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A four-degrees-of-freedom microstage for the compensation of eccentricity of a roundness measurement machine
International Journal of Machine Tools & Manufacture 44 (2004) 365–371 www.elsevier.com/locate/ijmatool
A four-degrees-of-freedom microstage for the compensation of eccentricity of a roundness measurement machine Chien Hung Liu a, Wen-Yuh Jywe b, a
b
Institute of Mechtronoptic Systems, Chienkuo Institute of Technology, Changhua, Taiwan, ROC Department of Automation Engineering, National Huwei Institute of Technology, Huwei, Yunlin 632, Taiwan, ROC Received 24 September 2003; received in revised form 2 October 2003; accepted 15 October 2003
Abstract This paper contains a description of four-degrees-of-freedom microstage, designed to replace manual adjustment mechanism in a roundness measurement machine for the compensation of eccentricity. Four-degrees-of-freedom motion (two-translational and two-rotational motion) was obtained by four piezoelectric actuators that were set up on the same plane to minimize the effect of the abbe’s offset. The microstage was fixed on a rotary table to compensate not only for the x- and y-position errors, but also for the angle errors about the x- and y-axis. Repeatability, calibration and experimental tests were carried out and the results showed the proposed design was easy to assemble for most types of roundness test machines and had sufficient capability to compensate for the eccentricity. # 2003 Elsevier Ltd. All rights reserved. Keywords: Roundness test machine; Eccentricity; Microstage; PZT; Self-compensation
1. Introduction For a roundness test to minimize measurement error, the rotary table should be adjusted to be horizontal and the relative centerline between the workpiece and rotary table should be adjusted to be concentric. These steps are normally carried out by a manual adjustment mechanism (the ball-screw driving mechanism). At the beginning of a roundness test, a larger working range probe has to be selected first for an initial test to obtain a rough eccentricity. Then, the manual adjustment mechanism is used to compensate for the eccentricity by manually adjusting the ball-screw driving mechanism to move the rotary table or the workpiece. Various probes with different measurement ranges and resolutions are selected for different measurement precision requirements. In general, the probe with the smaller measurement range can provide higher resolution but a small offset between the probe and workpiece is required. The selection of a proper probe is
Corresponding author. Tel.: +886-5-6335195; fax: +886-5-6331211. E-mail address: [email protected] (W.-Y. Jywe).
0890-6955/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2003.10.025
always determined by the eccentricity between the centerline of the workpiece and the rotary table, and the measuring range of the probe. Although manual adjustment can compensate for rough eccentricity, the compensated values cannot achieve the micrometer level and may often result in the worst results. Piezoelectric actuators have been widely used as actuators to produce the microdisplacement [1–3]. Jouaneh and colleagues [4] employed a piezoelectric actuator to provide a single axis movement for a laser welding application. James Li and Li [5] improved workpiece roundness by using a piezoelectric micropositioning controller. Moreover, high precision micropositioners are required to provide the motion in nanometer scales using piezoelectric devices [6,7]. In this paper, the design development of an automaticadjustment four-degrees-of-freedom microstage for the compensation of eccentricity during the roundness measurement is described. Four piezoelectric actuators were set up on the same plane to minimize the effect of the abbe’s offset and were used as the drivers to move and rotate the stage. Two of them provide the translational displacement and the others provide the
366
C.H. Liu, W.-Y. Jywe / International Journal of Machine Tools & Manufacture 44 (2004) 365–371
rotational displacement. This microstage was used as an automatic eccentricity compensation mechanism to improve the precision of a roundness machine. It can easily be fixed on the table of any roundness test machine and the four-degrees-of-motion (two-translational displacement and two-rotational displacement) can automatically compensate for the x- and y-axial eccentricity and rotate the rotary table (or the central line of a cylindrical workpiece) to meet the horizontal (or vertical) level. 2. Design of the four-degrees-of-freedom microstage A schematic of the tower fixture base of the microstage is shown in Fig. 1. Four piezoelectric actuators are set on the same plane to minimize the thickness of this compensator and provide two-translational and two-rotational motions. These piezoelectric actuators are driven by an amplifier (0–1000 DCV), which is controlled by a PC with a D/A interface card. Fig. 2 shows the assembled structure of the microstage and Fig. 3 shows two structures, the upper cover and the lower fixture base, of the microstage. As shown in Fig. 3, the main parts in microstage are composed of four piezoelectric actuators, a double T-slot with two slide blocks, two angular offset blocks, one master ball on the lower fixture and two master balls on the upper cover. The actuators, named piezo 1 and piezo 4, elongate/shorten their lengths to provide the x- and
Fig. 1. cover.
The structure of the microstage mechanism without upper
Fig. 2.
