Derivation of accelerated durability tests for ...

講演番号

335

文献番号

20185335

Derivation of accelerated durability tests for powertrain mounted components subject to engine vibrations Bram Cornelis 1) , Simone Delvecchio 2) , Claudio Manna 3) 1) Siemens Industry Software NV, Interleuvenlaan 68, B-3001 Leuven, Belgium (E-Mail: [email protected]) 2) NVH Consultant, Via Aminta 25, I-44123 Ferrara, Italy 3) Ferrari S.p.A., Via Abetone Inferiore 4, I-41053 Maranello, Italy

ABSTRACT: Powertrain mounted components are exposed to engine-induced vibrations that may lead to failure due to accumulated fatigue damage. Durability tests hence need to be performed during the development phase. This work presents a procedure to synthesize an accelerated but damage-equivalent durability test for testing the powertrain mounted components on an engine test bench. First, the induced real-life fatigue damage is quantified based on engine speed histograms. Second, an engine test bench drivecycle is synthesized such that the induced fatigue damage matches the real-life fatigue damage. A turbocharger component mounted on a supercar V8 engine is considered as application example. KEY WORDS: Vibration/Noise/Ride Comfort, power train/body (vehicle body)/engine mounting system (B3) 1. INTRODUCTION

Driven by the industry need to save weight and fuel, while

Automotive components and systems may be subjected to (1)

maintaining power and performance, various new combustion

high levels of vibration during their operational life . It is

engine technologies have been deployed in recent years (such as

therefore necessary to validate the most critical components

turbocharger, direct injection and variable valve timing, etc.). The

through durability tests in order to avoid the risk of failure. In

corresponding engine & powertrain mounted components, which

order to conduct a representative test, the environmental

enable these technologies, are of particular interest in this work.

excitations can be taken as a reference to synthesize the test profile,

Engine & Powertrain mounted components are typically

a so-called “Test Tailoring” or “Mission Synthesis” procedure(2).

exposed to sine-on-random vibration environments(4-6). In a

In recent years, a Mission Synthesis procedure based on the

traditional mission synthesis approach, operational accelerometer

Fatigue Damage Spectrum (FDS) has been proposed

(3)

and has

measurements have to be conducted in order to characterize the

been widely adopted by various industries(2). The methodology

total lifetime FDS, which represents the total accumulated fatigue

allows for accelerated lifetime tests, which are a practical

damage over the lifetime of the component. However, under the

necessity due to cost and feasibility reasons: the duration of the

assumption that the engine-induced vibrations are the dominant

excitation which acts on the component for its entire lifetime has

loading input to the component (which is the case for powerful

to be reduced, while the damage potential has to be preserved.

supercar engines), it was previously demonstrated(5) that the lifetime fatigue damage can be derived based on accelerometer measurements of only a run-up, in combination with engine speed histograms which characterize the lifetime mission. The engine speed histograms represent the distribution of the time durations that are spent in particular engine speed ranges during the total intended life of the component (e.g. the customer usage by a particular target driver group). Through this approach the measurement efforts and costs are hence greatly reduced. During the final step of the traditional Mission Synthesis procedure, a shaker test profile is synthesized(7) which matches the lifetime FDS. However, an alternative approach is to test the

Fig.1: Example V8 engine test setup with enginemounted components visible.

component while it is mounted on an engine test bench, where the

2018 JSAE Annual Congress (Spring) May 23 to 25 ， 2018 Issued on May 21 ， 2018 2018 JSAE Annual Congress Proceedings (Spring)

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Fig.2: Schematic overview of the FDS calculation. engine is running in closed-loop control at a desired RPM

2.2. Fatigue Damage Spectrum (FDS) calculation

(specified by the drivecycle), and where the component is excited

The FDS calculation is illustrated in Fig. 2. The response of

by the vibrating engine block. This can be advantageous because

each SDOF system to the (measured) base vibration is computed

the test conditions are likely more similar to the real-life vehicle

in the form of a relative displacement. It is assumed that the

conditions (e.g. similar boundary conditions, similar temperature,

response is directly related to the stress by means of Eq. (1). A

etc.), compared to the case where the component is to be mounted

cycle counting algorithm (e.g. Rainflow Counting(8)) is applied in

on a shaker(1). This paper proposes a novel procedure which

order to extract stress cycles. Assuming that the S-N curve

synthesizes a drivecycle for a durability test on the engine test

(otherwise known as Wöhler curve) is described by the Basquin’s

bench, such that the corresponding FDS on the bench matches the

equation as in Eq. (2), and that the damage follows a linear

lifetime FDS (derived from the vehicle mission).

