computer-controlled lapping system for granite surface plates

7
Journal of Manu[acturing Systems Vol. 19/No. 3 q 2000 Computer-Controlled Lapping System for Granite Surface Plates Jiexin Wang and Bi Zhang, Dept. of Mechanical Engineering, University of Connecticut, Storrs, Connecticut, USA Binyuan Xue, Dept. of Mechanical Engineering, Shanghai Jiaotong University, Shanghai, China Abstract Granite surface plates are traditionally finished by hand lapping, which is time consuming, strenuous, and costly. Surface quality and accuracies of such plates depend large- ly on the experience and skill level of the operator. In this study, a computer-controlled system is developed for ultra- precision lapping of granite surface plates. The system can easily achieve a high lapping efficiency and high flatness accuracy due to its capability of on-line measurement of flat- ness, optimization of the lapping process, and automation of the lapping operation. The system has been successfully applied to a number of granite surface plates, and the results show that a flatness error of less than 2 tJm over a 1 x 2 m area is obtained. This paper also presents the principle of on- line measurement of flatness and experimental results based on the computer-controlled lapping system. Keywords: Granite Surface Plate, Computer-Controlled Lapping, Flatness Error, On-Line Measurement, Lapping Optimization Introduction Granite, a kind of rock, is widely used for sur- face plates in high-precision machine tools and coordinate measuring machines due to its distinc- tive and versatile properties, such as superior wear and corrosion resistance, low thermal deforma- tion, and nondenting property) In general, a gran- ite plate is processed by hand lapping, in which abrasive grits are charged between a lap and the granite plate, while the lap is displaced over the workpiece surface by hand to accomplish material removal. However, hand lapping is a time-consum- ing and strenuous process through which it is dif- ficult to obtain high accuracy. In recent years, many advanced technologies and materials for loose abrasive processes, for example, lapping and polishing, have been developed to a significant degree, especially for the optics and semiconduc- tor industries. 2 Both conventional abrasives, such as A1203 and SiC, and superabrasives, such as dia- mond and cubic boron nitride, are used extensive- ly in lapping and polishing. The grit size of the abrasives can be less than 0.1 /am, or even down to nanometer scale. Lapping using both fixed and loose diamond abrasives ranging from 0.5 to 2.0 /am grit sizes has been reported. The resulting sur- face roughness can be as low as 0.9 nm Ra [Ref. 3]. Computer control techniques have also been widely used in machining, although in a more lim- ited manner in lapping. Computer-controlled mea- surement and compensatory machining has been applied to improve the geometric accuracy of sur- face plate machining and guideway preparation. 4,s Notably, a CNC polisher for large telescope mir- rors has been developed that can detect contour errors and feedback to the computer. In an iterative process, the system has made parts with a residual error of 0.7 arc-sec (3.5/arad). 6 In this study, a computer-controlled lapping sys- tem is developed with on-line measurement of flat- ness error to realize optimal lapping operation. The system can achieve good flatness and high lapping efficiency. This paper reports the application of the lapping system to granite surface plates and experi- mental results of computer-controlled lapping. Experimental Setup The lapping system consisted of a microcomput- er, a lap, and a frame that carried X, Y, and Z slide- ways. The lap was automatically controlled by the system during operation. The X and Y slideways were driven by the Xand Y stepping motors for posi- tional control of the lap, while the Z slideway was mainly used for loading and unloading the lap. A schematic of the lapping system is shown in Figure 1. A DC motor was used to rotate a spindle so as to drive a rocking mechanism through a transmission. The rocking mechanism then moved the lap back 149

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Page 1: Computer-controlled lapping system for granite surface plates

Journal of Manu[acturing Systems Vol. 19 /No. 3 q

2 0 0 0

Computer-Controlled Lapping System for Granite Surface Plates Jiexin Wang and Bi Zhang, Dept. of Mechanical Engineering, University of Connecticut, Storrs, Connecticut, USA Binyuan Xue, Dept. of Mechanical Engineering, Shanghai Jiaotong University, Shanghai, China

