multi-axis CNC machine tools by compensating for machine geometric and thermal errors in ... the machine accuracy by one order of magnitude using a laser ...
~
Int. J. Mach. Tools Manufact. Vol. 35, No. 4, pp. 593-605, 1995 Copyrightt~) 1994 ElsevierScience Ltd
) Pergamon
Printed in GreatBritain. All rightsreserved 0890-6955/9559.50 + .00
COMPUTER-AIDED ACCURACY ENHANCEMENT F O R MULTI-AXIS CNC MACHINE TOOL JENQ-SHYONG C H E N t
(Received 4 November 1993; in final form 1 March 1994)
Abstract--A computer-aided error compensation scheme has been developed to enhance the accuracy of multi-axis CNC machine tools by compensating for machine geometric and thermal errors in software way. Stationary geometric errors including the coupling effect of linkage errors between machine slides are calibrated off line. Dynamic thermal errors are predicted on line by an artificial neural network model. Because machine errors are variant with the cutting time and slide positions, a PC based compensation controller has been developed to upgrade commercial CNC controllers for real-time error compensation. The real-time compensation capability is achieved by digital I/O communication between the compensation controller and CNC controller without the need of any hardware modification to the machine servo-drive loops. The compensation scheme implemented on a horizontal machining center has been proven to improve the machine accuracy by one order of magnitude using a laser interferometer and cutting test.
INTRODUCTION
FOR A THREE-AXISmachine, the precision of the cut part is determined by the moving accuracy of an open kinematic chain consisting of three movable slides. That means the positioning accuracy at the cutting edge should be defined by the relative moving error between the cutting tool and workpiece. Any linkage errors existing on machine slides will then result in a positioning error at the cutting edge. Among the machine error sources, stationary geometric errors and thermally-induced errors of machine linkages are known to be key contributors. Stationary geometric errors of machine tools come from manufacturing defects, machine wear, static deflection of machine components due to the deadweights of moving machine slides, misalignments due to assembly and installation, and soft machine foundation. Geometric errors include linear errors of the leadscrews, straightness errors of the guideways, angular errors of machine slides and orthogonal errors among machine axes. To the geometric errors, angular errors (slideway pitch, yaw and roll, and orthogonal errors) associated with large Abbe offset length are considered to be the largest contributors to machine static positioning errors. Position sensing devices of machine servo-drive loops are usually attached at the slide driving mechanisms, which is in common with many machine tools on the market today (Fig. 1). This design will create a positioning error A at the cutting edge if an
Fir. 1. T h e A b b e offset induced error.
tDepartment of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan, R. O.C. 593
594
JENQ-SHYONGCHEN
Abbe offset length exists from the sensing device to the cutting edge and the movement of the machine slide possesses angular errors. The Abbe offset induced error is especially significant with medium-size and large-size machine tools for which a highly rigid machine structure is difficult to achieve and small angular motions of working table are amplified by the large traveling distances of feed axes. For machines with over 400 mm capacity, the Abbe offset induced error contributing to workpiece errors with a magnitude more than several tens ~m is not unusual. To attain higher levels of machine accuracy, the emphasis will be on not only the short-term repeatability and positioning accuracy caused by geometric errors, but also the long-term stability caused by thermal errors during machining. The thermal errors come from thermal expansions and thermal distortions of machine components due to internal or external heat sources such as motors, bearings, hydraulic systems, sunshine, etc. The thermal bending of C-shaped machine frames, thermal expansions of leadscrews, and thermal distortion of the spindle are usually the dominant error sources. A typical magnitude of spindle growth could be more than one hundred ~m from machine cold-start to warm-up if not equipped with any specific built-in temperature control capability. The thermal bending of a C-shaped machine and thermal expansions of leadscrews can produce positioning errors from several tens to > 100 ~m, too. In many cases, the dynamic thermal error is likely the most formidable obstacle to obtaining higher levels of machine accuracy. It has been reported that thermal errors could comprise 40-70% of the workpiece error in precision machining [1]. High machine accuracy can be achieved through designing a machine with precise components, good rigidity and low thermal distortion. There are, however, some physical limitations which inhibit the success of these efforts. Machine accuracy is limited and the cost for achieving this limit can be very high. In addition to the design approach, enhancing the machine accuracy through compensating