CMY
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ISSN 0860 - 097X Cena zł 26,25 z VAT
Zam. 98/2012 Nakład 200 FOLIA
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M
Y
K
403
ANDRZEJ SOBCZYK
Improvement of Hydraulic System Efficiency by Means of Energy Recuperation Poprawa sprawności hydraulicznych układów napędowych maszyn przez zastosowanie układów z rekuperacją energii
MECHANIKA
Y
seria
M
A. Sobczyk – IMPROVEMENT OF HYDRAULIC SYSTEM EFFICIENCY... / POPRAWA SPRAWNOŚCI HYDRAULICZNYCH ...
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POLITECHNIKA KRAKOWSKA im. Tadeusza Kościuszki
KRAKÓW 2011
strona 1 (tytu³owa)
Zam. 98/2012 Nak³ad 200
MONOGRAPH MONOGRAFIA 403
strona 2 (tytu³owa)
Zam. 98/2012 Nak³ad 200
TADEUSZ KOŒCIUSZKO CRACOW UNIVERSITY OF TECHNOLOGY
ANDRZEJ SOBCZYK
IMPROVEMENT OF HYDRAULIC SYSTEM EFFICIENCY BY MEANS OF ENERGY RECUPERATION
MECHANICS MONOGRAPH 403
•
CRACOW 2011
strona 3 (tytu³owa)
Zam. 98/2012 Nak³ad 200
POLITECHNIKA KRAKOWSKA im. Tadeusza Koœciuszki
ANDRZEJ SOBCZYK
POPRAWA SPRAWNOŒCI HYDRAULICZNYCH UK£ADÓW NAPÊDOWYCH MASZYN PRZEZ ZASTOSOWANIE UK£ADÓW Z REKUPERACJ¥ ENERGII
SERIA MECHANIKA MONOGRAFIA 403
•
KRAKÓW 2011
strona 4 (redakcyjna)
CHAIRMAN OF THE CRACOW UNIVERSITY OF TECHNOLOGY PRESS EDITIORIAL BOARD PRZEWODNICZ¥CY KOLEGIUM REDAKCYJNEGO WYDAWNICTWA POLITECHNIKI KRAKOWSKIEJ Jan Kazior
CHAIRMAN OF THE EDITORIAL BOARD PRZEWODNICZ¥CY KOLEGIUM REDAKCYJNEGO WYDAWNICTW NAUKOWYCH Józef Nizio³
SERIES EDITOR / REDAKTOR SERII Rafa³ Palej SCIENTIFIC EDITOR / REDAKTOR NAUKOWY Stanis³aw Micha³owski REVIEWERS / RECENZENCI Leszek Osiecki, Jaros³aw Stryczek SECTION EDITOR / SEKRETARZ SEKCJI Marta Wlaz³o PROOF READ BY / WERYFIKACJA JÊZYKOWA El¿bieta Han-Wierciñska TYPESETTING, PAGE MAKE-UP / SK£AD I £AMANIE Krystyna Gawlik
COVER DESIGN / PROJEKT OK£ADKI Jadwiga M¹czka
© Copyright by Politechnika Krakowska, Kraków 2011 © Copyright by Andrzej Sobczyk, Kraków 2011 ISSN 0860-097X
Wydawnictwo PK, ul. Skar¿yñskiego 1, 31-866 Kraków; tel.: 12 628 37 25, fax: 12 628 37 60 e-mail:
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5
Contents Nomenclature ........................................................................................................................................ 7 1. Introduction and state of the art of energy saving system in mobile machines ............................... 11 2. Energy saving system from boom mechanism................................................................................ 14 2.1. Energy storing in hydraulic accumulator ................................................................................ 15 2.2. Energy recuperation comparative study for excavator hydraulic system ................................ 20 2.3. Accumulator charging and pilot system supply from boom cylinder...................................... 28 2.4. The swing, boom turn, blade and additional equipment powering with stored energy ........... 29 2.5. Powering of the swing mechanism directly from boom cylinder ............................................ 30 3. Concepts of multi-chamber cylinder circuits .................................................................................. 32 3.1. Three chamber gas-oil cylinder .............................................................................................. 32 3.2. Three oil-chamber cylinder (3C) for energy recovery circuit ................................................. 33 3.3. Four oil-chamber cylinder (4C) energy recovery concept ...................................................... 34 4. Field tests of the excavator ............................................................................................................ 35 4.1. Calculation method of hydraulic system energy consumption during excavator working cycle .... 35 4.2. Tests results for the original hydraulic excavator system ....................................................... 37 4.2.1. Experimental tests ........................................................................................................ 37 4.2.2. Estimation of hydraulic system energy consumption ................................................... 38 4.3. Energy estimation for saved energy utilized in swing mechanism.......................................... 39 4.3.1. Estimation of energy consumption for a circuit with energy saving system with automatic control of pilot pump 3 ........................................................................ 40 4.3.2. Summary of original system field tests ........................................................................ 42 5. Energy recovery system using a 3C cylinder .................................................................................. 45 5.1. Structure of the hydraulic system............................................................................................ 45 5.2. Electronic control system........................................................................................................ 46 5.3. Operating principles of energy recovery system ..................................................................... 49 5.3.1. Operation with energy saving system switched off ...................................................... 49 5.3.2. Active energy saving system (boom lowering from A3) .............................................. 50 5.3.3. Active energy saving system (boom lifting from the accumulator to chambers A1, A3) .................................................................................................... 52 5.3.4. Manual discharge of accumulator ................................................................................ 53 6. Field tests of an excavator with 3C cylinder ................................................................................... 54 6.1. Experimental tests of 3C cylinder energy saving system ........................................................ 54 6.2. Estimation of power consumption with 3C cylinder energy saving system ............................ 59 6.3. Summary of field tests of an excavator with 3C cylinder ....................................................... 61 7. Proposal of improving energy saving by system modification ....................................................... 62 7.1. Energy recovery system modification..................................................................................... 62 7.2. Estimation of 3C cylinder diameters based on load characteristic .......................................... 63 8. Tests with original 301.5 mini excavator boom cylinder and energy saving system ESS .............. 68 8.1. Tests methodology .................................................................................................................. 70 8.2. Excavator 301.5 boom lowering tests with ESS ..................................................................... 71 8.3. Boom lowering tests with regenerative (regen) valve ............................................................. 77 8.3.1. Additional tests of ESS with regen valve ..................................................................... 81
6 8.4. Laboratory tests with accumulator energy utilization ............................................................. 83 8.4.1. Accumulator discharging tests ..................................................................................... 83 8.4.2. Energy storage for given cycle of operation ................................................................. 89 8.5. Summary of 301.5 excavator boom cylinder and energy saving system (ESS) tests .............. 97 9. Hydraulic Power Recovery (HPR) tests stand for scaled linkage of 320C excavator ..................... 99 9.1. Tests with accumulator to simulate boom lowering energy .................................................. 101 9.1.1. Tests for system with and without one-way clutch..................................................... 101 9.1.2. Tests of underpressure elimination system ................................................................. 105 9.1.3. Tests of system flow control ...................................................................................... 108 9.2. Design of scaled research stand for 320C hydraulic excavator ............................................. 111 9.2.1. Tests results for system with boom lowering under gravity ....................................... 115 9.2.2. Tests results for system with both boom cylinder chambers supply ........................... 118 9.2.3. Tests results for system with regenerative (regen) valve ............................................ 120 9.2.4. Engine transient analysis – Flywheel support system................................................. 122 9.2.5. Flywheel support system for HPR stand .................................................................... 125 9.3. Hydrostatic support system ................................................................................................... 126 9.4. Summary of Hydraulic Power Recovery (HPR) tests stand for scaled linkage of 320C excavator ................................................................................................................. 130 10. General conclusions .................................................................................................................... 133 10.1. Field tests of an excavator with 3C cylinder .................................................................... 133 10.2. 301.5 mini hex boom cylinder with energy saving system ESS ....................................... 133 10.3. Hydraulic Power Recovery (HPR) tests stand for scaled linkage of 320C excavator ....... 134 10.4. Future research ................................................................................................................. 135 Acknowledgments ............................................................................................................................. 137 Appendix A ....................................................................................................................................... 138 A.1. 3C Cylinder strength calculations .................................................................................... 138 A.1.1. Check of the piston rod for the inside and outside pressure ................................ 139 A.1.2. Check of the 3C rod for buckling ........................................................................ 141 A.1.3. Check of the cylinder tube for the inside pressure .............................................. 142 A.1.4. Check of the complete 3C cylinder for buckling ................................................. 144 A.2. Example of calculations for mini hex 301.5 3C cylinder ................................................. 145 A.3. Determination of optimal (diameters d1, d2 and d3 – wise) 3C cylinder ........................ 146 A.3.1. Primary selection of diameters ............................................................................ 146 A.3.2. Cylinder stress calculation .................................................................................. 148 A.3.3. Calculation of hollowed rod under outer and inner pressure load ....................... 149 A.3.4. Calculation of 3C rod buckling ........................................................................... 154 A.3.5. Cylinder tube for inside pressure check .............................................................. 156 A.3.6. Buckling calculation of the complete, extended cylinder .................................... 159 A.4. Determination of optimal diameters d1, d2 and d3, considering existing pipe and rod cylinder standard products, available on the Polish market ............................................ 161 A.5. Design of 3C cylinders .................................................................................................... 162 References ......................................................................................................................................... 164 Summary ........................................................................................................................................... 171 Zusammenfassung ............................................................................................................................. 172 Streszczenie ....................................................................................................................................... 173
7
Nomenclature A A1o A2o A1 A2 A3 B d d1 d2 d3 E Ec Ee Eh EIN Emax Em EOUT Ep Et Ē Ēe Ēemax F Fac1 Fac2 g H J J J L, l M M
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
area piston side cross section area of original cylinder rod side cross section area of original cylinder chamber C1 working area of 3C cylinder chamber C2 working area of 3C cylinder chamber C3 working area of 3C cylinder hydraulic fluid bulk modulus diameter diameter of chamber 1 of 3C cylinder diameter of rod of 3C cylinder (diameter of chamber 3) diameter of chamber 3 of 3C cylinder Young modulus, energy boom cylinder hydraulic energy during lowering effective energy hydraulic motor input energy input energy maximum value of energy hydrostatic motor mechanical energy output energy pump output energy total energy consumptions of system during excavation energy in non-dimensional domain effective energy in non-dimensional domain maximum of effective energy in non-dimensional domain force 3C cylinder force with chamber C1 supplied 3C cylinder force with chamber C1 and C3 supplied Earth gravity width, stroke radius of gyration cross-section moment of inertia reduced moment of inertia length mass torque
[m2] [m2] [m2] [m2] [m2] [m2] [Pa] [mm] [mm] [mm] [mm] [Pa] [J] [J] [J] [J] [J] [J] [J] [J] [J] [–] [–] [–] [N] [N] [N] [m/s2] [m] [m] [m4] [kgm2] [m] [kg] [Nm]
8
Md Me Mp Mm N Nak1 Nak1 Nc Nh Nm Np n nm np. Pkr p po po p1 p1 p2 p1 p2 p3 pa pb1 pb2 pb3 pg pp pcrtl pm po ps1 ps2 Q Qa Qak1 Qak2
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
pump driving torque electric motor shaft torque pump/electric motor shaft torque hydraulic motor torque power input power of accumulator during charging output power of accumulator during discharging boom cylinder hydraulic power during lowering hydraulic motor input power hydrostatic motor mechanical power hydraulic pump hydraulic power exponent in p-V gas thermodynamic equation hydraulic motor rotational velocity pump/electric motor rotational velocity critical compressive force pressure absolute accumulator charging pressure non-dimensional charging pressure absolute minimum, system accumulator, pressure ratio of pressure p1 to p2 absolute maximum, system with accumulator, pressure pump 1 working pressure pump 2 working pressure pump 3 working pressure accumulator gas pressure control signal boom cylinder piston side pressure boom cylinder rod side pressure boom cylinder chamber 3 pressure accumulator gas pressure pump output pressure boom lowering control signal pressure hydraulic motor input pressure hydraulic accumulator oil side pressure swing motor pressure swing motor pressure volumetric flow accumulator volumetric flow accumulator input flow during charging accumulator output flow during discharging
[Nm] [W] [Nm] [Nm] [W] [W] [W] [W] [W] [W] [W] [–] [rpm] [rpm] [N] [Pa] [Pa] [–] [Pa] [–] [Pa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [m3/s] [m3/s] [m3/s] [m3/s]
9
Qb Qc Qp Qvm q qm qp Re RH Rm r S SL SR T t U V Vb Vo Vp3 Vs1 Vs2 Vφm V1 V2 v vb x xa xb δ ε εp, εm σ λ λgr ω ωm
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
volumetric boom cylinder flow output volumetric flow from cylinder pump delivery hydraulic motor volumetric losses flow unit volume of pump or hydraulic motor per revolution unit volume of pump or motor per radian unit volume of pump per radian plasticity limit proportional limit tensile stress of material radius control signals swing mechanism joystick position signal left swing mechanism joystick position signal right temperature time voltage volume voltage signal for swing directional valve 6 volume of charging gas at pressure po voltage signal for pump 3 operation mode voltage signal for swing directional valve 7 voltage signal for energy saving directional valves 2 and 3 hydraulic motor, per radian, unit displacement volume of charging gas at pressure p1 volume of charging gas at pressure p2 linear velocity boom cylinder velocity linear displacement, safety factor displacement of accumulator piston linear displacement of boom cylinder dimension tolerance coefficient angular acceleration displacement parameter of pump and hydrostatic motor stress slenderness ratio for buckling slender limit angular velocity hydraulic motor angular velocity
3
[m /s] [m3/s] [m3/s] [m3/s] [m3] [m3] [m3] [Pa] [Pa] [Pa] [m] [–] [–] [–] [K] [s] [V] [m3] [V] [m3] [V] [V] [V] [m3] [m3] [m3] [m/s] [m/s] [m] [mm] [mm] [–] [l/s2] [–] [Pa] [–] [–] [rad/s] [rad/s]
10
η ηa ηL ηHM ηs ηt
– – – – – –
ηvm ηhmm ηhmp
– – –
efficiency coefficient hydraulic accumulator efficiency coefficient hydraulic line efficiency coefficient hydraulic motor hydro-mechanical efficiency Energy Saving System (ESS) efficiency coefficient Energy recovery system (installation-accumulator-motor) total efficiency coefficient hydraulic motor volumetric efficiency coefficient hydraulic motor hydro-mechanical efficiency coefficient hydraulic pump hydro-mechanical efficiency coefficient
[–] [–] [–] [–] [–] [–] [–] [–] [–]
11
1. Introduction and state of the art of the energy saving system in mobile machines The main goals of the research work on hydraulic system efficiency improvement by means of energy recuperation in heavy duty machinery were: an evaluation of the energy saving system for a mini excavator, taking into consideration the results of both stand tests and simulation, construction of a physical system equipped with necessary measurement, adjustment and control devices, testing the energy saving system for the given excavator working cycles and an analysis of the results for the evaluation of energy saving system efficiency improvement. Based on the conclusions from the first stage of the research work, as well as the author’s former experience in hydraulic system research [93–96, 98, 99], the main attention was focused on energy recovery from the lowered boom of the excavator type machine. To achieve this, the developing the system structure and control algorithms for optimal power saving and management also in the hydraulic system [33, 34, 91] of multi-actuator mobile hydraulic machines has been undertaken. Thus, displacement control was a greater challenge compared with throttle-controlled linear and rotary actuators, because such control of flow direction and velocity significantly reduces machine overall fuel consumption by avoiding throttling losses in delivered hydrostatic energy [35–37, 39, 40, 74,79, 80, 85, 101]. The machine hydraulic system efficiency was assumed to be obtained through: – boom mechanism potential energy estimation, – use of the hydraulic accumulator as energy storage, – new multi chamber (MC) cylinder design, – mini-hex (mini hydraulic excavator) laboratory and field tests, – improving energy recovery by means of the hydrostatic motor in Hydraulic Power Recovery (HPR) to maximize energy recovery as well as reduce and equalize engine power requirements. From the chronological point of view energy saving hybrid systems in vehicles have been studied for many years in the transportation sector [2, 14–21, 50–52, 64, 65, 97, 103–105, 107, 108, 110, 111, 113, 114, 116, 118] and more recently there has been a growing interest in the hybridization of off-highway vehicles such as construction, mining and agricultural machines due to both increasing fuel costs as well as more stringent emission regulations continuing to be placed on industry [3–9, 11, 22, 27–29, 31, 32, 38, 47, 48, 54–59, 69, 71–73, 75, 77, 78, 83, 84, 86, 92, 100, 109, 112, 117, 119]. Among them much of the focus has been on electric hybrid systems where companies such as Case, Kobelco, and Komatsu have
12
released or announced the release of hybrid construction equipment to the market. Only little focus, however, seems to have been placed on purely hydraulic hybrid systems. Significant research has been done on power management for vehicle drivetrains based on hydrostatic transmissions (HST) and power-split drives. Ossyra presented a control method for HST involving two real-time optimization loops: one feedback loop for the engine based on steady-state efficiency characteristics and the other for the HST based on detailed steady-state loss models of the hydraulic pump/motor units. However, there has been little work on engine power management for mobile hydraulic machinery in which the primary energy consumers are working functions rather than the propulsion drive [70]. A Japanese industrial R&D group controlled pump flow rates and engine speed on an excavator to improve overall efficiency by about 10% [43]. An Asian research group showed 26% fuel savings using similar methods [12]. A group in Canada constructed a displacement-controlled forestry machine, but did not report fuel measurements [53]. Recently, Alleyne et al. have developed control methods for optimizing the powertrains of earthmoving vehicles with respect to energy consumption [68]. Some selected solutions could be found in [60–63, 82] where the authors deal with energy saving by programmable valves, energy recovery efficiency in electro-hydraulic forklift and use of differential cylinder in closed hydrostatic circuit. There is no previous research on power management for excavators or similar machines using pump-controlled actuators [39]. Research on hybrid highway vehicles has been conducted for many years [106]. The motivation for this is clear because the primary operating cost of a passenger vehicle is fuel. In off-highway machines, such as construction equipment, time is much more costly than fuel, so system design has traditionally been focused on maximizing machine power and productivity and not on fuel consumption. Recent increases in fuel costs have given some incentive to look for more fuel efficient designs although the greatest push for fuel efficient hybrid systems has been the increasing emission regulations placed on OEMs by governments [42]. In the United States a new set of federal emissions regulations referred to as the Tier emission standards was implemented in the 1990s. The Tier standards represent a scheduled reduction in emissions to be allowed in off-road diesel engines which are to be phased in over time. As each new phase rolls in manufacturers are being forced to find new innovative methods to reduce their machines emissions without reducing productivity. This and similar standards being issued by governments around the world are driving advancements in hybrid technology for off-road machines [21]. Current research trends in hybrid off-road machinery seem to be copying the electric hybrid approach taken by hybrid passenger vehicle manufacturers. Several systems have already been announced for sale on the market. Komatsu released the PC200-8 hybrid 22 ton crawler excavator for sale in 2008 [45]. The series hybrid systems consists of a generator driven by the diesel engine, an electric motor to
13
drive the swing (rotation of the upper structure) and a capacitor bank to recover and deliver energy rapidly [23, 24]. Komatsu is claiming 25–30% fuel savings from the standard model although the machine cost has been reported to be from 25–50% more [23, 45, 120]. Since Komatsu’s release of their hybrid excavator several other companies including Case, Doosan, Hitachi and Sumitomo have developed electric hybrid excavators of the same general design and size and either announced their release to the market or unveiled prototypes [116, 120]. All of the above mentioned hybrids have maintained their original hydraulic systems for controlling the boom, stick, and bucket functions which require linear actuation. Kobelco has introduced a more complex hybrid system [42] which allows for energy recovery from the boom cylinder and reduced metering losses. This system is again a series hybrid where the engine drives a generator and there is an electric motor for the swing drive. However, in this system there are also three more electric motors for powering the pumps controlling the remaining actuator functions. Because the boom function has the most potential for recoverable energy it is actuated with electro-hydrostatic actuation. Besides excavators, Volvo announced the release of the market’s first electric hybrid wheel loader which offers 10% fuel savings and higher performance than the traditional machine, and Deutz and Atlas Weyhausen have teamed up to build a prototype electric hybrid wheel loader. There seems to have been much less interest in industry in purely hydraulic hybrid systems using accumulators to recover and store energy. Caterpillar developed such a system for a 50 ton excavator [26] where energy was recovered from boom operations. They claimed average fuel savings of 25–30% with the machine operating 5% faster than the standard system. While the savings were similar to that promised by newer electric hybrids, it has received little attention.
14
2. Energy saving system from boom mechanism This chapter of monograph contains description of the proposed hydraulic circuits with hydraulic energy recuperation and their operation designed for the Cat 301.5 excavator, driven by 2 main pumps with hydraulically controlled system supplied by a third pilot pump, called pump 3 in next chapters. After the theoretical analysis confirmed by a series of lab and field tests, two of the proposed energy saving cylinders, based on dimensions of the originally installed boom cylinder, were designed, built and extensively tested. The circuits, including a special design of the multi-chamber cylinder, are described in the next chapters of the monograph. In all cases where energy could be cached, then temporarily stored to be used further to supply or co-supply next working movement of the equipment, the pneumo-hydraulic accumulator was adopted as hydraulic energy storing device. Other types such as weight-loaded or spring-type accumulators were not taken into account due to their large size versus energy stored, low response and other working limitations. The gas-charged type accumulators store energy under the pressure of gas, usually nitrogen. The three types of gas-charged accumulators could be classified as piston type, bladder type and diaphragm type. The accumulators without oil-gas separation could not be used to avoid gas entry to hydraulic fluid. The gas-charged accumulator, which was used for energy storage during the tests, consists of a steel body containing two, bladder separated, chambers for oil and compressed nitrogen, which was pre-charged to certain pressure through the charging valve. When the accumulator is charged by high pressure oil, it is stored at high pressure under the action of compressed gas. The gas compression process is described by the equation: p0V0n = p1V1n = p2V2n = const
(1)
where: p0 – absolute accumulator charging pressure, gas pressure, [Pa], p1 – minimum absolute system pressure, p2 – maximum absolute system pressure, [Pa], V0 – volume of charging gas at pressure p0, [m3], V1 – volume of charging gas at pressure p1, [m3], V2 – volume of charging gas at pressure p2, [m3], n – exponent. The value of the exponent n varies from 1 to 1,4. For the isothermal process, n = 1; for the polytrophic process, 1 < n < 1,4 and for the adiabatic process, n = 1,4. Thus, only for slow compression process, gas temperature is kept constant and the relation between gas pressure and its volume has the form: p0V0 = p1V1 = p2V2 = const
(2)
15
2.1. Energy storing in hydraulic accumulator From several functions of the hydraulic accumulator in hydraulic systems energy storage in an energy saving system should be briefly analyzed [76]. Using the accumulator as an energy storage device, it is very important to estimate the mathematical expression for the total stored energy and the effective energy delivered by the accumulator to the system. The total energy which could be stored in the hydraulic accumulator is the increase in the compressed gas energy when compressed from charging pressure value p0 to pressure maximum system pressure p2. The value of energy could be calculated from equation: dE = –pdV
(3)
where the negative sign indicates that the stored energy increases with the decrease of compressed gas volume. For the polytrophic compression process: pV n = p0V0n = p1V1n = p2V2n
(4)
V ndp + npV n–1dV = 0
(5)
dV = −
or
V dp np
(6)
1
⎛ p ⎞n V p1 n V = ⎜ 0 ⎟ V0 Then dV = − 0( n +01) n dp np ⎝ p⎠
Then,
or
V0 p10 n E= n
∫
p2 p0
p −1 n dp
V0 p10 n ( n −1) n ⎡ p2 − p0( n −1) n ⎤⎦ E= ⎣ n −1
(7)
(8)
(9)
As can be seen from the last expression, the energy stored is highly dependant on charging pressure p0. The maximum value of stored pressure can be found for dE/dp0 = 0 from expression: p0 = n − n ( n −1) p2
(10)
16
Considering the adiabatic process, n = 1,4 – the maximum storage energy can be obtained from the above equation, for p0 = 0,308p2, and maximum energy can be estimated by substituting Eq. (10) into Eq. (9)
Emax =
V0 p2
n n ( n −1)
(11)
In non-dimensional domain E = E/Emax and p0 = p0/p2 we obtain nondimensional expression for accumulator energy, in case of the polytrophic process:
E=
n n ( n −1) 1 n ⎡ n −1 n p0 ⎣1 − p0( ) ⎤⎦ n −1
(12)
For the isothermal process, where n = 1, the total energy stored in the accumulator can be calculated as follows: pV = p0V0 = p2V2
(13)
pdV + Vdp = 0
(14)
p0V0 dp p2
(15)
dV = −
E = −∫
p2 p0
pdV = p0V0 ln ( p2 p0 ) = −V0 p2
p0 ⎛ p0 ⎞ ln ⎜ ⎟ = −V0 p2 p0 ln ( p0 ) p2 ⎝ p2 ⎠
(16)
dE = 0 or ln ( p0 ) = −1 and p0 = 1 e . dp0 Then, substituting in Eq. (16), the formula for the maximum energy is obtained
Thus, for maximum energy,
Emax = p2V0 e and E = E Emax = −ep0 ln ( p0 )
(17)
Fig. 1 presents graphically the relation between non-dimensional stored energy E and non-dimensional charging pressure p0 = p0 p2, for polytrophic (n = 1,3) and isothermal gas processes. The total stored energy obtains its maximum for p0 = 0,308 to 0,37, depending on the gas process.
E = E/Emax
17
n=1
n = 1.3
p 0 = p0 p 2
Fig. 1. Variation of the total energy stored in a hydraulic accumulator with charging pressure, calculated [76]
When the accumulator has to be a secondary source of energy to drive the hydraulic cylinder and/or motor, the system minimum pressure which can operate the output device has to be taken into acocunt. Thus the effective energy which can be reused can be calculated as: Ee = p1(V1 – V2)
(18)
Consequently, for the polytrophic gas process, effective energy can be calculated as: ⎡ ⎛ p ⎞1 n ⎤ Ee = p1V1 ⎢1 − ⎜ 1 ⎟ ⎥ ⎢⎣ ⎝ p2 ⎠ ⎥⎦
(19)
The value of maximum energy can be obtained when dEe/dp1 = 0, or n
⎛ n ⎞ p1 = ⎜ ⎟ p2 or p1 = 0,47p2 for n = 1,4 ⎝ n +1⎠
(20)
Thus, Ee max = p2V1
nn
( n + 1)
n +1
or Ee =
in non-dimensional domain, respectively.