accumulation according to the Miner’s rule as in Eq. (3), it is

The two discussed steps (derivation of lifetime FDS and synthesis of engine drivecycle) will be demonstrated on a real-life application example, i.e. a turbocharger component which is mounted on a supercar V8 engine.

possible to combine Eqs. (1)–(3) and obtain the (pseudo) fatigue damage induced by the environmental vibration with Eq. (4): (1)

𝜎(𝑓𝑛 ) = 𝐾 ⋅ 𝑧(𝑓𝑛 ) 𝑁𝑖 ⋅ 𝜎𝑖𝑏 = 𝐴𝑏

2. MISSION SYNTHESIS THEORY REVIEW 2.1. Introduction The main objective of the Mission Synthesis procedure is to

𝐷 = ∑𝑖 𝑑𝑖 = ∑𝑖

(2) 𝑛𝑖 𝑁𝑖

𝐾𝑏

𝐹𝐷𝑆(𝑓𝑛 ) = 𝐴𝑏 ∑𝑖 𝑛𝑖 (𝑓𝑛 ) ⋅ 𝑧𝑖𝑏 (𝑓𝑛 )

(3) (4)

develop a durability test specification based on the actual vibration

where in Eq. (1), 𝜎 and 𝑧 are the stress and the relative

environmental conditions which will be encountered by the

displacement responses, respectively, dependent on the chosen

component. Dedicated operational measurements are performed,

SDOF-system natural frequency 𝑓𝑛 ; 𝐾 is a constant factor relating

whereby an accelerometer is placed on the vibrating “host structure” onto which the component will be mounted. In order to assess the fatigue damage which is induced by the vibration excitation, a detailed model of the component would in principle be required in order to calculate the stress response at the critical locations. The considered procedure instead makes a simplified working assumption. Similar to the determination of the Shock

the displacement to the stress. In Eq. (2) 𝑁𝑖 is the maximum number of cycles that the component can sustain at a sinusoidal load with stress amplitude σ𝑖 and the parameters 𝐴 , 𝑏 are representing the intercept and the slope of the S-N curve, respectively. In Eq. (3), 𝑛𝑖 is the actual number of cycles at stress amplitude σ𝑖 to which the component is subjected. In Eq. (4), z𝑖 is the amplitude of the relative displacement between the SDOF

Response Spectrum (SRS), a fictitious Single-Degree-Of-

mass and base. The repetition of this computation, changing the

Freedom (SDOF) reference system with a variable resonance

natural frequency of the SDOF system in order to cover the entire

frequency is assumed. The SDOF reference system allows for an

targeted bandwidth, leads to the full Fatigue Damage Spectrum

assessment and comparison of the different environmental “input”

(FDS) which represents the fatigue damage potential of a certain

excitations, independently from the actual characteristics of the

vibration at each frequency of interest.

component. The fatigue damage potential of different input

A related damage potential function is the Maximum Response

excitations can then be quantified by the so-called Fatigue

Spectrum(3) (MRS). The remainder of the paper will focus on FDS,

Damage Spectrum (FDS).

but similar procedures can be followed for calculating the MRS.

2018 JSAE Annual Congress Proceedings (Spring)

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3. MISSION SYNTHESIS PROCEDURE FOR DURABILITY TESTING ON ENGINE TEST BENCH

In order to derive the FDS which corresponds to these engine speed histograms, it is now only required to measure the

