Friction characterization experiments on a single point diamond turning machine tool

Int. J. Mach.ToolsManufact. %Iol.34, No. 1, pp. 19-32, 1994. Printed in Great Britain

0890-6955/94$6.00+ .00 ~) 1993PergamonPress Ltd

FRICTION CHARACTERIZATION EXPERIMENTS SINGLE POINT DIAMOND TURNING MACHINE

ON A TOOL

S. CETINKUNT,t"W. L. Yo,t J. FILLmEN,~ and A. DONMEZ:~ (Received 11 June 1992; in final form 16 October 1992) Abstract--Sub-micnm precision machining requires very precise position and speed control of the motion of the machine tool axes. The accuracy of coordinated position control determines the profile accuracy of a part in contour m~Lchining, while the accuracy of speed control is the most significant factor in the resulting sub-surface damage that may occur in contour or non-contour machining. In high precision machining of brittle materials, it iLs desirable that the chip removal process be in the ductile regime of the material. The fundamental hypothesis is that if ductile regime chip removal is not accomplished, sub-surface damage will occur on the machined part. Although this can be partially corrected by removing the damaged layer by polishing, that is a very slow manual and costly operation. Therefore, it is desirable to machine such parts at the ductile regim~e to avoid sub-surface damage. Such a chip removal process requires precise control of feed rates at extremely slow speeds. This motion control problem is difficult due to the large friction and the unpredictable nature of the friction at very low speeds. The standard proportional-integral-derivative (PID) type servo control algorithms are not capable of delivering the desired precision in motion control. The friction must be accurately compensated for by the real-time control algorithm. This requires an accurate means of predicting the friction on-line. To this end, off-line experiments, designed with statistical considerations of factors affecting friction, were conducted. The data collected from these experiments were analyzed to understand the friction characteristics and to develop appropriate model structures for on-line predictions.

1. INTRODUCTION

HIG~I PRECISIONmachining is one of the few manufacturing processes by which very precise mechanJical components can be produced for many sophisticated high-tech engineering systems. Examples include the machining of precision metal mirrors, roller bearing elements for jet engines, high density magnetic storage devices and artificial hip-joint replacement components. As engineering systems become more and more sophisticated, the demand for the precision levels of parts also become more and more stringent. Hence, the precision capability of the machining processes used for production of such parts must be improved. The goal of this work is to improve the precision of a particular high precision machine tool at NIST (Fig. 1). The environmental conditions in the machining laboratory are very tightly regulated. The room temperature is regulated to within -+1°C. The machining room is vib,.ration-isolated from the rest of the building. This particular machine tool was designed and built for high precision machining applications (Fig. 1). The guide ways in the X - Y table portion are plain type double V-ways, where one flat surface slides over another flat surface. As a result, very large stiction and Coulomb friction exists in the X - Y table drives. Although the use of roller-type guide-ways would result in less friction, it has undesirable effects in precision machining. Specifically, the deformations of the roller elements induce inaccuracies on the machined part geometry. The signature of the roller element deformations is clearly observed on the machined parts. Furthermore, the plain type guide ways have much larger load capacity and longer life than the roller type guide ways. In high precisi~on machining, a machining defect called sub-surface damage is a major problem [1]. Such a defect severely limits the use of high precision parts, such as mirror components in optical systems. Although the defect can be partially removed

tDepartment of Mechanical Engineering, University of Illinois at Chicago, U.S.A. ~National Institute of Standards and Technology, Gaithersberg, Maryland, U.S.A. 19

20

S. CETINKUNTel al.

F1G. 1. Picture of the high precision machine tool used in the experiments.