(n + 1)n +1 P (1 − P 1 / n ) nn
1
1
(21)
18
For the isothermal process, (where n = 1), by substituting in Eqs. (20) through (21) it can be shown that effective energy obtains its maximum value for p1 = 0,5p2. ⎛ p ⎞ Ee = p1V1 ⎜1 − 1 ⎟ p2 ⎠ ⎝
(22)
Then,
Ee max = 0,5 p1V1
(23)
and
Ee = 4 p1 (1 − p1 )
(24)
Ee = Ee Ee max
where
and
p1 = p1 p2
(25)
E = E/Emax
The graphical relation between minimum pressure p1 and stored energy in nondimensional domain, for the isentropic and polytrophic cases, is show in Fig. 2. The maximum values of the described processes are placed for p1 = 0,47 for the polytrophic (n = 1,3) and p1 = 0,5 for the isothermal.
n=1 n = 1.3
p 0 = p0 p 2
Fig. 2. Variation of effective accumulator energy with minimum operating pressure to maximum pressure ratio, p1/p2, calculated [76]
It should be noted that the above considerations are based on theoretical processes and do not include some important phenomena such as pressure losses during charging and discharging accumulator. Neither is included the time of energy storage following fast charging which significantly affects the operation
19
efficiency of the accumulator measured as a ratio of output energy which could be re-used to drive certain mechanisms to input energy when the accumulator is being charged. Some results on this aspect are discussed and presented in the literature [40, 50], where the influence of accumulator stop time on charging – discharging process efficiency was tested. Selected results of the stand tests are shown in Figs 3 and 4, and present the decrease of hydraulic accumulator efficiency as a function of stop time. Another problem that needs consideration is also the ambient temperature in which the hydraulic system with accumulator operates, causing changes in the intensity of heat exchange between accumulator and surroundings. In that case the application of extra insulation could improve the efficiency of energy storing when the accumulator is not used in continuously hydraulic energy flow. It should be noted here that the total efficiency of the energy recuperation system with accumulator is more dependant on the level the energy which could be stored and the working cycle frequency. 40 30 3 Q /min] Q [dm [dm3/min]
20 10 0 -10 -20 -30 -40 100 80
TT [°C] [oC]
60 40 20 0 -20 16
pp[MPa] [MPa]
12 8 4 0
60
80
100
120 [s] tt [s]
140
160
180
200
Fig. 3. Selected results of temperature and pressure changes in charged accumulator as a function of stop time [53]
20 1 0.95
η [−]
0.9 0.85 0.8 0.75 0.7 0
5
10
15 Stop time [s]
20
25
30
Fig. 4. Accumulator efficiency versus stop time characteristic [53]
Accumulator efficiency ηa was defined as: ηa =
EOUT EIN
(26)
where: EOUT – hydraulic output energy during discharging after a different stop time, EIN – hydraulic input energy delivered to accumulator during charging. The results show that the efficiency of pneumo-hydraulic accumulator has the maximum value of 0,96 for continuous processes of charging and discharging but drop significantly up to 0,74 after stop time of 30 sec., due to pressure versus temperature decrease in time. The results of hydraulic accumulator efficiency testing presented below lead to the conclusion that in calculation of energy recuperation such phenomena as not even and not always repeatable working cycle parameters, additional pressure losses in installation necessary to connect the accumulator to the circuit, should be taken into consideration. Otherwise, the results of calculations could be far away from the results which can be obtained during field tests on a real machine and in real environment. Consequently, in what follows, differentiated research program of energy saving system configuration is presented, leading to some important conclusions and an energy saving system configuration, as well as to energy management algorithms.
2.2. Energy recuperation comparative study for excavator hydraulic system The experiments were conducted on 301.5 type mini excavator hydraulic system allowing to compare the amount of recovered energy by adding a hydraulic
20
25 21
11
1
22
1
2
3
22
T 2
100
105
M
22
R1
Pb8
100
R2
RV4
A8 Pa8 B7 (9F)
RV5
R4 B8 A9 Pa9 (6G)
22
B9
101
101
R3 16
103
100
KET CYLINDER 14
BOOM CYLINDER
15
12
A7
T
3
4
RVI
P1
8
D
D
B
B
(BG) (AH)
19
B
PP
A
RV9
P
T
T
OUT
7
(CI)
A
A
B
A6
RV2
C
C
A
6
T
A
C
B
5
9
A5
R1 1
RV6
(FK)
101
ARM CYLINDER
L1 Pa5 B5
101
(FL)
Pb5 L3
B6
16
23
A4
103
PB
(IC)
BOOM
B4
102
24
A
102
DB
Pb3 L2
P
R4 4
L4 A3 Pa3 B2 (9E)
R2 R3 T 3 2 BUCKET
Pb
B3
M
RV8
104
SWING MOTOR
RV7
Pa
B
13
Fig. 5. 301.5 excavator hydraulic system
RV10
P2
P
P
PP
PP
A
DR
12
TRAVEL MOTOR RIGHT
DR
TRAVEL MOTOR LEFT
A2
19
(9D)
L1 1
F
F
T
B1
E
E
P
A1
BLADE CYLINDER 17
ARM
SWING
T2
P3
BOOM SWING CYLINDER
L3 L2 3 2
RV3
(9C)
18
L4 4
10
24
21
22
accumulator with the energy used by the original factory system. A general scheme of the excavator hydraulic system with the basic measurement and control points is shown in Fig. 5. For clarity, Fig. 6 shows a detailed scheme of the supply section of the excavator hydraulic system which consists of three pumps: pump 1 – supplying boom and bucket cylinders or right travel motor, 2 – supplying arm cylinder or left travel motor and pilot system pump 3 – mainly to supply hydraulic control of excavator mechanisms, also used as a source of supply of the swing motor, boom swing cylinder and blade cylinder. The tests were carried out according to the adopted working cycle, which corresponds to real excavation conditions. A view of the excavator specially prepared for the series of tests on energy possible to capture, evaluation and different system configurations of reuse is presented in Fig. 7. to boom and bucket cylinder, travel motor left to arm cylinder, travel motor right
22
22
100
100
20
22
22
25 21
to swing motor, boom swing and blade cylinder
to pilot system
4
3
7
100 1
105
T
1
6
M
2
3 T
A
P
8
OUT
A
C
B
5
2 RV9 RV10
T
Fig. 6. 301.5 hydraulic excavator hydraulic supply system
Fig. 7. 301.5 hydraulic excavator with equipment for energy saving field test
23 4 5
(P a) 3 9
RV7
(V b) RV8
(V b)
(VS1,VS1,reset)
1 2
B8
(reset) 6
A8
(P ctrl) (9F)
(reset)
7
8
8
(V S2)
(V S1)
B3
(S L)
A3
(9E) (SR)
Fig. 8. Hydraulic energy saving system for capturing energy from boom lowering and reusing it to supply the swing motor, where: B8, A8 and B3, A3 – connections of boom cylinder and swing motor with original directional valves block (9F) and (9E); 101, 102 – input and output pressure transducers on boom cylinder and swing motor, respectively; 103 – boom cylinder displacement transducer and 104 – angular displacement of swing motor
This chapter contains description of two proposed energy saving circuits and their operation. The first circuit uses the energy from the lowered boom to charge the extra installed hydro-pneumatic accumulator, and further to power the swing mechanism, which is presented in Fig. 8. In the second circuit, the energy collected in the accumulator was used to power the pilot pressure control circuit and the swing mechanism, Fig 13. This allowed relief of pilot pump 3 responsible for the pilot control circuit pressure (the flow was directed to the tank if the pressure in the pilot system accumulator 6 was sufficient to power the circuit). The additional elements that were added to the circuit were numbered: 2, 6, 7 – directional valves, 3 – flow control valve, 4 – accumulator, 8 – check valves, 9 – relief valve (see also Table 1). The need to control the speed of boom lowering was expected, so a proportional flow control valve (3) was installed. However, it turned out (during experimental tests) that a simple throttle valve could be used instead. This led to setting the proportional flow control valve to a constant preset value. When the proper pre-charge pressure of the accumulator was selected, there was no need to
24
use the throttle valve, due to sufficient pressure drop in the hydraulic line. Fig. 8 presents the essential parts of the hydraulic circuit with an energy saving system, by capturing energy from the boom mechanism and reusing it in the swing mechanism. In this case the principle of operation of the energy recovery circuit is based on accumulation of energy from boom cylinder (1), (during lowering of the boom), in the hydro-pneumatic accumulator (4), and its reuse to power the swing mechanism (5). This circuit also allows partial unloading of pump 3, which is responsible for the swing mechanism, which was powered from a secondary energy source – the hydraulic accumulator (4). But because of the limited volume of the accumulator, after its total discharge, the task of powering the mechanism was taken over by pump 3 again. The process of charging the accumulator depends on the intensity of use of the boom mechanism (lowering) and the average depth of excavation in a given class of ground. Table 1. Hydraulic energy saving circuit elements shown in Fig. 6 No. 1 2 3 4 5 6 7 8 9
Name Boom Cylinder Directional Valve Proportional Flow Control Valve Accumulator Swing Motor Directional Valve Directional Valve Check Valve Safety Valve
Qt’y 1 1 1 1 1 1 2 2 1
Type 162-5851 4WE6 3.1/G24 NZ4 XQC2-12/NC50-12CAEN 2,5 [dm3] 144-5975 EVK 06EC312CA A-202 NG 10A DB10 3 12/315U
Producer Caterpillar Ponar Wadowice Comatrol Orsta Caterpillar Comatrol WSK Wrocław Ponar Wadowice Ponar Wadowice
Before physical tests an important assumption was made that the proposed energy saving system would not aggravate the machine characteristics. An electronic circuit was built which allowed automatic control of individual executive elements (directional valves). The block diagram of electronic control system is shown in Fig. 9 while Fig. 10 shows a view of control system components installed on the machine and detailed view of the swing mechanism joystick with micro switches for direction of rotation detection. The principle of operation of this circuit is based on four input signals and reset: – pa – voltage signal proportional to gas pressure in the accumulator, – pctrl – voltage signal proportional to control pressure of the boom lowering directional valve (used to detect the state of boom lowering), – sL and sR – two detecting signals of the swing mechanism joystick position (left or right, respectively), – reset signal for manual deactivation of control system.
25
The circuit contains three voltage output control signals: – Vs1 and Vs2 – two control signals responsible for additional swing directional valves (6 and 7), – Vb control signal responsible for valves (2 and 3) that enable energy transfer from the lowered boom cylinder to the accumulator.
2.2 MPa
6.5 MPa
0.5 MPa
Fig. 9. Operation principle of control circuit
Fig. 10. Control system installed on the excavator micro switches fixed in the swing mechanism joystick for direction of rotation detection
The electro-magnetic coils of the directional valves were supplied from additional 24V battery by means of appropriate relays. Signal pa was compared in comparators K1 and K2 with two reference values of pressure, which were set to 2,2 [MPa] and 6,5 [MPa]. As a result of this operation, a logical high state (logical 1) appeared on the output of comparator K1 when
26
signal pa exceeded 2,2 [MPa]. Otherwise its output was in low state (logical 0). On the output of comparator K2 a high state appeared when the value of pressure pa was lower than the reference value – 6,5 [MPa]. In case of a higher pa pressure the output value was at a low state. Comparator K3 was used as a boom lowering detector. When pctrl signal appeared, the output of K3 was in a high state. A high state on the output of comparator K1 indicates that the accumulator is charged and its energy can be used to drive the swing mechanism. In such case the appearance of a high state on input sL or sR causes a high state on output gates G1 or G2. This results in repositioning of the applicable hydraulic directional valves by control signals Vs1 or Vs2. When the pressure in the accumulator is lower than 2,2 [MPa], the output on K1 is in a low state. This causes the output state of gates G1 and G2 to be in a low state independent of sL or sR signal. Charging of the accumulator during lowering of the boom requires the following conditions to be fulfilled: – high state on the output of K3, – high state on the output of K2. The second requirement assures an optimum range of accumulator charging pressure. Compliance of both requirements causes the appearance of high state on output of gate G3, which causes switching of the adequate valves (signal Vb). As a result, the accumulator is charged with energy from the system during boom lowering. Fig. 11 shows the configuration of the excavator hydraulic system components with the energy saving system enabled. The red color indicates the flow of the pressurized working medium from the piston side of the boom cylinder and the blue color indicates the working medium path which supplied the cylinder rod side. During boom lowering (which is indicated by signal pctrl) control signal Vb switches the directional valve (2), to direct the flow of working medium to the accumulator (4). Vb signal from the control circuit also turns on the proportional flow control valve (3) to the pre-set value. The process of charging the accumulator can be carried out to a designated maximum value of pressure pa level. In the event of malfunction of the control circuit (overcharge of the accumulator above the specified safety level), the pressure relief valve (9) will be initiated. The next step of system modification was to create more flexible electric control system. The modernized electronic circuit allows automatic control of individual executive elements (directional valves). The principle of operation of this circuit is shown in Fig. 12.
27 4 5
(Pa) 3 9
RV7
(Vb) RV8
(Vb)
(VS1,VS1,reset)
1 2
B8
(reset) 6
A8
(Pctrl) (9F)
(reset)
7
8
8
(VS2)
(VS1)
B3
A3
(SL) (9E) (SR)
Fig. 11. Energy saving system during charging of the accumulator, where: B8, A8 and B3, A3 – connections of boom cylinder and swing motor with original directional valves block; 101, 102 – input and output pressure transducers on boom cylinder and swing motor, respectively; 103 – boom cylinder displacement transducer and 104 – angular displacement of swing motor
3.4 ; 4.5 MPa
6.5 MPa
0.5 MPa
Fig. 12. Principle of operation of control circuit
28
– – – – – –
Control of the circuit was based on three input signals: pa – voltage signal proportional to gas pressure in the accumulator, pctrl – voltage signal proportional to control pressure of the boom lowering directional valve (used to detect the state of boom lowering), s – detecting signal of the swing mechanism joystick position. The circuit contains three voltage output signals: Vp3 – which controls the directional valve (10) responsible for the type of work of pump 3, Vs – control signal responsible for the additional swing directional valve (13), Vb – control signal responsible for valves (8) that enable the energy transfer from the boom cylinder to the accumulator.
2.3. Accumulator charging and pilot system supply from boom cylinder Fig. 13 represents the principle of operation of the energy saving system during charging of the accumulator (12) by the boom cylinder (7). The red color indicates the flow of the pressurized working medium from the lowered boom to the accumulator and the pilot pressure system. 16 101
103
BOOM CYLINDER
(S)
(Pctrl)
SWING MOTOR
Control Valve AS
15 (9F)
17 (9E)
101
(Vb)
7
14
4
8 101
M
3
SPEED TRAVEL
13
T
105
(Vp3)
(Pa)
1 101
CONTROL PANEL
(VS)
12
6 RV9
2
OUT
101
A
C
5
B D
RV10
10
11
T
18
Fig. 13. Hydraulic system part showing energy saving by charging of the accumulator and alternative supplying the pilot pressure system, instead of pump 3, from boom cylinder during boom lowering
29
Installed pressure relief valve (18) prevents hydraulic accumulator from overcharging in case of an electronic control system failure.
2.4. The swing, boom turn, blade and additional equipment powering with stored energy Fig. 14 presents the principle of operation of the energy saving system, when the swing, boom turn, blade or additional equipment could be powered by the accumulator (12). The red color indicates the flow of the pressurized working medium from the accumulator (12) to the directional valves (16) and to the pilot pressure circuit. 16 101
103
BOOM CYLINDER
(V b )
(S)
(P ctrl)
Control Valve AS
101
15 (9F)
7
SWING MOTOR
14
17 (9E)
4
8 101
M
3
SPEED TRAVEL
13
T
105
(V p3)
(P a)
1 101
CONTROL PANEL
(V S)
12
6 RV9
2
OUT
101
A
C
5
B D
RV10
10
11
T
18
Fig. 14. Hydraulic energy saving system when mechanisms are powered by accumulator
When the boom mechanism joystick is positioned to the “lowering boom” position, Vb signal switches the directional valve (8), directing the flow to the accumulator (12). After the accumulator is charged to the set maximum value of pa level, the valve (8) is set to close the accumulator – boom cylinder path as shown in Fig. 9. While the accumulator is charged from the boom cylinder, the flow from control system pump (3) is directed through the open directional valve (10) to the tank, as shown in Fig. 13. The check valve (11) ensures that the oil from the boom
30
cylinder does not flow to the tank. To ensure that the flow from pump (3) does not flow through the excavator original directional valve block (16), the directional valve (13) remains in closed position. When the swing mechanism is initiated, the directional valve (13) is switched by VS signal. As a result, the flow is directed from the accumulator (12) to directional valves (16) and further to the swing mechanism. While the mechanisms are powered by the accumulator (12), the flow from pilot pump 3 is directed to the oil tank. In the discussed circuit, it is possible to power three different mechanisms (swing, blade and turn) by the accumulator. In the energy saving circuit tested the experiments were focused on the swing mechanism, as used most often during excavation.
2.5. Powering of the swing mechanism directly from boom cylinder Fig. 15 represents the principle of operation of the energy saving system when the swing mechanism is powered directly from the boom cylinder (7). The red color indicates the flow of the pressurized working medium from the boom cylinder (7) to the directional valves (16) and to the pilot pressure circuit. This is the case when the lowering of the boom and the swing of the body occur at the same time. 16 101
(S)
(P ctrl)
SWING MOTOR
Control Valve AS
15 (9F)
17 (9E)
(V b) 101
103
BOOM CYLINDER
7
14
4
8 101
M
3
SPEED TRAVEL
13
T
105
(V p3)
(Pa)
1 101
CONTROL PANEL
(V S)
12
6 RV9
2
101
OUT
A
C
5
B D
RV10
10
11
T
18
Fig. 15. Hydraulic energy saving when swing mechanism is powered directly from boom mechanism cylinder
31
Powering the swing mechanism directly from the lowered boom is possible when the swing mechanism is initiated after lowering of the boom begins. When the swing mechanism is initiated, the directional valve (13) is switched with VS signal. If the boom is lowered simultaneously, Vb signal from the control circuit repositions the directional valve (8), to direct the flow of the working medium directly to directional valves (16) and further to the swing mechanism (17). When the mechanism is powered by the lowered boom (7), the flow from the pump (3) is directed to the tank through the opened directional valve (10).
32
3. Concepts of multi-chamber cylinder circuits This chapter presents different concepts of the energy saving system based on multi-chamber cylinders. The principle of their operation is based on energy recovery from the boom mechanism and its reuse during raising of the boom. The proposed circuits would allow reduction of energy required while raising the boom, resulting in partial relief of the pump. This results in decreasing of the total energy used by the boom mechanism.
3.1. Three chamber gas-oil cylinder Fig. 16 shows a basic hydraulic system with a three chamber (3C) gas-oil cylinder. The additional chamber is filled with nitrogen and connected with a gas cylinder to increase the working volume of the gas. The two remaining chambers are filled with hydraulic oil as in a regular cylinder. Higher gas pressure in chamber 3 allows a decrease of pressure required to extend the boom cylinder while raising the boom. 30
A1B1
[MPa] p p[MPa]
20
Gas volume 0.5 dm3 0.6 dm3 0.7 dm3
10
0 0.7
0.8
0.12
0.9 ls [m]
1
0.08
[dm3]] ΔVΔV[dm
0.04
1.1
0
3
Fig. 16. Three chamber gas-oil cylinder in the boom hydraulic system
Fig. 17. Characteristics of nitrogen compression for different volumes of gas (accumulator gas volume)
33
It was assumed that gas pressure and its pressure characteristics as a function of piston displacement have to be matched to avoid uncontrolled movement of the boom in any position (caused by accumulator gas pressure). Minimum values of a load acting on the boom cylinder occur when the arm and bucket cylinders are extended to the maximum position. The positions of the arm (A) and bucket (B) cylinders were assigned accordingly as A1B1. The characteristics of gas compression (in chamber 3 and additional gas chamber of a three chamber boom cylinder) should be below the characteristics of pressure as a function of displacement of the piston for arm and bucket position A1B1, determined by the mathematical model of excavator equipment. The results of such adjustment is shown in Fig. 17, where the diameter of the rod closing chamber 3 is 22 [mm], ls is the total length of the boom cylinder, and ΔV is the change of volume after rod retraction. From Fig. 17 it is obvious that the best characteristics, from the adopted point of view, are found in a circuit with the gas volume of 0,6 [dm3].
3.2. Three oil-chamber cylinder (3C) for energy recovery circuit The presented circuit, with a three chamber cylinder with a gas cylinder, allows a decrease of pump operating pressure during boom raising. This leads to energy saving. However it is impossible to lift the boom without supplying one of the cylinder chambers by the pump. Keeping in mind the possibility of using the energy from lowering the boom to further raising of the boom without additional power a new circuit was proposed. In this circuit the additional chamber was proposed to be filled with oil (instead of gas) and controlled by additional distribution valves. A scheme of such a circuit is shown in Fig. 18. A1
A2
A3
Fig. 18. Concept of energy recovery circuit with 3C cylinder
34
When lowering the boom, the additional control valve is placed in position II. This charges the accumulator with oil flowing from chamber A1. During boom raising the control valve is placed in position I. This makes the fluid flow from the accumulator to chambers A1 and A3. This leads to higher ratio of (A1+A3)/A1, which causes an increase of the force during boom lifting with respect to the force occurring while lowering the boom. Thus, it is possible to lift the boom in some part of its motion without the supply of the cylinder from the pump. It is obvious that the movement of the boom will be smaller than during boom lowering. That is why further raising of the boom requires a supply from the pump.
3.3. Four oil-chamber cylinder (4C) energy recovery concept The simplification of the control valves that control the flow of the working medium from the cylinder to the accumulator can be obtained using a four chamber cylinder (4C), shown in Fig. 19. A1 A2 A4 A3
Fig. 19. Concept of energy recovery circuit with a 4C cylinder
The additional, fourth, chamber in the cylinder allows keeping the multiplication of pressure supplied to the accumulator without changing the existing structure of controlling the cylinder from the pump. This results in an unchanged function of control of velocity, and the additional control valve allows obtaining a greater cylinder force during lifting than lowering. The systems shown in Figs 16, 18 and 19, were analyzed for their functions. So far circuits based on multi-chamber cylinders have neither been built nor tested.
35
4. Field tests of the excavator The next step, after completing the energy saving system, was to test the circuits under real conditions to estimate the level of energy possible to recover. To achieve this and to assure data recurrence, the following assumptions were made: – a strict excavation test was established, lasting 1800 [s], composed of 75 cycles. Each cycle contained five stages of work. The first stage – excavation, consisted of work of the boom mechanism (lowering), the arm mechanism (closing), and the bucket mechanism (closing). The second stage – work with the boom mechanism (raising). The third stage – about 90 degree swing, work of the swing mechanism. The fourth stage – emptying the bucket, work of the arm mechanism (opening) and bucket (opening). The fifth stage – swing, work of the swing mechanism, return to the excavation position, – constant rpm of the engine was set to 2350 [rpm], under which the engine delivers approximately maximum torque, – the excavation process was always performed in the same spot to eliminate the influence of different density of soil, – selection of one operator to assure the same type of excavation. The test was repeated five times, for all circuits described above, to eliminate errors and to allow statistical analysis. Testing under true conditions was carried out in a specially prepared area located within the Cracow Technical University campus ground. During the field tests, data were collected using a computer based measuring system. The measured signals from the sensors were amplified and converted to digital signals using an A/D Advantech PCL 818HG card. The signals were sent to a computer where the data were saved, analyzed and visualized using computer software.
4.1. Calculation method of hydraulic system energy consumption during excavator working cycle To compare different energy saving systems, taking into consideration power consumption, it was necessary to determine the energy used during a strict excavation test. Total energy Et is the sum of energy consumption for particular pump Ei: 3
Et = ∑ Ei i =1
where: i – pump number (i = 1, 2, 3).
(27)
36
The energy used by a particular pump was calculated using the formula:
Ei =
∑ ΔE = ∑ 0,5 ⋅ ( N
18000 j =1
18000
ij
j =1
i ( j −1)
+ N ij ) ⋅ ( t j − t j −1 )
(28)
where: ΔEij – energy consumed by the pump number “i” during one sampling period, Nij – power of pump number “i” at the instant tj, j – number of date row ( j = 1, 2, ... 18000, total test time 1800 s and sampling rate 10 [Hz]). The graphical interpretation of the energy calculation method is shown in Fig. 20. NN Ni(j–1) ji ji i(j-1)
ΔΔΕ Ejiji
tt(j–1) tjj (j-1)
Fig. 20. Graphical interpretation of energy calculation
The calculations of instantaneous power were made using the formula:
N ij = pij ⋅ nij ⋅ qi
(29)
where: pij – pressure on particular hydraulic pumps, nij – rotational velocity of the hydraulic pump, qi – unit output of individual pumps. During the analysis the power of a particular pump was compared with the power obtained for the original circuit (calculated in the same way), therefore Eq. (29) does not take into consideration the pump volumetric efficiency. To register parameters required to determine energy used by particular pumps the measurement system shown in Fig. 21 was used.
37
Fig. 21. Block diagram of the measurement system
4.2. Tests results for the original hydraulic excavator system 4.2.1. Experimental tests To allow identification of particular phases of the excavator working cycle a series of additional parameters was registered. The block diagram of the measuring circuit is shown in Fig. 21, and the elements used are listed in Table 2. Table 2. List of measuring circuit elements No. 101
Name Pressure transducer
Qt’y 4
102
Pressure transducer
2
Type 8891.74.3315, class 0,3
Producer Trafag
8842.21, class 0,3
Trafag
103
Displacement transducer
1
HPS-750-V
Wobit
105
rpm transducer
1
PCID-5ZN Inductive,
Puh
121
Impulse counter
1
DAG – 2F060010
Kobold
122
Wiring terminal board
1
PCLD-8115
Advantech
123
Analog-Digital card
1
PCL 818HG
Advantech
38 p1,p2,p3 [MPa]
20 16 12 8 4
350 300
15
250
10
200
5
150
0 12
100
xb [mm]
400
20
ps1,ps2 [MPa]
pb1,pb2 [MPa]
0 25
8 4 0 6
N [kW]
4
2
0 0
10
20 t [s]
30
40
Fig. 22. Two selected cycles from field test
Fig. 22 presents selected time plots of registered data during the tests, where: pb1 – pressure inside the boom cylinder on the piston side (pink) [MPa], pb2 – pressure inside the boom cylinder on the rod side (light blue) [MPa], ps1 – pressure on the swing motor (green) [MPa], ps2 – pressure on the swing motor (violet) [MPa], p1(blue), p2 (red), p3 (black) – pressures on individual hydraulic pumps [MPa], N – power [kW] on individual hydraulic pumps, pump number one (blue), pump number two (red), pump number three (black), xb – boom cylinder displacement (black), [mm]. 4.2.2. Estimation of hydraulic system energy consumption
For each set of the excavation tests calculations of the energy used by individual pumps were made. The pumps energy and the total energy used by the excavator during the excavation process are shown in Fig. 23.
