Improving the quality of surface in the polishing

Int J Adv Manuf Technol DOI 10.1007/s00170-010-3109-1

ORIGINAL ARTICLE

Improving the quality of surface in the polishing process with the magnetic abrasive powder polishing using a high-frequency induction heating source on CNC table Seyed Saeed Mirian & Alireza Fadaei & Seyed Mohsen Safavi & Mahmoud Farzin & Mahmoud Salimi

Received: 1 October 2010 / Accepted: 30 November 2010 # Springer-Verlag London Limited 2010

Abstract In this research, polishing flat surfaces has been done by using a completely new and innovative method. In this method, rotary magnetic tool that carry magnetic abrasive powders, is placed in a very strong thermal induction field, and magnetic rotary tool frequently change its direction from clockwise (CW) to counterclockwise (CCW) and CCW to CW. The frequency of changing rotation direction is an important parameter of this innovation method. The intended pieces for polishing operations have been placed on a synchronic two-axis Cartesian CNC table, and the gap between rotary magnetic tool and the sheet surface can be controlled by a power transmission screw operating in the direction of the vertical axis. Several experiments have proved high performance of the new proposed method in the process of polishing. Keywords High-frequency induction heat source (HFIHS) . Data acquisition mechatronics . Abrasive powder polishing . Numerical control . Air gap Nomenclature HAPP Heating-assisted powder polishing PLC Programmable logic control MAP Magnetic abrasive polishing HFIHS High-frequency induction heating source CNC Computer numerically controlled RMT Rotary magnetic tool

S. S. Mirian (*) : A. Fadaei : S. M. Safavi : M. Farzin : M. Salimi Isfahan University of Technology, Khomeynishahr, Iran e-mail: [email protected]

1 Introduction A variety of research has been done in this field, based on which a new approach has been proposed in this paper, by using the fact that heating and cooling of the abrasive powder can improve the process of polishing. The whole experiments carried out indicate success of the method in the average air gaps. Review of the previous works carried out indicates that no measure has been so far undertaken about placing the rotary magnetic abrasive powder in a very intense thermal electromagnetic field and using the energy resulting from this field for polishing. While associating a kind of effective frictional brushing, it is a new subject to which the research work done has been paid. In this innovative method of polishing, rotating of magnetic rotary tool and meanwhile powering on–off of high-frequency induction heat source (HFIHS) will cause the abrasive powders frequently getting hot and cold. This heating and cooling of powders, helps the powders to be more fragile and the sharp edges of the powders will increase. At the same time, temperature shock of this frequent heating and cooling will affect polishing process and the abrasive powder will act more efficiently. In this point of view, this proposed method is an innovative method that no other references paid on it. The other advantage of this innovative method is cooling and heating of abrasive powders in short cycle times. Short cycle time of heating and cooling of abrasive powders is source of temperature shocking of this method. This temperature shock can help to improving of polishing process and using of HFIHS will cause Several advantages in comparison to other heating methods that the major advantages are listed below: 1-1 HFIHS can cause the heating process in short cycle times in comparison with other methods.

Int J Adv Manuf Technol

1-2 After powering off of HFIHS, rotating of magnetic rotary tool can help the cooling of abrasive powders in short cycle times. 1-3 In this method of temperature shocking system, no other facilities like oven and furnace is needed. 1-4 This method is more cost effective than other methods.

2 Literature review Special feature of MAP method is to create surfaces with desirable or flat high-quality curve, without having direct contact of the polishing tool with the intended surfaces [1]. In most of the research done, the workpiece intended to perform the polishing operations is being rotated, in which forced passing of the abrasive particles over the rotating workpiece has caused the workpiece surface to be polished [2]. Furthermore, combination of this polishing method with automatic computer numerically controlled (CNC) table, to automatically move the workpiece, is the topic on which many new research have been carried out [3, 4]; and a variety of works has been provided about mathematical modeling of this polishing method, among which ref [5] can be cited. Also, in many cases, researchers have used the magnetorheological gel instead of abrasive powder for the process of polishing, among which the refs [6, 7] can be cited. In research work conducted by Dabrowski et al. [6], workpiece and magnetic head have simultaneously rotated, due to which performance of this method has been increased. Ref [8] also has made internal polishing of austenitic steel capillary tubes by this method. Furthermore, ref [9] has polished the inner surface of aluminum–ceramic equipment using this method. Cooling and heating of abrasive powders with HFIHS in short times, and consequently, a temperature shock condition is a new topic that no other reference paid attention to it.