by a manual polishing operation, it is costly and time consuming. Therefore, avoiding the occurrence of the sub-surface damage in the machining process is more desirable than attempting to correct it later. The basic hypothesis is that the sub-surface damage occurs as a result of impact type chip removal in the machining process. If the chip removal is in the ductile regime, sub-surface damage would not occur at all. In order to achieve chip removal in the ductile regime, the feed rates must be very slow and well regulated. This translates to a very slow and well regulated speed control problem of the machine tool axes. The main difficulty in achieving high precision motion control is the presence of friction in the machine tool drive system [2, 3]. Understanding and predicting the friction phenemenon has been a subject of physical sciences for many years with little success [4-10]. Feedback control systems involving friction have been studied in various applications [11-16]. The control system of the machine tool can be divided into three sub-systems: (1) actuation system (i.e. servo motors), (2) sensing system (encoders, tachometers, laser interferometer etc.), and (3) control computer hardware and software. Although the technologies available for actuation and sensing sub-systems are rather standard offthe-shelf components, there is no standard solution for an appropriate control software. The standard PID-type control softwares are not capable of providing the desired motion control accuracy in the presence of large friction [12, 16, 17]. More advanced control algorithms than the standard PIDs are needed to explicitly address the friction problem. Friction compensation at low velocities using repetitive learning control techniques was studied on an X - Y bed of a machine tool [12, 15]. The differences between this work and [12] is that the machine tool X - Y bed used in our study has a much larger stiction friction, which varies significantly as a function of stage position, whereas the position dependence of friction was not significant in the X - Y bed of the machine tool used in Ref. [12]. Furthermore, the low velocity is not just a region of a move, but the whole cycles of moves are performed at very low velocities in the precision machining studied in this work. The design of the experiments and the analysis of the data obtained from the experiments for the characterization of friction in the machine tool axis drives are the focus of this paper. The outcome of this work in understanding the friction will ultimately be used in a real-time control algorithm in order to achieve more precise

Friction Characterization Experiments

21

machine tool control. Furthermore, the generic understanding of friction behavior in the context of a particular machine tool may be useful in many other mechanical systems where friction is a concern. 2. DESCRIPTION OF THE HIGH PRECISION MACHINE TOOL USED IN THE EXPERIMENTS

A picture showing the geometric features of the machine tool used in the experiments is shown in Fig. 1. Only one axis (Y) is used in this study. The characteristics of the other axis (X) are similar to those of the Y-axis, so they will have almost identical servo control problems. Once the Y-axis motion control problem is solved, it can be duplicated for the X-axis, and the multi-axis contour machining reduces to a motion coordination and planning problem. The Y-axis is driven by a brushless, frameless d.c. servo motor directly coupled with a highly sensitive tachometer and an incremental encoder. The guides are double V-way steel surfaces over steel surfaces without any rollers. This is indeed the main reason for the very straight line motion capacity of the machine. A directly coupled acme-type nut and lead screw mechanism exists between the stage and the motor. The static friction torque was measured to be between 3.4 and 5.6 Nm (30 and 50 lb in) depending on the position and direction of motion. The backlash was about 17.8 ~m (700 p,in) (Fig. 2). The frameless, brushless d.c. servo motor has about 8.20 Nm (72.7 lb in) peak torque, and 2.99 Nm (26.5 lb in) continuous torque capacity at stall. The motor torque constant is 0.82 Nm/A (7.27 lb in/A), the rotor inertia is 1.16 x 10 -4 kg m 2 (1.03 x 10-31b in sec2). The incremental encoder resolution is 1024 lines per revolution which provides 4096 counts per revolution using x 4 factor in the decoding circuit of the digital controller board. The servo motor is powered by a linear servo amplifier which can be used in ~elocity or current mode. The amplifier commutates the motor phase currents using the encoder signals. An important element is the high sensitivity tachometer which provides a high signal to noise ratio at very slow speeds. The tachometer has an output of 55.7 V/(rad/sec) (or 5.8328 V/rev/min), with a maximum terminal voltage of 118 V, which limits the use of the tachometer to a maximum of 20 rev/min. The maximum ripple voltage ratio of peak to peak to nominal value is specified to be within 0.75%, but the actual observed noise was about 40 mV at any nominal voltage output. If a very high resolution position feedback system is used, the resolution must be sufficient even at very low speeds to obviate the need for the tachometer feedback. A PC-bus-based motion controller board using a Motorola 56001 DSP (30 MI-Iz), is used for position control as well as velocity control loop depending on the amplifier mode. The board's servo control algorithm accepts only encoder compatible feedback signals. 3. THE LIMITATIONS OF PID CONTROLS AND NEED FOR FRICTION CHARACTERIZATION