In this section, a mission synthesis methodology for

acceleration during a run-up maneuver (for example measured

powertrain mounted components will be presented. The

while driving on a long straight section on a test track). The run-

methodology consists of two steps. In the first step (cf. Section

up data is segmented into M non-overlapping segments, whereby

3.1), a lifetime FDS representing the fatigue loading over the

each segment corresponds to a certain RPM range which matches

entire component lifetime is derived. In particular, only

one of the bins of the engine speed histograms (cf. Fig. 3, where

accelerometer measurements of a run-up, in combination with

M = 14). An FDS is calculated for each run-up segment, hence

engine speed histograms, are required to calculate the lifetime

resulting in M separate FDS results. The different FDS results are

FDS. In the second step (cf. Section 3.2), an optimization

finally summed together (assuming Miner’s linear damage

approach is applied in order to synthesize a damage-equivalent

accumulation, Eq. (3)), whereby repetition factors based on the

drivecycle that can be applied on an engine test bench.

engine speed histogram are applied. The repetition factors (𝑅𝐹𝑚 ) are given by the following Eq. (5):

3.1. Derived FDS Methodology The main assumption of this paper is that the engine is the

𝑅𝐹𝑚 = ⌈

3600 . 𝐻lifetime,𝑚 𝑇runup,𝑚

⌉

(5)

dominant source of excitation loading for the engine & powertrain

In Eq. (5), ⌈.⌉ is the round-up operator, 𝐻lifetime,𝑚 is the number

mounted components. As in this case the excitation levels

of hours spent in RPM range m (cf. Fig. 3), and 𝑇runup,𝑚 is the

generally increase as the engine speed increases(5), the engine

duration (in seconds) of the run-up segment corresponding to

speed “working point” will be of major importance to the induced

RPM range m. The FDS functions are multiplied by these

vibration levels (and fatigue damage). It is then sufficient to know

repetition factors before summing all together, so that an

the engine speed histograms or duty cycles(4), in order to

extrapolation is made to the intended lifetime of the component.

characterize the lifetime FDS of the component. The engine speed

An overview of the Derived FDS method is illustrated in Fig. 4.

histogram represents the time duration that is spent in a certain engine speed range (quantified in Revolutions-Per-Minute, RPM) during the operational life. Fig. 3 shows the engine speed histograms for the application case considered in this paper (axis units are normalized). The RPM range between idle and redline was hereby segmented into 14 bins, and the duration spent in each bin was determined through real-life vehicle recordings. It can be observed that for “Mission 3” relatively more time is spent in higher RPM ranges than for the other missions. This is because “Mission 3” corresponds to the racing variant of the vehicle, where more aggressive driving styles are encountered, compared to the base vehicle versions.

Fig.4: Derivation of Lifetime FDS from segmented run-up measurement and engine speed histogram 3.2. Drivecycle synthesis algorithm It was previously established how to derive a lifetime FDS, which quantifies the potential total fatigue damage accumulation caused by the engine operation over the intended lifetime of the powertrain mounted component. In this section, it will be explained how a drivecycle can be synthesized for application on an engine test bench, where the component is excited through the vibrating engine block. The drivecycle should be such that it causes the same amount of damage to the component(s) as in the

Fig.3: Engine speed histograms for 3 target missions


real-life vehicle conditions, but in a shorter amount of time (i.e., an accelerated lifetime test).

3

In a first step, accelerometer measurements are performed on

By minimizing the cost function in Eq. (7), a solution is found

the engine test bench, while the engine is performing run-ups and

which matches the Lifetime FDS as close as possible. Optionally,

certain other prescribed operations (e.g. resonance dwells where

it can be specified to only match the Lifetime FDS inside a critical

the engine is fixed to a certain RPM working point). The run-up

bandwith (i.e., between 𝑓𝑚𝑖𝑛 and 𝑓𝑚𝑎𝑥 ). As the optimization

data can be further segmented into shorter segments, in a similar

focuses only on matching the FDS functions, there is no guarantee

manner as in previous section. Each of these short blocks of

that a short test duration is obtained. Conversely, the cost function

timeseries data (originating either from a resonance dwell or from

in Eq. (8) directly quantifies the test duration (i.e., the factors 𝛿𝑙

a run-up segment) will be referred to as an “element”. For each

represent the duration of each element), so that minimizing this

element, a corresponding “Element FDS” can be calculated using

function can lead to a shorter test duration. The constraint

the standard procedure as explained in Section 2.2.