moved up and down by a power transmission screw, and can change the distance between magnetic tool and the surface of the circular flat pieces. Due to some restrictions, just polishing the top of circular flat pieces has been considered in the present research, and polishing of threedimensional pieces with this new method, has been postponed to the next research works. Furthermore, in this proposed system, the polishing forces were measured with and without the presence of HFIHS by using a data acquisition system as well as system of monitoring the current passing through the stepper motor drives (which is a symbol of the forces). These forces have been measured in two following cases, 1. The powder and the magnetic tool are not placed in an inductive thermal electromagnetic field. 2. The powder and the magnetic tool are placed in an inductive thermal electromagnetic field The difference between these forces in the two cases above, as well as the quality of polished surface, is one of output parameters of the experiments. The main components of this proposed system are: 3-1 Two-axis CNC table, whose spindle in the Z direction can be moved by a power transmission screw that can adjust the gap distance between the tool and workpiece. By using two stepper motors whose drives are controlled by a PC base controller, table is capable of automatically moving on relevant proposed route. This system shown in Fig. 1

3 Introduction of system and components In the proposed method, there is the ability to move flat sheets in the horizon plane through designing and constructing a two-axis Cartesian CNC table. Due to some restrictions, just polishing the flat sheets has been studied in the present research, and polishing the three-dimensional sheets has been postponed to the next research works. In the proposed method, it will be possible to move the circular flat pieces in horizon plane by the use of a two-axis automatic CNC table. Furthermore, the third axis of system (Z), on which three-phase motor of magnetic tool has been placed, can be

Fig. 1 Equipment controlling table and spindle


3-2 Mechatronic set of the system includes drive and programmable logic controller (PLC) to control the speed, direction, and frequency of the three-phase motor driving the magnetic head, as well as stepper motor drives with data acquisition equipment and pulse generator and direct current (DC) power supply. Figure 2 shows this complete set. 3-3 High-frequency induction heating source This system (as shown in Fig. 4) has a copper coil that abrasive powder will insert in this coil and when this source run it can immediately heat the abrasive powder. This heating source can frequently be on and off by PLC and this action will affect the polishing process. The heated abrasive powder could act better than normal powder and this is the main difference between this method and previous methods. 3-4 Special magnetic rotary tool, in which high-intensity magnetic discs are placed at maximum mode of about 8,400 gausses; and the number of magnetic discs inside it will determine the vertical magnetic field intensity. 3-5 Software collection and computer It includes the following software: & & & &

Labview for monitoring polishing forces; Mastercam for extracting CNC code related to the automatic motion magnetic head; Mach3 to convert the CNC code into motion pulses, and to send them on the PC base controller of the table's driving system; and Ladder master for programming logic controller of three-phase motor system and controlling speed and directions of successive clockwise and counter-

Fig. 2 Complete set

clockwise rotation of the system's spindle and controlling the corresponding time. 3-6 Abrasive powder Abrasive powder used in this system includes the materials required in sandblast systems, with brand of grate steel and size of 70 μm. Each component will be separately described as follows: CNC table In this table, which is made by an innovative mechanism without using LM and ball screw, guide pin, pulley time, and timing belt are to be used. By using two stepper motors with accuracy of 1.8 deg/ pulse, this table is capable of automatically moving with various well-known motion trajectories in CAD/ CAM applications. These methods include the following: & & & &

zigzag, spiral motion from inside to outside, spiral motion from outside to inside, one-way method of motion. In the cross of two guide pins of x, y, one holder has been prepared, on which the intended flat workpieces can be placed before the process of polishing. Furthermore, the spindle placed in the system, which is responsible for carrying the rotating magnetic head, has the ability to move up and down and thus to change the air gap between the rotating magnetic head and the workpiece, by a cast-iron plate connected to the power transmission screw in the direction of z axis. The spindle can be fully controlled by its inverter and PLC, with regard to the speed,