for the repeatable geometric errors in software way is becoming popular as a cost-effective method to improve machine accuracy. For example, backlash and pitch value compensations of leadscrew are now standard functions to commercial CNC controllers. In many cases, compensating for machine errors in software way has been found to be less expensive and more efficient than design modifications. It must be emphasized that, however, the error compensation method must not be considered an alternative to the design effort but rather an addition to it. It is generally accepted that building the best machine possible is the first step to control machine accuracy. In response to the increasing demand of higher machine accuracy, compensations of the straightness errors of a feed axis and the perpendicular errors among feed axes have recently become available at some CNC controllers. However, very few CNC controllers are able to compensate for two of the most important error sources: the angular error and thermal error. Compensations of the angular errors and thermal errors need real-time error compensation capability. The Abbe offset induced error caused by angular errors is spatial-variant across the machine working zone because the Abbe offset length is variant with the travel of feed axes. Besides the spatialvariant characteristic, the positioning error of a machine tool is also time-variant due to the dynamic effect of thermal errors. Recently, with the aid of an external PC, compensation of the angular errors and thermal errors on CNC machine tools have been achieved [2-8]. The external computer calculates the spatial-variant and time-variant positioning error at the cutting edge during machining and sends a correspondent compensation signal to the CNC machines. Previous research has shown some exciting achievements in the enhancement of machine accuracy through the computer-aided error compensation techniques. Laboratory reports proved that improvement by one to ten times on the turning machine and the machining center is achievable. Commercial spindle growth compensation schemes are available now and improvement by a factor of ten is not unusual for a general cutting process [6]. The objective of this research is to develop a computer-aided error compensation
Computer-aided Accuracy Enhancement
595
scheme which enhances machine accuracy by compensating for both geometric errors and thermal errors in real time. The spatial-variant and time-variant position error at the cutting edge caused by the geometric errors and thermal errors were synthesized and formulated by a kinematic model using homogeneous coordinate transformation. Stationary geometric errors including the coupling effect of linkage errors between machine slides were calibrated off line, while dynamic thermal errors were predicted on line. Because thermal errors are highly nonlinear with cutting conditions, precise prediction of thermal errors under unpredictable cutting conditions is a key step for accurate thermal error compensation. In this research, the thermal errors were predicted on line through an artificial neural network (ANN) model which correlates thermal errors to temperature measurements. The predicting precision of ANN under new cutting conditions and measurement noise was also studied. Since most CNC controllers available today are not able to compensate for the Abbe offset induced errors and thermal errors in real time, a PC based compensation controller has been developed to upgrade commercial CNC controller for real-time error compensation. This scheme was implemented on a horizontal machining center equipped with a DynaPath Delta20 CNC controller and a series of tests were conducted to verify the effectiveness of this compensation scheme. SYNTHESIS OF GEOMETRIC AND THERMAL ERRORS
To compensate for machine errors, the positioning error of the cutting tool and workpiece at any location within the machine working zone must be identified first. One way is to measure directly the relative error between the cutting tool and workpiece across over the machine working zone and to express the errors as 3D error maps. Since the error map method is time-consuming in measurement and impractical for thermal error compensation, this research is to measure the geometric and thermal errors existing on machine linkages. Those linkage errors are then synthesized by a kinematic model which is built based on each specific machine configuration and is to calculate the corresponding positioning errors at the cutting edge caused by the geometric and thermal errors. The kinematic model has been developed by using the homogeneous coordinate transformation method which transforms the position and orientation of a rigid body in one coordinate frame to another coordinate frame. For example, assume that a movable x-axis slide with a coordinate frame B is moving on a machine base with a coordinate frame A (see Fig. 2). Then, under small angular error assumption, the coordinate of a point P fixed on the moving slide can be transformed into the coordinate frame A as
PA
=
TB =
T~PB ~, -13 0
(1) 1 a 0
--or 1 0
O,+80x+x+Sxoy+8oy+sy Oz+8Oz+Sz 1
'
FIG. 2. Homogeneous coordinate transformation.