39 6
total energy
EE[MJ] [MJ]
4 pump 1 pump 2
pump 3
2
0
Fig. 23. Energy used by individual pumps and total energy consumed by the hydraulic system
4.3. Energy estimation for saved energy utilized in swing mechanism For each field test, calculations of the energy used by particular pumps and the total energy used by the excavator during five series of the excavation process were made. These energies are shown in Fig. 24 for five tests. The average arithmetic energy is shown in Fig. 25. 6 total energy
EE [MJ] [MJ]
4 pump 1
2
pump 2
pump 3
0
Fig. 24. Energy used by particular pumps and total energy for energy saving system supplying swing motor 6
total energy
4
E [MJ]
E [MJ]
pump 1 pump 2 2
pump 3
0
Fig. 25. Arithmetic average energy used by particular pumps and total average energy for energy saving system supplying swing motor
40
Comparisons of the energy used by the circuit with energy saving system (yellow) and without the energy saving system (green) are shown in Figs 26 and 27. Fig. 26 presents the arithmetic average energy and Fig. 27 presents dispersion of energy using Box-Whisker plots, where the red lines indicate arithmetic average. 6 total energy
E [MJ]
4
E [MJ]
pump 1 pump 2
pump 3
2
0
Fig. 26. Comparison of average energy of energy saving system with the original system pump 1
pump 2
pump 3
3.2
3.2
3.2
2.8
2.8
2.8
2.4
2.4
2.4
total energy 6.2
6
2
E [MJ] E [MJ]
2
E [MJ] E [MJ]
2
E [MJ] E [MJ]
E [MJ] E [MJ]
5.8
5.6
5.4 1.6
1.6
1.6
1.2
1.2
1.2
5.2
5
Fig. 27. Comparison of energy dispersion for the energy saving system (yellow) with the original system (green)
The analysis of excavator operation showed that the energy used by pump 3 was about 30 percent of the total energy used during the test. However, the energy used to power the swing mechanism was very small, and most of the energy was lost due to the requirement of adequate pressure in the pilot pressure circuit (3,9 [MPa]). This led to a new design of the energy saving system in which pilot pump 3 was automatically turned on and off. 4.3.1. Estimation of energy consumption for a circuit with energy saving system with automatic control of pilot pump 3
For each test of work calculations of the energy used by particular pumps and the total energy used by the excavator during the excavation process were made.
41
These energies are shown in Fig. 28 for five tests. The average arithmetic energy is shown in Fig. 29. total energy
5
4
pump 1
E [MJ]
E [MJ]
3
2 pump 2 pump 3 1
0
Fig. 28. Energy used by individual pumps and summary energy for system with automatic control of pilot pump 5 total energy
EE[MJ] [MJ]
4
3
pump 1
2
pump 2 pump 3
1
0
Fig. 29. Average energy used by individual pumps and average total energy for system with automatic control of pilot pump
Comparisons of the energy used by the circuit with the energy saving system (brown) and without such system (green) are shown in Fig. 30. Fig. 31 presents dispersion of energy using Box-Whisker plots, where the red lines indicate the arithmetic average. 6 total energy
E [MJ] E [MJ]
4 pump 1
2
pump 2
pump 3
0
Fig. 30. Comparison of average energy of energy saving system with the original system
42 pump 1
pump 2
pump 3
3.2
3.2
3.2
2.8
2.8
2.8
2.4
2.4
2.4
2
2
2
total energy 6.5
1.6
E E[MJ] [MJ]
1.6
E [MJ] E [MJ]
EE[MJ] [MJ]
E [MJ] E [MJ]
6
1.6
1.2
1.2
1.2
0.8
0.8
0.8
5.5
5
4.5
0.4
0.4 E1
0.4 E2
4 E3
Fig. 31. Comparison of energy dispersion for energy saving system (brown) with the original system (green)
4.3.2. Summary of original system field tests
During the conducted experiments two variants of energy saving circuit were tested. The operation principle of the first variant lies in transfer of energy from the boom cylinder to the accumulator and its further transfer to the swing mechanism during the swing motion. It should be noted that pilot pump number 3 was working under load of relieved pressure during the entire cycle. In the second variant, the energy from the boom mechanism was used to power the pilot control circuit and the swing mechanism. This allowed the relief of pump 3 mentioned (directing the flow to the tank), whenever there was sufficient pressure in the accumulator for the pilot control circuit. However, when the pressure in the accumulator was insufficient, pump 3 automatically charged up the accumulator to the required level. In the circuit in question the operation of the swing mechanism was automatically controlled. The operation of mechanisms powered by pump 3, such as blade, boom swing and additional equipment required hand switching of the electronic control circuit. Further development of the circuit to allow powering of these mechanisms was intended. The conducted experiments allowed estimation of the energy used for the original circuit and two described energy saving system circuits. Fig. 32 presents a breakdown of energy used in the excavation process for individual circuits, and Fig. 33 represents the energy dispersion for five respective tests, where: 1 – factory installed circuit (green), 2 – energy saving circuit directly from the boom to the swing mechanism (yellow), 3 – recovery circuit with automatic control of pump 3 (brown).
43 8
1
6
2
E [MJ] E [MJ]
3 4
2
0
Fig. 32. Comparison of energy used for tested systems individual circuits
6.5
6
EE[MJ] [MJ]
5.5
5
4.5
4 E d
Fig. 33. Breakdown of summary energy for individual circuits
Recovering energy [%]
25 20 15 10 5 0
Fig. 34. Percentage of energy recovered for individual variants of the circuit
44
The amount of energy used during the excavation process depends not only on the circuit itself but also on many other factors that are impossible to take into consideration. Such factors include: the method of excavation by the operator (intensity of use of the boom and bucket mechanisms), soil properties (type, density, moisture, etc.). This explains the dispersion of energy for individual circuits. Assuming the value of required energy in the original circuit to be 100%, the energy recovery for individual circuits was obtained as shown in Fig. 34. For the first circuit the recovered energy was 7% (yellow), and for the second circuit the recovered energy was 24% (brown).
5. Energy recovery system using a 3C cylinder 5.1. Structure of the hydraulic system The schematic diagram of a hydraulic energy recovery system using a threechamber cylinder (3C) is shown in Fig. 35. The operating principle of the energy recovery system involves the storage of energy generated by a lowered boom (chamber A3 in cylinder 4) in a hydro-pneumatic accumulator. The energy was then utilized in the boom mechanism and transferred to chambers A1, A3. On account of variable effective areas of the cylinder, during the boom lowering and raising stage, the system provides pressure multiplication, at the same time the piston rod protrusion is shorter in relation to its retraction during lowering. 4
7
3
6
2
5
1
Fig. 35. Hydraulic energy saving system with 3C cylinder
46
New elements added to the conventional hydraulic excavator design are designated as 2, 3, 4, 5, 6, 7 (distribution valves block 3, 3C cylinder 4, other control valves 2, 5 and 6, accumulator 7) and shown in Fig. 35. The detailed specification is provided in Table 3. Table 3. List of additional hydraulic elements No. 2 3a, b 3c, d 4 5 6 7
Name Directional valve poppet Directional valve poppet Directional valve poppet Boom Cylinder Proportional pressure relief valve Proportional Flow Control Valve Accumulator
Qt’y 1 2 2 1 1 1 1
Type EVH 06/C3-12C-DG1/2” EVH 06/CA3-12C-DG1/2” EVH 06/CA5-12C-DG1/2” 3C XMP 06/250-12C-A-LG1 1/2” XQC2-12/NC50-12CAEN 2,5 [dm3]
Producer Comatrol Comatrol Comatrol C.U.T. Comatrol Comatrol Orsta
The results of tests performed within the framework of the previous research project [86] reveal that the rate of accumulator (7) loading and unloading in systems without a flow control valve is sufficient, that is why this flow control valve (6) is eliminated minimizing the flow resistance in the whole circuit. In the diagrams further on this flow control valve is omitted accordingly.
5.2. Electronic control system The energy recovery system has to be supported by a specially designed and engineered control system. Each of the spool valves in the hydraulic system (2, 3a, 3b, 3c, 3d) in the configuration shown in Fig. 35 have to be controlled separately. Independent control of coils in all these proportional valves allow providing time delays in valve opening and closing, thereby tuning the energy recovery system. Fig. 36 shows the concept of the electronic control circuit designed. The control of the energy recovery system uses four input signals: – pg – signal proportional to gas pressure in the accumulator, – pbd – signal proportional to control pressure whilst the boom is lowered, – pbu – signal proportional to control pressure whilst the boom is raised, – on – binary signal, activating the energy recovery system. The five binary signals generated control the corresponding coils in valves. In order to determine the conditions at which the state of output signals should change, threshold levels are provided. Input signals are compared with the threshold values in the comparator and a binary signal (0, 1) is generated accordingly on the comparator outputs. When the comparator input value (+) is greater than its output value, we get (1), otherwise the output value is (0).
47 + -
11.0
pgmax
10.7 +
pg
-
pbd
+
1.0
on
-
pbd1 +
pbd2
2.5
v1 v2
-
pgmin
v3
8.0 +
8.2
pbu
-
v4
+
v5
-
+
0.3
-
pbu1
pg1 8.4 + -
+
8.6
-
Fig. 36. Principle of operation of control circuit
The following threshold levels are defined: – pgmax – the energy recovery system is switched off during the boom lowering phase when the maximal gas pressure in the accumulator is exceeded, – pgmin – the energy recovery system is switched off during the boom lifting phase when the gas pressure in the accumulator reaches its predetermined minimal value, – pbu1 – used for detecting the state of boom raising, – pbd1 – used for detecting the state of boom lowering, – pg1 – controls the valve (5) during the boom raising phase, – pbd2 – controls the valve (5) during the boom lowering phase. These thresholds are introduced to reduce the sensitivity of the system to instantaneous, small fluctuations of control signal values, which might induce transient states in the control system. The threshold values are determined on the basis of proof tests. The operating principles of the system for two working cycles are shown in Fig. 37.
48 1
on
0 j
pg
pgmax
f
pbd pbu
b a
pg1 pgmin
l
g i
c
pbd2 pbd1
h
d
e
k
o
pbu1
v1 v2 v3 v4 v5 Fig. 37. Control system operation in typical working cycles
Description of states of the control system: – the control circuit operates as long as the control signal on is in the high state, when this condition is not met the output state will not be varied (v1-0; v2-0, v3-1, v4-1, v5-0), no matter how other signals should change, – (a) – raised boom, changing the position of the joystick lever in the lowering direction leads to an increase of the control pressure pbd, to the change of state (0; 1; 0; 1; 0) and accumulator loading, – (b) – stronger changing the joystick position increases the pressure in the control system and after reaching the threshold pbd2 the high state appears at the output v5 (0; 1; 0; 1; 1), – (c), (d) – joystick release causes the system to return to the neutral state (0; 0; 1; 1; 0) – (d), prior to that signal v5 is switched off – (0; 1; 0; 1; 0) – (c), – (e) – shifting the joystick position towards the boom raising function generates control pressure signal pbu and leads to the change of the state of the system to (1; 0; 1; 0; 1) – boom raising using the energy recovered from the accumulator,
49
– (f) – when the gas pressure in the accumulator reaches the threshold value pg1 during the boom raising, the signal is switched off v5 – (1; 0; 1; 0; 0), – (g) – when the gas pressure in the accumulator reaches the value pgmin, the outputs are switched to the neutral state – (0; 0; 1; 1; 0), – (h), (i) – start-up of the second working cycle (analogous to a and b) – raised boom, changing the position of the joystick lever in the lowering direction generates the control pressure signal and leads to the change of state (0; 1; 0; 1; 0) and accumulator loading begins. Further shifting of the joystick increases the pressure in the control system which exceeds the threshold value pbd2, giving rise to the high state at the output v5 (0; 1; 0; 1; 1), – (j) – when the gas pressure in the accumulator reaches the value pgmax the outputs are switched to the neutral state – (0; 0; 1; 1; 0), – (k), (l) – shifting the joystick position towards the boom raising function generates the control pressure signal and leads to the change of the state of the system to (1; 0; 1; 0; 1) – boom raising using the energy recovered from the accumulator; when gas pressure in the accumulator reaches the threshold value pg1 during the boom lifting phase the signal v5 is switched off (1; 0; 1; 0; 0) – analogous to e and f, – (o) – releasing of the joystick causes the system to return to the neutral state (0; 0; 1; 1; 0).
5.3. Operating principles of energy recovery system 5.3.1. Operation with energy saving system switched off Fig. 38 shows a schematic diagram of a hydraulic-powered boom mechanism when the energy recovery system is off. This state occurs when: – the energy recovery system is switched off by pressing a button, – accumulator (7) is loaded up to pressure pmax and boom lowering is to be continued, – during the boom raising, when the accumulator is unloaded down to pressure pgmin. The configuration of distribution valves (3), (3a) and (3b) in an open position, (3c), (3d) in a closed position) ensures that the original distribution valve in the excavator (1) is directly connected with chambers A1, A3. When the energy recovery system is off, the boom can be lowered or raised without the hydraulic accumulator (7).
50 4
7
3
2
5
1
Fig. 38. Boom cylinder hydraulic system with energy saving switched off
5.3.2. Active energy saving system (boom lowering from A3) Fig. 39 shows the operating principle of the system with an on-state energy recovery circuit; the accumulator is loaded from chamber A3. The liquid flows associated with the supply system are indicated in orange color, red color indicates the flow of the working fluid to the accumulator. The return flow is marked in blue. During the boom lowering, the distribution valve (1) shifts to the lowering position, as a consequence the pump in this configuration directly supplies chamber A2 of the cylinder 3C (4). The configuration of distribution valves (3): (3a) and (3b) are open and (3b), (3d) are closed. This configuration opens the path from chamber A3 through an open distribution valve (3c) right through to the accumulator (7), thus enabling the storage of energy transferred from chamber A3. The open valve (3a)
51
provides the connection between chamber A1 and the return line. The valve (2) is opened to minimize the resistance of oil flow from chamber A1 to the reservoir. This state occurs only when the boom lever is fully shifted to the lowering position (at small lowering rates the distribution vale (2) remains closed and oil has to flow through the distribution valve (1) from chamber A1 to the reservoir. When the accumulator (7) loading from chamber A3 is over (end of cycle or reaching the maximum pressure pgmax), the intermediate state of the control system is reached (valves (2) and (3c) are closed and 3c and 3d remain closed), afterward the system configuration becomes that shown in Fig. 38. 4
7
3
2
5
1
Fig. 39. Energy saving system during accumulator charging
52 4
7
3
2
5
1
Fig. 40. Active energy saving system during boom raising
5.3.3. Active energy saving system (boom lifting from accumulator to chambers A1, A3) Fig. 40 shows the operating principle of the boom mechanism with the active energy recovery system (from the accumulator to chambers A1, A3). The fluid flow from the supply system is indicated in yellow, the flow of the working fluid under pressure from the accumulator is indicated in red. Flows in the return line are indicated in blue. When the boom is raised, the valves (1) and (2) change their position. In consequence, the pump delivery is directed to the return line. The group of valves (3) have the configuration: (3a), (3b)-closed; (3c), (3d)-open. This configuration opens the path from the accumulator (7) to chambers A1, A3 thereby allowing for the transfer of energy stored in the accumulator. Chamber A2 is connected to the return line directly, via the distribution valve (1). When the energy stored in the accumulator (7) pgmin is all used up, the system is switched to the mode whereby the cylinder (4) is supplied from the pump. An intermediate state
53
occurs in between, when the valve (2) is closed and then the system switches to the configuration shown in Fig. 38. The intermediate state was introduced to minimize the negative impacts produced when the valves (3) switch from the accumulator supply to the pump supply mode. 4
7
3
2
5
1
Fig. 41. Energy saving system during manual discharge
5.3.4. Manual discharge of accumulator Fig. 41 shows the configuration of valve connections enabling the manual discharge of the accumulator. The flows of the working fluid under pressure from the previously loaded accumulator to the return line are indicated in red. The accumulator is manually unloaded through changing the position of the valve (5), to connect the accumulator with the oil tank. At the same time valves (3c) and (3d) should remain in closed position.
54
6. Field tests of an excavator with 3C cylinder For better evaluation of the functional properties of the cylinder 3C energy recovery system in the experimental tests the same procedure as described in chapter 5 was used. Also the same method of energy calculation during repeated working cycle was adopted.
6.1. Experimental tests of 3C cylinder energy saving system Testing under real operating conditions was carried out in the area located within the Cracow University of Technology campus ground. During field tests, the data were collected using a computer based measuring system. The measured signals from the sensors were amplified and converted to digital signals using an A/D Advantech PCL 818HG card. The signals were sent to a computer where the data were saved, analyzed and visualized using computer software. Fig. 42 shows the excavator with installed instrumentation during field tests. The tests were carried out using a 2,5 liter accumulator to recover energy, and the following parameters were set: pre-charge pressure of the accumulator of 7,6 [MPa] and maximum accumulator charging pressure of 10,5 [MPa].
Fig. 43. Block diagram of the measurement system
During the field tests the measurement circuit shown in Fig. 43 was used. Elements used in this measuring circuit are listed in Table 4. To generate control
55
signals for energy saving system a pressure transducer was installed in the gas connector of the accumulator and original hydraulic control circuit. Table 4. List of elements used in the measurement system Name Pressure transducer Pressure transducer Pressure transducer Displacement transducer Impulse counter Rpm transducer Impulse counter Wiring terminal board Analog-Digital card
Qt’y 3 4 2 1 1 1 1 1 1
Type 8891.74.3315, class 0,3 8220.74.5017.35.17.P class 0,15 8891.74.3315, class 0,3 VRVT 190/500 EM-10-V PCID-5ZN Inductive DAG – 2F060010 PCLD-8115 PCL 818HG
Producer Trafag Trafag Trafag Penny & Giles Penny & Giles Puh Kobold Advantech Advantech
p1,p2,p3 [MPa]
20 16 12 8 4
pb1,pb2,pb3 [MPa]
450 400 350 300 250 200 150 100 50 0
20 15 10 5 0 10
pg [MPa]
9.5 9 8.5 8 7.5 5 4 3 2 1 0 1700
1710
1720
1730 t [s]
1740
1750
Fig. 44. Selected work cycles from the entire test
1760
xb [mm]
0 25
N [kW]
No. 101 102 103 104 105 106 121 122 123
56
Fig. 44 presents random selected cycles of hydraulic system with operation parameters taken from the entire process of excavating, where: – pb1 – boom cylinder pressure in piston side A1 (red) [MPa], – pb2 – boom cylinder pressure in rod side A2 (light blue) [MPa], – pb3 – pressure in the boom cylinder chamber A3 (magenta) [MPa], – pg – pressure in the gas volume of the accumulator (green) [MPa], – p1 (black), p2 (blue), p3 (red) – hydraulic pumps outlet pressure [MPa], – N – power [kW] of individual hydraulic pumps, pump 1 (black), pump 2 (blue), pump number 3 (red), – xb – displacement of boom cylinder (black) [mm].
p1 [MPa]
16 12 8 4 0 pb1,pb2,pb3 [MPa]
16 12 8 4 0 10.5 pg [MPa]
10 9.5 9 8.5 8
xb [mm]
7.5 450 400 350 300 250 200 150 100 50 0 100 v [mm/s]
50 0 -50 -100 -150 1246
1248
1250
1252
1254
1256
t [s]
Fig. 45. Boom cylinder velocity during lowering of the boom with 3C cylinder energy saving system, where: v – speed of boom cylinder (blue) [mm/s]
57
xb [mm]
xb [mm]
The analysis of the energy saving system with 3C cylinder proved some differences related to the original excavator circuit. It was concluded that these differences are related mainly to the boom cylinder speed. During lowering of the boom, i.e. charging of the accumulator, the average velocity of the boom cylinder vb was 150–130 [mm/s] (Figs 45, 46). Boom lowering velocity in the original excavator is between 75 to 80 [mm/s] as shown in Fig. 47. 450 400 350 300 250 200 150 100 50 0 100
vv [mm/s] [mm/s]
50 0 -50 -100 -150 1120
1160
1200 [s] tt [s]
1240
1280
Fig. 46. Boom cylinder displacement and velocity for the 3C cylinder energy saving system for selected time period 400
200
b
xxb [mm] [mm]
300
100 0 80
[mm/s] vv[mm/s]
40 0 -40 -80 -120 1600
1640
1680
1720
1760
1800
[s] tt [s]
Fig. 47. Boom cylinder velocity for the original hydraulic system of excavator
The differences in boom lowering speed are attributable to the reduction of the effective area A2 and the decrease of the flow resistance between chamber A1 and
58
the tank, achieved when the valve (2) was provided and the throttling in the return line in the distribution valve (1) in the excavator was eliminated, shown in Fig. 47. To ensure slow and high-precision lowering of the boom the valve (2) opens when control pressure exceeds the value pbd2.
p1 [MPa]
16 12 8 4 0 pb1,pb2,pb3 [MPa]
16 12 8 4 0 10 pg [MPa]
9.6 9.2 8.8 8.4 8
xb [mm]
7.6 450 400 350 300 250 200 150 100 50 0 150 v [mm/s]
100 50 0 -50 -100 -150 820
824
828 t [s]
832
836
Fig. 48. Boom cylinder velocity during raising of the boom with 3C cylinder energy saving system
Fig. 48 shows the plots of the parameters of the energy recovery system with a 3C cylinder during the phase of boom lifting. When the energy stored in the accumulator is utilized in this process, the average raising speed is 115 [mm/s] (the plot section to the left of the red vertical line). When the accumulator is unloaded
59
completely and the system is supplied from a pump the average lifting speed is 50 mm/s (the plot section to the right of the red line). The difference in the boom lifting velocity is associated with the accumulator unloading characteristics and depends on the actual configuration of the working equipment. In the original system the lifting velocity falls between 50 and 60 [mm/s] (Fig. 48). The movements that take place in excavations are mostly high speed, that is why they are not regarded as dangerous but useful as the working cycles can get shorter, particularly when the bucket and arm movements are well synchronized. In the original system the boom lifting speed is limited by the pump volumetric delivery.
6.2. Estimation of power consumption with 3C cylinder energy saving system The energy used by individual pumps and the total energy used by the excavator during the whole excavation process was calculated for each test and is presented in Fig. 49 and 50. 5500
total energy 5000 4500 4000
pump 1+2
E [kJ]
E [MJ]
3500 3000 2500 2000
pump 3
pump 1 pump2
1500 1000 500 0
Tests
Fig. 49. Energy used by individual pumps and total energy
Comparison of energy used by the 3C cylinder energy saving system (yellow) with the energy used by the original system (green) is shown in Figs 51 and 52. While Fig. 51 presents the arithmetic average energy, Fig. 52 presents dispersion of
60
energy using Box-Whisker plots, where the red lines indicate the arithmetic average. 5000
total energy
4000
pump 1+2
E E[MJ] [kJ]
3000
pump 3 2000
pump 1
pump2
1000
0
Fig. 50. Arithmetic averaged energy used by individual pumps and averaged total energy
6000
total energy 5000
pump 1+2
EE [MJ] [kJ]
4000
3000
pump 1
2000
pump2
pump 3
1000
0
Fig. 51. Comparison of average energy used by 3C cylinder energy saving system with the original system
61 pump 1 2600
pump 2
pump 3
2000
2200
1800
2000
total energy 6000
2400
EE [MJ] [kJ]
2200 2000
5600 1600
1800
1400
1600
1200
1400
1800
5200
1600 1400
4800
Fig. 52. Comparison of energy dispersion for energy saving system (yellow) with the original system (green)
6.3. Summary of field tests of excavator with 3C cylinder The 3C cylinder with the energy recovery system was extensively tested to check its functional parameters and potentials of power savings. – The tests confirmed good performance of the 3C cylinder applied in the energy recovery system for an excavator Cat 301.5. – The energy savings in the tested system run up to 14%. – Apart from the actual system configuration other factors affect the amount of energy used up in the excavation processes though they cannot be precisely quantified for individual tests. These factors include: the manner of making an excavation by the operator ( intensity of arm and bucket mechanism utilization), soil parameters (soil type, compactness, moisture contents). – Application of a 3C cylinder and reduction of flow resistance in the lines supplying the cylinders (elimination of throttling in the original distributor in the boom) led to an increase of the boom lowering speed. Flow resistance had to be reduced to relieve the supplying pump as higher pressure values were now becoming necessary to lower the boom due to the reduction of the effective area A2. – The boom moving speed is increased also when the 3C cylinder is powersupplied from the accumulator (boom lifting). That is evidenced by the accumulator unloading characteristics (greater flow rates). – It is suggested that a flow control valve (6) be placed between the accumulator (7) and the distributors unit (3) to eliminate too rapid changes of the boom lifting and lowering speed. However, in this configuration the performance of the energy recovery system might be deteriorated. The performance of a 3C energy recovery system could be fully evaluated when the integrated valve block is built to combine the functions of the original system with the energy recovery application.