The assembly diagram of the compensator mechanism.
y-translational motion. A double T-slot block with two slide blocks, shown in Figs. 3 and 4, is designed to avoid the effect of shear stress between the piezo 1 and piezo 4 actuators. Piezo 1 and piezo 4 actuators are connected with two slide blocks, respectively. When the piezo 1 elongates/shortens its length, the slide block will avoid the effect of shear stress on piezo 4. A master ball is machined on the top of the T-slot block and is well assembled with a ball socket machined on the upper cover. The actuators change their lengths to move the master ball of the T-slot block and transfer the translational movements to the upper cover. The actuators, named piezo 2 and piezo 3, elongate/shorten their lengths to provide the angular motion about xand y-axis. Two other designed master balls, machined on the upper cover which is in good contact with the two angular offset motion blocks on the lower fixture base, ensure the transfer of translational motion to rotational motion from the lower fixture base to the upper cover. Fig. 5 shows the angular error compensation method on piezo 3 side, and the same occurs on the piezo 2 side. The actuators change their lengths to move two angular offset motion blocks and the motion is transferred to the upper cover via the master ball to provide x- and y-rotational motion. By the movement described above, the upper cover of the microstage
C.H. Liu, W.-Y. Jywe / International Journal of Machine Tools & Manufacture 44 (2004) 365–371
Fig. 3.
Photograph of the upper cover and lower fixture base of the four-degrees-of-freedom microstage.
carries the workpiece to do the four-degrees-of-motion. Because of the effect of abbe’s offset, the design of the four-degrees-of-freedom microstage was arranged in a single layer plane to reduce the height and weight of the total measuring device. In the actual application, this compensator mechanism (four-degrees-of-freedom microstage) is easily fixed on the top of a rotary table and can be applied to most types of roundness test machines. 3. The relation between the microstage and rotary table Fig. 6 shows the error components of a rotary table without consideration of the abbe’s offset. There are three linear positioning errors: x-axis (dx ðhÞ), y-axis (dy ðhÞ) and z-axis (dz ðhÞ) and angular errors ex ðhÞ, ey ðhÞ and ez ðhÞ. For the compensation of eccentricity of a
roundness test machine, the positioning errors in the x-axis (dx ðhÞ) and y-axis (dy ðhÞ) and the angular errors (ex ðhÞ and ey ðhÞ) have to be considered. Let the {T}-coordinate system be embedded in the center of the rotary table of the roundness test machine and the {C}-coordinate system be embedded in the center of the cover of the microstage. The relation between the {T}- and {C}-coordinate systems is shown Fig. 7. Let pm be the vector of the elongational displacement of the piezoelectric actuator, i.e. pm ¼ ½ p1 p4 p2 p3 T . Let xm ¼ ½ xm ym be the translational value and am ¼ ½ am bm be the tilt error along the x- and the y-axes, respectively, in the {C}-coordinate system. Then, the relation between pm, xm and am can be shown as follows:
xm ym
1 ¼ 0
0 1
p3 tanw1 l1 p tanw 4 2 bm ¼ tan1 l2
am ¼ tan1
Fig. 4.
367
Photograph of the double T-slot block.
p1 p4
ð1Þ ð2Þ ð3Þ
Fig. 5. The angular error compensation method on piezo 3 side.
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and the designed parameters in this paper are w1 ¼ w2 ¼ 45
v
l1 ¼ l2 h ¼ 0; the relation between pm, x and a is x 1 0 p1 ¼ y 0 1 p4 p 3 a ¼ tan1 l1 p4 b ¼ tan1 l1 Fig. 6. The error components of a rotary table.
ð5Þ ð6Þ ð7Þ
4. The performance test of the microstage 4.1. Drift (repeatability) test results of the microstage
As shown in Fig. 5 where wi (i ¼ 1 2) is the angle of angular offset motion blocks, li (i ¼ 1 2) is the distance between the centers of two balls. Suppose x ¼ ½ x y is the eccentricity value and a ¼ ½ a b is the tilt error in the {T}-coordinate system. As shown in Fig. 7, the relation of coordinate transformation between x and xm can be obtained as x cosh sinh xm ¼~ r0 þ ð4Þ y ym sinh cosh where h is the angle orientation between the {T}-coordinate system and {C}-coordinate system. The vector ~ r0 ¼ ½xC ; yC is the position vector between points T and C in {T}-coordinate system. Because the eccentricity value obtained is in the {T}-coordinate system
Fig. 7. Relation between the {T}- and {C}-coordinate system.