Abstract Granite surface plates are traditionally finished by hand

lapping, which is time consuming, strenuous, and costly. Surface quality and accuracies of such plates depend large- ly on the experience and skill level of the operator. In this study, a computer-controlled system is developed for ultra- precision lapping of granite surface plates. The system can easily achieve a high lapping efficiency and high flatness accuracy due to its capability of on-line measurement of flat- ness, optimization of the lapping process, and automation of the lapping operation. The system has been successfully applied to a number of granite surface plates, and the results show that a flatness error of less than 2 tJm over a 1 x 2 m area is obtained. This paper also presents the principle of on- line measurement of flatness and experimental results based on the computer-controlled lapping system.

Keywords: Granite Surface Plate, Computer-Controlled Lapping, Flatness Error, On-Line Measurement, Lapping Optimization

Introduction Granite, a kind of rock, is widely used for sur-

face plates in high-precision machine tools and coordinate measuring machines due to its distinc- tive and versatile properties, such as superior wear and corrosion resistance, low thermal deforma- tion, and nondenting property) In general, a gran- ite plate is processed by hand lapping, in which abrasive grits are charged between a lap and the granite plate, while the lap is displaced over the workpiece surface by hand to accomplish material removal. However, hand lapping is a time-consum- ing and strenuous process through which it is dif- ficult to obtain high accuracy. In recent years, many advanced technologies and materials for loose abrasive processes, for example, lapping and polishing, have been developed to a significant degree, especially for the optics and semiconduc- tor industries. 2 Both conventional abrasives, such as A1203 and SiC, and superabrasives, such as dia-

mond and cubic boron nitride, are used extensive- ly in lapping and polishing. The grit size of the abrasives can be less than 0.1 /am, or even down to nanometer scale. Lapping using both fixed and loose diamond abrasives ranging from 0.5 to 2.0 /am grit sizes has been reported. The resulting sur- face roughness can be as low as 0.9 nm Ra [Ref. 3]. Computer control techniques have also been widely used in machining, although in a more lim- ited manner in lapping. Computer-controlled mea- surement and compensatory machining has been applied to improve the geometric accuracy of sur- face plate machining and guideway preparation. 4,s Notably, a CNC polisher for large telescope mir- rors has been developed that can detect contour errors and feedback to the computer. In an iterative process, the system has made parts with a residual error of 0.7 arc-sec (3.5/arad). 6

In this study, a computer-controlled lapping sys- tem is developed with on-line measurement of flat- ness error to realize optimal lapping operation. The system can achieve good flatness and high lapping efficiency. This paper reports the application of the lapping system to granite surface plates and experi- mental results of computer-controlled lapping.

Experimental Setup The lapping system consisted of a microcomput-

er, a lap, and a frame that carried X, Y, and Z slide- ways. The lap was automatically controlled by the system during operation. The X and Y slideways were driven by the Xand Y stepping motors for posi- tional control of the lap, while the Z slideway was mainly used for loading and unloading the lap. A schematic of the lapping system is shown in Figure 1. A DC motor was used to rotate a spindle so as to drive a rocking mechanism through a transmission. The rocking mechanism then moved the lap back

149

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Journal of Manufacturing Systems Vol. 19/No. 3 2000

~'~ Z-motor Lapping frame--~ ~ ~ X-motor - otor

~ Granite plate

Figure 1 Lapping System for Granite Plates

and forth to form a translational motion, as shown in Figure 2. The spindle moved along the cross guide- way that was driven by the X, Y stepping motors along the side guideways. The spindle motion in the X and Y directions formed the positional motion of the lap. In fact, the lap movement was a combination of both the translational and positional motions, but material removal was mainly accomplished through the translational motion of the lap because the trans- lational motion was much faster than the positional

Tension spring ~ ! ~~7!