(2)
596
JENQ-SHYONG CHEN
where T,~: homogeneous coordinate transformation matrix from frame A to frame B; x: travel of the moving slide; Ox, Oy, Oz: offset distances between the origins of frames B and A when x is zero; 8Ox, 8Or, 8Oz: drifts between the origins of frames B and A due to thermal error; 8x, By, 8z: translational errors of a slide deviating from its nominal movement and a, 13, ~/: rotational errors of a slide in the x, y and z axes. An important feature of the homogeneous coordinate transformation is that the coordinates of one object with respect to several different coordinate frames can be found by a series of multiplications as P i = T i •+ 1 • qpi+2 *i+l " ... •
TJ-IPj
(2)
•
As shown in Fig. 3, now consider the three slides of the machining center as an open kinematic chain of linkages. Assume that three local coordinate systems B, C and D are assigned and fixed to the three movable slides. Also, a global coordinate system A is assigned to the machine base. Then position vectors of the tool and workpiece after any movement can be transformed to the global coordinate A by using corresponding homogeneous coordinate transformation matrices. After the coordinate transformation, if there are no linkage errors, these two position vectors must be coincident. The linkage errors, however, will produce a relative positioning error between the cutting tool and workpiece. This error is then Ap
=
D
TAPtool
B
C
(4)
-- TATBPworkpiece
where AP: relative position error between cutting tool and workpiece Ptool: position vector of cutting edge at the cutting tool Pworkplcce: position vector of cutting edge at the workpiece B TB, C T,~: homogeneous coordinate transformation matrices. TA, Note that both the geometric and thermal errors of each machine linkage are encoded into the corresponding homogeneous coordinate transformation matrix and equation (4) is the kinematic model of the machining center which calculates the corresponding positioning error between the cutting tool and workpiece across over the machine working zone. For more information about the kinematic model see [3]. MEASUREMENT
OF GEOMETRIC
AND
THERMAL
ERRORS
A laser interferometer measurement system and an electronic differential level were used to measure machine linkage errors. Those errors include linear errors of feed
FIG. 3. C o n f i g u r a t i o n o f t h e m a c h i n i n g c e n t e r .
Computer-aided Accuracy Enhancement
~
597
0.10 1 0.06 f 0.08 0.04 o.o2 0.00 -0.02 o 2bo 4oo 6oo 8oo Travel along the x-axis (mm) •
•
•
•
•
FIG. 4. The positioning error of the x-axis.
mechanisms, straightness errors of guideways, angular errors of machine slides, outof-squareness errors among machine axes, thermal expansions of leadscrews, thermal bending of machine column and thermal drifts of the coordinate references of feed axes. To the thermal errors of spindle, five capacitance sensors were used to measure three translational drifts of the tool cutting edge at the x, y and z directions, and two angular inclination errors of the cutting tool axis. The measurement result shows that the positioning errors of the x-axis (90 Ixm of a 750 mm travel, Fig. 4) and the z-axis (157 i~m of a 500 mm travel) are far larger than the specifications (+_20 ~m) provided by the machine vendor• The angular errors of machine slides created by the heavy deadweight of the working table are mainly responsible for driving the machine out of specifications• The pitch angular errors of the working table with magnitudes of 12 arcsec (Fig. 5) and 46 arcsec were found in the x- and z-axes, respectively. Since the x- and z-axes slides of machine tools are stacked, pitch angular motions of the working table are amplified by the large Abbe offset length associated with this machine configuration. Most previous work related to error compensation either on machine tools or CMM adopted the kinematic rigid body assumption. This assumption implies that the geometric errors of each linkage depend only on its own coordinate and are not influenced by the movements of other linkages. That is, there are no coupling effects of linkage errors between machine slides. The large angular errors of the working table, however, imply that the rigidities of the foundation, machine structures and guideway systems are not sufficient to support the heavy deadweight of the working table and to keep deformations within permissible limits. This result is a warning signal that the stacked x- and z-axes may violate the kinematic rigid body assumption• Indeed the test result shows that the pitch errors of the x-axis were affected by the movement of the z-axis slide, Fig. 6. To the thermal errors, thermal expansions of leadscrews with magnitudes of 25, 120 and 40 p,m were found in the x-, y- and z-axes, respectively, after a 6 hr run. Thermal expansion of the z-axis also caused a 82 p,m drift at the coordinate reference of the z-axis. Translational thermal drifts of the spindle in all three directions were significant 10.