It is of importance to calibrate the performance of the microstage before it is employed for any application. Therefore, a laser interferometer (HP5529) was set up to check the drift of the microstage. The variation output was monitored and the results are shown in Fig. 8. It was found that the actuator of the microstage needed at least 15 min to warm up. After warming up, the drift could be maintained at less than 0.2 lm in the x-axis, y-axis or z-axis. Thus, the drift (repeatability) test results prove the effectiveness of the application of the microstage for eccentricity compensation in a roundness test. 4.2. Calibration of the microstage The microstage was calibrated with the HP5529A laser interferometer throughout its possible working ranges and applied input voltages. The input voltage was set from 0 to 700 V. The output in each of the axes of the microstage was at a range of about 0–53 lm. Fig. 9 shows the calibrated results in the x-axis. It was found that the hysteresis effect, which occurs while
Fig. 8. Drift test for piezoelectric actuator of the compensator mechanism.
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369
applied without any problem. To obtain high precision measurement results, probes with smallest possible working range are generally employed. A probe with a long working range was employed for an initial test to obtain the eccentricity between the center of the workpiece and the center of the rotary table of the roundness test machine. Then, the microstage, set on the top of the rotary table, was employed to compensate for the eccentricity. The flowchart of the compensation procedure is shown in Fig. 11. The small movements in the x-axis and y-axis and two rotational angles are of micrometer dimension, which cannot be executed by a general Fig. 9.
Calibration results for the microstage.
sampling the same nominal target at different sampling directions, causes a dead zone in the output. The data of the relative results can be recorded in the database for the compensation of eccentricity for an open loop control system. 4.3. Loading test of the microstage For the application of the compensation of eccentricity on a roundness test, the loading capability of the microstage should be at a range of the weight of a general tested part. Thus, a loading performance test was carried out. Four test parts, weighing from 2 to 10 kg, were loaded on the microstage within a range of 100– 900 V driving force. The average results of the loading tests for several runs in the x-axis were shown in Fig. 10. The data of the relative results can be recorded in the database for the compensation of eccentricity. 5. Experimental tests for the compensation of eccentricity in a roundness test In the actual application, the compensation microstage is set on the rotary table. For most types of roundness test machines, this mechanism can be
Fig. 10. The loading test result of the compensator mechanism.
Fig. 11. The flowchart of the compensation procedure for eccentricity.
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ball-screw driving mechanism like the manual adjustment mechanism. 5.1. Off-line error separation calculation method As shown in Fig. 12, a simple measurement device is set up to measure the error components of the rotary table. A position sensitivity detector with an associated fixture is set on the rotary table while a laser diode is set on its top, supported by a fixture. During the test, the quadrant sensor is carried with the rotary table. The unideal movement of the rotary table makes the laser diode project the laser light on different positions of the quadrant sensor. Thus, the quadrant sensor can collect the movement by outputting the 2-D positioning signal. The obtained error components of the rotary table can be further used to separate the error components obtained via real workpiece measurement. As seen in Fig. 12, in order to obtain the same error signals of the rotary spindle from a position sensitivity detector and probe, the heights h1 and h2 should be the same. This off-line method can be employed for the error separation of the workpiece and rotary spindle if good repeatability of the rotary table is found. The data sampled by the probe can be expressed by the following equation: Sp ðhÞ ¼ Ec ðhÞ þ Ew ðhÞ þ Er ðhÞ þ Eabbe ðhÞ
ð8Þ
where Sp(h) is the sampled data of the probe, ec(h) is the eccentricity between the workpiece and the rotary table, ew(h) is the error produced by the rotary table (obtained via a quadrant sensor), er(h) is the error of the workpiece, eabbe(h) is the error due to abbe’s offset. The sampled data of the probe can be obtained via A/D card and computer. The eccentricity between the centerline of the workpiece and the centerline of the rotary table can be analyzed by the minimum zone technique provided by Jywe et al. [8]. The rotary table error can be pre-measured via the quadrant sensor outputs.
The error due to abbe’s offset is normally not considered for this application because only out-of-roundness is under consideration (the radius error is not considered). The out-of-roundness is defined as the minimum error band between the maximum and minimum circles, of which sampled data are included. The radius error is defined as the error between the nominal radius and the analyzed radius by the least square fitting or minimum zone technique. In this application, due to the rotary table, errors were pre-measured via the quadrant sensor outputs, the individual errors of the workpiece can be separated from the total sampled data. 5.2. The experimental results of the test First of all, the microstage was used to adjust the horizontal level of the table using the tilt angle compensation. The tilt angle compensation can also be used to compensate the centerline of the workpiece, especially for cylindricity measurement. Then, a round part was set on the stage. A probe with a long working range was selected for an initial test. The measurement result is shown in Fig. 13(a). A large eccentricity (5 lm, 32 lm) was obtained. After compensating the eccentricity using the microstage, a high precision probe with a small working range was selected for more precise measurement. The measurement result is shown in Fig. 13(b). The eccentricity (1.2 lm, 2.8 lm) shows a sufficient improvement using the microstage. Fig. 14 shows the measuring result of rotary table errors using a laser diode and a position sensitivity detector. For the off-line error separation method, the rotary table errors (Fig. 14, obtained from the position sensitivity detector) can be separated from the measurement result (Fig. 13, obtained from probe) to obtain the real error of the workpiece. Fig. 15 shows the final result with the roundness of workpiece being 6.7 lm.