62
7. Proposal of improving energy saving by system modification 7.1. Energy recovery system modification In order to explore energy saving potentials in excavator hydraulic systems, it was advisable that additional tests should be run for modifications of the excavator system and systems enabling utilization of stored energy. Fig. 53 shows a suggested modification to an energy recovery system. The system uses 3-way, 2-position distribution valves in place of the group of valves (3). Such configuration would simplify the control procedure. Further modifications are possible. For example, the stored energy can be also utilized to power-supply the bucket mechanism, as shown in Fig. 54. 4 7
3a 6
3b 2
5 1
Fig. 53. Suggested modification of energy recovery system
63 Original Bucket Cylinder
3C Boom Cylinder
Main (original) distribution valve
Main (original) distribution valve
Fig. 54. Energy recovery in bucket mechanism
7.2. Estimation of 3C cylinder diameters based on load characteristic Primary choice of the dimensions of the 3C cylinder, mainly diameters d1, d2, d3 of particular chambers, based on real force F characteristic taken from the experiments during boom lowering and raising. This force varies for different arm and bucket configuration as well as for bucket load from diggings. Force F characteristic of the boom cylinder during lowering without excavating material (for example to the trench) is utilized, with initially adopted cross section areas of the chambers, to accumulator volume estimation and its preload pressure, required for energy saving during boom lowering. Fig. 55 presents the range of real force F characteristic during boom lowering as a function of the actual cylinder lengths lb, for different configuration of the arm and bucket, taken from the field tests of a mini excavator 301.5, consisting of 75 working cycles. From the distribution of the force values limited by lines F1 and F2, shown in Fig. 55, the range of the most possible values of force F was determined. The next step was to size cylinder chambers diameter, assuming that the difference between areas of the
64
new 3C cylinder and original one should not be greater than ±10%. It is expressed by formulas, where δ1, δ2 are tolerance coefficients:
δ1 =
A1o − ( A1 + A3 )
δ2 =
A1o
⋅ 100%
(30)
A2 o − A2 ⋅ 100% A2 o
(31)
where: A1o, A2o – cross section areas of the original cylinder A1, A2, A3 – equivalent cross section areas of the 3C cylinder, respectively. Fm 9761 lb 4800 Fm 9761 lb +3238.5
20000
F1 16000
F F[N] [N]
12000
F2
8000
4000
0 0.7
0.8
0.9 lb [m]
1
1.1
lb [m]
Fig. 55. Boom cylinder real force F characteristic during lowering taken form 75 working cycles
Having initially chosen the diameters of particular chambers and knowing cylinder force F characteristic, it is possible to calculate pressure in chamber 3 (C3) during boom lowering: pb 3 =
F1 A3
pb 3′ =
F2 A3
(32)
where: F1, F2 – upper and lower force value limit during boom lowering, pb3, pb3’ – upper and lower limit of pressure value in chamber 3C.
65
The character of the cylinder load, taken from the experiment and calculation, allows determining accumulator volume and its preload pressure. To select gas accumulator the equation for pressure changes due to its gas volume can be used: pa = po ⋅
Vn (V − Vo ) n
(33)
p [MPa]
where: pa – accumulator pressure, po – preload pressure, V – maximum accumulator volume, Vo – actual accumulator volume. When determining the preload pressure one should remember that it works in the full range of boom cylinder stroke rather infrequently. So, the curve of the accumulator charging pressure (pa) crossing the curve of the piston side cylinder pressure during its lowering (pb3’) is acceptable.
lb [m]
Fig. 56. Pressure characteristics in chamber C3 (pb3 lower limit, pb3’ upper limit) and selected accumulator pressure during its charging from boom cylinder
The next stage of the procedure is to check whether the level of force value which can be obtained from the accumulator pressure is high enough to overcome the cylinder force (taken from the real test, see Fig. 56), and in consequence be able to raise the boom using the energy stored in the accumulator during lowering. Boom cylinder force characteristic during its raising is different in real tests, that is why its value was restricted between two curves F3, F4, as shown in Fig. 57. These curves are a reference for checking whether the force coming from accumulator pressure is able to overcome these forces and enable raising the boom.
66
Force characteristics coming from accumulator pressure were calculated from equations: Fac1 = pa ⋅ A1
Fac 2 = pa ⋅ ( A1 + A3 )
(34)
50000
40000
F4
F [N] F [N]
30000
20000
10000
F3
0 0.7
0.8
0.9 Lb [m]
1
1.1
lb [m]
Fig. 57. Boom cylinder force characteristic during its raising (taken from 75 cycles of field tests)
35000 Fac2 30000
F4
25000
FF[N] [N]
20000
F3
Fac1
15000
10000
5000
0 0.7
0.8
0.9 L b [m] lb [m]
1
1.1
Fig. 58. Force characteristics as a function of boom cylinder length during boom raising
In Fig. 58 force characteristics during raising the boom F3 and F4, together with force coming from accumulator pressure, are presented. Curve Fa1 is obtained
67
when the energy stored is transferred from accumulator to chamber C1 of 3C cylinder, while curve Fa2 – when the stored energy is transferred to both 3C cylinder chambers C1 and C3. If the force coming from accumulator pressure is higher than the force which is present during boom lowering, it can be assumed that the diameters of the cylinder chambers have been adjusted correctly and the next step is to check the cylinder dimensions in respect to strength of material. The goal is to develop a suitable control system which enables, by measuring actual load of the boom cylinder, an automated change of the force characteristic (coming from accumulator pressure) from Fa1 to Fa2, in relation to actual load of the boom cylinder enabling its raising from the stored energy. The range of energy reuse depends on accumulator charge coefficient on one hand and volume of chamber 3C on the other, limiting the range of cylinder movement from the stored energy. The guidelines of 3C cylinder design for estimated pressure values of its operation in adopted heavy duty machine equipment working cycle as well as strength calculations – are presented in Appendix A.
68
8. Tests with original 301.5 mini excavator boom cylinder and energy saving system ESS The main goal of the research described in this chapter was to develop a more advanced energy saving concept with pump-motor as a component of a hydraulic energy storage and reuse system which enables lowering energy consumption by equalized engine load. It required designing and building a special laboratory test stand, which is presented in Fig. 59. 301.5 mini hex
Load (cycle)
Main (original) distribution valve Mp ENGINE (electric motor)
np
Mm
np
nm
one-way clutch Proportional relief valve
Proportional flow control
Fig. 59. Hydraulic energy saving system (ESS)
The Energy Saving System (ESS), compared with that described in previous chapters, allowed managing energy distribution by different configurations of energy flow. The ESS test stand presented gives a possibility of transferring hydrostatic energy from the mini excavator boom cylinder to the hydrostatic motor and, in this way, reducing the main (electric) engine torque necessary to drive the pump. So, the efficiency of energy recovery process is obvious. Furthermore, we can store energy in the hydraulic accumulator and then use it to support the main drive (electric motor and pump) in the phase of maximum power consumption. The installed measurement devices allow us to evaluate power and energy at different system points and phase of its operation and, in consequence, to determine the efficiency of the energy storage process. Table 5 shows a list of hydraulic components used in the stand. Measurement transducers, shown in Fig. 59, are connected to the acquisition system, equipped with an A/D computer card, as presented in Fig. 60. This
69
measurement system allowed us to register such parameters as pressure, torque, rotational velocity, flow and temperature.
Fig. 60. Block diagram of the measurement system Table 5. List of hydraulic components of ESS test stand No.
Name Variable displacement axial piston pump with electric control Variable displacement motor with electric control Accumulator One-way clutch Electric motor 1 Directional poppet valve 2, 5 Directional poppet valves 3 Directional valve poppet 4 Proportional directional valve 6 Proportional relief valve 7 Proportional Flow Control Valve 8 Relief valve
Qt’t 1 1 1 1 1 1 2 1 1 1 1 1
Type PV032 32[cm3/rev] – 350 [bar] A6VM28EP1 28[cm3/rev] – 400 [bar] Piston 6 [dm3] FB 37 SF 22 [kW] EVH 06/CA5-12C-DG1/2” EVH 06/C3-12C-DG1/2” EVH 06/A3-12C-DG1/2” XQ2 12/NC-12C-DG1/2” XMP06 XQC2-12/NC50-12CAEN DBW
Producer Parker Bosch-Rexroth Parker Radius Indukta Comatrol Comatrol Comatrol Comatrol Comatrol Comatrol Ponar Wadowice
70
8.1. Tests methodology Boom lowering tests were performed after the 301.5 mini hex system was connected to ESS stand in the configuration presented in Fig. 61. The piston side of the boom cylinder was connected to distribution valve 4 while the rod side was connected to the return line. During boom lowering valves 3 and 4 were in open position and valves 1, 2 and 5 were closed, thus the oil from boom cylinder flowed to the hydrostatic motor supporting the electric engine. Proportional relief valve 6 was used to keep pressure in the pump outlet. So the torque necessary to drive the pump was covered by both motors: electric and hydrostatic. 301.5 mini hex
Load (cycle)
Main (original) distribution valve Mp ENGINE (electric motor)
np
Mm
np
nm
one-way clutch
Proportional flow control
Proportional relief valve
Fig. 61. Hydraulic system during boom lowering tests
A number of boom lowering tests were done for different electric motor rpm, different potential energy of boom (executed by adding mass into the bucket), for different boom lowering velocity controlled by hydrostatic motor displacement. A detailed list of the boom lowering tests is presented in Table 6. Table 6. List of boom lowering tests Electric engine rpm level 1000 1500 2000 2500
Without load in bucket Yes Yes
With load 52 [kg] in bucket Yes Yes Yes Yes
Boom cylinder velocity range [mm/s] (25–220) (25–220) (25–220) (25–220)
71
One of the main aspects of tests was an evaluation of the energy recovery efficiency in the system based on hydrostatic motor as energy transformer. This efficiency was calculated according to the formula: k
E η= m = Ec
∑ 0,5 ⋅ ( N i= j k
m ( i −1)
+ N mi ) ⋅ (ti − ti −1 )
∑ 0,5 ⋅ ( Nc (i −1) + Nci ) ⋅ (ti − ti −1 )
(35)
i= j
where: Ec – total energy of boom lowering process measured on boom cylinder outlet, Em – total energy on hydrostatic motor shaft, Nc – hydrostatic power on the boom cylinder outlet, Nm – power on hydrostatic motor shaft, i – current row number, j, k – first and last row number of boom lowering phase, respectively. Hydrostatic power on the boom cylinder outlet and on hydrostatic motor shaft were determined following the equation:
N c = pb1 ⋅ Qc
(36)
N m = M m ⋅ ωm
(37)
where: pb1 – pressure in the piston side outlet of boom cylinder, Qc – volumetric flow in the boom cylinder outlet, Mm – hydrostatic motor torque, ωc – hydrostatic motor angular velocity.
8.2. Excavator 301.5 boom lowering tests with ESS Selected plots of one cycle of system parameters during boom lowering tests on ESS stand are presented in Figs 62–67. where: εm – displacement control parameter of motor (purple), Uv4 – proportional directional valve 4 control voltage [V] (red), Qc – boom cylinder flow [dm3/min] (orange), pb1 – pressure in piston side of boom cylinder [MPa] (magenta), pm – pressure in hydraulic motor inlet [MPa] (blue), pp – pressure in pump outlet [MPa] (red), Mm – hydrostatic motor torque [Nm] (blue), Mp – electric engine torque [Nm] (red), nm – hydraulic motor rotational velocity [rpm] (blue), np – electric engine rotational velocity [rpm] (red), xb – displacement of boom cylinder [mm] (black), vb – velocity of boom cylinder [mm/s] (magenta).
72
Fig. 62. Selected plots of system parameters for 1000 [rpm] of electric engine – one cycle
Fig. 63. Selected plots of system parameters for 1500 [rpm] of electric engine – one cycle
73
Fig. 64. Selected plots of system parameters with additional load 52 [kg] for 1000 [rpm] of electric engine – one cycle 10 8
0.6
6
0.4
4
0.2
2
0
0
20
40 0
vb [mm/s]
Qc [dm3/min]
16
Uv4 [V]
εm
1 0.8
12
-40 8
-80
4 0
-120
pp,pm,pb1 [MPa]
16 12 8 4
400
30
300
20
200
10
100
np, nm [rpm]
0 1600
0
1200 800 400 0 144
146
148
150
t [s]
Fig. 65. Selected plots of system parameters with additional load 52 [kg] for 1500 [rpm] of electric engine – one cycle
152
xb [mm]
Mp, Mm [Nm]
0 40
74 10
6
0.4
4
0.2
2
0
0
30
50
Uv4 [V]
8
0.6
0 20
-50 -100
10
vb [mm/s]
Qc [dm3/min]
εm
1 0.8
-150 0
-200
pp,pm,pb1 [MPa]
20 16 12 8 4
400
30
300
20
200
10
100
np, nm [rpm]
0 2500
xb [mm]
Mp, Mm [Nm]
0 40
0
2000 1500 1000 500 0 262
263
264
265
266
t [s]
Fig. 66. Selected plots of system parameters with additional load 52 [kg] for 2000 [rpm] of electric engine – one cycle
8
0.6
6
0.4
4
0.2
2
Uv4 [V]
10
0
0
25
40
20
0
15
-40
10
-80
5
-120
0
-160
vb [mm/s]
Qc [dm3/min]
εm
1 0.8
pp,pm,pb1 [MPa]
20 16 12 8 4 0 400
40
300
30 200
20
100
10
0
np, nm [rpm]
0 3000 2000 1000 0 172
174
176
t [s]
Fig. 67. Selected plots of system parameters with additional load 52 [kg] for 2500 [rpm] of electric engine – one cycle
178
xb [mm]
Mp, Mm [Nm]
50
75
Based on the data collected during the tests performed on the ESS stand, energy possible to recover during boom lowering was calculated, and mechanical energy transferred from the hydrostatic motor to pump shaft was determined. Taking into consideration these two energies, in the boom lowering phase, the efficiency of energy recovery process can be evaluated following Eq. (27). Fig. 68 shows energy recovery efficiency as a function of hydraulic motor displacement, while Fig. 69 presents the efficiency in relation to boom cylinder velocity, for different engine rpm and different load in excavator bucket. 0.6
tests without load in excavator bucket for 1000 engine rpm
0.4
ΝΝΝ ηΝΝ[–]
tests without load in excavator bucket for 1500 engine rpm tests with 52 kg load in excavator bucket for 1000 engine rpm test with 52 kg load in excavator bucket for 1500 engine rpm tests with 52 kg load in excavator bucket for 2000 engine rpm
0.2
tests with 52 kg load in excavator bucket for 2500 engine rpm
0 0
0.2
0.4
0.6
0.8
1
8 εΝmmΝ[–]
Fig. 68. Efficiency as a function of motor displacement
0.6
tests without load in excavator bucket for 1000 engine rpm tests without load in excavator bucket for 1500 engine rpm tests with 52 kg load in excavator bucket for 1000 engine rpm tests with 52 kg load in excavator bucket for 1500 engine rpm tests with 52 kg load in excavator bucket for 2000 engine rpm tests with 52 kg load in excavator bucket for 2500 engine rpm
η [–] η [−]
0.4
0.2
0 0
50
100
150
200
250
[mm/s] v v[mm/s]
Fig. 69. Efficiency as a function of boom cylinder velocity
76
As can be seen, maximum efficiency varies from 0,25 to 0,6 and depends on boom cylinder velocity as well as electric motor rpm (in the range of 1000 to 2500 [rpm]). The analysis of the efficiency plots proved that efficiency is heavily affected by hydrostatic motor efficiency (due to volumetric displacement) and hydraulic line losses (between cylinder and motor). To illustrate the influence of the above parameters on the total efficiency of the boom cylinder ESS, hydraulic line and motor losses for 1000 [rpm] and 2500 [rpm] were determined, according to formulas: ηL =
pm po
ηHM =
– efficiency of hydraulic line,
(38)
M m ⋅ ωm – total efficiency of hydraulic motor, Qb ⋅ pm
ηs = ηHM ⋅ ηL
(39)
– total efficiency of system,
(40)
where: pm – input pressure of hydrostatic motor, po – output pressure of boom cylinder, Mm – torque of hydrostatic motor, ωm – rotational velocity of hydrostatic motor, Qb – output volumetric flow from boom cylinder. The results of partial efficiencies together with their product are shown in Figs 70 and 71. 1
0.8
hydraulic efficiency of line motor total efficiency of hydraulic hydrulic motor total efficiency of system
η [–] η [−]
0.6
0.4
0.2
0 0
40
80
120
160
vbb [mm/s] [mm/s]
Fig. 70. Efficiency as a function of boom velocity for 1000 engine rpm
77 1
0.8
hydraulic efficiency of line hydraulicmotor total efficiency of hydrulic motor total efficiency of system
ηη[–] [−]
0.6
0.4
0.2
0 80
120
160
200
240
vvbb[mm/s] [mm/s]
Fig. 71. Efficiency as a function of boom velocity for 2500 engine rpm
It can be observed that for 2500 [rpm] and boom cylinder velocity range from 80 to 240 [mm/s], line efficiency varies from 0,9 to 0,6, while motor efficiency varies from 0,2 to 0,3. Such low efficiency of the motor results mainly from its work in the low range of pressure and displacement control parameter of the motor below 0,5.
8.3. Boom lowering tests with regenerative (regen) valve To run boom lowering tests with a regen valve, the stand (Fig. 72) was modified by installing an extra electro-controlled distribution valve 5. During boom lowering, distribution valve 5 is in position, presented in Fig. 72, connecting boom cylinder chambers. Through opened valves 4 and 3, oil flows from the boom cylinder to hydrostatic motor. Valves 1 and 2 remain in closed position, while the pump is loaded using proportionally controlled relief valve 6. The tests were performed with an empty bucket for three values of electric engine rpm and different hydrostatic motor displacement, resulting in different boom cylinder velocity (Table 7). Table 7. Specification of tests Electric engine rpm 1000 1500 2000
Without load in bucket Yes Yes Yes
Boom cylinder velocity range [mm/s] (80 – 190) (80 – 190) (80 – 190)
78 301.5 mini hex
Load (cycle)
Main (original) distribution valve Mp
np
ENGINE (electric motor)
M
np
nm
one-way clutch Proportional relief valve
Proportional flow control
Fig. 72. ESS stand and minihex boom cylinder with regen valve 10
6
0.4
4
0.2
2
0
0
30
40 0
20 -40 10 -80 0
pp,pm,pb1, pb2 [MPa]
Uv4 [V]
8
0.6
vb [mm/s]
Qc [dm3/min]
εm
1 0.8
-120
20 16 12 8 4 0 400 300
20
200 10 100
0 1200
np, nm [rpm]
xb [mm]
Mp, Mm [Nm]
30
0
800 400 0 514
516
518
520
t [s]
Fig. 73. Selected plots of system parameters with regen valve for 1000 [rpm] of engine (one cycle)
Selected plots of system parameters are shown in Figs 73–75, where: εm – displacement control parameter of motor (purple), Uv4 – proportional directional valve 4 control voltage [V] (red), Qc – boom cylinder flow [dm3/min] (orange), pb1 – pressure in the piston side of boom cylinder [MPa] (magenta), pb2 – pressure in the rod side of boom cylinder [MPa]
79
pp,pm,pb1, pb2 [MPa]
0.8
8
0.6
6
0.4
4
0.2
2
Uv4 [V]
10
0
0
25
40
20
0
15
-40
10
-80
5
-120
0
-160
vb [mm/s]
Qc [dm3/min]
εm
1
20 16 12 8 4
400
30
300
20
200
10
100
np, nm [rpm]
0 1600
xb [mm]
Mp, Mm [Nm]
0 40
0
1200 800 400 0 210
211
212
213
214
215
t [s]
Fig. 74. Selected plots of system parameters with regen valve for 1500 [rpm] of engine (one cycle)
pp,pm,pb1, pb2 [MPa]
10
6
0.4
4
0.2
2
0
0
50
50
40
0
Uv4 [V]
8
0.6
-50
30
vb [mm/s]
Qc [dm3/min]
εm
1 0.8
-100 20
-150
10
-200
0
-250
20 16 12 8 4
400
30
300
20
200
10
100
np, nm [rpm]
0 2000
0
1600 1200 800 400 0 122
123
124
125
126
127
t [s]
Fig. 75. Selected plots of system parameters with regen valve for 2000 [rpm] of engine (one cycle)
xb [mm]
Mp, Mm [Nm]
0 40
80
(green), pm – pressure in the hydraulic motor inlet [MPa] (blue), pp – pressure in the pump outlet [MPa] (red), Mm – hydrostatic motor torque [Nm] (blue), Mp – electric engine torque [Nm] (red), nm – hydraulic motor [rpm] (blue), np – electric engine [rpm] (red), xb – displacement of boom cylinder [mm] (black), vb – velocity of boom cylinder [mm/s] (magenta). 0.25
1000 engine rpm 1500 engine rpm 2000 engine rpm
0.2
η η[–] [−]
0.15
0.1
0.05
0 60
80
100
120
140
160
180
v [mm/s] vb [mm/s] b
Fig. 76. Efficiency of energy recovery as a function of boom cylinder velocity for system with regen valve
0.6
tests without load in excavator bucket for 1000 engine rpm tests without load in excavator bucket for 1500 engine rpm tests without load in excavator bucket with regen valve for 1000 engine rpm tests without load in excavator bucket with regen valve for 1500 engine rpm tests without load in excavator bucket with regen valve for 2000 engine rpm
ηη [–] [−]
0.4
0.2
0 0
50
100
150
200
250
[mm/s] v v[mm/s]
Fig. 77. Comparison of energy recovery efficiency for system, with regen valve and one without
81
Energy recovery efficiency was determined employing formula (35) (see section 8.1). Fig. 76 shows energy recovery efficiency as a function of boom cylinder velocity. A comparison of energy recovery efficiency for a system with the regen valve and one without is presented in Fig. 77. The efficiency of the system with the regen valve is below 0,2 and is lower than that for the conventional system, which can be explained by an extremely low value of hydrostatic motor displacement control parameter (in the range up to 0,13), despite high boom cylinder velocity (from 80 to 170 [mm/s]). 8.3.1. Additional tests of ESS with regen valve
To observe the phenomena related to regen valve operation additional tests were performed in which time delay between switching valves 5 and 3 was introduced. These made it possible to measure and analyze pressure and boom cylinder displacement transients. The tests were done for two different time delays: 8 sec (Fig. 78) and 1,1 sec (Fig. 79). As a background for comparison, in Fig 80 tests results for simultaneous switching of valves 5 and 3 was presented.
Fig. 78. Selected plots of system parameters with regen valve for different time of regen valve and hydrostatic motor switching (with time delay 8 sec)
82
Fig. 79. Selected plots of system parameters with regen valve for different time of regen valve and hydrostatic motor switching (with time delay 1,1 sec) 1
εm
0.6 0.4
pp,pm,pb1, pb2 [MPa]
Qc [dm3/min]
0.2 0
0
50
50
40
0 -50
30
vb [mm/s]
Valve 3 on/off
1 0.8
-100 20
-150
10
-200
0
-250
20 16 12 8 4
400
30
300
20
200
10
100
np, nm [rpm]
0 2000
xb [mm]
Mp, Mm [Nm]
0 40
0
1600 1200 800 400 0 122
123
124
125
126
127
t [s]
Fig. 80. Selected plots of system parameters with regen valve for the same time of regen valve and hydrostatic motor switching
83
Regen valve switching affects boom lowering about 60 mm of cylinder stroke in spite of hydrostatic motor not working. Also, at the same time, a significant pressure increase was observed in the hoses connecting boom cylinder with ESS stand. This leads to the conclusion that at this time all the oil flow from boom cylinder goes to build up pressure in elastic hoses.
8.4. Laboratory tests with accumulator energy utilization Taking into consideration the increase of hydrostatic motor displacement control parameters, a 6 liter hydro-pneumatic piston accumulator was used as an energy source for hydrostatic motor supply instead of limited energy from boom cylinder. Valves 1 and 2 (Fig. 81) were used to achieve different system operation phases (accumulator charging and discharging).
Load (cycle)
Mp ENGINE (electric motor)
np
Mm
np
nm
one-way clutch Proportional relief valve
Proportional flow control
Fig. 81. ESS stand with accumulator
8.4.1. Accumulator discharging tests
Tests were performed for four values of electric motor rpm (1000, 1500, 2000, and 2500) and for different hydrostatic motor displacement. Selected plots of system parameters are shown in figures 82–85,
25 20 15 10 5
20
500
16
400
12
300
8
200
4
100
0
Qa [dm3/min]
0 600
30
1200
20
800
10
400
0
ne [rpm]
Mm [Nm]
xak [mm]
pp, pg, po, pm [MPa]
84
0
1 0.8
εm
0.6 0.4 0.2 0 280
320
360
400
440
t [s]
25 20 15 10 5
30
500 20
400 300
10
200 100
0 2000
30
Mm [Nm]
Qa [dm3/min]
0 600
1600 20
ne [rpm]
xak [mm]
pp, pg, po, pm [MPa]
Fig. 82. Selected plots of system parameters with accumulator for 1000 [rpm] of engine
1200 800
10
400 0
0
1
εm
0.8 0.6 0.4 0.2 0 100
200
300
400
t [s]
Fig. 83. Selected plots of system parameters with accumulator for 1500 [rpm] of engine
where: εm – displacement control parameter of motor (blue), i – accumulator flow (green) [dm3/min], xak – displacement of accumulator piston (black) [mm], po – pressure in outlet accumulator (violet) [MPa], pp – pump pressure (red) [MPa], pm – hydraulic motor pressure (blue) [MPa], pg – accumulator pressure (green) [MPa], Mm – hydrostatic motor torque (blue) [Nm],
85
25 20 15 10 5
40
500
30
400
20
300 200
10
100
0
Qa [dm3/min]
0 600
40
2500
30
2000
ne [rpm]
Mm [Nm]
xak [mm]
pp, pg, po, pm [MPa]
Mp – electric engine torque (red) [Nm], ne – hydraulic motor rpm (blue) [rpm].