PID-type conllrol is the industry standard in servo motion control [14, 17]. The controller used for our machine tool also implements a variation of the standard PID algorithm for the motion control of each axis. The exact form of the digital PID algorithm is shown in Fig. 3. The power amplifier is used in current mode by setting K2(s) = Kdc and Kl(s) = 1, which are normally used for tuning if the amplifier is used in velocity mode. It has been known that friction acts as a slowly varying disturbance on the control system. If no integral action is used in the PID algorithm (PD action only), there will be a steady-state positioning error equal to the friction torque divided by the d.c. gain of the loop transfer function. Integral action is included in the PID algorithm in order to increase the d.c. gain, and hence reduce the steadystate error. UndLer PD control, the system eventually stops with a finite steady-state positioning error that is not large enough to generate a control action to break the static friction. Under PID control, however, the integral control action builds up the control action due to finite positioning error until the stiction is overcome. The system generally results in overshoot, and is stopped by the stiction friction. This cycle con-

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Schematic illustration of the control system hardware for a very high precision diamond turning and grinding machine.

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24

S. CETINKUNT et al.

tinues, resulting in limit cycle oscillations involving stiction between each half cycle about the desired final position [14]. Friction causes limit cycle oscillations under PID control. One way of eliminating the problem is to accurately estimate the friction online, and compensate for it with feedforward control before it causes limit cycle oscillations through the interaction with the integral control. The limit cycle phenomenon in the position control under PID was observed in the single point diamond turning machine used in the experiments. In addition to the positioning accuracy, velocity control accuracy is also very important in machining applications concerned with sub-surface damage. To investigate the velocity regulation accuracy, the existing control system was tuned to its best possible parameters and commanded to perform various test motions. The tracking accuracies for a step and parabolic change of position command are shown in Fig. 4.(a), and (b). Clearly, the quality of velocity regulation is very poor compared to what can be achieved if there was no friction. Therefore, the friction must be estimated and compen-

FIG. 4. Position and velocity response of the axis motion in response to a commanded motion under the standard PID control algorithm. (a) Commanded motion: step function position command; (b) commanded motion: parabolic function position command.

Friction Characterization Experiments

25

sated for in a real-time control algorithm in order to significantly eliminate frictioninduced inaccuracy problems in motion control. 4. DESIGN OF EXPERIMENTS AND ANALYSIS OF DATA FOR CHARACTERIZATION OF FRICTION IN THE MACHINE TOOL AXIS At very low speed motions, over 80% of the torque delivered by the m o t o r is used to overcome friction in the machine tool axis drive system. In order to assure accurate speed control, the friction must be predicted and compensated for accurately. The factors affecting friction are: 1: 2: 3: 4:

t e m p e r a t u r e of the machine tool axis drive system components, position oll the machine tool axis, speed, an6 direction of motion.

Experiments were conducted at different times under the same conditions of the above factors, in order to take into account the fact that there are different microscopic interferences between the guide-ways [18], the slides, and the lead screw-nut mechanism. The friction must be characterized as a function of the above variables. Two sets of experiments were designed and conducted on the machine tool: one set for the dynamic:, and the other set for static friction estimation. The purpose was to understand the factors affecting friction in order of importance, and to develop a model

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26

S. CEnr~KtJNT et al.

from which the friction could be predicted in real-time given process variables such as direction of motion, position, speed and temperature. Furthermore, the total distance traveled was predicted as a function of torque pulse height and width. Such results can be directly useful in point to point position control applications [14]. The basic approach taken in the experiments for dynamic friction characterization was to send a pulse current command to the servo amplifier which was in current mode, so that effectively an amplified form of the current was developed at the axis drive motor (Fig. 5). The electrical time constant of the servo amplifier in current mode and of the servo motor was negligibly small for the time scale of our interest. The position and velocity of the axis as a result of this pulse were recorded as functions of time. Since the transition from stiction friction to Coulomb friction occurs rather steeply in the low velocity range, different pulse height and width (effectively motor torque magnitude and duration) combinations were experimented with to obtain a data set that was rich in terms of the information at low velocities. As a result, the velocity factor was determined by two factors: 1: pulse height (current command, effectively the motor torque magnitude), and 2: pulse width (duration). The basic approach in statistical experiment design is that if all the variables affecting the outcome could be tested in all possible combinations (the so-called full factorial experiment design) and the resultant experimental data are recorded, the statistical analysis of this complete set of data would reveal or uncover the relationships between the variables and the interactions of the variables. Among those uncovered relationships, there may be some that were not known or not expected by previous engineering insights [19, 20]. Conducting a full factorial experiment is not always practical. The number of experiments to conduct can easily reach the tens of thousands which makes it impractical in terms of time and cost. Therefore, some good engineering judgements need to be made regarding how many discrete temperatures, positions and pulse heights and widths to consider. The goal is to collect as rich a data set as possible containing the type of information needed with as few experiments as possible. The following conditions were considered in the experiments: 1. 2. 3. 4. 5.