𝐹𝐷𝑆𝑇𝑒𝑠𝑡 ≥ 𝐹𝐷𝑆𝑇𝑎𝑟𝑔𝑒𝑡 (again, between 𝑓𝑚𝑖𝑛 and 𝑓𝑚𝑎𝑥 ) is added

The bench elements can be viewed as “elementary maneuvers”

in order to prevent the trivial solution (𝑤1 = 𝑤2 = ⋯ = 0). The

which can be created on the test bench, and which excite the

obtained solution may however be too severe at some frequencies.

components mounted on the engine block (and hence cause a

In general, it is not possible to predict a priori which alternative

small amount of fatigue damage). In addition, the previously

may lead to the best result, so that both options should be explored.

derived lifetime FDS respresents the total damage accumulation

Finally, once an optimal solution for the weight factors 𝑤𝑙 has

over the lifetime of the component, which should be matched on

been found, a feasible drivecycle still has to be constructed which

the test bench in a short amount of time. The objective is hence to

matches this solution. This is a key difference with the proving

find the optimal mix of bench elements (including the number of

ground test scheduling(9), where the weight factors directly

times each has to be repeated), such that the total sum FDS

indicate the number of times each test track segment has to be

(denoted as 𝐹𝐷𝑆𝑇𝑒𝑠𝑡 ) matches as close as possible the lifetime

driven. In this work, a novel post-processing algorithm was added

FDS (denoted as 𝐹𝐷𝑆𝑇𝑎𝑟𝑔𝑒𝑡 ). Namely, the total sum FDS

in order to construct a feasible drivecycle. Although a fully

reproduced on the test bench is given by following Eq. (6):

detailed algorithmic description will not be presented, some of the

𝐹𝐷𝑆𝑇𝑒𝑠𝑡 = ∑𝐿𝑙=1 {𝑤𝑙 . 𝐹𝐷𝑆𝑙 }

(6)

where the weight factors 𝑤𝑙 are the unknown repetition factors which have to be determined, 𝐹𝐷𝑆𝑙 are the calculated FDS

main points are given below. In essence, the algorithm constructs a drivecycle assuming a set of rules which must be fulfilled: 

RPM) has to be found, which can be repeated until the

functions for the corresponding bench elements, and where L is the total number of available elements. The problem statement is very similar to the “Optimum track mixing” methodology(9), which aims at constructing an optimal proving ground testing schedule for full vehicle durability testing. Similar as in this approach, two alternative optimization strategies are considered: 

intended test duration (cf. cost function Eq. (8)) is reached. 

There should be no sudden gaps or jumps in the RPM.



The RPM gradient should never be steeper than a predetermined threshold.



Preference is given to run-ups instead of run-downs.

In order to fulfill these rules, a small modification to the optimal weights 𝑤𝑙 is allowed during the synthesis (and

Histogram optimization: in this case, the following

automatically determined by the algorithm). Examples will be

optimization problem is solved:

presented in the following section.

𝑓𝑚𝑎𝑥

min ∑ 𝑤𝑙

𝐿

2

[𝐹𝐷𝑆𝑇𝑎𝑟𝑔𝑒𝑡 (𝑓𝑛 ) − ∑{𝑤𝑙 . 𝐹𝐷𝑆𝑙 (𝑓𝑛 )}]

𝑓𝑛 =𝑓𝑚𝑖𝑛

4. EXPERIMENTAL RESULTS

𝑙=1

Subject to constraint: 𝑤𝑙 should be positive integers 

The smallest “closed” cycle (with start and end at the same

(7)

The previously discussed methodologies will be illustrated through a real-life application case. In this example, a durability

Runtime optimization: in this case, the following

test procedure was sought for a turbocharger component that is

optimization problem is solved:

mounted on a supercar V8 engine. Accelerometer measurements

𝐿

were performed both in the vehicle (i.e., test drives on a test track)

min ∑{𝑤𝑙 . 𝛿𝑙 } 𝑤𝑙

Subject to constraints:

and on the engine test bench. In addition, the total lifetime

𝑙=1

missions were also available in the form of engine speed

𝐹𝐷𝑆𝑇𝑒𝑠𝑡 ≥ 𝐹𝐷𝑆𝑇𝑎𝑟𝑔𝑒𝑡

and 𝑤𝑙 should be positive integers

(8)

histograms (cf. Fig. 3). The following sections will report an initial exploration of the measured data, a validation of the “Derived FDS methodology” of