~ O
0
.~-10 -20 0 200 400 " 600 800 Travel along the x-axis (ram) FIG, 5. The pitch angular error of the x-axis.
598
JENQ-SHYONG CHEN
6
Z--0mm
'
.......
-2'
...............
__
".., \
ZdS00mm
.,
-6
0
!
I
!
200
400
600
800
Travel along the x-axis(ram) FIG. 6. The nonkinematic rigid body effect of the x-axis.
after a seven hour run with 1000 rpm (100, 60 and 20 t~m in the x, y and z directions). Thermal inclinations of the spindle axis were about 30 arcsec and 20 arcsec in the tiltup and lateral directions. The column was also subject to significant thermal bending which caused a 12 arcsec thermal variation in the pitch error of the y-axis and a 15 arcsec thermal variation in the y - z squareness• A 12 arcsec thermal variation of the yaw error in the y-axis was also found despite the fact that the machine structure is symmetric. Examining the temperature field of the machine structure, the column had a 4°C temperature gradient from the left-hand-side to the right-hand-side. The reason is that some heat sources of the machining center such as the hydraulic system and the power amplifiers of motors are clustered in the left-hand-side of the machine column. ON-LINE THERMAL ERROR PREDICTION
Precise and on-line prediction of dynamic thermal errors is a key step for accurate thermal error compensation. Since thermal errors exhibit highly nonlinear interaction [9], a precise quantitative prediction is difficult to achieve by using a theoretical heat transfer analysis. Quantitative prediction of thermal errors is usually achieved by empirical models which correlate machine thermal errors to temperature measurements through experiments and curve fitting techniques• One difficulty in establishing the empirical models of thermal errors is that the thermal drifts at the spindle cutting edge of a machining center with a C-shaped frame design are due to a combination of thermal distortions from several machine components with different thermal time constants• For example, the thermal distortions of the spindle, the thermal expansion of the leadscrew and the thermal bending of the machine column all contribute to the thermal drifts at the spindle cutting edge. Due to the difference in their heat capacities, the spindle heats up and cools down quickly but the column has a very sluggish response to generated heat. This makes the thermal drifts at the spindle cutting edge very sensitive to the spindle speed, feed speed and the temperature history (warm-up or cool-down status) as shown in Figs 7 and 8. 60 50 30 20 10 0
~ 2100 rpm •
a
100
•
!
200
•
!
300
•
!
400
500
Time (mm) FIG. 7. Spindle thermal drift (spindle speed effect).
Computer-aided Accuracy Enhancement
' f~=~ool_down 100"
I
599
~
" " ~ ' ~ * . ~ ,,.,.~. ~.~. J
0
!
0
200
•
!
400
•
!
•
600
!
800
l O00
Time(rain) FIG. 8. Spindle thermal drift (temperature history effect).
Therefore a multiple variable empirical model is necessary to include the thermal effects from the spindle, leadscrew, column and even the environment. In this research, the thermal errors have been predicted on line through a kind of artificial neural network (ANN) with multiple-layer feedforward architecture as shown in Fig. 9. Input layer is the input buffer of the temperature measurements and output layer is the output buffer of the predicted thermal errors. Layers between the input and output buffers are called hidden layers. The functions of the hidden layers are to perform feature extraction and noise suppression between the input temperature measurements and output thermal errors. Although there can be more than one hidden layer of a MLP, it has been proved that any nonlinear function between the inputs and outputs can be mapped with only one hidden layer if the number of nodes in the hidden layer is large enough. One of the features of the ANN is that it fits thermal errors and temperature measurements in a multiple-input and multiple-output approach which significantly reduces the tedious task on the established empirical thermal error models. For example, all of the five thermal errors (three translational drifts and two angular inclinations) at the spindle cutting edge can be predicted with only one ANN model. The nonlinear and interaction characteristics of the thermal errors were represented in the form of connected weights between neurons which were obtained through a supervised backpropagation training algorithm. Supervised training requires the training pairing of each input vector with a target vector representing the desired output. Usually a network is trained by a number of such training pairs. The training pairs should include all of the patterns of an application if possible. When an input vector is applied, the output of the network is calculated and compared with the corresponding target vector. The error between the network output and target is then fed back through the network to adjust the weights. The training will be iterated until the error of the entire training set reaches an acceptably low level. For more information about the ANN on thermal error modeling see [ 10]. Figure 10 shows the curve fitting result of the spindle thermal drifts in the z direction after training and it shows that the ANN can fit the thermal drifts very well. These training data were collected from five constant spindle speed tests at 600, 1000, 1500, 2100 and 2600 rpm. For each constant spindle speed test, the machining center was
ATI
~
81
AT2 •
52 •
o
ATn ~
•
~m input layer
hidden layer
ouput layer
FIG. 9. Three layer feedforward ANN for thermal error modeling.