Guideway ~/L~] I~

I

A

I II/ ! I] ~ 4 ~ 1 ~ Transmission

[~:~ I~---..~ De motor

ng mechanism

Holder

Granite plate _1

Figure 2 Translational Motion Mechanism of the Lap

motion. A computer was connected to a digital out- put port and a digital-to-analog converter to control all the stepping motors and a DC motor. These motors, in turn, controlled the positional and trans- lational motions of the lap. The lap was made of granite material and was supported by a holder that allowed the lap to tilt and move up and down freely so that wear of lap did not affect lapping accuracy. In most cases, tap water was used as the lubricant, which is consistent with standard practice in pro- duction manufacturing practice. Lapping oil was also used for better surface finish. The lap was grooved to accommodate abrasives and lubricant.

The translational motion of the lap provided the lap with a uniform velocity and an even wear at any point of the lap during lapping operation. Therefore, a high quality of surface finish could be obtained.

On-Line Measurement of Flatness The on-line measurement of flatness was per-

formed with the computer control. Two measure- ment schemes--diagonal and rectangular--were utilized to measure and assess flatness, as shown in Figure 3. Each measurement scheme was assigned with a particular track arrangement. 7 An electronic level with a resolution on the order of 0.2 arc-sec was used. A carriage, to which the level was attached, moved along the measurement tracks at an equal interval. The angular displacement of the car- riage was indicated by the output signals of the elec- tronic level that were amplified and fed into a low- I

(a) Diagonal scheme

I _

(b) Rectangular scheme Figure 3

On-Line Flatness Measurement Schemes for Lapped Granite Surface Plates

1 5 0

Page 3: Computer-controlled lapping system for granite surface plates

Journal of Manufacturing Systems Vol. 19/No. 3

2000

AZ

Figure 4 Flatness Error Definition

pass filter, then into a 12-bit A/D converter. To avoid the reading error due to the swing of level sensor, the computer monitored the input signals until the stable signal was read in. After the measurements along all the tracks were completed, the input data was saved to a file, and then flatness error was calculated. Similar to straightness error, flatness error is defined as the perpendicular distance between the maximal and minimal deviation points from a geometric ref- erence plane, as shown in Figure 4. 8,9

In many cases, a machined surface does not have a specified orientation for a reference plane but is only required to be as flat as possible. However, to determine flatness errors, the orientation of a refer- ence plane must be specified. Two calculation meth- ods are used for the assessment of flatness error: the least squares method and the min imum zone method) ° Each of the methods requires a reference plane for flatness assessment. The following pro- vides a description of the two methods.

Least Squares Method A reference plane can be determined by the least

squares method for a set of measurement data Po (X~, Yj, Z0) and is expressed by the following equation:

Z = a X + b Y + c (1)

The deviation between the reference plane and mea- surement data is given as follows:

Zi j - (aX i +bYj +c) (2) AZii = a2 b 2

~,/1 + +

"9 )- S = AZij ( i=1 ..... N ; j = I ..... M) (3)

where parameters a, b, and c will be found to mini- mize the sum of square AZ#. In practical flatness measurements, the inclination of a surface to be measured is adjusted to be as small as possible to obtain higher measurement accuracy. In t~s case, !t can then be assumed that a,b << 1 so that -,,'l + a 2 + b 2 = I. Equation (2) is reduced to the following:

AZij = Z i j - (aX i +bYj +c) (4)

The parameters a, b, and c, which satisfy ~)S/~a = 0, 3S/3b = 0, ~S/Oc = 0, can be obtained by solving the following matrix equation:

EEx/ EEx, x

ZEx,

=/zzz,jx / 1_ zzz, j

zz 2 zx /×

(5)

Consequently, flatness error c can be obtained using the difference between the maximum and the mini- mum of deviations AZ~ from the least squares plane.

c=max(AZo)-min(AZj ) ...... (i=1 ..... K: j = l ..... L) (6)

Minimum Zone Method With the minimum zone method, flatness error c

is determined by the minimum distance between two parallel planes that contain all measurement points, u Assuming the two parallel planes defined by the following:

Z = a X + b Y + G

and

Z = a X + b Y + c 2

for plane A

for plane B

(7)

then, all measured points are contained between plane A and plane B. The minimum zone method is to search for the two parallel planes that are as close as possible. Flatness error e can be written as follows:

e = ~ l + a 2 +b2

which is a function of a and b. The solution to e (a, b) becomes nonlinear. An optimization algo- rithm is applied to solving the problem. Is The results calculated in both methods can be shown in two

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Journal of Manufacturing Systems Vol. 19/No. 3 2000

dimensions or three dimensions. The minimum zone method always provides a low value of flatness and yet is more complicated in the algorithm.