Temperature: Direction of motion: Position (mm (in)): Pulse height (%): Pulse width (msec):

Cold +12.7 (0.5) 40 90

Warm -+ 25.4 (1.0), . . . 241.3 (9.5) 100 (70) 270 (180)

The standard full factorial design with these values of variables requires 152 (2 x 19 x 2 x 2) experiments in one direction, and a total of 304 (2 x 2 x 19 x 2 x 2) experiments in both directions. Some salient considerations in statistical experiment design [19-21] suggest that a few mid-point experiments are very useful in validating the derived prediction equation without significantly increasing the number of experiments. For every pulse height, pulse width, and position combination, a mid-point experiment was conducted using the mid-value for these variables between two consecutive experiment settings. For a set of experiments where two positions (i.e. 50.8 mm (2 in) and 203.2 mm (8 in) locations along the axis), two pulse height and two pulse width cases were studied, one mid-point experiment for every eight experiments must be performed. This is not a significant increase in the number of experiments. The advantages of such additional experiments outweigh the cost of conducting them [19] (Fig. 6). Randomization of the order of the experiments was another experiment design consideration used to eliminate potential contamination of conclusions from possible drifts in the data.

Friction Characterization Experiments

27

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Exp. set

Conditions of experiment

Number of experiments conducted

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36

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PH{70%}, PW{180 ms}; + - , - +; X~ (mm): {127, 177.8, 50.8, 203.2, 101.6, 127, 152.4, 50.8, 228.6, 76.2, 127} ((in): {5", 7", 2", 8", 4", 5", 6", 1", 9", 3", 5"}); 4xll

44

PH{40, 100%}, PW{90, 270 ms}; X~ mm (in): {50.8 (2"), 203.2 (8")}; + - , Repeat 5 times; 2x2x2×2x5

80

PH{40, 100%}, PW{90, 270 ms}; Xi mm (in): {25.4 (1") . . . . . 228.6 (9")} +, - , - , +; (2 x 2 x 9 + 1) × 4

148

PH{40, 55, 70, 85, 100%}; + - ; PW{90, 135, 180, 225, 270 ms}; Xi mm (in): {50.8 (2"), 127 (5"), 203.2 (8")}; 45 x 2

90

PH{40, 70, 100%}; + - ; PW{90, 180, 270 ms}; repeat 5 times; X~ mm (in): {50.8 (2"), 127 (5"), 203.2 (8")}; 9 x 11 x 2 Total

198 672

A n o t h e r c o n s i d e r a t i o n in the friction e x p e r i m e n t s was the o r d e r o f m o t i o n d i r e c t i o n . W o u l d t h e e x p e r i e n c e d friction be the s a m e for t h e two t y p e o f m o v e s s h o w n in Fig. 6 (1 a n d 2 o r 1' a n d 2' m o t i o n s ) ? T h e t a b l e m o v e s b a c k a n d forth f r o m a p a r t i c u l a r p o s i t i o n e n d i n g u p at the original position. T h e only d i f f e r e n c e b e t w e e n t h e two m o v e s

S. CETINKUNTet al.

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TABLE2. STATICFRICTIONVALUESMEASUREDALONGTHE MACHINETOOLAXIS Position X (mm (in))

+ Torque (Nm (lbin))

0.0 (0.0) 25.4 (1.0) 50.8 (2.0) 76.2 (3.0) 101.6 (4.0) 127 (5.0) 152.4 (6.0) 177.8 (7.0) 203.2 (8.0) 228.6 (9.0) 254 (10.0)

5.36 5.36 4.79 5.07 4.51 5.36 4.79 5.36 5.64 5.07 5.64

- Torque (Nm (Ibin))

(47.5) (47.5) (42.5) (45.0) (40.0) (47.5) (42.5) (47.5) (50.0) (45.0) (50.0)