4

(a)

(c)

(b)

Fig.5: Accelerometer measurement on engine reference point during 1 lap of the Fiorano circuit (a); Vehicle speed and engine speed recorded synchronously with accelerometer data (b); Fiorano circuit satellite view with vehicle speed overlay (c) Section 3.1, and examples of the drivecycle synthesis method of

A run-up measurement was performed by driving on the long

Section 3.2. It will be shown that a new drivecycle can be

straight section of the circuit. A time-frequency analysis and an

synthesized based on a derived FDS from a vehicle mission.

order extraction were performed on the accelerometer data, cf.

Moreover the method can also be applied in order to further

Figs. 6 and 7. Also from this analysis, it is evident that the

optimize an already existing drivecycle.

vibration data is dominated by engine orders. Due to the particular engine design (flat-plane crank V8), in particular the 2nd order is

4.1. Data exploration

dominant. In Fig. 7, a critical bandwidth is indicated where the

Acceleration signals and engine speed (RPM) time traces were

highest levels of the 2nd order are observed. This critical

recorded during test drives performed on the Fiorano circuit

bandwidth will be used to set 𝑓𝑚𝑖𝑛 and 𝑓𝑚𝑎𝑥 in the drivecycle

(Maranello, Italy), cf. Fig. 5. In addition to run-up measurements,

synthesis method (cf. Sections 4.3 and 4.4).

which are required for the “Derived FDS methodology”, measurements were also made while driving laps around the circuit. Although the latter is not a required input for the “Derived FDS methodology”, it can be used for validation purposes (cf. Section 4.2). When the raw accelerometer data (cf. Fig. 5-a) is compared to the engine speed time trace (cf. Fig. 5-b), a strong correlation is evident. This asserts the main assumption that the engine speed working point is of major importance to the induced vibration levels, which can hence be exploited to derive the FDS.

Fig.7: Order Tracking applied on run-up acceleration data

4.2. Validation of Derived FDS methodology Vibration measurements were performed not only for run-ups, but also while driving entire laps on the circuit. The RPM time traces were also recorded in both situations. Hence, it was possible to validate the accuracy of the proposed Derived FDS methodology, similarly as in previous work(5). The measurements were divided into two datasets: Fig.6: Time-Frequency analysis of run-up acceleration data




1 lap on Fiorano circuit performed by driver 1.



Run-ups performed by drivers 2 and 3.

5

The measurements were hence performed while 3 different

As previously discussed, there are 2 alternative optimization

drivers were driving the vehicle. In all cases vibrations were

strategies (histogram optimization and runtime optimization).

measured on the same engine reference point. It was observed that

Results for both approaches are presented here: histogram

the lateral (Y) direction was the most severe. Hence, the Y

optimization in Figs. 10 and 11, and runtime optimization in Figs.

direction data will be used in the remainder of the paper.

12 and 13.

The RPM time trace of the lap data was processed in order to create an engine speed histogram (similar as in Fig. 3). In this case, the “mission” is hence 1 lap on the Fiorano track as driven by driver 1. The raw vibration data of the lap is processed using the standard FDS calculation (cf. Section 2.2 and Fig. 2). The result is denoted as 𝐹𝐷𝑆𝑎𝑐𝑡𝑢𝑎𝑙,1 . The run-up data was processed using the “Derived FDS methodology” (cf. Section 3.1 and Fig. 4). The vibration data is segmented into non-overlapping segments corresponding to particular RPM ranges. The FDS is calculated for each segment, repetition factors (derived from the engine speed histogram and Eq. (5)) are applied, and the sum FDS is calculated. In this case, the procedure is applied independently on two different run-ups

Fig.9: Derived FDS for Mission 1

(measured for driver 2 and for driver 3). The results are denoted as 𝐹𝐷𝑆𝑑𝑒𝑟𝑖𝑣𝑒𝑑,2 and 𝐹𝐷𝑆𝑑𝑒𝑟𝑖𝑣𝑒𝑑,3 . A comparison between the actual FDS and the two independent derived FDS functions is shown in Fig. 8. It is evident that a good correspondence is found, hence proving the efficacy of the method.