Lapping Path Optimization The goal of optimizing the lapping path is to

achieve a desired accuracy as fast as possible so that the material removed during lapping can be mini- mized. Assuming V~j is the volumetric material removal in the section (i, j)

(9)

where AZ,:/ is the deviation of data point Po with respect to the reference plane and represents the mean height value in the section (i, j ) . A Z o is normally greater than or equal to zero. Therefore, the reference plane used for calculating material removal is selected in such a way that the bottom data point Pro, is in the plane. It can be expressed as follows:

Z:a(X-Xm)+b(r-Y,,) or (10)

Z = a X + b Y - a X m - bY,,

in addition, e is the allowable flatness error, s is the area of the section (i, j) , k is a function of (AZ 0 - ~) and can be written as follows:

k : l AZj - ~ > 0 1

k = O AZ~j-~<O] (ll)

It means that the lapping process is needed only when the height value is greater than the allowable flatness error in which a lapping path is determined. The total volume of material removal ~ (mm 3) is obtained in the following equation:

(12)

According to Eq. (2), AZ/j is a function of the refer- ence plane chosen, which is expressed in Eq. (10). (~ is also a function of the reference plane because and s are constants and k is only a selective func- tion. In fact, to optimize the lapping path is to search for a reference plane, which can result in a minimum value of material removal. The objective function can be found as follows:

Minimize: ¢ : f ( a , b) =

s x k (13)

where a, b, and c are coefficients for the reference plane, but according to Eq. (10) cb can be found as a function of a and b, as follows:

G, = Z,,,, - aX, , - b I1,,, (14)

Powell's direct numerical search-conjugate direc- tion method was applied in the optimization pro- gram to determine the optimal lapping path." It is an efficient method for finding the minima of a func- tion without calculating its derivatives.

Computer-Control led Lapping Experiment

Material removal takes place as the lapping tool travels across the granite surface plate. Because many parameters could affect the material removal, a series of lapping tests was conducted to obtain information on the effect of the lapping parameters, such as tool velocity, lapping time, abrasive size, and lapping pressure, on the material removal process, u Figure 5 shows the effect of lapping velocity on material removal under the conditions of lapping pressure 0.5 N/cm 2 and the average grit size of SiC abrasives of 5 ILtm. A larger material removal rate was obtained at the speed of 300 mm/s than at 150 ram/s, which indicates that a higher lapping velocity results in a higher material removal rate, and vice versa. It is also observed from Figure 5 that the material removal rate decreases with the progress of

300 mm/s

• 150 mm/s

I 1

0.5 1.0 1.5 2.0

..~:=~J"-~ iI- -- -~ -

2.5 3.0

Time, min.

Figure 5 Effect of Lapping Velocity on Material Removal

152

Page 5: Computer-controlled lapping system for granite surface plates

Journal o/'Manu/acturing Systems Vol. 19/No. 3

2000

¢ 10 ~m

-43-- 5 pm

-~- 0.5 om ~ ~ . . _ _ . _ _ ~

/

0.5 1.0 1.5 2.0 2.5 3.0

Time, min.

Figure 6 Effect of Abrasive Grit Size on Material Removal

lapping at both velocities. The decreasing rate might be due to breakdown of the abrasive grits)

Figure 6 shows the effects of abrasive grit size on material removal under the condition of lapping velocity 150 mm/s and lapping pressure of 0.5 N/cm z. An overall trend in Figure 6 is that material removal rate increases with the increase in grit size. The abrasives with a smaller grit size show a quick- er drop in material removal rate than do larger ones. This phenomenon might be attributed to two rea- sons: wear and breakdown of abrasive grits and lap plate loading. During the lapping process, wear and grit breakdown is anticipated to o c c u r , 7 which results in smaller and smaller grit sizes. On the other hand, smaller grits can easily load the lap plate and cause a decrease in material removal rate. For the abrasives of 0.5 ~tm grit size, the material removal rate approaches zero after 1.5 minutes of lapping. However, the smaller abrasives result in a better surface finish.