1500
20
1000
10
500
0
0
1 0.8
εm
0.6 0.4 0.2 0 100
200
t [s]
25 20 15 10 5 0 600
50
500
40
400
30
300
20
200
10
100
0 3000
ne [rpm]
Mm [Nm]
40 30
2000
20
1000
10 0
0
1 0.8
εm
Qa [dm3/min]
xak [mm]
pp, pg, po, pm [MPa]
Fig. 84. Selected plots of system parameters with accumulator for 2000 [rpm] of engine
0.6 0.4 0.2 0 120
160
200
240
t [s]
Fig. 85. Selected plots of system parameters with accumulator for 2500 [rpm] of engine
86
The analysis of collected data allowed building the characteristics of energy efficiency as a function of hydrostatic motor inlet pressure. These characteristics for different motor displacement are illustrated in Figs 86–89. 1
0.8
εm = 0.10 εm = 0.17
0.6
[–] ηηtt [−]
εm = 0.23 εm = 0.29 εm = 0.36
0.4
εm = 0.42
0.2
0 4
6
8
10
12
14
16
18
ppmm [MPa]
Fig. 86. Efficiency of energy recovery system with accumulator as a function of motor pressure for different displacement for 1000 engine rpm 1
εm = 0.10
0.8
εm = 0.17 εm = 0.23 εm = 0.29 εm = 0.36
0.6
ηηtt [–] [−]
εm = 0.42 εm = 0.49 εm = 0.55
0.4
εm = 0.62 εm = 0.74 0.2
0 4
8
12
16
20
24
ppmm [MPa]
Fig. 87. Efficiency of energy recovery system with accumulator as a function of motor pressure for different displacement for 1500 engine rpm
87 1
0.8
εm = 0.10 εm = 0.23 εm = 0.36
0.6
ηtη[–][−]
εm = 0.49
t
εm = 0.62 εm = 0.74
0.4
εm = 0.87
0.2
0 4
8
12
16
20
24
[MPa] pp mm[MPa]
Fig. 88. Efficiency of energy recovery system with accumulator as a function of motor pressure for different displacement for 2000 engine rpm
1
0.8
εm = 0.10
0.6
ηt η[–][−]
εm = 0.23
t
εm = 0.36 εm = 0.49
0.4
εm = 0.62 εm = 0.74
0.2
0 4
8
12
16
20
24
[MPa] pmpm[MPa]
Fig. 89. Efficiency of energy recovery system with accumulator as a function of motor pressure for different displacement for 2500 engine rpm
88
To determine the influence of pressure losses in the hydraulic line on energy recovery efficiency partial efficiency of line and hydrostatic motor were calculated and plotted in Fig. 90 for hydrostatic motor displacement control parameter εm = 0,23 and in Fig. 91 for εm = 0,74. 1
0.8
ηηt [–] t [-]
0.6
0.4
hydraulic efficiency of line total efficiency of hydraulic motor total efficiency of system
0.2
0 4
8
12
16
20
24
pmm [MPa]
Fig. 90. Efficiency of line and motor as a function of motor inlet pressure for εm = 0,23 and 2500 [rpm] of electric engine 1
0.8
ηηt [–] t [-]
0.6
0.4
hydraulic efficiency of line total efficiency of hydraulic of motor total efficiency of system
0.2
0 0
4
8
12
16
20
pmm [MPa]
Fig. 91. Efficiency of line and motor as a function of motor inlet pressure for εm = 0,74 and 2500 [rpm] of electric engine
89
For a small hydrostatic motor displacement (εm = 0,23) pressure losses in the line are not visible while for hydrostatic motor displacement control parameter εm = 0,74 they are significant due to the increased volumetric flow, but still the energy losses in hydrostatic motor determine the total efficiency of the system. 8.4.2. Energy storage for given cycle of operation
cycle nr
0 12 11
100 250 200 150 100 50 0 120 80 40 0 -40 4 3 2
10
xb [mm]
200
xa [mm]
300
alfa [o]
BOOM RAISING PHASE
400
phase nr
4
500
TRANSPORT AND UNLOADING PHASE
8
DIGGING PHASE
20 16 12 8 4 0 20 16 12 8 4 0 20 16 12 8 4 0 12
BOOM LOWERING PHASE
ps1,ps2 [MPa]
pa1,pa2 [MPa]
pb1,pb2 [MPa]
p1,p2,p3 [MPa]
The first step of energy storage tests was to determine power cycle, similar to the real cycle of mini hex operation. As a base for this analysis, data from field tests were taken. The whole digging operation consists of about 75 cycles divided into 4 phases: boom lowering, digging, boom rising, transport and unloading of excavated material. Fig. 92 shows system parameters of selected operation cycle.
N [kW]
1 10 8 6 4 2 0 290
295
300
305
310
315
t [s]
Fig. 92. Plots of system parameters in selected cycle of 301.5 excavator operation
A set of field tests data was used to determine mean values of system parameters such as pressure and volumetric flow, the product of which gave mean values of power in particular phases of the cycle, as well as mean level of power in the whole cycle, which is presented in Fig. 93.
90 8
boom lowering phase digging phase boom raising phase transpotr/unloading phase whole cycle
7
6
NN[kW] [kW]
5
4
3
2
1
0 0
20
40
60
80
ccidid
Fig. 93. Mean values of power for particular phases of the cycle and for whole cycle as a function of cycle number (cid)
In the same way the duration of particular phases of the cycle were calculated and presented in Fig. 94, while Fig. 95 shows these characteristics completed with mean value of whole cycle time estimation.
10
8
[s] t [s]
6
4
boom lowering phase digging phase boom raising phase transpotr/unloading phase whole cycle
2
0 0
20
40
60
80
ccidid
Fig. 94. Mean values of particular phases duration as a function of cycle number (cid)
91 30
boom lowering phase digging phase boom raising phase transpotr/unloading phase whole cycle
[s] tt [s]
20
10
0 0
20
40
60
80
ccidid
Fig. 95. Mean values of cycle and its phases duration as a function of cycle number (cid)
A list of mean values of duration and power for particular phases and whole cycle is presented in Table 8. Table 8. Mean values of duration and power for particular phases and whole cycle No. 1 2 3 4 Whole cycle
Phase Boom lowering Digging Boom rising Transport and unloading
t [s] 5,13 3,72 7,29 6,99 23,13
N [kW] 2,5 5,8 3,4 2,4 3,28
Using the determined values of power and duration a typical cycle of power was established, as presented in Fig. 96, where the black line indicates mean power in the whole cycle. Assuming that power in both boom lowering phase and transport/unloading phase is at a similar level, the power cycle could be simplified to the form shown in Fig. 97, where only three phases are separated (boom lowering and transport/unloading phases were combined). As can be visible, the power level in third (boom raising) phase is equal to the mean value in the whole cycle. The tests were performed on ESS stand in configuration presented in Fig. 81. The main control parameters were: displacement control parameter of pump, hydrostatic motor displacement, and flow through proportional control valve. An extra predetermined control file was added to data acquisition program to allow
92
proper control of specified parameters due to phase of working cycle. In phase I the pump power is divided into two streams, the first is used to charge the hydropneumatic accumulator and the second is treated as a system output (flow through the flow control or relief valve). In phase II of the power cycle the energy stored in accumulator is used to support electric engine driving the pump under high load. In phase III system power is at a mean level so the accumulator is not used (electric engine power is sufficient to cover the cycle load). Selected plots of system parameters are presented in Figs 98 and 99. 6
NN [kW] [kW]
4
2
0 0
5
10
15
20
25
tt [s] [s]
Fig. 96. Typical power cycle for Cat 301.5 excavator
8
N [kW]
N [kW]
6
4
2
0 0
5
10
15
tt [s] [s]
Fig. 97. Simplified power cycle
20
25
5
0.8
4
0.6
3
0.4
2
0.2
1
0
0
Uf [V]
εm, εp
93 1
500
40
400 30 300 20
200
10
xb [mm]
Qp, Qa [dm3/min]
50
100
0
0
pp,pm,pg [MPa]
16 12 8 4
Md Mp, Mm [Nm]
0 50 40 30 20 10
np, nm [rpm]
0 2500 2000 1500 1000 500 0 0
40
80
120
t [s]
1
5
0.8
4
0.6
3
0.4
2
0.2
1
0
0
Uf [V]
εm, εp
Fig. 98. Selected plots of system parameters for 2000 [rpm] of engine
500
40
400 30 300 20
200
10
100
0
0
pp,pm,pg [MPa]
16 12 8 4
Md Mp, Mm [Nm]
0 50 40 30 20 10
np, nm [rpm]
0 2500 2000 1500 1000 500 0 20
25
30
35
40
t [s]
Fig. 99. Selected plots of system parameters for 2000 [rpm] of engine – one cycle
45
xb [mm]
Qp, Qa [dm3/min]
50
94
where: εp – displacement control parameter of pump (red), εm – displacement control parameter of motor (blue), Uf – control voltage of proportional flow controller 7 [V] (magenta), Qp – pump delivery [dm3/min] (red), Qa – accumulator flow [dm3/min] (green), xa – displacement of accumulator piston [mm] (black), pp – pump pressure [MPa] (red), pm – hydraulic motor pressure [MPa] (blue), pg – accumulator pressure [MPa] (green), Mm – hydrostatic motor torque [Nm] (blue), Mp – electric engine torque [Nm] (red), Md – torque necessary to drive the pump [Nm] (black), nm – hydraulic motor rpm [rpm] (blue), np – electric engine and pump rpm [rpm] (red). The torque plots show the difference between electric engine torque (red line) and torque which is necessary to drive the pump (black line), in the phase of high system load. So, owing to the energy saving system consisting of a hydropneumatic accumulator and hydrostatic motor leveling of the engine torque is possible. Obviously, it is important what the efficiency of the energy recovery process is. Determination of system efficiency required calculation of power and energy in particular phases of the cycle and at specified points of the circuit. Energy and power during charging in the accumulator pressure line, energy and power during discharging in the line between the accumulator and hydraulic motor, as well as energy and power for the hydraulic motor, were given. For calculation, the following formulas were used, respectively: – Outlet power and energy of the pump N p = Qp ⋅ p p
(41)
t2
E p = ∫ Q p ⋅ p p dt
(42)
t1
where: Qp – pump delivery, pp – pump pressure, t1 – beginning time, t2 – end time. – Power and energy in accumulator inlet during charging
N ak 1 = Qak1 ⋅ po
(43)
t2
Eak 1 = ∫ Qak 1 ⋅ po dt t1
where: Qak1 – accumulator flow, po – oil pressure in accumulator inlet.
(44)
95
– Power and energy in accumulator outlet during discharging N ak 2 = Qak 2 ⋅ po
(45)
t4
Eak 2 = ∫ Qak 2 ⋅ po dt
(46)
t3
where: Qak2 – accumulator flow, t3 – beginning time, t4 – end time. – Input power and energy of hydraulic motor
N h = Qak 2 ⋅ pm
(47)
t4
Eh = ∫ Qak 2 ⋅ pm dt
(48)
t3
where: pm – pressure in hydraulic motor inlet. – Output power and energy of hydraulic motor N m = M m ⋅ ωm
(49)
t4
Em = ∫ M m ⋅ ωm dt
(50)
t3
where: Mm – hydrostatic motor torque, ωm – hydrostatic motor angular velocity. The calculated values of energy at specified points of the system for four cycles are presented in 3D bar plots (Fig. 100). Additionally, in Fig. 101 the same energies are set up in 2D bar plots, where the areas between particular energies indicate energy losses in defined circuit parts. These energy losses are marked ΔEL1 – energy losses in the line between pump and accumulator, ΔEak – energy losses in the accumulator, ΔEL2 – energy losses in the line between accumulators and HM, ΔEm – energy losses in HM. Using the energies above it is possible to calculate the total efficiency of the energy recovery system as well as its partials, according to formulas: ηL1 =
Eak 1 E E E , ηL 2 = h , ηak = ak 2 , ηm = m , ηt = ηL1 ⋅ ηak ⋅ ηL 2 ⋅ ηm Ep Eak 2 Eak 1 Eh
(51)
where: ηL1 – efficiency of the line between pump and accumulator during charging, ηL2 – efficiency of the line between accumulator and motor,
96
ηak – accumulator efficiency, ηm – hydraulic motor efficiency, ηt – total efficiency.
E [J]
outlet energy of the pump energy in the accumulator inlet during charging energy in the accumulator output during discharging input energy of the hydraulic motor output energy of hydraulic motor
Cycle number
Fig. 100. Energy at specified points of ESS
16000
Ep Eak1
ΔEL1 ΔEak
Eak2 Eh
12000
ΔEL2
EE[J][J]
ΔEm 8000
Em
Em energy loses in line between pump and accumulator energy loses in the accumulator energy loses in line between accumulator and HM energy loses in HM output energy of HM
4000
0 0
1
2
3
4
5
Cycle number number Cycle
Fig. 101. Energy losses in defined segments of ESS circuit
97 1
ηL1 ηL2 ηak
0.8
ηm ηt
ηη
0.6
0.4
0.2
0 0
1
2
3
4
5
Cyclenumber number Cycle
Fig. 102. Total efficiency of energy recovery process with its partials
The estimated values of the energy recovery system efficiencies described above are shown in Fig. 102.
8.5. Summary of 301.5 excavator boom cylinder and energy saving system (ESS) tests Within the framework of energy saving system (ESS) a test stand was designed and built. This stand was powered by 22 kW electric motor and was equipped with two main, electronically controlled hydrostatic units: a variable displacement pump and a variable displacement hydrostatic motor. The ESS stand enables different configurations of energy flow, including the mini hex boom mechanism and hydropneumatic accumulator, so a variety of energy saving systems could be tested on it. The main part of tests performed on the ESS stand was aimed at to boom potential energy recovery using the hydrostatic motor and its energy utilization to drive the system’s pump, supporting the electric engine. The tests were performed for a number of pump rpm and for different boom cylinder velocity. Based on the collected data the efficiency of energy recovery was calculated, together with partial efficiencies of the particular system components (hydraulic line, hydrostatic motor). The results of efficiency evaluation were presented. The achieved values of total efficiency were below 0,6. Maximum values were reached for low engine rpm (1000 [rpm]) and for boom cylinder velocity in the range of 75–125 [mm/s]. Lower value of efficiency for higher engine rpm results from a decrease of hydrostatic motor displacement (displacement control parameter εm below 0,5). Lowering of efficiency for high boom cylinder velocity (above 125 [mm/s]) on the other hand
98
results from increasing pressure losses in the hydraulic line as well as lower hydrostatic motor efficiency. When comparing tests results for a system with the regen valve in relation to a system without it significant lowering of energy recovery efficiency can be observed. This is the effect of further hydrostatic motor displacement decrease due to flow lowering. The achieved values of efficiency for a system with the regen valve (below 0,2) are shown with relation to tests without the regen valve. The second part of tests was aimed at determination of energy system properties with a hydro-pneumatic accumulator. Utilization of energy stored in the accumulator to power the hydraulic motor and in this way to support the electric engine allowed extending of motor displacement range operation. Similarly to boom lowering tests, with energy recovery in the hydrostatic motor, in tests with accumulator the efficiency of energy utilization was calculated. The results of these tests and calculations are illustrated as a function of motor pressure, for different displacement and for different engine rpm. Based on the characteristic developed the optimal range of motor operation can be determined. The next step in tests on the ESS stand with accumulator was to evaluate energy storage process efficiency in a selected cycle with engine torque leveling. To work out a proper cycle of power, an analysis of mini excavator 301.5 field tests results was done and, as a result, a typical power cycle was adopted (Fig. 96). In these tests control of system parameters such as displacement control parameter of pump, hydrostatic motor displacement, and flow through proportional control valve was executed by a predetermined file. The acquired data of system operation are presented in Figs 98 and 99, where we can observe the difference between the torque necessary to drive the pump and electric engine torque, which shows the effect of torque leveling. Taking into consideration the presented parameters, the efficiency of energy storage and reusing process was calculated and presented in Fig. 102. For the adopted power cycle (where hydrostatic motor operates in displacement control parameter range from εm = 0,3 to εm = 0,5), the total efficiency of energy storage process is about 50%. Calculation of energy losses in particular components of the system, such as: hydraulic lines, accumulator and motor, shows that hydraulic motor is the main contributor to energy losses.
99
9. Hydraulic Power Recovery (HPR) tests stand for scaled linkage of 320C excavator Chapter 9 presents an energy saving concept developed and tested, with a hydrostatic motor as a hydraulic transformer of energy from boom lowering and/or stored in the hydraulic accumulator to reduce energy consumption and equalize diesel engine load. It required designing and building an extension to the existing Energy Saving System (ESS) test rig. Fig. 103 presents a scheme of the hydraulic power recovery (HPR) test stand, which allowed different configurations of energy flow. The HPR stand gives a possibility to transfer hydrostatic energy from the scaled excavator 320C boom mechanism to hydrostatic motor and, in this way, to reduce electric engine torque necessary to drive the pump. Thus, the efficiency of energy recovery process can be determined. Also, we can test different aspects such as the necessity to use oneway clutch, control system properties, including: elimination of underpressure in the hydraulic motor inlet, elimination of over-speed and control of the regen valve. The measurement devices installed allowed evaluating energy at different system points and phases of its operation and, in consequence, determining the efficiency of energy for different control systems. Table 9 shows a list of hydraulics components used in the stand structure [13, 25]. pg hydraulic accumulator
9
2
1 3 Load (cycle)
10 8
6
Control pressure
pm
pp ne
Me
p
m
Mm
motor
M Engine (electric motor)
Proportional relief valve
Uv 4 5
pump
one – way clutch ON/OFF
Fig. 103. Hydraulic power recovery system (HPR)
100 Table 9. List of hydraulic components No.
1 2 3 4 5 6 8
Name Qt’t Type Variable displacement axial piston PV032 32 [cm3/rev] – 350 1 pump with electric control [bar] Variable displacement motor with A6VM28EP1 28 [cm3/rev] 1 electric control – 400 [bar] Accumulator 1 Bladder 18 [dm3] One-way clutch 1 FB 37 SF Electric motor 1 22 [kW] Directional poppet valve 1 EVH 06/CA5-12C-DG1/2” Directional poppet valve 1 EVH 06/C3-12C-DG1/2” Directional poppet valve 1 EVH 06/A3-12C-DG1/2” Proportional Directional Valve 1 D1FP Cylinder 1 Proportional relief valve 1 XMP06 Relief valve 1 DBW
Producer Parker Bosch-Rexroth Ponar Wadowice Radius Indukta Comatrol Comatrol Comatrol Parker Orsta Comatrol Ponar Wadowice
Measurement transducers, shown in Fig. 103, are connected with the data acquisition system, equipped with an A/D computer card, as presented in Fig. 104. This measurement system allowed measurement and registration of parameters such as: pressure, torque, rotational velocity (rpm), flow and temperature. Detailed information about sensors and transducers, used in the system is listed in Table 11.
Fig. 104. Block diagram of the measurement system
101 Table 10. List of elements used in the measurement system No. p.. Qo Mm Mp nm np Lc To 10 11 12 13 14
Name Pressure transducer Flow transducer Torque transducer Torque transducer Rpm transducer Rpm transducer Displacement transducer Temperature transducer Integrated torque and rpm meter Impulse counter Temperature meter Wiring terminal board Analog-Digital card
Qt’y 6 1 1 1 1 1 1 1 2 1 1 1 1
Type 8891.74.3315, class 0,3
Producer Trafag Kral Sensor At Sensor At Sensor At Sensor At Peltron Czaki Sensor At
Mt 200 Mt 200 Mt 200 Mt 200 Thermocouple type K Beta 2002 MKS EMT 101 PCLD-8115 PCL 818HG
Czaki Advantech Advantech
9.1. Tests with accumulator to simulate boom lowering energy 9.1.1. Tests for system with and without one-way clutch In the first phase of the tests an 18 liter hydro-pneumatic bladder accumulator was used as an energy source for hydrostatic motor suppl instead of boom cylinder energy during lowering. Digitally controlled valves 1 and 2 (Fig. 105) were used to achieve different system operation phases (accumulator charging and discharging). pg hydraulic accumulator
9
2
1 3 10
Load (cycle)
8
6
Control pressure
pm
pp ne
Me
p
m
Mm
motor
M Engine (electric motor)
pump
one – way clutch ON/OFF
Proportional relief valve
Uv 4
Lc
Fig. 105. Hydraulic system with accumulator
5
102
The main goal of the tests was to check an advantage of using one-way clutch connecting the pump and motor. Another problem was to determine underpressure in the hydrostatic motor inlet when the hydraulic motor is running without supply. Hydraulic cylinder 5 (Fig. 105) allowed monitoring underpressure. When underpressure appears in the motor inlet hydraulic cylinder the rod begins to retract (Lc). Series of tests were done for different electric motor rpm, different hydrostatic motor displacement and different system of displacement control (manual and automatic). A detailed list of tests is presented in Table 11. Table 11. List of tests for system with accumulator Control system Manual, automatic Manual, automatic Manual, automatic Manual, automatic Manual, automatic
0.8
10
0.6
9.6
εp, εm
9.2
0.4
8.8
0.2
8.4
0 pp, pg, po, pmi, pmo [MPa]
Digital
Electric engine rpm level Without one way clutch With one way clutch 500 Yes Yes 1000 Yes Yes 1500 Yes Yes 2000 Yes Yes 2500 Yes Yes
8
20 16 12 8 4 0 40 30 20 10
LC [mm]
0 160
100 80
120
60
80
40
40
20
ne [obr/min]
0
vc [mm/s]
Me, Mm [Nm]
50
0
2500 2000 1500 1000 500 0 114
116
118
120
t [s]
Fig. 106. Selected plots of system parameters for constant 500 [rpm] of electric engine without clutch
10
0.6
9.6
εp, εm
9.2
0.4
8.8
0.2
8.4
0 pp, pg, po, pmi, pmo [MPa]
Digital
103 0.8
8
20 16 12 8 4 0
60 40 20
0 160
160
120
120
80
80
40
40
ne [obr/min]
0
vc [mm/s]
LC [mm]
Me, Mm [Nm]
80
0
2500 2000 1500 1000 500 0 62
63
64
65
66
67
t [s]
Fig. 107. Selected plots of system parameters for 500 [rpm] of electric engine with clutch
Selected plots of HPR system parameters during manual control of motor displacement are presented in Figs 106 and 107, where: εm – displacement control parameter of motor (blue), εp – displacement control parameter of pump (red), Digital – digital control signal (black), pp – pressure in pump outlet [MPa] (red), pg – pressure of accumulator gas [MPa] (green), po – pressure in accumulator joint [MPa] (black), pm – pressure in hydraulic motor inlet [MPa] (blue), pmo – pressure in hydraulic motor outlet [MPa] (cyan), Mm – hydrostatic motor torque [Nm] (blue), Me – electric engine torque [Nm] (red), Lc – displacement of boom cylinder [mm] (red). vb – velocity of boom cylinder [mm/s] (violet), nm – hydraulic motor rotational velocity [rpm] (blue), np – electric engine rotational velocity [rpm] (black). Exemplary plots of system parameters during automatic control of motor displacement (by parabolic motor inlet pressure function Fig. 108) are presented in Figs 109 and Fig. 110. It can be observed that for a system with and without oneway clutch and also for both motor displacements control systems, underpressure in the motor inlet is present. So, after discussions with Caterpillar Tech Center Hydraulic Research, it was decided to remove one-way clutch from the drive system as a component, which did not provide elimination of hydraulic motor underpressure.
104 1
0.8
εmm
0.6
0.4
0.2
0 0
4
8
12
16
20
[MPa] ppmm [MPa]
1
10
0.8
9.6
0.6
9.2
0.4
8.8
0.2
8.4
pp, pg, po, pmi, pmo [MPa]
0
Digital
εp, εm
Fig. 108. Automatic motor control by use of parabolic function of pressure
8
20 16 12 8 4 0
60 40 20
0 160
160
120
120
80
80
40
40
ne [obr/min]
0
0
2500 2000 1500 1000 500 0 120
124
128 t [s]
132
136
Fig. 109. Selected plots of system parameters for 2500 [rpm] of electric engine without clutch
vc [mm/s]
LC [mm]
Me, Mm [Nm]
80
10
0.8
9.6
0.6
9.2
0.4
8.8
0.2
8.4
pp, pg, po, pmi, pmo [MPa]
0
Digital
εp, εm
105 1
8
20 16 12 8 4 0
60 40 20
0 160
160
120
120
80
80
40
40
ne [obr/min]
0
vc [mm/s]
LC [mm]
Me, Mm [Nm]
80
0
2500 2000 1500 1000 500 0 32
36
40 t [s]
44
48
Fig. 110. Selected plots of system parameters for 2500 [rpm] of electric engine with clutch
9.1.2. Tests of underpressure elimination system Another aspect of the tests was to determine underpressure value and introduce an underpressure elimination system. The value of underpressure was measured by specially installed pressure transducer punder (Fig. 111).
Fig. 111. Hydraulic system with underpressure transducer
106
After installation of the underpressure transducer tests were performed for two values of electric motor rpm (1000, 2000,) and for different hydrostatic motor displacement. Selected plots of system parameters are shown in Fig. 112, where: εm – displacement control parameter of motor (blue), εp – displacement control parameter of pump (red), pp – pressure in pump outlet [MPa] (red), po – pressure in accumulator inlet [MPa] (black), pm – pressure in hydraulic motor inlet [MPa] (blue), punder – pressure in hydraulic motor inlet [MPa] (red), Mm – hydrostatic motor torque [Nm] (blue), Mp – electric engine torque [Nm] (red), Uv4 – proportional directional valve 4 control voltage [V] (green). 1
εp,
0.6
0
0.4
ON/OFF Valve 2
1
0.8
0.2 0
-1
1
1 Uv4 [V]
εm
0.8 0.6 0.4 0.2
punder [MPa]
pp, pm, pmp [MPa]
0
0
16 12 8 4 0 0
-0.02 -0.04 -0.06 Me, Mm [Nm]
80 60 40 20 0 64
68
72
76
t [s]
Fig. 112. Selected plot for system parameters for 1000 [rpm]
As can be seen, underpressure value depends on motor displacement parameter and also on engine rpm. Based on the data collected during the tests performed on the HPR stand, underpressure as a function of motor displacement control parameter was calculated for both ranges of engine rpm. Fig. 114 shows motor inlet underpressure as a function of hydraulic motor displacement. The tests showed underpressure up to 0,05 [MPa], so the system of its elimination was introduced in the next phase of research. A scheme of this system is presented in Fig. 114.