600
JENQ-SHYONG
350300.
~
~
100-
CHEN
:1
experiment ANN
•
5o;
!
o: - 5 0 1 - 600rpm- " 1000rpm - " -,1500~. m-- " : .2100mm'_._L____.-• , i • | | 200 300 400 500 600 700 0 100 Data number
I
2600m. 800
FIG. 10. The curve fitting result of the spindle thermal drift in the z direction by ANN. 250 "~200 150
~,
5o e~
m
,
~=~
spindle speed
K° m experiment ANN
0 0" '2" '4" '6" '8" i0' I'2"14 Time (hour)
Fro. 11. Spindle thermal drift Az (1250 rpm). run continuously for 6 hr to warm-up and then stopped for 10 hr to allow the machine to cool down. In order to realize the performance of the ANN, a series of tests were conducted to verify the predicting precision under new cutting conditions and measurement noise. New observations of the spindle drift in the z direction were collected from two tests with new cutting conditions. For the first test, the spindle was run continuously at a constant spindle speed (1250 rpm) over 6.5 hr until thermally stable and then stopped for cooling down. The second type of test was a random spindle speed test. The machine was initially run with a constant spindle speed for 30 min and then stopped for 15 min. After that the machine was set at another spindle speed and the same test done again. The test was continuous over 8 hr and the changes of the spindle speed were selected randomly. Figures 11 and 12 show that the ANN can predict the new observations well under new or varying cutting conditions. The noise resistance robustness of the A N N was evaluated by adding a 0.4 C noise level at all temperature
~ 250
random spindle speed
~100
O'f' . 0
. . . . . . . 2 4 6 Time (hour)
8
FIG. 12. Spindle drift Az (random speed).
Computer-aided Accuracy Enhancement 250 _,
0
'2
_
601
spindle speed1 '4 '6 Time (hour)
'8
FIG. 13. The noise resistance robustness of the ANN. measurements during the 1250 rpm constant spindle speed test. Figure 13 shows the ANN can predict the spindle thermal growth well under the 0.4 C noise level. ERROR COMPENSATION SCHEME Most CNC controllers available today are not able to compensate for Abbe offset induced errors and thermal errors in real time. Therefore, a PC based compensation controller (see Fig. 14) has been developed to upgrade the commercial CNC controller for real-time error compensation. The positions of three machine slides are accessed through a quadrant encoder input and digital output board (Q/D board) which counts the encoder pulses and outputs the current slide coordinates in decimal format. Stationary geometric errors including the coupling effect of linakge errors are stored as data bank. Although these errors may be quite stationary over a period of time, they need to be periodically updated on a yearly basis to include the long-term variations of the machine wear, material stability and foundation. Dynamic thermal errors are predicted on line through ANN models and 23 thermocouples installed on the machine structures. These 23 thermocouples were scanned by a 16 bit A / D converter and updated at a sampling rate of every 2 s. Predicted thermal errors from the ANN models include thermal expansion of leadscrews, thermal drifts at spindle head, thermal variation of squareness errors, thermal drift of axis references and thermal bending (angular errors) of the machine structure and spindle. The system software of the compensation controller was written using a C language. The compensation controller sends compensation values in digital byte format to the PLC board of a CNC controller through a digital I/O port. The advantage of using the digital I/O technique is that the compensation scheme can be implemented on almost any CNC controllers without any hardware modification to the machine servodrive systems. The CNC controller will periodically fetch the compensation signal in
H ,
digitalVO] •
~1
[ thermocouples I
I
enc°der -- I fotxlback
signal
- data bank
PC
Delta 20T CNC c°ntr°Uer
FIG. 14. The block diagram of the error compensation scheme.