direction, and the amount of rotation which is among the parameters affecting the process of polishing. CNC table, as well as inverter and spindle are shown in Fig. 1. Mechatronic set This set includes two stepper motor drives with PC base controller to convert the CNC motion codes into pulse-width modulation (PWM) for drives using the Mach3 software. Furthermore, three-phase motor inverter and the system's PLC are among other components of the system. DC power supply is used for operating stepper motor drives; and data acquisition card is also used for measuring and recording the polishing forces, by getting and recording data of current passing through each drive (in each 0.01-s-interval times). Furthermore, PLC is responsible for controlling three-phase motor. Another duty of PLC is controlling (on–off) high-frequency induction heating source. The frequency of on–off of this heating source is one of important parameters. The time of heating could not select more than 10 s because it may melt the powder and it could not select lower that 0.5 s because in this case the abrasive powder could not be heated perfectly. The optimum time of on-off of this system that obtained during experiments was 3-s on and 7-s off that this cycle frequently repeated. Figure 3 shows the block diagram of complete set during experiments. Fig. 3 Complete block diagram of system

As shown in Fig. 3, the flat sheet for polishing is located on top of the container, and under the flat sheet is a vacant space that the abrasive slurry filled it. Figure 4 shows this object schematically. In this method, top and bottom of sheets will be polished with two different methods. Top of sheets will be polished with HAS (heating-assisted system) and bottom of sheet will be polished by effect of abrasive slurry. This slurry abrasive is magnetic sensitive and wants to move toward the magnetic rotary tool and existing of flat sheet, prevent this motion and thus cause to polishing of bottom side of sheet. In this kind of polishing one can compare these two kinds of polishing with another and thus at the same time heating-assisted polishing and traditional use of abrasive slurry in polishing, will be possible. High-frequency induction heating source The induction heat source works at 220 V electricity and its working frequency is equal to 100 kHz. Its maximum voltage and current intensity are 12 A and 220 V, respectively. The maximum input power is equal to 9.5 kW and a tank with at least 50 L of water, as well as a pump with discharge capacity of 2 L/min and head of 0.1 MPa are needed, in order to cool the copper coil. With minor change in the hand steering pedal of the thermal source, the system can be automatically controlled by the pulses sent from the PLC.


Thus, the PLC outputs controlling the process include y0 and y1 for creating successive clockwise and counterclockwise rotations of the set's spindle, as well as output y2 for switching the pedal of induction heating source. As is shown in Fig. 4, during the process of polishing, while the rotary magnetic tool is placed within the copper coil of the induction heating source, sheet is moved by CNC table in accordance with the proposed CAD/CAM strategy; and polishing occurs by hot magnetic abrasive particles. The abrasive particles will have two motions (rotation and transitional motion) which include rotation around the vertical axis (to follow rotation of the magnetic tool) as well as traversing the direction (to follow the magnetic tool). Polishing operations of the flat surface happen faster and easier, due to successive hot and cold temperatures of the abrasive particles within the copper coil of induction machine, as well as their successive clockwise and counterclockwise rotations. In Fig. 5 high-frequency heating source during heating of abrasive powder is shown. Magnetic rotary tool This tool has been so designed and built that a certain number of magnetic discs with specified field intensity can be fed within it, and the intended test can be done. The more number of discs, the higher rotating field intensity, and consequently the stronger abrasive brush. This tool, in terms of field intensity, is very strong, and as is shown in Fig. 6, is capable of carrying a 5kg mass in the case that the magnetic discs (whose structure has been described in Fig. 7) have filled one half of it. It should be noted that to connect this tool

Fig. 4 Polishing of bottom and top side by two different methods

to the three-phase motor, direct coupling with the motor shaft is used, and that the motor output is directly transferred to the rotating magnetic tool. Computer and software collection Mastercam software has been used to extract CNC motion codes by well-known methods and strategies, such as the different methods of pocket and center contour as clockwise or counterclockwise. The pieces selected for polishing operations include sheets with 150-mm diameter; and to extract motion codes in the software, the intended CAD geometry is drawn as circles with diameters of 150 mm. Furthermore, the intended CAM will include the use of known pocket methods on the related CAD as well as extraction of CNC codes related to any strategy. One of the strategies including a spiral motion from inside to outside in the clockwise system is shown in Fig. 8 Furthermore, programming of the set's PLC controller is done by ladder master software. It includes control of speed, direction, and time of clockwise and counterclockwise rotations of the magnetic rotary head. This software also controls the switching pedal of the high-frequency induction heating source, and programs the system's PLC, which is the type of vigor with eight inputs and six outputs, with the ladder logic method. Magnetic abrasive powder Different abrasive powders, including steel grate powders for sandblasting, and sintered powder of aluminum oxide and iron carbonyl, have been used during stages of relevant experiments. Due to their high melting temperature and resistance against melting in high-frequency induction heating environment, it is necessary to use aluminum oxide and steel grate.