107
Fig. 113. Characteristic of underpressure as a function of motor displacement control parameter (for 1000 engine rpm – black, for 2000 engine rpm (red))
Fig. 114. Hydraulic system with underpressure transducer and low pressure hydro-pneumatic accumulator
This underpressure elimination system consists of small diameter hydraulic cylinder 5 pressurized by low pressure hydro-pneumatic accumulator 11, and proportional directional valve 4. While the inlet pressure of hydraulic motor drops,
108
its displacement is de-stroked to 0. During hydrostatic motor de-stroking the oil flow going from cylinder 5 prevents the hydraulic motor from cavitation. After hydrostatic motor de-stroking and accumulator discharge the pressure goes down (close to 0) and valve 4 is in open position, so the motor sucks in the oil from its return line. The next tests were performed for the underpressure elimination system described, and selected plots of system parameters are shown in Fig. 115. To illustrate the influence of valve 4 on underpressure value, after hydrostatic motor de-stroking and accumulator discharge, a series of valve 4 manual switching on/off was performed (after disabling of automatic control algorithm of underpressure system elimination), which is represented by the plot in green color. 1
1
ON/OFF Valve 2
εp
0.8 0.6 0.4 0
0
1
10
0.8
8
0.6
6
0.4
4
0.2
2
0
0
Uv4 [V]
εm
0.2
pp, pm [MPa]
12 8 4 0 120
0.04
80
0
40
-0.04
Lc [mm]
punder [MPa]
160 0.08
0
Me, Mm [Nm]
80 60 40 20 0 388
392
396
400
404
t [s]
Fig. 115. Selected plot for system parameters for 2000 engine rpm
It can be seen that when proportional directional valve 4 is closed (disabling underpressure elimination system) underpressure is about minus 0,02 [MPa], but when the system is activated (proportional directional valve 4 is open when the motor is not supplied), underpressure is eliminated. 9.1.3. Tests of system flow control The main idea of tests with flow control was to establish a proper value of the flow going from the hydrostatic accumulator. This flow will be equivalent to cylinder velocity in the next phase of research test (after installing the boom mechanism). This was done through setting the flow from the accumulator in
109
a different way: by joystick position or by slider position. An additional goal of the control algorithm is to avoid over-speed of the electric engine. The system should ensure control of the flow which can be consumed by the hydraulic motor due to its displacement and shaft rpm. Also, the torque generated by the hydraulic motor cannot be greater than the torque of the pump running at the same rpm. When the required flow is greater than motor consumption, overflow is directed to the tank through proportional valve 4, Fig. 114. Control algorithm is based on the following calculations consisting of two conditions: Required flows: Qm = ε m ⋅ qm ⋅ nm / ηvm
(52)
where: εm – motor displacement control parameter, qm – motor displacement, nm – motor shaft rpm, ηvm – volumetric efficiency of motor. Torque condition (the torque of pump cannot be greater than the torque of hydraulic motor):
M m ≤ M p ⇒ ε m ⋅ pm ⋅ qm ⋅ ηhmm ≤
ε p ⋅ qp ⋅ pp
(53)
ηhmp
where: εp – pump displacement control parameter, qp – pump displacement, pp – pump outlet pressure, ηhm – hydro-mechanical efficiency. Taking relevant formulas into account, the value of motor displacement control parameter can be obtained from the following expression:
⎡ ⎛ Qc ε p ⋅ qp ⋅ pp 1 ε m = min ⎢ min ⎜ ⋅ ηvm , ⋅ ⎜ pm ⋅ qm ηhmp ⋅ ηhmm ⎢⎣ ⎝ nm ⋅ qm
⎞ ⎤ ⎟⎟ ,1⎥ ⎠ ⎥⎦
(54)
To calculate the value of overflow through valve 4 (Fig. 116), the following formulas can be used: Qv 4 = Qc − Qm Qv 4 = Qc − ε m ⋅ qm ⋅ nm ⋅
1 ηvm
(55)
After inserting the above calculations into the control algorithm series of tests were done for different electric motor rpm (1000 and 2000) and for different input function (ramp, step) of the flow control signal.
110 Qc
Qv4
Qm
Fig. 116. Flow distribution in HPR system
Selected plots of system parameters are shown in Figs 117 and 118. 1
1
ON/OFF Valve 2
εp
0.8 0.6 0.4 0
1
10 8
0.6
6
0.4
4
0.2
2
0
0
60 40 20 0 10 8 6 4 2 0
Me, Mm [Nm]
80 60 40 20 0 28
32
36
40
t [s]
Fig. 117. Selected plots of system parameters for step input function of flow (10 [dm3/min]) and 1000 [rpm]
Uv4 [V]
0 0.8
punder, pp, pm [MPa] Qc, Qcm, Qm [dm3/min]
εm
0.2
111 1
1
ON/OFF Valve 2
εp
0.8 0.6 0.4 0
1
10 8
0.6
6
0.4
4
0.2
2
0
0
Uv4 [V]
0 0.8
punder, pp, pm [MPa] Qc, Qcm, Qm [dm3/min]
εm
0.2
60 40 20 0 10 8 6 4 2 0
Me, Mm [Nm]
80 60 40 20 0 32
36 t [s]
40
Fig. 118. Selected plots of system parameters for ramp input function of flow and 1000 [rpm]
9.2. Design of scaled research stand for 320C hydraulic excavator The research project was assumed to perform tests for Cat 320 Hydraulic Excavator (320 HEX) equipment [66, 67, 81]. It is a medium size excavator but overall dimensions of the original equipment are too large for tests in the Cracow University of Technology Fluid Power Laboratory. So it was agreed to design and build a scaled Cat 320 HEX boom mechanism, ensuring pressure and velocity characteristics similar to the original machine. The parameters of the scaled mechanism were – boom cylinder: • diameter of piston – 0,08 [m], • area of piston side – 0,005 [m2], • stroke – 0,6 [m], • velocity – 0,2 [m/s]; – HPR supply system: • flow rate – 60 [dm3/min], • pressure level – from 10 to 15 [MPa], • power – 15 [kW]. The construction of the stand base, boom and arm was simplified for faster and easier production. The stand base was made from 6 meters long U-irons. For the
112
boom and arm typical steel sections were used. Kinematics for the stand was established in simulations using Working Model 2D software (WM2D). Different configurations were checked in order to receive typical characteristic for excavator equipment. As an example 301.5 excavator was tested. For comparison, Fig. 119 shows two equipment structures: mini hex 301.5 of original dimension, and scaled 320 hex and their boom cylinder pressure characteristics obtained in static calculations. The characteristics for both mechanisms were compared. The value of additional load required for the assembly on arm end point to achieve the necessary level of pressure was determined. During calculations the assumed level of working pressure about 15 [MPa] was obtained (with an additional load of 750 [kg]). Fig. 120 presents pressure characteristic as a function of cylinder stroke for different additional load for arm cylinder in retract position.
Fig. 119. Working Model 2D interactive window
Obviously, each change of arm position causes changes of pressure characteristic and value of the needed load. The characteristic of boom cylinder head pressure, for arm cylinder in extended position, is shown in Fig. 121. Additionally, to reach the assumed level of pressure in each configuration of equipment (for limited load) extra joints were designed enabling connection of
113
“loading” cylinder between the stand base and the boom. The cylinder can be assembly parallel to the main cylinder to give extra load. It is an independent type of load, which can allow obtaining a higher value of pressure or a different shape of load characteristic. For example, Fig. 122 shows pressure characteristic as a function of boom cylinder stroke for 200 [kg] load and extra force from “loading” cylinder.
PRESSURE OF CYLINDER PISTON SIDE [MPa] PRESSURE OF CYLINDER PISTON SIDE [MPa]
20
16 750kg
12 500 kg
8 200kg
50kg
4
0 1000
1200 1400 CYLINDER STROKE [mm] CYLINDER STROKE [mm]
1600
Fig. 120. Pressure characteristic as a function of cylinder stroke for additional load (arm cylinder in retract position)
PRESSURE OF CYLINDER PISTON SIDE [MPa] pressure of cylinder piston side [MPa]
20
16
12
750 kg
500 kg 8
200 kg 4
50 kg
0 1000
1200
1400
1600
cylinder stroke [mm] CYLINDER STROKE [mm]
Fig. 121. Pressure characteristic as a function of boom cylinder stroke for additional load (arm cylinder in extend position)
114
pressure of cylinder piston side [MPa] PRESSURE OF CYLINDER PISTON SIDE [MPa]
20
30 kN 16
20 kN 12
10 kN
8 1000
1200
1400
1600
cylinder stroke [mm] CYLINDER STROKE [mm]
Fig. 122. Pressure characteristic as a function of boom cylinder stroke for 200 [kg] load and extra force from “loading” cylinder
The results of static calculations presented in the form of pressure characteristics confirm the adopted stand configuration and its dimensions. Table 12 presents data of boom and “loading” cylinders. Table 12. List of cylinders to research stand Point of destination Boom cylinder Additional cylinder
Length + stroke [mm] 1000 + 600 1340 + 1085
Diameter [mm] 80/50 63/36
Company Wropol Engineering Wropol Engineering
A separate step of stand design was to verify each part of construction strength. Based on maximum forces, determined with Working Model 2D, the construction elements were checked for: – bending stresses of boom and arm, – bending and shearing stresses as well as pin unit pressure. Strength calculations confirmed the adopted material and its dimensions for: – structural section – 200x160x6 from 18G2A steel, – pin – unified diameter 50 [mm] from 16HG steel. Then, engineering specification was prepared for manufacturing. Fig. 123 presents a 2D view of stand construction, while Fig. 124 shows a 3D view of stand construction.
115
6 5
1
2
3
4
Fig. 123. General assembly 2D view of 320 scaled research stand: 1 – base, 2 – boom, 3 – boom cylinder, 4 – additional cylinder, 5 – connector, 6 – arm
Fig. 124. 3D view of steel construction for research stand
As distinct from tests with a hydro-pneumatic accumulator the scaled stand allowed simulation of 320 C excavator equipment operations. Boom lowering tests were performed with a hydraulic motor over-speed elimination control system for three cases of boom cylinder supply: – lowering under gravity, only cylinder head side supplied during raising, Fig. 125, – lowering by supply of cylinder rod side, shown in Fig. 129, – lowering by supply of cylinder rod side with regen valve operation, Fig. 132. For all configurations, series of boom lowering tests were done for: – two different electric motor rotational velocities (1000 and 2000 [rpm]), – two different potential energies of boom (done by adding mass on the end of stick: 300 [kg] and 600 [kg]), – different values of pump displacement control parameter, – different input function of boom velocity (step, ramp, trapezoid). 9.2.1. Tests results for system with boom lowering under gravity
Selected plots of parameters for a system with boom lowering under gravity of mass are shown in Fig. 125.
116
Fig. 125. System with boom cylinder lowering under gravity
1
p
4
0.2
2
0
0
0
500
-50
400
-100
300
-150
200
-200
100
-250
0
pp, pm [MPa]
15 10 5
Me, Mm [Nm]
0 80 60 40 20 0
η
1 0.8 0.6 0.4 0.2 0 0
100
200 t [s]
Fig. 126. Plots of system parameters for load 300 [kg] during lowering under gravity
Uv4 [V]
m
6
0.4
xc [mm]
8
0.6
ε,ε vz, vc, [mm/s]
10
0.8
117
Based on the presented data collected in the tests performed on the HPR stand, energy possible to recover during boom lowering was calculated and mechanical energy transferred from the hydrostatic motor to pump shaft was determined. With these two energies, for boom lowering phase of operation cycle, the efficiency of energy recovery process was evaluated using the formula:
η=
M m ⋅ ωm A ⋅ vc ⋅ pm
(56)
where: Mω – hydrostatic motor torque, in [Nm], ω – motor angular velocity, in [rad/sec], A – area of boom cylinder piston side, in [m2], vc – piston velocity, in, [m/sec], pm – motor inlet pressure, in [Pa]. Fig. 127 shows the energy recovery efficiency defined above as a function of boom cylinder velocity for different pump displacements, and engine rpm of 1000 and 2000 [rpm]. Fig. 128 presents a comparison of efficiency in relation to boom cylinder velocity, for different engine rpm and load of 300 kg. The efficiency decrease, seen on the characteristics above, for higher boom cylinder velocity results from opening of motor bypass valve (valve 4) when the hydrostatic motor cannot consume all the oil flow from cylinder. Therefore, the maximum of energy recovery efficiency depends on rotational velocity, pump displacement and pressure. For full pump displacement (εp = 1) the maximum of efficiency is reached for boom cylinder velocity 90 [mm/s] in case of rpm of 1000 and 180 [mm/s] in case of rpm of 2000. a)
b) 1000 rpm, εp = 1
1
2000 rpm, εp = 1
1
1000 rpm, εp = 0,5
2000 rpm, εp = 0,5
1000 rpm, εp = 0,25
2000 rpm, εpp = 0,25
0.8
0.8
0.6
ηη
ηη
0.6
0.4
0.4
0.2
0.2
0
0
40
80
120
vvcc [mm/s] [mm/s]
160
200
40
80
120
160
vcc [mm/s] [mm/s]
Fig. 127. Energy recovery efficiency as a function of boom cylinder velocity a) for 1000 engine rpm, b) for 2000 engine rpm
200
118 1
1000 rpm, εp = 1 2000 rpm, εp = 1
0.8
ηη
0.6
0.4
0.2
0 40
80
120
160
200
[mm/s] vvcc [mm/s]
Fig. 128. Comparison of energy recovery efficiencies as a function of boom cylinder velocity for different engine rpm and for 300 [kg] load
9.2.2. Tests results for system with both boom cylinder chambers supply Selected plots of parameters for a typical system with both cylinder chambers supplied are shown in Fig. 130. These tests were performed for a system without the regen valve. In the presented system (Fig. 129), a new circuit was introduced to achieve pilot pressure for the hydrostatic motor and valves together with a system of hydrostatic motor underpressure elimination (the blue hidden line).
Fig. 129. System with both boom cylinder chambers supplied
m p
0.4
ε,ε
0.6
4 0 -4
0.2
-8
vc, [mm/s]
0 50
500
0
400 300
-50
200 100
-150
0
25 20 15 10 5 0 100
Me, Mm [Nm]
pp, pb1, pb2 ,pm [MPa]
-100
xc [mm]
8
0.8
U [V2] , U [V1], U [V4]
119 1
80 60 40 20 0
η
1 0.8 0.6 0.4 0.2 0 122
123
124
125
126
127 t [s]
128
129
130
131
132
Fig. 130. Plots of system parameters during lowering for typical system with both boom cylinder chambers supplied for 600 kg load
In Fig. 131 a comparison of energy recovery efficiency as a function of boom cylinder velocity for different engine rpm is presented. 1
Qv4 -- Qv4 -- 0.8
η η
0.6
0.4
LEGEND 1000 rpm, εp = 1
0.2
2000 rpm, εp = 1
0 0
40
80
120
160
200
c [mm/s] vc v[mm/s]
Fig. 131. Comparison of energy recovery efficiency as a function of boom cylinder velocity for different engine rpm and for 600 [kg] load
120
Energy recovery efficiency characteristics for a typical boom mechanism system with both cylinder chambers supplied are very similar to those presented before for a system with boom lowering under gravity. 9.2.3. Tests results for system with regenerative (regen) valve
The next task of investigation was to test the HPR system with the regen valve installed between the head and rod side of the cylinder (Fig. 132) which connects both chambers of the cylinder during boom lowering.
Fig. 132. System with regen valve
Selected plots of parameters for a system with the regen valve are shown in Fig. 133. In the same way as for the previous systems, energy recovery efficiency characteristics were worked out and shown in Fig. 134 which presents a comparison of energy recovery efficiency in relation to boom cylinder velocity, for different engine rpm. As expected, the flow through the regen valve increases energy losses, which results in efficiency drop. This can be observed on the characteristics plots presented above, where the achieved values of efficiency are by about 20% lower in relation to systems without the regen valve.
121 8 4 0 -4
0.2
-8
0
500
-40
400 300
-80
200 100
-160
0
25 20 15 10 5 0 100
Me, Mm [Nm]
pp, pb1, pb2 ,pm [MPa]
-120
20
80
16
60
12
40
8
20
4
0
0
Q regen dm3/min
vc, [mm/s]
0
xc [mm]
m p
0.4
ε,ε
0.6
U [V2] , U [V1], Ur, U [V4]
engine 2000 [rpm], load [600 kg]
1 0.8
η
1 0.8 0.6 0.4 0.2 0 242
244
246 t [s]
248
250
Fig. 133. Selected parameters plots of system with regen valve, for 600 [kg] load and 100 [mm/s] cylinder velocity
1
0.9
0.8
0.7
ηη
0.6
0.5
0.4
LEGEND 1000 rpm 2000 rpm
0.3
0.2
0.1
0 0
40
80
120
160
200
240
[mm/s] vvcc [mm/s]
Fig. 134. Comparison of efficiency in relation to boom cylinder velocity for different engine rpm for 600 [kg] load obtained from the tests with regen valve
122
9.2.4. Engine transient analysis – Flywheel support system In the frame of the research program a concept of applying a flywheel to reduce over-speeding and smooth load of engine has been analyzed [30, 41]. A model of the system is shown in Fig. 135. The data for the model were taken from a 320 hex diesel engine.
Diesel engine
JF
Me, Js
Load
Fig. 135. Fflywheel support system
The law of motion for rotary system is described by the formula:
JH
M e M load
(57)
where: J – moment of inertia, İ – angular acceleration, Me – torque of diesel engine, Mload – torque of load. The characteristic of diesel engine torque as a function of angular velocity (lug curve) is presented in Fig. 136. 800
600
400
e
M Me [Mn] [Nm]
MM e1e1
200
0 80
100
120
140
160
Z Z [rad/s] [rad/s]
180
Z Z11
200
Fig. 136. Lug curve for 320 hydraulic excavator diesel engine
ZZ22
220
123
For modeling, linear torque characteristic for angular velocity in the range of ω1 to ω2, was adopted. Thus, engine torque formula can be written as:
M e = M e1
M e1 ω2 − ω ω2 − ω1 ω2 − ω1
(58)
where: Me1 – diesel engine torque for angular velocity ω1. Using step function of the load torque in the form:
M load = 1(t ) M 0
(59)
a differential equation for angular velocity ω is obtained:
J
M e1 ω2 dω = M e1 − M0 − ω dt ω2 − ω1 ω2 − ω1
(60)
Solving this equation, with initial condition ω = ω2, the formulas for angular velocity and engine torque can be written as: M e1 t ⎞ ⎛ M0 J ( ω1 −ω2 ) ⎟ ω ( t ) = ω2 + ( ω1 − ω2 ) ⎜⎜1 − e ⎟ M e1 ⎝ ⎠
(61)
M e1 t ⎞ ⎛ J ( ω1 −ω2 ) ⎟ M e ( t ) = M 0 ⎜1 − e ⎜ ⎟ ⎝ ⎠
(62)
Selected plots of 320 hex engine transient parameters for step load characteristic are presented in Fig. 138. The continuous line indicates parameters for a system without additional inertia (engine moment of inertia J = 1,135 [kgm2]), while the hidden line relates to a system with 25 [kgm2] of additional flywheel, which could be necessary to achieve diesel engine torque transient in pre-adopted time period of about 5 [s]. To calculate the moment of inertia, which is necessary to achieve smooth engine torque transient for different values of engine torque M e (T ) = kM 0
(63)
can be adopted, where: T – time for engine torque smoothing, k – factor (k < 1, e.g. k = 0,99).
124
Mload, Me [Nm]
600
400
without additional inertia with additional inertia 25 kgm2
200
ω [rad/s]
0 220
210
200
190 0
1
2
3
4
5
6
t [s]
Fig. 137. Engine transient parameters for different moments of inertia
We could not set k of 1, because it would give infinite time of torque transient, so after some simple calculations a formula for determination of necessary moment of inertia is obtained. M e1 T ⎞ ⎛ J ( ω1 −ω2 ) ⎟ kM 0 = M 0 ⎜1 − e ⎜ ⎟ ⎝ ⎠
e
M e1 T J ( ω1 −ω2 )
=1− k
(64)
M e1 T = ln (1 − k ) J ( ω1 − ω2 ) J=
M e1T ( ω1 − ω2 ) ln (1 − k )
(65)
Selected values of the moments of inertia for given diesel engine torques, calculated using the above formula, are presented in Table 13 (where: r – radius of flywheel, h – width of flywheel).
125 Table 13. Selected values of moments of inertia for given diesel engine torques No. M1 [Nm] J [kgm2] m [kg] (r = 0,25 m) h [m] for steel
1 100 4,04 129,2
2 200 8,07 258,3
3 300 12,11 387,5
4 400 16,15 516,6
5 500 20,18 645,8
6 600 24,22 774,9
0,08
0,17
0,25
0,33
0,42
0,5
9.2.5. Flywheel support system for HPR stand
Based on the equations presented in chapter 9.2.4 some calculations for the electric motor installed on the HPR test stand were done. For calculations flywheel radius r = 0,22 [m] was adopted as a maximum possible flywheel dimension which could be installed on the existing stand. Calculations were done for two values of moment of inertia listed in Table 14, where the first one (J = 2,6 [kgm2]) fulfills the requirement of five seconds engine torque transient (equation 7), while the second one (J = 1,44 [kgm2]) is in the middle of the range. The calculated torque and angular velocity in time domain are presented in Fig. 138 for different moments of inertia. Table 14. Selected values of flywheel parameters for two moments of inertia No. M1 [Nm] J [kgm2] m [kg] (r = 0,22 m) h [m] for steel
1 72 2,6 107
2 72 1,44 60
0,09
0,05
Mload, Me [Nm]
80
60
40
without additional inertia with additional inertia J=1.44 kgm2 with additional inertia J=2.6 kgm2
20
0 300
ω [rad/s]
290
280
270
260 0
1
2
3
4
5
6
t [s]
Fig. 138. HPR stand engine transient parameters for different moments of inertia
7
126
Applying additional inertia, as can be seen, allows receiving smooth engine transient, however, the achieved dimensions and mass of the flywheel makes this system impractical. Following this conclusion it was decided not to install a flywheel in the HPR stand for testing.
9.3. Hydrostatic support system Fig. 139 presents a hydrostatic system of engine torque smoothing. It consists of the main unit (pump/motor) and two accumulators: one is high pressure pH and the other one is low pressure pL. Additionally, the system is equipped with pressure make-up and flushing circuit to maintain the pressure in suction line on a proper level and generate oil exchange in the closed line between accumulators to perform cooling and filtering.
Fig. 139. Hydrostatic system of engine transient smoothing
The aim was to achieve the linear function of the main hydrostatic unit (working in this situation as a motor) in case of step characteristic of load torque, which is presented in Fig. 140. In this case the required HM torque could be described as a time function by the formula: M m t
t· § M 0 ¨1 ¸ © T¹
where: M0 – load torque, T – time for engine torque smoothing.
(66)
127 M0
Torques: Mm
M load, Mm
Mload
-1
0
1
2
3
4
t [s]
5
6
7
8
T
Fig. 140. Required hydrostatic motor torque
The main parameters of the system cam be calculated based on the set of equations: M m = ε mVϕm Δpm ηhmm Q = ε mVϕm ω + Qvm
(67)
Δpm = pH − pL
where: Mm – HM torque, εm – displacement control parameter, Vφm – HM displacement per rad., ηhmm – hydro – mechanical efficiency, ω – angular velocity, Qvm – leakage flow, Δpm – pressure difference, pH, pL –pressure in high and low pressure lines, respectively. Pressures pH and pL depend on thermo-dynamic processes in accumulators for the ideal gas, and described by the formula: p V n = p0V0 n = p2V2 n
(68)
where: p0, V0 – initial pressure and accumulator volume, n – polytrophic process coefficient, p2, V2 – maximum accumulator pressure and corresponding gas volume. The gas volume of high pressure accumulator during the discharging process is a function of outgoing oil flow, and can be expressed as: V = V2 + ∫ Qdt
(69)
128
Neglecting: pL, ηhmm, Qvm and using simplification Δpm = p, the following calculations can be performed: εm = Q=
Mm Vφm p
Mm M ω Vφm ω = m Vφm p p
(70)
dV M m ω = dt p
Volume V is a function of pressure p and accumulator initial parameters p0, V0: 1
⎛ p ⎞n V = V0 ⎜ 0 ⎟ ⎝ p⎠
(71)
thus, after derivation a differential equation for pressure p is obtained: 1 ⎡ ⎤ d ⎢ ⎛ p0 ⎞ n ⎥ M m ω V0 ⎜ ⎟ = dt ⎢ ⎝ p ⎠ ⎥ p ⎥⎦ ⎣⎢
(72)
Taking into consideration equation 25 for the HM torque a set of equations for accumulator pressure p, gas volume V and motor displacement control parameter εm is obtained: ⎧ dp M 0 ωn ⎛ t 1− ⎪ =− 1 ⎜ dt T ⎝ ⎪ V0 p0 n ⎪ 1 ⎪ ⎛ p0 ⎞ n ⎪ ⎨V = V0 ⎜ ⎟ ⎝ p⎠ ⎪ ⎪ M0 ⎛ t⎞ ⎪ε m = ⎜1 − ⎟ Vφm p ⎝ T ⎠ ⎪ ⎪ ⎩
1
⎞ n ⎟p ⎠
(73)
The solution of the above set of equation leads to time functions of system parameters in the following form:
129
⎧ ⎪ n ⎪ 2 n −1 ⎛ n −1 ⎞ ⎪ ⎛ ⎞ M t ω 0 n 1 ⎜t − ⎟⎟ ⎪ p ( t ) = ⎜⎜ p2 − ( n − 1) n 2T ⎠ ⎟⎠ V p 0 0 ⎝ ⎪ ⎝ ⎪ 1 1− n 1− n ⎪ ⎛ ⎞ M 0ω ⎛ t2 ⎞⎟ ⎪ ⎜ 1− n ⎛ p0 ⎞ n t− ⎨V ( t ) = ⎜ V0 ⎜ ⎟ − ( n − 1) ⎟ n ⎜ p0V0 ⎝ 2T ⎠ ⎟⎟ ⎝ p2 ⎠ ⎜ ⎪ ⎝ ⎠ ⎪ ⎪ t⎞ ⎛ M 0 ⎜1 − ⎟ ⎪ T ⎝ ⎠ ⎪ε m ( t ) = n ⎪ n −1 2 n −1 ⎛ ⎞ ⎛ ⎞ t ωM 0 ⎪ Vφm ⎜ p2 n − ( n − 1) 1 ⎜t − ⎟⎟ ⎪ ⎜ n T ⎠ ⎟⎠ 2 V p 0 0 ⎝ ⎝ ⎩
for t ∈ [ 0;T ]
for t ∈ [ 0;T ]
(74)
for t ∈ [ 0;T ]
This set of functions can be used to determine the capacity of accumulator V0 and motor displacement Vφm with conditions: ⎧⎪V ( t ) ≤ V0 ⎨ ⎪⎩ε m ( t ) ≤ 1
(75)
The maximum value of V(t) is for t = T, so it is quite easy to solve the first condition and find a minimum necessary accumulator capacity: V0 =
M 0T ω 1 − n 1− n 2 p0 1 − p0 n
( )
(76)
p2
To solve the second condition it is necessary to find the maximum of function εm(t) and then put time tm to the condition for motor displacement control parameter, so it is necessary to solve a set of formulas: ⎧ d εm ( t = tm ) = 0 ⎪ ⎨ dt ⎪ε m ( t = t m ) ≤ 1 ⎩
(77)
After some calculations a formula for minimum necessary hydrostatic motor displacement is obtained:
130
Vφm
⎛ p n ⎜ (1 − n ) 1−n 2 1−n ⎜ p2 n − p0 n ⎝ 1−n
n +1 M = 0 ( n + 1) 2( n −1) kp0
n ⎞ ⎟ ( 2n )1− n ⎟ ⎠
(78)
where: k – coefficient k < 1. Fig. 141 presents selected characteristics of the required geometric displacement of hydrostatic motor as a function of torque, for different work pressures. For calculations the following values of parameters were adopted: coefficient k = 0,8 and initial accumulator pressure of 0,2*p2 (where p2 is max. accumulator pressure). For the same parameters the necessary capacity of hydropneumatic accumulator as a function of torque was estimated and presented in Fig. 142. 50
400
p= 20 [MPa]
p= 20 [MPa] 40
p= 25 [MPa]
p= 25 [MPa] 30
3
V00 [dm [dm3]] V
3
[cm3/rev] /rev] qq mm[cm
300
200
p= 30 [MPa]
p= 30 [MPa] 20
100
10
0
0 100
200
300
400
500
600
M M [Nm] [Nm]
Fig. 141. Required hydrostatic motor geometric displacement as a function of torque for different work pressures and parameters: k = 0,8, p0 = 0,2*p2
100
200
300
400
500
600
[Nm] MM[Nm]
Fig. 142. Required initial volume of accumulator as a function of torque for different work pressures and parameters: k = 0,8, p0 = 0,2*p2
9.4. Summary of Hydraulic Power Recovery (HPR) tests stand for scaled linkage of 320C excavator The modified stand for Hydraulic Power Recovery system operation enabled testing 320 hex scaled boom mechanism. Hydrostatic motor operation in higher displacement range (close to maximum rpm) was achieved. Two options of energy transfer between the hydrostatic motor and pump, with or without one-way clutch, have been tested. One of task was to determine the influence of one-way clutch between the hydrostatic motor and pump on the system properties, particularly on pressure changes in the motor inlet when the hydraulic motor was not supplied.