602
JENQ-SHYONG CHEN 0,30
befo•
°o:ol
:/o:1 0"00~0 -0.05
0.30 0.25
°n
1"00 200
300 40C
500 60C
Travel of z-axis (nun) (1) x=35mm, y=65mm
beforec ~
"~ o.20
~
m ns:,on
0.15 0.05 0.00 -0.05
ioo ~oc ~00 4"0o ~oc 600 Travel of z-axis (mm)
2 (2) x=640mm, y=385mm x
F~G. 15. The distance errors in the z-axis without and with compensation.
from the PLC's I/O port and then compensate for machine errors by shifting the coordinate origins of three axes. According to the execution speed of the PLC's software, the Delta20 controller can compensate for machine errors within 10 ms per cycle. However, the overall compensation speed may be delayed by the error calculation time, about 10 ms, taken by the 386-PC based compensation controller. In summary, the overall compensation rate of this scheme would be within 20 ms which is considered to be fast enough to compensate for the positioning errors caused by static geometric errors and quasistatic thermal effects in real time. EXPERIMENTAL RESULTS
The effectiveness of the error compensation scheme has been verified by a HP laser interferometer system in three categories: spatial-variant error compensation, dynamic thermal error compensation and nonkinematic rigid body compensation. The first test is for spatial-variant error compensation. In this test, the distance errors of the z-axis at two xz planes within the machine working zone were measured without and with compensation. The first xz plane is at y = 65 mm and the second xz plane is at y = 385 mm. For each plane, six lines distributing equally across the plane were tested. Notice that this test covers the position variations in all three axes. Let us single out one line from each plane for discussion. The maximum errors without compensation were 160 ~m at line 1 and 250 t~m at line 2 (Fig. 15). With compensation they were reduced to within a 10 Ixm range. Actually, the errors along all 12 lines were all within - 10 ~m after compensation compared with 160-250 ~m before compensation. To evaluate the dynamic thermal error compensation, the machine was run under a typical cutting cycle for 6 h. The distance errors of the y-axis were measured periodically with and without compensation. Figure 16 shows that without compensation the distance errors along the y-axis varied from - 3 5 ~m at cold-start to 110 txm after a
0.10
after 6 hour run
....
~0.05 o.oo
-
-
.oo,0L 100 200
300 400 500 600 Travel of y-axis (mm)
FIG. t6. Positioning errors of y-axis without compensation.
Computer-aided Accuracy Enhancement
603
0.15 0.10
~0.05 0.00 -0.05 0 - 10021)0-3()0 400- 5(10 600 Travel of y-axis (nun) FIG. 17, Positioning errors of y-axis with compensation. Y
FIG. 18. Arrangement for the non-rigid body effect compensation test. 120 . ^
I-*-line 1
Ioo I .-*- line 2 80.] -----line 3
0
,#'
Y " _ . ~
] / /
200 400 600 800 Travel along the x-axis (mm) Fro. 19. ~c before compensation.
0
200 400 600 800 Travel along the x-axis (mm)
Fio. 20. &x after compensation (using kinematic rigid body algorithm). 6 hr run due to the time-variant thermal effect. With compensation, machine errors have all been kept within _ 10 ~m for the entire 6 hr run (Fig. 17). To evaluate the compensation for non-rigid body kinematic effect, four lines (see Fig. 18) across the machine working zone have been tested. Figure 19 shows that the distance errors along these four lines vary from 70 to 115 t~m before compensation. The errors were compensated for first by an algorithm which adopts the traditional rigid body kinematic assumption. Figure 20 shows that the error magnitudes after
604
JENQ-SHYONGCHEN
-1°1 0
, 200
."°-, linel4 , 460 660
/ 800
Travel along the x-axis (mm) FIG. 21. Ax after compensation (using nonkinematic rigid body algorithm). 1
Axl
uncompensated
4
I
I
Ay~
I ay2
% Ax2
3
xl=x2--41Onun,yl=y2=304mm, ~1=~2=~3=~4=90
compensated
Axl (~tm) Ax2 (gin) Ayl (l~m)
28.9 30.9 92.3
-18.9/4.8" -16.8 / 6.1" 0.2
Ay2 (lain) AB1 (arcsec)
92.4 7.4
7.2 2.2
AB2 (arcsec)
-7.4
1.4
A83 (arcsec)
8.7
2.3
A54(arcsec)
-8.7
-1.5
* after correction of non-kinematic-rigid body effect