Fig. 7 Special structure of a rotating magnetic tool

Fig. 5 Induction heating source during heating of abrasive powder

4 Complete set As is shown in Fig. 3, since rotating magnet tool is placed inside copper coil of the induction heating source in this innovative method, it is impossible for the rotary magnetic head to be moved on the plane XY. So, the workpiece should be automatically moved by the CNC table under the head. Furthermore, the amount of air gap between the rotary magnetic tool and surface of sheet (in which powder of abrasives are placed), is one of the important parameters of the set of tests which can be changed with axis-z

Fig. 6 High magnetic power of a rotating head to keep a 5-kg castiron weight

manually powered transmission screw; and the effect of which can be observed on the intended outputs, including the surface smoothness and polishing force. PLC, as a central system controller, can switch the pedal of induction source. It also can make the abrasive powder hot and cold. Furthermore, the frequency of successive switching of the high-frequency induction heating source is another input parameter in the series of the experiments conducted. The gap can be changed with axis-z manually powered transmission screw, whose effect can be observed on the intended outputs, including the smoothness of the surface

Fig. 8 CAD/CAM strategy required for polishing the sheet surface


and polishing force. The three-phase motor drive related to the set's spindle, on which a volume is embedded, is capable of creating rotational speeds, from 5 to 14,00 rpm. The successive clockwise and counterclockwise rotation of the magnetic tool at different times is another parameter being controlled by PLC, and is one important parameter in the set of experiments conducted. PLC program of the inverter is so planned that it can create a wide range of different frequency modes of the spindle's clockwise and counterclockwise rotations. However during the experiments carried out, only eight cases have been actually considered. Furthermore, 32 analog input channels and eight digital inputs can be received in data acquisition card of the system, among which two analog input channels are actually used to measure the polishing forces (ch0, ch1). The channel ch0 measures the polishing forces in the direction x, proportional to current of motor, x; and the channel ch1 measures the polishing forces in the direction y, proportional to current of motor, y. The third analog channel Ch2 can be also used for measuring and recording the current of the three-phase motor spindle. As the central controller of the system, PLC can fully control the three-phase motor. Furthermore, depending on which PLC input is active, the time of clockwise and counterclockwise rotations of the magnetic head rotating around itself can be controlled. For example, when the PLCrelated input ×3 is excited, the spindle motor will successively rotate for 5 s CW and 5 s to CCW. These clockwise and counterclockwise rotations of the rotating magnetic tool and consequently powder of abrasives as well as frequently heating and cooling of magnetic abrasive powder have significant effects on the process of polishing. PLC has been so programmed that the least time of clockwise and counterclockwise rotation is for 0.5 s by stimulating ×0; and the most time occurs in the stimulation ×7 (i.e., constant clockwise rotation of 3,600 s). The complete set of experiments inputs are such below: 1. Air gap between the magnetic rotary tool and the workpiece surface (from 0.5 to 10 mm for every 0.5 mm of a experiment) can be changed for total of 20 experiments; 2. Rotational speed of the magnetic device connected to a three-phase motor (from 5 to 1,400 rpm with an increase of 100 rpm totally for 14 experiments); 3. Frequency and time of clockwise and counterclockwise rotations of the three-phase motor (from 0.5 to 3,600 s); 4. Feed rate in the CNC table, to automatically move the workpiece (very varied, from 10 to 1,000 mm/min); 5. Number of the discs supplying rotating magnetic field (20 discs);