131
Series of tests were performed using two types of motor displacement control: manual and automatic, which has shown that for a system with and without oneway clutch, for manual motor displacements control systems, underpressure in the motor inlet was still present. Since one-way clutch did not ensure elimination of hydraulic motor underpressure, it was removed from the drive system. As an alternative solution, to eliminate underpressure, a special control algorithm was developed. Its task was to de-stroke motor displacement, together with opening of directional valve 4, in case of an insufficient supply flow. The algorithm eliminates underpressure in the hydraulic motor inlet port, except the transient phase immediately after stopping the suppl flow. Time delay of motor response was the main cause of these phenomena. So, in addition to the control algorithm described two types of anti-cavitation systems were designed and implemented into the HPR system. These systems ensured motor underpressure elimination for the whole range of system operation. The next task of the research described in the chapter was to develop and test a boom lowering velocity control system including hydraulic power recovery with additional function, such as: engine over-speed and hydrostatic motor underpressure elimination. After initial tests of the flow control algorithm with the hydro-pneumatic accumulator used as energy source, a scaled boom mechanism was installed and put to tests. Boom lowering tests were performed for three cases of boom supply: lowering under gravity, only cylinder head side supplied during rasing, lowering by supply of cylinder rod side, and for lowering by supply of cylinder rod side with regen valve operation. The main goal of investigation was to determine energy recovery efficiency. As can be seen from the presented results, energy recovery efficiency depends on rotational velocity, pump displacement and pressure. Efficiency characteristics for a typical boom mechanism system (with both cylinder chambers supplied) are very similar to the system with boom lowering under gravity. As expected, the flow through the regen valve results in increased energy losses, which, in turn, results in about 20% efficiency drop. For maximum pump displacement (εp = 1) the maximum value of energy system recovery efficiency is around 85% for a system without the regen valve and 65% for a system with the regen valve. The efficiency drop for higher boom cylinder velocity, proved by the characteristics, results from of the motor bypass valve (valve 4) opening when the hydrostatic motor cannot consume all the oil flow from the cylinder. The final stage of Hydraulic Power Recovery research was aimed at engine transient analysis. Two engine torque-smoothing systems were analyzed: flywheel support system and hydrostatic support system. The mathematical models of engine transient developed and solved allowed formulation of rules for sizing components such as flywheel, hydrostatic motor and accumulator. The calculations done for the flywheel support system led to a conclusion that application of additional inertia allows receiving smooth engine transient, however, the achieved
132
dimensions and mass of the required flywheel make the system impractical. Based on this conclusion it was decided not to install a flywheel in the HPR stand for testing. The developed nomograms of hydrostatic motor displacement and accumulator capacity as functions of engine torque can be helpful in initial sizing of hydrostatic support system components.
133
10. General conclusions 10.1. Field tests of an excavator with 3C cylinder Tests on a mini excavator 301.5 with a prototype design 3C cylinder confirmed good functional properties and improved efficiency of the hydraulic system. Depending on operation and environment parameters such as the manner of making an excavation by the operator (intensity of arm and bucket mechanism use), soil parameters (soil type, compactness, moisture content) and depth of digging, energy savings vary from some to 14% for the adopted at the beginning, repeatable digging test. Additionally, the change in the installation structure due to the application of a 3C cylinder decreases pressure losses in the lines supplying the cylinders by elimination of throttling losses in the original distribution valve, allowing also a controlled increase of the boom lowering velocity. The boom moving velocity can also be increased when the 3C cylinder is power-supplied from the charged accumulator, which takes place during boom lifting. Observation and tests results led to a particular conclusion that for elimination of rapid changes of boom lifting and lowering velocity, the flow control valve should be installed between the accumulator (7) and the distributors unit (3) of the energy saving system, despite the fact that energy efficiency of energy recovery system can be slightly lower than that obtained during tests. The performance of a 3C energy recovery system of a hydraulically controlled excavator system can be fully evaluated provided that an optimally designed, integrated valve block is be applied to connect the functions of the original system with energy recovery tasks [87, 88].
10.2. 301.5 mini hex boom cylinder with energy saving system ESS By introducing hydraulic energy transition between the boom cylinder and pump driving system energy saving system (ESS) allowed extending the range of hydrostatic energy which can be captured irrespective of its level and state of pressure in the hydro-pneumatic accumulator [89]. Such flexibility was possible by attaching to the electric engine shaft two electronically controlled hydrostatic units: a variable displacement pump and a variable displacement hydrostatic motor. Such an energy saving system structure enabled a different strategy of energy flow, including the mini hex boom mechanism and hydro-pneumatic accumulator. The total efficiency of energy recovery was determined based on tests data, and reached
134
the maximum value of 60% for 1000 [rpm] of the drive shaft and for the boom cylinder velocity in the range of 75 to 125 [mm/s]. A lower value of efficiency for higher engine rpm resulted from hydrostatic motor displacement decrease (lowering displacement control parameter εm below 0,5). On the other hand, lowering of efficiency for high boom cylinder velocity (above 125 [mm/s]) was a result of increased pressure losses in the hydraulic line as well as lower hydrostatic motor efficiency for such conditions of its operation. A reasonable estimate of ESS was done on a laboratory stand with accumulator by evaluation of energy storage process efficiency in selected cycles with engine torque leveling. An adequate cycle of power was adopted based on the analysis of mini excavator field tests results. The performed tests showed a difference between the torque value necessary to drive the pump and electric engine torque, which was named an effect of torque leveling. For the adopted power cycle (where the hydrostatic motor operated in rather not recommended, from efficiency point of view, displacement control parameter range from εm = 0,3 to εm = 0,5), the estimated total efficiency of energy storage process was about 50%. It should be noted here that the calculated energy losses in particular components of the system, such as hydraulic lines, accumulator and motor indicate that the efficiency of hydraulic motor had a major contribution to energy losses (smaller unit volume variable displacement hydrostatic motor was not available for test with mini excavator boom).
10.3. Hydraulic Power Recovery (HPR) tests stand for scaled linkage of 320C excavator The research stand equipped with a medium size 320 hydraulic excavator scaled boom mechanism and HPR system, driven by a 22 [kW] electric motor with frequency controlled rpm, allowed the application and control of different configurations of energy flow from the hydro-pneumatic accumulator, and a scaled boom mechanism cylinder as an energy source [90]. One-way clutch between the hydrostatic motor and pump also gave a possibility to control the mechanical driving torque. To prevent hydrostatic motor from cavitation a special control algorithm was developed. The main function of this algorithm was to de-stroke motor displacement, together with opening directional valve 4, in case of an insufficient supplying flow. The algorithm eliminates underpressure in the hydraulic motor inlet port, except the transient phase just after stopping the supplying flow. Time delay of motor response is the main cause of those unwanted phenomena. Consequently, two types of anti-cavitation systems were designed and implemented into HPR system as an additional control algorithm (chapter 8). These
135
systems ensure motor underpressure elimination for the entire range of system operation. As a result of the tests boom lowering velocity control system, including hydraulic power recovery, engine over-speed and hydrostatic motor underpressure elimination control algorithm was developed. Three cases were taken into consideration: boom lowering under gravity (only cylinder head side is supplied during raising), boom lowering by supplying the cylinder rod side and boom lowering by supplying the cylinder rod side with regen valve operation. The energy recovery efficiency, as a function of boom cylinder velocity for different load and engine rpm, shows that energy recovery efficiency clearly depends on pump rotational velocity and its displacement, and operation pressure. Efficiency characteristics for a typical boom mechanism system (with both cylinder chambers supplied) are very similar to a system with boom lowering under gravity. As was expected, the flow through regen valve result in increased energy losses, which results in about 20% efficiency lowering. For full pump displacement (εp = 1) the maximum value of efficiency is around 85% for a system without the regen valve and 65% for a system with the regen valve. The efficiency decrease for a higher boom cylinder velocity results from of motor bypass valve (valve 4) opening when the hydrostatic motor cannot consume all the oil flow from the cylinder. The performed calculations and analyses for a flywheel support system led to a conclusion that applying additional inertia allows receiving smooth engine transient, however, the achieved dimensions and mass of the required flywheel make the system impractical. On the basis of the HPR system tests in a wide range of operation and for different structures nomograms were developed of hydrostatic motor displacement and accumulator capacity as a function of engine torque, which could be helpful as a tool in initial sizing of hydrostatic support system components. To determine transient parameters of the analyzed engine torque-smoothing system, a dynamic model of the system, in Mathlab/Simulink was developed, which could be used successfully.
10.4. Future research The present monograph offers a solution of an energy saving and recovery system for hydraulic excavator, evaluated from the point of view of efficiency. As was mentioned in some tests summaries, some problems of dynamic properties of energy saving systems should be taken into account. The future research should be targeted at dynamic parameters optimization in the aspect of both control quality and ergonomic and safety. Another area to investigate is improvement of hydraulic system efficiency by a design and implementation of new, more efficient, electronically controlled components, including pumps, motors and valves, as well
136
as integrated, quality control oriented, monitoring systems of system operating parameters. Furthermore, using the experience of future research into electric hybrid vehicles and some “pilot” mobile machines systems, hydraulic hybrid displacement control systems with energy storage capabilities should be analyzed and developed. As a result, an excavator hydraulic system with hydraulic energy storage and embedded integrated electro-hydraulic control hardware could be worked out. Finally, all innovation, especially in hydraulic driven heavy duty machines, should take into consideration balanced solution covering machine manufacture cost, cost of operation and quality of machine control as well as ergonomics of operator’s workplace.
137
Acknowledgments The author would like to acknowledge that the monograph was executed on selected results of the research projects done for Caterpillar Inc. Peoria, USA in the years 2002–2006. Following the Agreement signed between the Cracow University of Technology, Cracow, Poland and Caterpillar Inc. Center of Excellence (former T&SD), Peoria, Ill. USA, publication of the research results was subject to five year confidentiality restriction. The author was involved in the project as a principal investigator and Project Manager. Laboratory and field test were possible to perform thanks to delivery by Caterpillar Inc., for this purpose, of a mini excavator, mid-size production linkages as well as professional package of Mathlab Simulink installation with dedicated laptops and xPC Target control module. The author would like to thank the Cracow University of Technology Fluid Power Laboratory team for their input in preparing and performing laboratory and field tests, according to the specific methodology. The author also expresses his gratitude to Prof. Stanisław Michałowski for consultation during the execution of Projects 4–6.
138
Appendix A A.1. 3C Cylinder strength calculations Fig. A.1 presents a scheme of 3C cylinder structure with the main dimensions and chambers (C1, C2 and C3) marked.
Hollowed piston rod
C3
C2
Cylinder tube
d2 d3 d1 d0 d4
C1
3C rod
Fig. A.1. 3C cylinder
For calculation of a 3C cylinder four load cases have been taken into account. These are: – Check of the hollowed piston rod for the inside and outside pressure, – Check of the 3C rod for buckling, – Check of the cylinder tube for the inside pressure, – Check of the 3C cylinder for buckling.
139
A.1.1. Check of the piston rod for the inside and outside pressure
On the basis of the analysis of load conditions of the hollowed piston rod of 3C cylinder, resulting from pressure, two typical cases can be specified: – the hollowed piston rod is loaded by the inside pressure in chamber C3, while its outside surface is not loaded (Fig. A.2a – this case occurs during boom lowering phase when chamber C3 is used), – the hollowed piston rod is loaded by the outside pressure in chamber C2, while its inside surface is not loaded (Fig. A.2b – this case occurs during simultaneous supply of chambers C1 and C2). b)
a)
pA3
pA2
pA1 pA1
Fig. A.2. Two cases of pressure loading of hollowed rode
To determine rod stresses under pressure load a thick walled pipe model has been applied (Lame case), which gives formulas for radial – σr, circumferential – σc and longitudinal – σl stresses, as follows: for the first configuration of the pressure load (Fig. A.2a):
140
p A 2 − p A3 r22 ⋅ r32 p A 2 ⋅ r22 − p A3 ⋅ r32 ⋅ 2 − r22 − r32 r r22 − r32
(A.1)
− ( p A 2 − p A3 ) r22 ⋅ r32 p A2 ⋅ r22 − p A3 ⋅ r32 ⋅ 2 − r22 − r32 r r22 − r32
(A.2)
σr =
σc =
σl = −
p A1 ⋅ A1 Ar
(A.3)
where: pA2 – atmospheric pressure. For the second configuration of the pressure load (Fig. A.2b):
p A 2 − p A3 r22 ⋅ r32 p A 2 ⋅ r22 − p A3 ⋅ r32 σr = 2 ⋅ 2 − r2 − r32 r r22 − r32
σc =
− ( p A 2 − p A3 ) r22 ⋅ r32 p A2 ⋅ r22 − p A3 ⋅ r32 ⋅ 2 − r22 − r32 r r22 − r32 σl = −
p A1 ⋅ A1 − p A 2 A2 Ar
(A.4)
(A.5)
(A.6)
where: pA2 – outside pressure, pA3 – inside pressure (in chamber C3), r – radius, r2 – rod outside radius, r3 – rod inside radius, Ar – area of rod cross section. The values of radius r2 and r3 are adopted as values taken from respective diameters. The total rod reduced stress for both cases can be obtained from H-M-H formula:
σT = σ r2 + σc2 + σl2 − σ r ⋅ σc − σ r ⋅ σl − σc ⋅ σl
(A.7)
The reduced value of rod stress should be referred to the tensile stress for rod material Rm, to check the following condition:
σT ≤ σ max =
Rm x
where: Rm – tensile strength of the material, x – safety factor.
(A.8)
141
If the condition is fulfilled, the hollowed rod wall thickness is correct for the expected pressure load. A.1.2. Check of the 3C rod for buckling
The next stage of strength calculation is the check of the 3C rod for buckling. The scheme of the 3C rod and its calculation model is shown in Figs A.3a and A.3b. In the model for buckling calculation it was assumed that one of its ends is restrained and the other one is free. The maximum force comes from the C3 chamber pressure, limited by the relief valve, and acts along the pin axis. a)
b)
F
F
d3
d4
Fig. A.3. Pin load for buckling calculation
The critical compressive strength from the buckling condition (resulting in loss of rod stability) is determined by the length of the element, cross section area and shape, its material and the way of its end fixing. Hence, the dimensional features for buckling calculation are defined as follows:
i= λ=
J A lb i
minimum radius of gyration slenderness ratio
142
where: A – rod cross section area,
J=
π ⋅ ( d34 − d 44 )
, 64 lb – modified length for the given buckling model (Fig. A.3b); lb =2 l. According to the value of the slenderness ratio λ, two cases of buckling calculation are carried out using the formulas: – calculation according to Euler for: λ > λgr, – calculation according to Tetmajer for: λ ≤ λgr, where: λgr is the slender limit given by the equation: J – cross-sectional moment of inertia;
λ gr = π ⋅
E RH
(A.9)
where: E – Young modulus, RH – proportional limit. In case where λ > λgr strength limit can be calculated from equation: σ kr =
π2 ⋅ E ⋅ J lb2 ⋅ A
(A.10)
whereas, when λ ≤ λgr the strength limit can be calculated from equation: ⎛ R − RH ⎞ RH σkr = Re − ⎜ e ⋅ ⋅λ E π ⎟⎠ ⎝
(A.11)
where: Re – plasticity limit The buckling condition to be fulfilled can be reduced to the expression: F σ kr ≤ A x
(A.12)
where: F – acting vertical force, x – factor of safety. A.1.3. Check of the cylinder tube for the inside pressure
In the analysis of the load (caused by pressure) of the main cylinder tube of the 3C cylinder the case when the cylinder chamber C3 is under inside pressure while the outside is normally not under pressure (atmospheric pressure only) should be taken into consideration (see Fig. A.4 – it takes place during boom raising).
143
pA2
pA1
Fig. A.4. Main cylinder pressure load
To determine cylinder tube stresses under pressure load a thick walled pipe model has been applied (Lame case) which gives formulas for radial – σr, circumferential – σc and longitudinal – σl stresses, as follows: p A0 − p A1 r02 ⋅ r12 p A0 ⋅ r02 − p A1 ⋅ r12 ⋅ 2 − r02 − r12 r r02 − r12
(A.13)
− ( p A0 − p A1 ) r02 ⋅ r12 p A0 ⋅ r02 − p A1 ⋅ r12 ⋅ 2 − r02 − r12 r r02 − r12
(A.14)
p A2 ⋅ A2 Ac
(A.15)
σr =
σc =
σl =
where: pA0 – outside pressure, pA1 – inside pressure ( in chamber C1), r – radius, r0 – outside radius, r1 – inside radius, Ac – area of cylinder wall cross section, values of r1 and r2 are calculated from cylinder diameters:
144
Ac =
r0 =
d0 2
(A.16)
r1 =
d1 2
(A.17)
π ⋅ d 02 π ⋅ d12 − 4 4
(A.18)
The total reduced stress from pressure can be determined by formula:
σT = σ r2 + σc2 + σl2 − σ r ⋅ σc − σ r ⋅ σl − σc ⋅ σl
(A.19)
The reduced value of cylinder stress should be referred to tensile strength for cylinder material Rm, to check the condition:
σT ≤ σ max =
Rm x
(A.20)
where: Rm – tensile strength, x – factor of safety. If the above condition is fulfilled, the hollowed cylinder wall thickness is correct for the expected pressure load. A.1.4. Check of the complete 3C cylinder for buckling
Schemes of the complete 3C cylinder load with its model for buckling calculation are shown in Figs A.5a and A.5b. The complete cylinder is an element with different stiffness at joints at both ends. The maximum vertical force acting along the axis of the cylinder comes from the pressure which occurs in chambers C1 and C3 and its value depends on the relief valve adjustment. For such an adopted buckling model Jasinski formula can be applied (for a rod of different cross section area). The critical value of the load (compressive force limit) can be determined from the formulas:
Pkr ⋅l E ⋅ J2 ⎛ Pkr ⎞ tan ⎜⎜ ⋅ l2 ⎟⎟ ⎝ E ⋅ J2 ⎠
+
Pkr ⋅l E ⋅ J1 ⎛ Pkr ⎞ tan ⎜⎜ ⋅ l1 ⎟⎟ ⎝ E ⋅ J1 ⎠
=0
(A.21)
where: E – Young modulus, J1, J2 – moment of inertia, l – length of complete 3C cylinder, l1, l2 – length of cylinder segments of different stiffness.
145 a)
b)
F
F
l
l
J1
J2
Fig. A.5. Complete 3C cylinder calculation
The value of the critical compressive force divided by the safety factor should be referred to the maximum force acting on the cylinder, and should be not greater than the result of division: F≤
Pkr x
(A.22)
A.2. Example of calculations for mini hex 301.5 3C cylinder Two cases of the 3C cylinder sizing are presented: – determination of an optimal (diameters d1, d2 and d3 – wise) 3C cylinder, – determination of optimal diameters d1, d2 and d3, considering the existing pipe and rod cylinder standard products, available on the Polish market.
146
A.3. Determination of optimal (diameters d1, d2 and d3 – wise) 3C cylinder A.3.1. Primary selection of diameters
Primary selection of the diameters was done adopting about ±10% tolerance between a 3C and original cylinder cross section areas, which, actually, is not reached in a real cylinder design. Cross section areas of the original cylinder are: – piston side: A1o =
π ⋅ d o21 4
(A.23)
A1o =
π ⋅ 602 4
(A.24)
A1o = 2827 [mm2]
(A.25)
– rod side: A2 o =
A2 o =
π ⋅ ( d o21 − d o22 ) 4 π ⋅ ( 602 − 302 ) 4
A2 o = 2121 [mm2]
(A.26)
(A.27)
(A.28)
Initially, the 3C cylinder diameters were set up as:
d 0 = 75 [mm] d1 = 63 [mm] d 2 = 42 [mm] d3 = 32 [mm] d 4 = 8 [mm] per cent difference between piston area of a 3C cylinder A1 + A3 and the original one A1o is: δ1 =
A1o − ( A1 + A3 ) A1o
⋅ 100%
(A.29)
147
⎛ ⎛ π ⋅ 632 π ⋅ 322 ⎞ π ⋅ 322 ⎞ π ⋅ 602 − ⎜⎜ ⎟− ⎟+ 4 ⎠ 4 ⎠ 4 ⎝ 4 ⎝ δ1 = ⋅ 100% 2 π ⋅ 60 4
(A.30)
δ1 = 10,3 %
(A.31)
per cent difference between rod side piston area of a 3C cylinder A2o the and original one A2 n is: δ2 =
A2 o − A2 n ⋅ 100% A2 o
π ⋅ ( 602 − 302 ) δ2 =
4
−
(A.32)
π ⋅ ( 632 − 422 )
π ⋅ ( 602 − 302 )
4
⋅ 100%
(A.33)
4 δ2 = 18,3 %
(A.34)
20
pb3'
16
pb3
p [MPa] p [MPa]
12
pac 8
4
0 0.7
0.8
0.9
1
1.1
[m] lb l [m] b
Fig. A.6. Pressure characteristics in chamber C3 (pb3, pb3’) and selected accumulator pressure (pac) during its charging
148
The next step of the procedure described before was to convert the force loading cylinder, present during boom lowering (Fig. A.6), to a necessary pressure to receive data for sizing the accumulator (volume and preload pressure), as follows:
Vn (V − Vo ) n
(A.35)
2,51.4 (2,5 − Vo )1.4
(A.36)
pA = p ⋅ p A = 10 ⋅
This step was followed by checking whether the cylinder force from accumulator pressure, acting only on area A1 or A1+A3, is higher than the force needed to raise the boom (Fig. A.7). 40000 Fac2 35000 Fac1 30000
FF[N] [N]
25000
F4
20000 F3 15000
10000
5000
0 0.7
0.8
0.9
1
1.1
[m] lLbb [m]
Fig. A.7. Force characteristics as a function of boom cylinder length during boom raising
Since forces characteristics from accumulator, (Fac1 or Fac2), are above the cylinder raising pressure characteristics (F3 and F4) it is concluded that cylinder diameters were chosen correctly energy saving–wise. The next step is to analyze the stress of the selected cylinder. A.3.2. Cylinder stress calculation
Fig. A.8 shows the scheme and sizing of a 3C cylinder with C1, C2 and C3 chambers marked.