FIG. 22. The dimensional errors without and with compensation (after 8 hr run). compensation were between 10 and - 3 0 p,m. Notice that the errors on line 2 and line 4 were overcompensated due to the non-rigid body kinematic effect. The test was repeated but using the proposed non-rigid body approach for the pitch errors of the x-axis. The result shows that the errors at these four lines were all kept within --- 10 I~m (see Fig. 21). The effectiveness of the error compensation scheme has also been verified by cutting tests. Two kinds of machining jobs were evaluated on an aluminum workpiece. First, several holes were made under cold start and after an 8 hr run. This is to evaluate the effectiveness of the compensation in the x-axis and the y-axis. Second, several strip-like surfaces were milled under cold start and after an 8 hr run. The depth difference of the milled surface was used to evaluate the compensation in the spindle growth (in the z-axis of the machine). The cut workpiece was inspected using a Sheffield Cordax CMM. The results shows that the maximum positioning errors of these holes were reduced from 92.4 to 18.9 ~xm (Fig. 22) in a dimension of 404 x 310 mm 2 and can be further improved to 6.1 fxm after correction of the nonkinematic rigid body effect. Also notice that the squareness errors of the workpiece were improved from 8.7 arcsec to 2.3 arcsec. The difference of these milled surfaces was reduced from 196 to 8 I~m (Fig. 23).
cold~
196gm
afterthe8
IT
h°ur mn
uncompensated
I
coldk~87 compensated
I
FIG. 23. The surface jumps without and with compensation.
h°"rmn
Computer-aided Accuracy Enhancement
605
CONCLUSIONS
Enhancing the machine accuracy through computer-aided error compensation has gained much attention recently in response to the increasing demand for higher machining precision and product quality. Techniques have evolved from simple backlash mwl ieadscrew pitch value compensation of a leadscrew to the straightness error compensation of a guideway and squareness error compensation between feed axes. Commercialized spindle thermal growth compensation is also available now. The research has demonstrated that with the aid of a PC, the angular errors of machine slides, thermal expansion of leadscrews, thermal drifts of spindle cutting edge, thermal inclinations of the cutting tool axis and thermal bendings of machine column can also be compensated for. The efficiency of this computer-aided error compensation scheme has been proved. Test result shows that the accuracy of a horizontal machining center has been improved by one order of magnitude after compensation. Dimension errors of a cut part were reduced from 92.4 to 18.9 o,m in a dimension of 404 x 310 mm 2 and the depth difference of milled surfaces was reduced from 196 to 8 ~m. REFERENCES [1] J. B. BXYAI~,International status of thermal error research, Ann. CIRP 16(1), 203 (1968). [2] M. AmAs^rPA et al., Error correction methodologies and control strategies for numerical control machine, Control Methods for Manufacturing Process, DSC-Vol. 7 (1988). [3] JENQ-SHvoSG CnEN, Real-time compensation of time-variant volumetric error on a machining center, Ph.D. Dissertation, University of Michigan (1991). [4] M. A. DONMEZ et al., A general methodology for machine tool accuracy enhancement by error compensation, Precision Engng 8(4) (1986). [5] K. C. FAr~, J. F. LIs and S. S. Lu, Measurement and compensation of thermal error on a machining center, Proc. 29th Int. M A T A D O R Conf., England (1992). [6] J. JANECZKO,Machine tool thermal distortion compensation, Report from 4th Biennial Int. Mach. Tool Technol. Conf. (1988). [7] KURTOGLU,The accuracy improvement of machine tools, Ann. CIRP 39(1) (1990). [8] M, A. WovTowrrz et al., Tool path error analysis for high precision milling with a magnetic bearing spindle, Trans. ASME 129-142 (1989). [9] M. H. ATn^ and L. Kovs, Nonlinear thermoelastic behavior of structural joints--solution to a missing link for prediction of thermal deformation of machine tools, Trans. A S M E J. Engng Ind. 101 (1979). [10] J. S. CnEN, J. X. YuA~, J. NI and S. M. Wu, Thermal error modeling for volumetric error compensation, ASME Winter Annual Meeting (1992).
35-4°H