Fig.10: Histogram optimization result: (zoomed-in) Target FDS vs. FDS for synthesized drivecycle

Fig.8: Comparison “Derived FDS” versus “Actual FDS” 4.3. Synthesis of drivecycle based on real-life vehicle mission This section reports the results of the drivecycle synthesis, based on a real-life vehicle mission. In order to obtain 𝐹𝐷𝑆𝑇𝑎𝑟𝑔𝑒𝑡 , the “Derived FDS methodology” is applied. The engine speed histogram for Mission 1 (cf. Fig. 3) is considered in this example. The resulting FDS is shown in Fig. 9. In this figure, a “critical bandwidth” is indicated. This is the frequency range wherein (roughly speaking) important resonance frequencies of the component are expected. The outer limits of this bandwidth will be set as 𝑓𝑚𝑖𝑛 and 𝑓𝑚𝑎𝑥 in the subsequent optimization step.


Fig.11: Histogram optimization result: drivecycle

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optimization closely matches the target FDS, whereas the runtime optimization overshoots the target FDS at some of the targeted frequencies. Figures 11 and 13 show the obtained drivecycles for both approaches. These drivecycles have to be repeated for the indicated number of times (also determined by the algorithm). It can be seen that in this case, runtime optimization obtains the shortest overall test duration (a total of 150 hours, compared to 176 hours for histogram optimization). It is again noted that in general, it is difficult to predict a priori which approach will result in a superior result, so that both approaches have to be explored. Fig.12: Runtime optimization result: (zoomed-in) Target FDS vs. FDS for synthesized drivecycle

4.4. Optimizing an already existing drivecycle Another related application is where an already existing drivecycle (and corresponding durability test program) has to be optimized. This drivecycle may have been previously obtained from empirical knowledge and long-term experience (e.g. it may be known from past experiences that a certain drivecycle was severe enough to adequately cover a particular target customer mission). However, there is an interest in optimizing the drivecycle such that the total test duration can be reduced. The methodology of this work will be applied in order to synthesize an alternative drivecycle which is applied in a shorter durability test. Although the test duration is reduced, the new drivecycle still preserves the same damage potential as the original drivecycle. In order to tackle this problem, it is first required to quantify the fatigue damage potential of the original drivecycle. The

Fig.13: Runtime optimization result: drivecycle

Derived FDS methodology of Section 3.1 can be applied for this purpose. The drivecycle definition is first processed in order to generate an engine speed histogram. The run-up segmentation

In both cases, it was observed that it is difficult to match the

process, which was outlined previously (cf. Fig. 4), is then applied

entire 𝐹𝐷𝑆𝑇𝑎𝑟𝑔𝑒𝑡 curve. This may be due to several reasons. There

in order to find the FDS corresponding to the original drivecycle.

may be slight differences between vehicle conditions and bench

In the second step, the optimization problem is solved whereby

conditions such that it is difficult to reproduce all physical effects

𝐹𝐷𝑆𝑇𝑎𝑟𝑔𝑒𝑡 is now set equal to the FDS corresponding to the

on the bench. It is also possible that there are too few bench

original drivecycle (instead of a FDS for a vehicle mission as was

“elements” (i.e., too small L), such that mathematical difficulties

done in the previous section). As our goal is to obtain a drivecycle

arise (overdetermined inconsistent system of equations). A

and corresponding durability test which is as short as possible, we

solution is then to focus the optimization on a smaller critical

use the runtime optimization method of Eq. (8). In order to be able

bandwidth, i.e. to set closely-spaced values for 𝑓𝑚𝑖𝑛 and 𝑓𝑚𝑎𝑥 .

to reduce the time duration, we make use of the prior knowledge

Figures 10 and 12 display the zoomed-in FDS functions (in the

that the important component resonances are expected to lie in a

critical bandwidth), which are obtained by both approaches. The

small critical bandwidth (as was done in previous sections). The

original target FDS (cf. Fig. 9) is again displayed for reference,

parameters 𝑓𝑚𝑖𝑛 and 𝑓𝑚𝑎𝑥 are set equal to the outer limits of this

together with the FDS corresponding to the synthesized drivecycle.

critical bandwidth.