6. Parameter of handling tool in each step over, in each of the motion trajectories, from 3/4 of tool diameter to 0.1 of tool diameter; 7. Induction field intensity of the high-frequency induction heating source; 8. Induction field voltage; 9. Conducting experiments and acquiring data about the current of drivers (the polishing forces and the current of the stepper motors), as well as measuring surface smoothness in the following cases: a. without heating induction field b. in the presence of heating induction field 10. Frequency and time of switching pedal of the highfrequency induction heating source. As is clear, the use of statistical methods or design of experiments using Taguchi approach with these experiments will actually include a great number of experiments. So, it was decided that it is selected among a limited range of I/Os, including four inputs parameters in four levels of access, and outputs in two levels, including two parameters of surface smoothness and current of stepper motor drives to be selected proportional to the polishing force. Input parameters have been listed in Table 1. In addition abrasive temperature indeed is the key factor that affects the performance of this kind of polishing. By use of a non contact temperature measurement system (infrared system) the mean temperature of abrasive particles has measured in various frequencies of heating operation and listed in Table 2. As it is mentioned before, under the flat sheet is a container which is filled with a slurry abrasive .This slurry can polish the sheet from bottom side and is an identification for comparing the quality of surface with another side of sheet (top side) that is in contact with hot abrasive particles

Table 1 Constant parameters during the experiments Value

Parameter

220 V 18 A Spiral pocket from inside to outside in clockwise system 20

Induction heat source voltage Induction heat source current Motion trajectory

200 mm/min 3/4 of the tools' diameter

Number of the magnetic discs providing magnetic field Motion feed of table Distance between cases of pass-over in automatic motion of table

Int J Adv Manuf Technol Table 2 Mean temperature conditions based on frequency

Frequency

0.05 Hz

0.1 Hz

0.2 Hz

0.5 Hz

0.75 Hz

0.9 Hz

1 HZ

Mean T(°C)

550°C

500°C

430°C

400°C

390°C

370°C

350°C

Relevant experiments with the data acquisition related to these experiments are performed in four output cases as follows: 1. Measuring the polishing forces without high-frequency induction heating source 2. Measuring the polishing forces with high-frequency induction heating source 3. Measuring the surface smoothness without highfrequency induction heating source 4. Measuring the surface smoothness with high-frequency induction heating source Furthermore, the parameter of air gap was considered as input for the set of experiments. So, four series of experiments were totally designed and carried out, whose results will be analyzed in the next section. It should be noted that a rotational speed of 500 rpm has been selected for the spindle, and a feed rate of 200 mm/min for the table in all these experiments.

5 Analysis of the results Data analysis and results of the experiments conducted were obtained by the statistical methods such as variance analysis and examination of input factors affecting the process outputs, including current of the stepper motors and surface smoothness of the ground pieces, as well as the equations between the inputs and outputs of the regression method. Fig. 9 Diagram of changes in the surface roughness, based on changes in air gap and the testing time

Finally, conditions of the experiment tests which lead to optimization of the output values is a separate subject that will be separately discussed in other papers. Here, just a few important figures and results are discussed. Among the total parameters affecting the experiments, the effect of air gap is examined on the two outputs, i.e., surface roughness and current passing through the stepper motors (proportional to the polishing force). These results are examined in the two following cases: 1. The rotary magnetic tool is not placed in a thermal induction field; 2. The rotary magnetic tool is placed in a inductive heating field. As is shown in Fig. 9, highest attainable surface smoothness without high-frequency induction source occurs for the lowest gap (i.e., 1 mm), and increase in the testing time will lead to better results. According to this diagram, it is clear that almost all the diagrams follow the same trend in the case of the presence of high-frequency induction field, and that rotational speed of 500 rpm has been selected for the rotary magnetic head in all these experiments. Furthermore, a frequency of once every 5 s has been selected for clockwise and counterclockwise rotations of the rotary magnetic tool. The effect of air gap on surface roughness in the presence of magnetic thermal induction field is shown in Fig. 10. As it is clear, firstly low air gap (1 or 2 mm) has little effect on the smoothness of final surface in these circumstances; and secondly, the best surface smoothness is related to air gap