Figure 7 shows the effects of lapping pressure on material removal under a lapping velocity of 150 mm/s and the average grit size of 5 ~tm. A higher lapping pressure caused more material removal under the same lapping conditions.

In this study, all the experimental results were stored in the computer as a process reference data file. Based on the file and the optimal lapping path, the material removal data file was generated by means of a computer algorithm, which included the amount of material removal in terms of sections along the lapping path. Because material removal was related to lapping time in the process reference data file, a desired amount of material can be pre- cisely removed by controlling lapping time on the individual segments along the lapping path.

2

0 0

---~-- P=I.0 N/cm 2

/'=-0.5 N/cm ~

ff

0.5 1.0 1.5 2.0 2.5

i~3J"-

3.0

Time, min.

Figure 7 Effect of Lapping Pressure on Material Removal

Lapping time T U expended in section (i, j) can be written as follows:

(15) L - G G

The total lapping time, T, is as follows:

2 = (16) • G

where G represents material removal rate and is related to the lapping parameters.

As a general guideline, a large grit size of abra- sives, large pressure and high velocity are recom- mended for coarse lapping whereas a small grit size, low pressure and velocity are for fine lapping. The lapping process can be repeated until the desired accuracy is obtained.

Figure 8 shows the flow diagram for the lapping process that includes construction of reference data file, acquisition of profile data, optimization of lapping path, control of lapping operation, and flatness measurement. All the above steps can be displayed on a computer screen, which facilitates an easy monitoring and control of the lapping operation. It took approximately one hour to com- plete one operation cycle. The lapping system developed has successfully been used to process a number of granite plates.

Figure 9 shows the flatness of the granite plate with the dimensions of 1 x 2 x 0.35 m from which a flatness of 1.13 ~tm was obtained over the area of 1 x 2 m. The flatness data of the plate is also plotted in Figure 10 in a three-dimensional view.

It is worth noting that this result is far better than the ISO standard of the same size of granite

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Journal of Manufacturing Systems Vol. 19/No. 3 2000

( >r Acquisiti°n°f ~--~ Start profile data

Stop ) N o ~

Optimization of lapping path

Flatness measurement

Process reference data file

l Control of

lapping operation

Figure 8 Flow Diagram of Lapping Process

surface plates. The measurement was made by an electronic level and verified by a laser interfer- ometer with a high accuracy and resolution on the order of 0.1 arc-see, which was considered to be adequate for comparison. The results obtained by the electronic level and the laser interferome- ter were in a good agreement.

Conclusion A computer-controlled lapping system was

developed for granite surface plates. The system significantly improves the lapping process over the strenuous and time-consuming hand lapping process. The results show that the system can lap granite plates to a flatness better than 2 lain over an area of 1 × 2 m under the following condi- tions: SiC abrasives with 0.5 ~tm grit size, 100 mm/s lapping velocity, and 0.5 N/cm ~ lapping pressure. The system can be applied to ultra-pre-

Yj lm Unit: pm

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.5 0.4 0.7 0.4 0.3 0.3 0.0 0.1 0.0 0.8 0.6

0.9 0.9 0.7 0.3 0.8 0.4 0.3

0.8 0.6 1.1 0.3 0.6 0.8 0.8 0.5 0.8 0.5 0.1

0.9 0.7 0.9 0.6 0.8 0.7 0.8

0.0 0.5 0.8 0.5 0.4 0.4 0.3 0.1 0.5

~X 0 Close error=0.3 Flatness= 1,13 m Figure 9

Flatness Data Measured Using Minimum Zone Method

cision lapping automation for surface plates of granite and other materials.