As previously mentioned, in order to obtain a feasible drivecycle,

The results of the approach are displayed in Fig. 14 and Fig. 15.

the algorithm may apply a small modification to the optimal

The target FDS, which was derived for the original drivecycle

weigths 𝑤𝑙 . The intermediate FDS (for optimal 𝑤𝑙 ) is also

using the approach of Section 3.1, is displayed in Fig. 14 for

displayed for reference. It can be observed that the histogram

reference. It can be observed that the FDS for the synthesized


7

drivecycle corresponds well with the target FDS inside the critical

The efficacy of the “Derived FDS methodology” was

bandwidth (i.e. between 𝑓𝑚𝑖𝑛 and 𝑓𝑚𝑎𝑥 ), as was intended through

demonstrated through a validation experiment.

the optimization. The synthesized drivecycle is shown in Fig. 15.

In the second step, a drivecycle is synthesized such that the

As indicated in the figure (and automatically reported by the

component can be durability tested directly on an engine test

algorithm), this drivecycle has to be repeated until a total test

bench (instead of a shaker). A novel procedure was developed

duration of 54 hours is reached. In comparison, for the original

which aims at constructing the drivecycle such that the

drivecycle, a total test duration of 72 hours was required. Hence

corresponding FDS on the bench matches the lifetime FDS, but

the newly found drivecycle indeed results in an accelerated

where the test duration is as short as possible. To achieve this, the

lifetime test with shorter duration.

method applies an optimization approach (where two optimization alternatives were discussed). Results for a real-life application (turbocharger component on V8 engine) were presented. In addition, it was shown that the method can also be applied in order to optimize already existing drivecycles (i.e. to further reduce the test duration, while preserving the damage potential). REFERENCES (1) L. Wang, R. Burger, A. Aloe, “Considerations of Vibration Fatigue for Automotive Components”, SAE International Journal of Commercial Vehicles 10.2017-01-0380 (2017), pp. 150-158. (2) CEEES Technical Advisory Board, “A Review of Methodo-

Fig.14: Target FDS (original drivecycle) vs. FDS for new synthesized drivecycle

logies for Deriving Vibration and Shock Test Severities”, (2008), [Online] available at http://www.ceees.org/tab_Mechanical_Environments.htm (3) C. Lalanne, “Mechanical Vibration and Shock Analysis – vol. 5: Specification Development”, third ed., John Wiley & Sons, Inc - ISTE, London, (2014). (4) L. Wang, R. Burger, Y.-L. Lee, K. Li, “Random Vibration Testing Development for Engine Mounted Products Considering Customer Usage”, SAE International Journal of Materials & Manufacturing, Vol. 6, No.2, SAE (2013), pp. 254-261. (5) B. Cornelis, B. Dendas, A. Carrella, “Qualification testing of racecar equipment subject to engine-induced vibrations: how to derive a test profile using a mission synthesis procedure”, in Proc. of ISMA, Leuven, Belgium, (2014). (6) D. Delaux, F. Kihm, “Synthesis of an Engine Vibration

Fig.15: Optimized drivecycle: total test duration 54 hours (compared to 72 hours for original drivecycle)

Specification and Comparison with existing Qualification Specifications”, in Proc. ASTELAB, Paris, France, (2010). (7) A. Angeli, B. Cornelis, M. Troncossi, “Synthesis of Sine-on-

5. CONCLUSIONS This paper presented a methodology for synthesizing an

Random vibration profiles for accelerated life tests based on fatigue damage spectrum equivalence”, Mechanical Systems and

accelerated but damage-equivalent durability test for testing the

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powertrain mounted components on an engine test bench. The

(8) M. Matsuishi, T. Endo, “Fatigue of metals subjected to varying

methodology consists of 2 major steps.

stress”, Proc. Japan Society of Mechanical Engineers, Fukuoka,

In the first step, a target FDS is derived based on acceleration

Japan, (1968).

signals measured during a run-up on a test track, and an engine

(9) B. Gründer, M. Speckert, M. Pompetzki, “Design of Durability

speed histogram which represents the lifetime customer mission.

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