3.66 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 4.51 5.36

(32.5) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (40.0) (47.5)

is the order of the motion direction. In order to investigate the dependency, if any, of the friction to the order of direction, the direction related experiments were conducted as shown in Fig. 6. Hence the total number of experiments required would be increased by a factor of four which would result in a total of 2 × 4 × 19 × 2 × 2 × (9/8) = 684 experiments. Since the repeatability of the friction in time is an important issue, repeating all of the experiments under the same conditions a number of times (say 20 times) to characterize the statistical distribution friction may be considered. That would result in a total of 684 × 20 = 13,680 experiments. Clearly, the number of experiments needs to be reduced using good engineering judgement and statistical considerations, while minimizing the loss of information in the data. The experiments actually conducted were influenced by statistical considerations of factors such as randomization, factorial coverage, balance, and mid-point validation experiments. Details of the experiments are summarized in Table 1 in the order they were conducted.

SINGLE-PULSE FRICTION ANALYSIS OF LOW-VELOCITY TURNING MACHINE EXPERIMENT#1

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Friction Characterization Experiments

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EXPERIMENT 12 REPEATABILITY ANALY818

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The second set of experiments were conducted for static friction estimation of different points on the machine tool axis. The torque command was progressively increased until motion began. The torque level calculated from the measured command current to the amplifier was then the static friction. The average stiction friction measurements are displayed in Table 2.

S. CETINKUNT et al.

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(d) FIG. 8. Repeatability analysis of the friction: results of the experiments conducted at table position 5.0 in. 20 times. (a) Distance traveled as a function time. (b) Velocity as a function of time. (c) Total distance traveled as function of the experiment repeat number from 1 to 20 repeats. (d) Probability distribution of the total distance traveled for the same experiment conditions over 20 repeats. 5. R E S U L T S A N D DISCUSSIONS

A total of 672 experiments were conducted for the dynamic friction characterization (Table 1). In addition, stiction friction (static friction) was measured at various points on the machine tool axis. Static friction measurements were rather simple and reliable because they do not involve any motion. The results are shown in Table 2 which indicate a large variation of friction as a function of position along the axis and of direction of motion. Static friction in the reverse direction at various positions was measured after the backlash was removed so that the measurements were not influenced by the backlash factor. The analysis of the dynamic friction experiments is summarized in Figs 7-9. Figure 7 shows the position as a function of time for 9 x 4 = 36 experiments conducted as a full factorial set (Table 1, experiment No. 1). Notice that the ninth four experiment

Friction Characterization Experiments Pulse

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set is the mid-point experiment set. The factors in the experiments were position (50.8 mm (2.0 in) and 203.3 mm (8.0 in)), pulse height (40 and 100% of maximum pulse) and pulse width (90 and 270 msec). For each set of experiments, the table was moved first in the positive ( + ) direction and then in the negative ( - ) direction, followed by the negative ( - ) and the positive ( + ) direction, which was 4 experiments per set. The data clearly display the directional dependence of friction. This was also confirmed by the static friction experiments (Table 2) when large directional dependence was measured. Repeatability of friction behavior is a very important issue. The purpose of experiment set No. 2 (Table 1) was to assess the repeatability of friction. The distance traveled, and the velocity are shown in Fig 8(a) and (b) as a function of time for 20 repetitions. Figure 8(c) shows the total distance traveled by each repeat of the experiment. Figure 8(d) shows the distribution of total distance traveled over the total number of experiments. It should be noted that experiment set No. 2 (Table 1) was started when the machine was cold. Hence, the results indicate a reasonable repeatable friction behavior. The results in Fig. 9 show the relative importance of factors affecting friction. The steeper the slope of a factor or a combination of factors, the more significant the effect of this factor on friction. The values of the slopes indicated in the figure should be interpreted relative to each other. They do not have an absolute direct physical un:it. Current activities focus on conducting more experiments to establish very reliable repeatable data, and to form friction prediction hypersurfaces as functions of position, speed, direction, and temperature taking into account the statistical behaviour characterizing the repeatability of the friction. Repeatability analysis of the data obtained from tile experiments clearly indicate that although the friction is quite repeatable after a few initial moves, it is still not perfectly repeatable. Therefore, it may best be modelled as a random variable with an average expected mean value, plus its variance and auto-correlation functions.