Int J Adv Manuf Technol Fig. 10 Effect of air gap on surface roughness in the presence of thermal induction field

of 5 mm. According to the diagram, it seems that frequent hot temperatures of abrasive powder in low air gaps not only don't help the created quality of surface, but also reduce the quality of surface, due to the local corrosions and sintered powder in the area; while this problem doesn't exist in the air gap of 5 mm or more. Comparison of the above diagram with the diagram of Fig. 9 shows that if the rotary magnetic head is placed in thermal induction field, the surface roughness will be achieved. In this case, it will be approximately 0.12 μm at best, while in the diagram (9), quality improvement of relevant surface for a gap of 5 mm has been reported to be approximately 0.2. Similarly, it is clear that for the air gap 7.5 mm, the surface quality in the presence of a thermal induction field is better than that in Fig. 11 Effect of air gap on the polishing forces without induction heat source

the absence of the field. Presence of thermal induction field practically has little impact for higher gaps. So according to the sum of these diagrams, it can be concluded that induction heat source has little effect in improving the quality of surface for low gaps (1 and 2 mm) and high gaps (10-mm high); and best performance of induction heat source occurs in the medium gaps. As is shown in Fig. 11, minimum current passing through the stepper motors (and thus the least polishing force in this case) occur for high gaps. It suggests that in this case, high air gaps cannot lead to high-quality surfaces. Furthermore, it is clear that in the early stages of polishing operations (i.e., until the first 30 min), minimum air gap (1 mm) can draw maximum current from the motors; and

Int J Adv Manuf Technol Fig. 12 Effect of air gap on the polishing forces in the presence of induction heat source

then, almost all diagrams will obtain similar behavior. So, it can be concluded that for air gap of 1 mm, almost the highest volume of polishing takes place until the first 30 min of polishing operations. Descending movement of the diagram for intervals of 2, 5, and 7.5 mm is also indicated that in these air gaps, increased time of operations will lead to less current passing through the motors. Therefore, it can be concluded that increased time in the process will cause surface quality improvement. Effect of air gap on the polishing forces in the presence of induction heat source is shown in Fig. 12. According to this diagram, it is clear that induction heat source causes increase in the polishing forces in the average air gaps. Thus, increasing the polishing forces in the average air gaps in the presence of thermal induction field can lead to better surface quality than that in the absence of the field above. What can also deduce from this diagram is that the induction heat source plays decisive role in the surface quality in cases that the air gap is neither too much nor too little. So, the best case for the use of induction heat source, in case that average plate surface, is (Fig. 12): Selected for the air gap of the rotary magnetic tool. Moreover, during the experiments it was observed that some values of abrasive powder can escape from the area of gap in the low gaps, while it was not seen in case of using the induction heat source. Considering the diagrams relating to Figs. 9, 10, 11 and 12, it can be generally concluded that: 1. High-frequency induction heat source has a significant effect on the quality of the pieces' surface in all air gaps.

2. The surface quality improvement occurs for the average air gaps in this method. 3. Maximum polishing forces occurs in the least air gaps, but this does not necessarily mean that the surface quality improvement occurs in the same distances.

References 1. Cheung FY, Zhou ZF, Geddam A, Li KY (2008) Cutting edge preparation using magnetic polishing and its influence on the performance of high-speed steel drills. J Mater Process Tech 208: I96–I204 2. Shankar MR, jain VK, Ramkumar j (2009) Experimental investigations into rotating workpiece abrasive flow finishing. J Wear wear267:43–51, Elsevier 3. Jain VK, Singh DK, Raghuram V (2008) Analysis of performance of pulsating flexible magnetic abrasive brush (P-FMAB). J Machining Sci Technol 12(1):53–76 4. Grzesika W, Rechb J, Wanat T (2007) Surface finish on hardened bearing steel parts produced by superhard and abrasive tools. Int J Mach Tool Manufact 47(2):255–262 5. Das M, jain VK, ghoshdastidar PS (2008) Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process. Int J Mach Tool Manufact (Science Direct) 48(3-4):415–426 6. Dabrowski L, Marciniak M, Szewczyk T (2006) Analysis of abrasive flow machining with an electrochemical process aid. Proc Inst Mech Eng, B: J Eng Manuf 220(3):397–403 7. De Chiffre L, Kunzmann H, Peggs GN, Lucca DA (2003) Surfaces in precision engineering, microengineering and nanotechnology. CIRP Annals-Manufacturing Technology 52(2):561–577 8. Yamaguchi H, Shinmura T, Ikeda R (2007) Study of internal finishing of austenitic stainless steel capillary tubes by magnetic abrasive finishing. J Manuf Sci Eng 129(5):885 9. Yamaguchi H, Shinmura T (2004) Internal finishing process for alumina ceramic components by a magnetic field assisted finishing process. J Precision Eng 28(2):135–142