Acknowledgment The authors would like to express their apprecia-

tion to the engineers of Shanghai Machine Tool Works for their enthusiastic support of this work.

References 1. A.Z. Abdin, "Investigation on Granite as a Material for Metrology

Aids," Annals of the CIRP (v27, nl, 1978), pp377-381. 2. R. Komanduri, D.A. Lucca, and Y. Tani, "Technological Advances in

Fine Abrasive Process," Annals of the CIRP (v46, n2, 1997), pp545-596. 3. M. Touge and T. Matsuo, "Removal Rate and Surface Roughness in

High-Precision Lapping of Mn-Zn Ferrite," Annals qfthe CIRP (v45, hi, 1996), pp307-310.

4. J. Wang, B. Xue, and J. Pei, "Computer Control System tbr Compensating Straightness Error in Grinding," ASME Winter Annual Meeting, Dallas, TX, 1990 (v45), ppl-7.

5. C.W. Park, K.E Eman, and S.M. Wu, "An In-Process Flatness Error Measurement and Compensatory Control System," ASME Journal of Engg. .for Indust~ (v110, 1988), pp263-270.

6. K. Becker and K. Beckstette, "A Pair of Machines tbr Computer- Controlled Fine Correction of Optical Surface," Ultra-Precision in Manufacturing Engineering (Berlin: Springer-Verlag, 1988), pp212-223.

7. W. de Bruin and J. Meijer, "Analysis of Flatness Measurement and Form Stability of a Granite Surface Plate," Annals of the CIRP (v29, nl, 1980), pp385-390.

8. C. Kirsten and E Ferreira, "Verification of Form Tolerances, Part 1:

Y

0

Figure 10 Three-Dimensional Display of Flatness of Granite Surface Plate

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Journal of Manufacturing Systems Vol. 19/No. 3

2000

Basic Issues, Flatness, and Straightness" Precision Engg. (v17, n2, 1995), pp131-141.

9. M. Oya et al., "A Study on Improvement of the Accuracy of a Three- Coordinate Measurement Machine: A Method of Error Correction," Int'l Journal of the Japan Society Mechanical Engg. (v30, 1987), pp344-349. 10. J. Meijer, "Accuracy of Surface Plate Measurement-General Purpose Software for Flatness Measurement," Annals of the CIRP (v39, nl, 1990), pp545-548. 11. T.S.R. Murthy and S.Z. Abdin, "Minimum Zone Evaluation of Surface," lnt l Journal of Machine Tool Design and Research (n20, 1980), pp123-136. 12. M. Fukuda and A. Shimokohbe, "Algorithms for Form Evaluation Methods for Minimum Zone and Least Squares," Proc. of Int'l Syrup. on Metrology for Quality Production, Tokyo, 1984, pp197-202. 13. M.J.D. Powell, "An Efficient Method for Finding the Minimum of a Function of Several Variables Without Calculating Derivatives," Computer Journal (v7, 1964), pp155-162. 14. J. Wang, J. Shi, and B. Xue, "The Research on Lapping Experiments for Granite Plate" Chinese Journal of Grinding and Grinders (n3, 1992), pp26-34.

Authors' Biographies Dr. Jiexin Wang is currently a senior engineer with Carten Controls Inc.

in Connecticut. He was a research scientist at the Precision Manufacturing Institute of the University of Connecticut (UConn) during 1996-98. He received his PhD degree from Shanghai Jiao Tong University in 1986.

Dr. Bi Zhang is an associate professor of mechanical engineering at the University of Connecticut. Prior to joining UConn in 1992, he was a postdoctoral research associate at Oklahoma State University. His area of expertise is in manufacturing systems and processes, with par- ticular emphasis on grinding-related research. He received his MS and PhD degrees from Tokyo Institute of Technology in 1985 and 1988, respectively.

Professor Binyuan Xue is professor emeritus with the Dept. of Mechanical Engineering at Shanghai Jiao Tong University. His area of expertise is in pre- cision machining systems.

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