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S. CE'nNKU~Tet al. 6. CONCLUSIONS

The aim of this work was to improve the precision of a high precision single point diamond turning machine tool to achieve machining in the sub-micron precision range without producing sub-surface damage in the machined part. This requires very accurate position and velocity control of the machine tool axes at very low speeds. The performance of the machine tool under a standard PID-type servo control was tested and observed to be unsatisfactory for the stated aims of the project. The friction must be accurately compensated for by a servo control algorithm in real-time. To this end, statistically designed experiments were conducted to collect data for the characterization in friction in the machine tool axes. The data were analyzed to understand the characteristics of the friction, and to develop appropriate model structures for on-line friction prediction and compensation. Acknowledgements--This work was supported in part by the National Science Foundation and the National Institute of Standards and Technology through a research fellowship program administered by the American Statistical Association. The encouragement of Dr Robert Lundegard, Chief of Statistical Engineering Division at NIST, and the provision of the necessary resources during the course of this project are greatly appreciated. REFERENCES [1] Z. NAKASUJI,S. KODERA, H. MATSUNAGA,N. IKAWAand S. SHIMADA,Diamond turning of brittle materials for optical components, Ann. CIRP 39/1, 89-92 (1990). [2] S. KATO, N. SATOand T. MATSUBAYASHI,Some considerations on characteristics of static friction of machine tool slideway, J. Lub. Technol. 94, 234-247 (1972). [3] D. P. HESS and A. SooM, Friction at a lubricated line contact operating at oscillating sliding velocities, J. Tribol. 112, 147-152 (January 1990). [4] B. DUDLEYand H. SwiFt, Frictional relaxation oscillations, Phil. Mag. 40, 849-861 (1949). [5] E. RAalNowlcz, Stick and slip, Sci. Am. 194(5), 109-118 (May 1956). [6] C. SHEr~and H. WAN6, Nonlinear compensation of a second- and third-order system with dry friction, IEEE Trans. Ind. Appl. 83, 128-136 (March 1964). [7] J. Tou and P. M. SCHULTHEISS,Static and sliding friction in feedback systems, J. appl. Phys. 24(9), 1210-1217 (1953). [8] B. ARMSTRONG-HELOUVRY,Stick-slip arising from Stribeck friction, in Proc. 1990 Int. Conf. Robotics Automation, pp. 1377-1382, IEEE, Cincinnati, OH (May 1990). [9] P. DAHL, Solid friction damping of mechanical vibrations, AIAA J. 14, 1675-1682 (December 1976). [10] M. MASOS and Y. WAN6, On the inconsistency of rigid-body frictional planar mechanics, in Proc. 1988 Int. Conf. Robotics Automation pp. 524-528, IEEE, Philadelphia, PA (April 1988). [11] W. L. NELSON, Pulse-width relay control in sampling systems, J. Basic Engng 65-76 (March 1961). [12] E. TusG, G. ANWARand M. TOmZUKA,Low velocity friction compensation and feedforward solution based on repetitive control, Proc. 1991 ACC, Boston, MA, 3, 2615-2620 (1991). [13] C. WALRATH,Adaptive bearing friction compensation based on recent knowledge of dynamic friction, Automatica 20, 717-727 (1984). [14] S. YANG and M. TOMIZUKA,Adaptive pulse width control for precise positioning under the influence of stiction and Coulomb friction, ASME J. Dyn. Sys. Meas. Control 110, 221-227 (1988). [15] J.-S. Hu and M. TOMIZUKA,Adaptive asymptotic tracking of repetitive signals - - a frequency domain approach, Proc. 1991 ACC, Boston, MA, 3, 2621-2628 (1991). [16] S., CET1NKUNT,W. L. Yu, J. FILLIBEN and A, DONMEZ, Friction characterization experiments for precision machine tool control at very low speeds, 1992 Am. Control Conf., 24-26 June, Chicago, IL (1992). [17] DC Motors, Speed Controls, Servo Systems, 5th edition. Electro-Craft Corp. (1980). [18] J. HALLIr~G(ed.), Principles of Tribology. MacMillan Education Ltd (1989). [19] G. E. P. Box, W. G. HUNTERand J. S. HUr~TER,Statistics for Experimenters. John Wiley, New York (1978). [20] J. FILLIBEN,Experiment Design for Scientists and Engineers. NIST (1990). [21] T. B. BARKER,Quality by Experimental Design. Marcel Dekker Inc., New York (1985).