149
Hollowed piston rod
C3
C2
Cylinder tube
d2 d3 d1 d0 d4
C1
3C rod
Fig. A.8. 3C cylinder sizing
In 3C cylinder strength calculations four cases of the load are taken into consideration: – Hollowed rod calculation under outer and inner pressure load, – 3C rod buckling calculation, – Cylinder tube for inside pressure check, – Buckling calculation of the complete, extended cylinder. A.3.3. Calculation of hollowed rod under outer and inner pressure load
In the analysis of the 3C cylinder hollowed piston rod load, caused by pressure, two characteristic cases were specified: – when the hollowed piston rod is loaded by inside pressure while its outside surface is not loaded (Fig. A.9a – the case takes place during lowering when chamber C3 is used), – when the hollowed piston rod is loaded by outside pressure while the inside is not loaded (Fig. A.9b – the case takes place, for example, during digging
150
process when the cylinder is stopped but subjected to outside forces causing passive pressure rising up to opening of the relief valve. b)
a)
pA3
pA2
pA1 pA1
Fig. A.9. Hollowed piston rod pressure load
To determine the stress of the rod material for both cases above a model for thick vessel was used (known as a Lame model): case a) for case a) radial stress σr, circumferential σc and longitudinal σl as a function of radius r of 16 [mm], are described by the equation below and amount to: Radial stress – σr
σr =
p A 2 − p A3 r22 ⋅ rr2 p A 2 ⋅ r22 − p A3 ⋅ rr2 ⋅ 2 − r22 − rr2 r r22 − rr2
(A.37)
151
σr =
0 − 21,5 212 ⋅ 162 0 ⋅ 212 − 21,5 ⋅ 162 ⋅ − 212 − 162 16 2 212 − 162
σr = −21,5 [MPa]
(A.38) (A.39)
circumferential σc σc =
− ( p A 2 − p A3 ) r22 ⋅ rr2 p A2 ⋅ r22 − p A3 ⋅ rr2 ⋅ 2 − r22 − rr2 r r22 − rr2
(A.40)
σc =
−(0 − 21,5) 212 ⋅ 162 0 ⋅ 212 − 21,5 ⋅ 162 ⋅ − 212 − 162 16 2 212 − 162
(A.41)
σc = 81,0 [MPa]
(A.42)
longitudinal σl ⎛ π ⋅ ( d12 − d32 ) ⎞ ⎟ p A1 ⋅ ⎜ ⎜ ⎟ 4 ⎝ ⎠ σl = − 2 2 π ⋅ ( d2 − dr )
(A.43)
4 ⎛ π ⋅ ( 632 − 31,62 ) ⎞ ⎟ 21,5 ⋅ ⎜ ⎜ ⎟ 4 ⎝ ⎠ σl = − 2 2 π ⋅ (42 − 32 ) 4
σl = −86,3 [MPa]
(A.44)
(A.45)
where: pA1 – chamber C1 pressure, pA2 – outside pressure, pA3 – inside, C3 chamber pressure, r – radius, r2 – outer rod radius, rr – inner rod radius, where radiuses r2 and r3 are given by:
r2 =
d2 2
(A.46)
r3 =
d3 2
(A.47)
152
The total rod reduced stress can be calculated from the equation and is: σT = σ r2 + σc2 + σl2 − σ r ⋅ σc − σ r ⋅ σl − σc ⋅ σl σT =
( −21,5 )
2
(A.48)
+ 81,02 + ( −86,3) − ( −21,5 ) ⋅ 81,0 − ( 21,5 ) ⋅ ( −86,3) − 81,0 ⋅ ( −86,3) 2
(A.49) σT = 146,1 [MPa]
(A.50)
case b) for this case radial stress σr, circumferential σc and longitudinal σl as a function of radius r of 16 [mm], are given by the formula and are, respectively: radial stress σr
p A 2 − p A3 r22 ⋅ rr2 p A 2 ⋅ r22 − p A3 ⋅ rr2 ⋅ 2 − r22 − rr2 r r22 − rr2
(A.51)
21,5 − 0 212 ⋅ 162 21,5 ⋅ 212 − 0 ⋅ 162 ⋅ − 212 − 162 16 2 212 − 162
(A.52)
σr = σr =
σr = 0 [MPa]
(A.53)
circumferential σc σc =
− ( p A 2 − p A3 ) r22 ⋅ rr2 p A2 ⋅ r22 − p A3 ⋅ rr2 ⋅ 2 − r22 − rr2 r r22 − rr2
(A.54)
σc =
−(21,5 − 0) 212 ⋅ 162 21,5 ⋅ 212 − 0 ⋅ 162 ⋅ − 212 − 162 16 2 212 − 162
(A.55)
σc = −102,5 [MPa]
(A.56)
longitudinal σl ⎛ π ⋅ ( d12 − d32 ) ⎞ ⎛ π ⋅ ( d12 − d 22 ) ⎞ ⎟ − pA2 ⋅ ⎜ ⎟ p A1 ⋅ ⎜ ⎜ ⎟ ⎜ ⎟ 4 4 ⎝ ⎠ ⎝ ⎠ σl = − π ⋅ ( d 22 − d r2 ) 4
(A.57)
153
⎛ π ⋅ ( 632 − 31,62 ) ⎞ ⎛ π ⋅ ( 632 − 422 ) ⎞ ⎟ − 21,5 ⋅ ⎜ ⎟ 21,5 ⋅ ⎜ ⎜ ⎟ ⎜ ⎟ 4 4 ⎝ ⎠ ⎝ ⎠ σl = − 2 2 π ⋅ (42 − 32 ) 4
σl = −22, 2 [MPa]
(A.58)
(A.59)
where: pA1 – chamber C1 pressure, pA2 – outside pressure, pA3 – inside pressure (in chamber C3), r – radius, r2 – outer radius of rod, rr – inner radius of hollowed rod, where radiuses r2 and r3 are given by:
r2 =
d2 2
(A.60)
r3 =
d3 2
(A.61)
The total rod reduced stress can be calculated from the equation and is: σT = σ r2 + σc2 + σl2 − σ r ⋅ σc − σ r ⋅ σl − σc ⋅ σl
(A.62)
σT = 02 + ( −102,5 ) + ( −22, 2 ) − 0 ⋅ ( −102,5 ) − 0 ⋅ ( −22, 2 ) − ( −102,5 ) ⋅ ( −22, 2 ) 2
2
(A.63) σT = 93, 4 [MPa]
(A.64)
With the total reduced stress it is possible to refer it to tensile strength for rod material, which, in our case, is Rm = 980 [MPa], checking the condition: σT ≤ σ max =
Rm x
(A.65)
980 4 146,1 [MPa] ≤ 245 [MPa] meets the condition 980 for case b) 93, 4 ≤ σ max = 4 93,4 [MPa] ≤ 245 [MPa] meets the condition where: Rm – tensile strength (for 34HNM steel Rm = 980 [MPa]), x – factor of safety (x = 4 for our case). for case a) 146,1 ≤ σ max =
154
Taking into consideration the calculation result it can be assumed that the hollowed piston rod fulfills the strength conditions from pressure. A.3.4. Calculation of 3C rod buckling
A schema for 3C rod buckling calculations with load character is shown in Figs A.10a and A.10b, where the following calculation model has been adopted: one end of the 3C rod is restrained and other one is free. Maximum compressive force comes from pressure in chamber C3 (which is equal to relief valve opening pressure) and acts along the rod axis. a)
b)
F
F
d4
l
l
d3
Fig. A.10. 3C rod for buckling calculation
As mentioned before, the critical compressive strength from the buckling condition (causes loss of rod stability) is determined by the length of the element, cross section area and shape, its material and the way of its end fixing. Hence, the dimensional features for buckling calculation are defined as follows and have values: – minimum radius of gyration:
i =
J A3
(A.66)
155
48750
i =
⎛ π ⋅ ( 31,62 − 82 ) ⎞ ⎜ ⎟ ⎜ ⎟ 4 ⎝ ⎠
(A.67)
i = 8,15 [mm]
(A.68)
– slenderness ratio lb i
(A.69)
360,5 8,15
(A.70)
λ = 44, 24
(A.71)
λ=
λ=
where: A3 – hollowed rod wall cross section area, J – cross section moment of inertia; for the hollowed rod the moment of inertia is given by the formula: J=
J=
π ⋅ ( d34 − d 44 )
64
π ⋅ ( 31,64 − 84 )
64
J = 48750 [mm4]
(A.72)
(A.73) (A.74)
where: lb – buckling modified length for the given buckling model (Fig. A.10b):
lb = 0,7 ⋅ l
(A.75)
lb = 0,7 ⋅ 515
(A.76)
lb = 360,5 [mm]
(A.77)
Based on the value of slenderness ratio λ, two cases of buckling calculations are carried out using the formulas: elastic range, calculation according to Euler for: λ > λgr non-elastic range, calculation according to Tetmajer for: λ ≤ λgr where: λgr is the slender limit given by the equation:
156
E RH
(A.78)
2,1 ⋅ 105 882
(A.79)
λ gr = π ⋅
λ gr = π ⋅
λ gr = 48, 48
(A.80)
where: E – Young modulus E = 2,1 ⋅ 105 , RH – proportional limit RH = 0,9 · Rm. RH = 882 [MPa]
(A.81)
Since we have a case where λ < λgr strength limit can be calculated from the equation: ⎛ R − RH ⎞ RH σkr = Rm − ⎜ m ⎟⋅ E ⋅λ π ⎝ ⎠
(A.82)
882 ⎛ 980 − 882 ⎞ σkr = 980 − ⎜ ⋅ 44, 24 ⎟⋅ 5 π ⎝ ⎠ 2,1 ⋅ 10
(A.83)
σkr = 890,6 [MPa]
(A.84)
The buckling condition to be fulfilled can be reduced to the expression: F σ kr ≤ A3 x
15780
(A.85) 890,6 3
(A.86)
21,5[MPa] ≤ 296,9[MPa]
(A.87)
⎛ π ( 31,6 − 8 ⎜ ⎜ 4 ⎝ 2
2
) ⎞⎟
≤
⎟ ⎠
where: F – force F = pA3 · A3, x – safety factor, adopted as 3. A.3.5. Cylinder tube for inside pressure check
In the analysis of a 3C cylinder load from pressure one particular case was selected. This is when the cylinder is subjected to inside pressure while the outside
157
surface is not under pressure. (For example when the boom is being raised – Fig. A.11).
pA2
pA1
Fig. A.11. Cylinder (tube) load by inside pressure
To determine the stress of the cylinder tube material, a model for thick vessel was used (Lame model), where radial stress σr, circumferential stress σc and longitudinal stress σl as a function of radius r of 31,5 [mm] are described by the equations below and amount to: radial stress σr:
p A0 − p A1 r02 ⋅ r12 p A0 ⋅ r02 − p A1 ⋅ r12 ⋅ 2 − r02 − r12 r r02 − r12
(A.88)
37,52 ⋅ 31,52 0 ⋅ 37,52 − 21,5 ⋅ 31,52 0 − 21,5 ⋅ − 37,52 − 31,52 31,5 2 37,52 − 31,52
(A.89)
σr = σr =
σr = −21,5 [MPa]
(A.90)
158
circumferential stress σc: σc =
σc =
− ( p A0 − p A1 ) r02 ⋅ r12 p A0 ⋅ r02 − p A1 ⋅ r12 ⋅ 2 − r02 − r12 r r02 − r12
− ( 0 − 21,5 ) 37,52 − 31,52
⋅
(A.91)
37,52 ⋅ 31,52 0 ⋅ 37,52 − 21,5 ⋅ 31,52 − 31,5 2 37,52 − 31,52
(A.92)
σc = 124,6 [MPa]
(A.93)
longitudinal stress σl: σl =
p A2 ⋅ A2 Ac
(A.94)
⎛ π ⋅ ( 632 − 422 ) ⎞ ⎟ 21,5 ⋅ ⎜ ⎜ ⎟ 4 ⎝ ⎠ σl = 2 2 ⎛ π ⋅ ( 75 − 63 ) ⎞ ⎜ ⎟ ⎜ ⎟ 4 ⎝ ⎠
(A.95)
σl = 28,6 [MPa]
(A.96)
where: pA0 – outside pressure, pA1 – inside pressure (present in chamber C1), r – radius, r0 – outer radius of the cylinder, r1 – inner radius of the cylinder, where r1 and r2 are related to diameters of the cylinder as follows:
Ac =
r0 =
d0 2
(A.97)
r1 =
d1 2
(A.98)
π ⋅ ( d 02 − d12 ) 4
(A.99)
159
The total reduced stress from pressure can be determined by the formula: σT = σ r2 + σc2 + σl2 − σ r ⋅ σc − σ r ⋅ σl − σc ⋅ σl σT =
( −21,5 )
2
(A.100)
+ 124,62 + 28,62 − ( −21,5 ) ⋅ 124,6 − ( −21,5 ) ⋅ 28,6 − 124,6 ⋅ 28,6 (A.101) σT = 128,6 [MPa]
(A.102)
The reduced value of cylinder stress should to be referred to tensile strength for cylinder material Rm, to check the following condition: σT ≤ σ max =
Rm x
(A.103)
128,6 ≤ σmax = 600 4
(A.104)
128,6 [MPa] ≤ 150 [MPa]
(A.105)
where: Rm – tensile strength (St 52.3 steel Rm = 600 [MPa]), x – factor of safety. Since the above condition is fulfilled, it can be concluded that thickness of cylinder wall was properly designed for the expected pressure load. A.3.6. Buckling calculation of the complete, extended cylinder
The final stage of 3C cylinder calculation was buckling calculation of the complete cylinder. A scheme of the cylinder and the buckling model adopted are shown in Figs A.12a and A.12b. The following model was adopted: the cylinder as a complete element has different stiffness along its lengths, cylinder ends have articulated joints, maximum force acting on the cylinder along its axis comes from relief valve pressure in chambers C1 and C3. For the adopted model the Jasinski formula for rod with different stiffness has been used. The critical value of load (compressive force limit) can be determined from the formulas:
Pkr ⋅l E ⋅ J2 ⎛ Pkr ⎞ tan ⎜⎜ ⋅ l2 ⎟⎟ ⎝ E ⋅ J2 ⎠
+
Pkr ⋅l E ⋅ J1 ⎛ Pkr ⎞ tan ⎜⎜ ⋅ l1 ⎟⎟ ⎝ E ⋅ J1 ⎠
=0
(A.106)
160
Pkr Pkr ⋅ 1100 ⋅ 1100 5 2,1 ⋅ 10 ⋅ 779900 2,1 ⋅ 10 ⋅ 101300 + = 0 (A.107) ⎛ ⎞ ⎛ ⎞ Pkr Pkr tan ⎜⎜ ⋅ 520 ⎟⎟ tan ⎜⎜ ⋅ 580 ⎟⎟ 5 5 ⎝ 2,1 ⋅ 10 ⋅ 779900 ⎠ ⎝ 2,1 ⋅ 10 ⋅ 101300 ⎠ 5
Pkr = 256, 2 [kN]
(A.108)
where: E – Young modulus, J1, J2 – moment of inertia, l – length of complete 3C cylinder, l1, l2 – lengths of different stiffness cylinder segments a)
b)
F
F
l
l
J1
J2
Fig. A.12. 3C cylinder buckling model
161
Fb ≤
Pkr x
(A.109)
p A3 ⋅ ( A1 + A3 ) ≤
Pkr x
21,5 ⋅ ( 2,333 + 0,734 ) ≤
(A.110)
232, 4 3
65,9 [kN] ≤ 85,4 [kN]
(A.111) (A.112)
The value of the critical compressive force divided by the safety factor is greater than maximum force acting on the cylinder, which fulfills the buckling condition.
A.4. Determination of optimal diameters d1, d2 and d3, considering existing pipe and rod cylinder standard products, available on the Polish market The calculation has been done using the same procedure as before and its results are listed in Table A.1. Table A.1
Cylinder diameters
Area tolerance Area tolerance Piston rod for inside pressure
Piston rod for outside pressure 3C rod for buckling Cylinder tube for inside pressure Complete 3C cylinder for buckling
Symbol do d1 d2 d3 d4 δ1 δ2 σr σc σI σT σr σc σI σT σb σr σc σI σT Fb
Unit 75 63 mm 42 32 8 10 % –18 –21,5 81,0 –86,3 146,1 0,0 –102,5 MPa –22,3 93,5 21,5 –21,5 124,6 28,6 128,5 kN 65,9
162
A.5. Design of 3C cylinders The calculation has been done using the same procedure as presented before and its results for three alternative designs are listed in Table A.2, where: σr – radial stresses, σc – circumferential stresses, σI – longitudinal stresses, σT – total stresses, pac – accumulator pressure, pb3, pb3’ – upper and lower limit of pressure value in chamber 3C. Table A.2 Symbol
Cylinder diameters
Area tolerance Area tolerance
Piston rod for inside pressure
Allowable stress for 34HNM steel
Piston rod for outside pressure
Allowable stress for 34HNM steel 3C rod for buckling Allowable stress for 34HNM steel
Cylinder tube for inside pressure
Allowable stress for St52.3 steel (DIN 2391/C or 2393) Complete 3C cylinder buckling force Compressive force limit
do d1 d2 d3 d4 δ1 δ2 σr σc σI σT
Unit
mm
%
I 75 63 42 32 8 10 –18 –21,5 81,0 –86,3 146,1
Variant II 78 65 42 32 8 17,3 –8,8 –21,5 81,0 –93,7 152,0
σdop
245
245
σr σc σI σT
0,0 –102,5 –22,3 93,5
0,0 –102,5 –22,3 93,5
245
245
σdop
MPa
III 78 65 45 32 8 17 –18 –21,5 65,5 –69,3 118,4 245 0,0 –87,0 –22,0 78,4 245
σb
21,5
21,5
21,5
σdop
296,8
296,8
296,8
σr σc σI σT
–21,5 124,6 28,6 128,5
–21,5 119,2 28,5 123,5
–21,5 119,3 25,4 124,2
150
150
150
σdop Fb Fdop
kN
65,9 85,4
70,2 86,2
72,6 124,8
Fig. A.13. Design of 3C cylinder for CAT 301.5 excavator
163
164
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Sobczyk A., Water Hydraulic Drive and Control – Mobile Application, Proc. of International Scientific-Technical Conference Hydraulics and Pneumatics 2007, ISBN 978-83-87982-27-0, 2007, 375-395. Sobczyk A., Energooszczędne i ekologiczne wodne układy napędu i sterowania – akwatronika (Energy Saving and Environment Friendly Water Hydraulic Drive and Control Systems – Aquatronics), in Polish, Proc. of International Scientific-Technical Conference Hydraulics and Pneumatics’2005, on “Problems and Development Tendencies in the Beginning Decade of the 21st Century”, Wroclaw, 17–19 maj 2005, 332-344. Sobczyk A., Pobędza J., Kucybała P., Badania symulacyjne hydraulicznego układu odzysku energii w pojazdach i maszynach roboczych (Simulation of Energy Saving System in Vehicles and Heavy Duty Machines), in Polish, Proc. of „XII Warsztaty Naukowe Polskiego Towarzystwa Symulacji Komputerowej, Sarbinowo Morskie 2005. Sobczyk A., Tora G., Grader Blade Stabilization System, Elsevier – Automation in Construction, 7(1998), 385-389. (This work constitute a part of the Research Project No. 7 TO7B 032 10 financed by KBN (Polish Committee for Scientific Research) in the period of 1996–1998). Sobczyk A., Water Hydraulics – the Industrial Perspective – chapter of “Water Hydraulics. The Natural Choice” book, ed. Mads Grahl Madsen, ISBN 82-7709-071-4, Bergen University College, Bergen 2004, 34-67. Song L., Bin Y., Energy-saving Control of Single-rod Hydraulic Cylinders with Programmable Valves and Improved Working Mode Selection, SAE Transactions – Journal of Commercial Vehicle, SAE 2002-01-1343, 2002, 51-61. Sprockhoff V., Untersuchungen von Regelungen am Hydrostatischen Zylinderantrieb mit Servopumpe, Ph.D. Thesis, RWTH, Aachen 1979. Stecki J.S., Garbacik A., Hydraulic Control Systems – System Design and Analysis, Fluid Power Net Publications, 2000. Stecki J.S., et al. Development of a Hydraulic Drive for a Novel Hybrid Diesel-Hydraulic System for Large Commercial Vehicles, 5th JFPS International Symposium on Fluid Power, Nara 2002. Stecki J., Matheson P., Advances in Automotive Hydraulic Hybrid Drives, Proc. of the 6th JFPS International Symposium on Fluid Power, Tsukuba 2005. Stelson K.A., Meyer J.J., Alleyne A.G., Integrated Algorithms for Optimal Energy Use in Mobile Fluid Power Systems, Research project overview, The Center for Compact and Efficient Fluid Power University of Minnesota, Minnesota 2011. Stelson K.A., Meyer J.J., Alleyne A.G., Hencey B., Energy Saving Control of a Hydraulic Hybrid Passenger Vehicle, Proc. of the 7th Japan Society of Fluid Power International Symposium on Fluid Power, Toyama 2008, 143-148. Stryczek S., Napęd hydrostatyczny (Hydrostatic Drives), in Polish, WNT, Warszawa 1984. Szumanowski A., Hybrid Electric Vehicle Drives Design, Wydawnictwo ITE-PIB, Warszawa 2006. Tikkanen S., Kliffken M., Ehret C., Baseley S., Hydraulic Hybrid Systems for Working Machines and Commercial Vehicles, Proc. of the 51st National Conference on Fluid Power, NCFP I08-19.4, Las Vegas, Nevada 2008. Triet H.H., Ähn K.K., Comparison and Assessment of a Hydraulic Energy-saving System for Hydrostatic Drives, Proc. of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 225, No. 1, February 1, 2011, 21-34. Van de Ven J.D., Olson M., Li P.Y., Development of a Hydro-Mechanical Hydraulic Hybrid Drive Train with Independent Wheel Torque Control for an Urban Passenger Vehicle, International Fluid Power Exposition, Las Vegas 2008.
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Summary The main subject presented in the monograph are selected research results of theoretical and experimental project works done mainly for Caterpillar Inc., Peoria, Ill., USA in the years 2003–2006. The major goal of analyses and laboratory experiments was to show the possibility of hydraulic energy recuperation in hydraulic driven earth-moving machinery, such as an excavator. The mechanism selected for the study was the boom mechanism as the most suitable for energy recuperation. This results from the significant moving mass of the equipment (boom, stick and bucket) as well as the stroke volume of the hydraulic fluid in boom cylinder, which can be stored under pressure in the hydraulic accumulator or transferred directly to another subsystem of the machine. The subsequent steps of the investigations included experiments allowing measurement of the potential energy which can be captured during a simulated typical excavator digging cycle. Another important task of the research were calculations and design of an energy saving system using an appropriate hydro-pneumatic accumulator and control of energy flow to and from the storage device, to be utilized in the system in the next cycle. Two different concepts of stored energy utilization are discussed. One is the possibility to use the accumulated energy as a supporting energy to raise the boom, which in consequence, reduces energy (from the hydraulic pump) necessary for the operation. To improve the ratio of possible pressure level which could be used to support the boom cylinder, a special three chamber (3C) cylinder design has been developed and tested on a stand and real machine in field tests. The other concept was the supply, connected to machine engine shaft, of the hydrostatic motor. Making use of a specially developed energy flow control system the motor enables utilization of energy saved, reducing the torque which is necessary to drive the system pump working under given load pressure. As was assumed, the presented solutions improve the total efficiency of the machine, which means both lowering fuel consumption and improving the durability as well as lowering the pollution due to the engine working in the most effective region of its characteristic.
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VERBESSERUNG DER HYDRAULISCHEN EFFIZIENZ DER AUFTRIEBSSYSTEME DURCH EINSATZ DER SYSTEME MIT ENERGIERÜCKGEWINNUNG Zusammenfassung Die Hauptfrage der Monographie ist die Anwendung der Rekuperation von Energie in hydraulischen Auftriebs und -Steuerungssystemen der Arbeitsmaschinen, belegt mit ausgewählten Ergebnissen der breit durchgeführten theoretischen und experimentellen Forschungsarbeiten, geführt hauptsächlich im Rahmen des internationalen Projektes für die Firma Catepillar Inc. aus Peoria in den USA. Das Ziel der Forschungsarbeiten war Verbesserung der Energieeffizienz von Betriebsmaschinen am Beispiel des Hydrauliksystems der Bagger. Besondere Aufmerksamkeit hat man dabei dem Antriebssystem von Bewegungen des Auslegers eines Hydraulikbaggers geschenkt, bei welchem aufgrund der hohen Masse des Auslegers, des Arms und des Löffels sowie des verhältnismäßig großen Betriebsdurchmessers des Hydraulikzylinders, und wo die Arbeitsflüssigkeit während der Senkbewegung aufgenommen und in dem hydraulischen Akkumulator gespeichert oder direkt in ein anderes Mechanismus der Maschine übertragen werden kann, besonders viel Energie rückgewonnen werden kann. Von zentraler Bedeutung waren die Untersuchungsarbeiten, welche die quantitative Bewertung der während einer Simulation des typischen Aushebevorgangs zurückzugewinnenden Energie ermöglicht haben. Anschließend wurde ein Energierückgewinnungssystem erarbeitet durch Anpassung des entsprechenden hydraulischen Akkumulators und des Durchflusssteuerungssystems in den Akku und aus dem Akku, damit die eingespeiste Energie in dem nächsten Arbeitszyklus der Maschine freigesetzt werden kann. Die Analyse ergab zwei Konzepte für die Nutzung der gespeicherten Energie. Das erste Konzept stellte die Möglichkeit der Nutzung der akkumulierten Energie für den zusätzlichen Antrieb der Hebebewegung des Auslegers dar, was die Reduzierung des Energiebedarfs seitens der Hauptpumpe in diesem Arbeitszyklus ermöglicht hat. In diesem Fall zum Zwecke der Nutzungssteigerung der eingespeisten Energie in einem breiteren Bereich der Betriebsdrucke, wurde ein 3-Kammer-Zylinder (3K) entworfen, erzeugt und sowohl am Prüfstand als auch an der Maschine in den Geländetests untersucht. Das zweite Konzept war die Nutzung der gespeicherten Energie zur Versorgung des mit der Treibwelle des Hauptantriebs verbundenen Hydraulikantriebs. Durch Einsatz eines Algorithmus zur Energiedurchflusssteuerung wird die Verringerung des Drehmoments des Hydraulikantriebs ermöglicht, welcher zum Antrieb der unter dem Betriebsdruck arbeitenden Maschinen benötigt wird. Wie der Beitrag belegt, erhöhen die dargestellten Lösungen die energetische Effizienz einer hydraulisch angetriebenen Maschine, was sich in der Praxis sowohl in der Verringerung des Treibstoffverbrauchs als auch in der Lebensdauererhöhung des Systems durch Ausgleich des Belastungsmoments eines Verbrennungsmotors bei gleichzeitiger Senkung der Abgaseemission des im optimalen Charakteristikbereich arbeitenden Motors.
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POPRAWA SPRAWNOŚCI HYDRAULICZNYCH UKŁADÓW NAPĘDOWYCH MASZYN PRZEZ ZASTOSOWANIE UKŁADÓW Z REKUPERACJĄ ENERGII Streszczenie Głównym zagadnieniem prezentowanym w monografii jest zastosowanie rekuperacji energii w hydraulicznych układach napędu i sterowania maszyn roboczych poparte wybranymi wynikami szeroko prowadzonych prac teoretycznych i badań eksperymentalnych, głównie w ramach projektu międzynarodowego dla firmy Caterpillar Inc. z Peorii w USA. Celem prac było wykazanie możliwości poprawy sprawności energetycznej układów napędowych maszyn roboczych na przykładzie hydraulicznego układu napędowego koparek. Szczególną uwagę poświęcono układowi napędu ruchów wysięgnika jako najbardziej interesującego ze względu na wielkość energii możliwej do odzyskania, wynikającą z dużej masy wysięgnika, ramienia i łyżki, jak również, związanej z tym, relatywnie dużej objętości roboczej cylindra wysięgnika, z którego ciecz robocza może być przechwycona w czasie ruchu opuszczania i zmagazynowana w akumulatorze lub bezpośrednio przekazana do układu napędowego innego mechanizmu maszyny. Istotnym etapem były więc badania doświadczalne pozwalające na ocenę ilościową energii możliwej do odzyskania w czasie symulacji fizycznej typowego cyklu kopania. Następnie został opracowany system odzysku energii poprzez odpowiedni dobór akumulatora oraz układu sterowania przepływem do i z akumulatora, aby następnie zgromadzoną energię wykorzystać w kolejnym cyklu pracy maszyny. W wyniku analizy pojawiły się dwie koncepcje wykorzystania zmagazynowanej energii. Pierwsza to możliwość użycia zakumulowanej energii, jako dodatkowej energii wspomagającej ruch podnoszenia wysięgnika, w celu obniżenia zapotrzebowania energii w tej fazie cyklu ze strony pompy głównej. W tym przypadku w celu bardziej efektywnego wykorzystania zmagazynowanej energii w szerszym zakresie ciśnień roboczych został zaprojektowany, wykonany i przebadany doświadczalnie na stanowisku i na maszynie w testach poligonowych, cylinder 3-komorowy (3C). Druga koncepcja to użycie zmagazynowanej energii do zasilania silnika hydrostatycznego połączonego z wałem napędowym silnika głównego maszyny. Dzięki zastosowaniu odpowiedniego algorytmu sterowania przepływem energii silnik hydrostatyczny umożliwia obniżenie momentu obrotowego potrzebnego do napędu pomp pracujących pod ciśnieniem roboczym. Udokumentowane w pracy rozwiązania zwiększają sprawność energetyczną napędzanej hydraulicznie maszyny roboczej, co w praktyce oznacza obniżenie zużycia paliwa, a także zwiększenie trwałości układu poprzez wyrównanie momentu obciążenia silnika spalinowego, przy jednoczesnym obniżeniu emisji spalin silnika pracującego w optymalnym zakresie swojej charakterystyki.