6. Conclusion
Fig. 12. The set up to measure the error of the rotary table.
In the roundness measurement, the difficulty of microadjustment at micrometer level is overcome in this paper by the designed automatic adjustment microstage. The four-degrees-of-motion (two-translational displacement and two-rotational displacement) can automatically compensate for the x- and y-axial eccentricity and rotate the rotary table or the central line of a cylindrical workpiece to meet the horizontal or vertical level. The automatic adjustment microstage can replace manual adjustment mechanism (the ballscrew driving mechanism) and can be applied to most roundness measurement machines.
C.H. Liu, W.-Y. Jywe / International Journal of Machine Tools & Manufacture 44 (2004) 365–371
371
Fig. 15. Roundness test result using the off-line error separation method.
Acknowledgements The work was supported by the National Science Council, Taiwan, Republic of China (Number NSC-892212-E-150-037).
References
Fig. 13. Roundness measurement result.
Fig. 14. Spindle error measured using a laser diode and a position sensitivity detector.
[1] H. Goto, T. Sasaoka, Vertical micro positioning system using PZT actuator, Bull. Japan Soc. Prec. Eng. 22 (1988) 277–283. [2] M. Taniguchi, M. Ikeda, A. Inagaki, R. Funatsu, Ultra precision wafer positioning by six-axis micro-motion mechanism, Int. J. Japan Soc. Prec. Eng. 26 (1992) 35–40. [3] N. Henmi, K. Sato, S. Wada, A. Shimikohbe, A six degrees of freedom fine motion mechanism, Mechatronics 2 (1992) 445–457. [4] R. Yang, M. Jouaneh, R. Schweizert, Design and characterization of a low-profile micropositioning stage, Prec. Eng. 18 (1) (1996) 20–29. [5] C. James Li, S.Y. Li, To improve work-piece roundness in precision diamond turning by in-situ measurement of a control, Mechatronics 6 (1996) 523–535. [6] A.R. Smith, S. Gwo, C.K. Shih, A new high-resolution twodimensional micropositioning device for scanning probe microscopy applications, Rev. Sci. Instrum. 65 (1994) 2252–2254. [7] C.W. Lee, S.W. Kim, An ultraprecision stage for alignment of wafers in advanced microlithography, Prec. Eng. 21 (1997) 113– 122. [8] W.Y. Jywe, C.H. Liu, C.K. Chen, The min–max problem for evaluating the form error of a circle, Measurement 26 (1999) 273– 282.
A four-degrees-of-freedom microstage for the compensation of eccentricity of a roundness measurement machine Chien Hung Liu a, Wen-Yuh Jywe b, a
b
Institute of Mechtronoptic Systems, Chienkuo Institute of Technology, Changhua, Taiwan, ROC Department of Automation Engineering, National Huwei Institute of Technology, Huwei, Yunlin 632, Taiwan, ROC Received 24 September 2003; received in revised form 2 October 2003; accepted 15 October 2003
Abstract This paper contains a description of four-degrees-of-freedom microstage, designed to replace manual adjustment mechanism in a roundness measurement machine for the compensation of eccentricity. Four-degrees-of-freedom motion (two-translational and two-rotational motion) was obtained by four piezoelectric actuators that were set up on the same plane to minimize the effect of the abbe’s offset. The microstage was fixed on a rotary table to compensate not only for the x- and y-position errors, but also for the angle errors about the x- and y-axis. Repeatability, calibration and experimental tests were carried out and the results showed the proposed design was easy to assemble for most types of roundness test machines and had sufficient capability to compensate for the eccentricity. # 2003 Elsevier Ltd. All rights reserved. Keywords: Roundness test machine; Eccentricity; Microstage; PZT; Self-compensation
1. Introduction For a roundness test to minimize measurement error, the rotary table should be adjusted to be horizontal and the relative centerline between the workpiece and rotary table should be adjusted to be concentric. These steps are normally carried out by a manual adjustment mechanism (the ball-screw driving mechanism). At the beginning of a roundness test, a larger working range probe has to be selected first for an initial test to obtain a rough eccentricity. Then, the manual adjustment mechanism is used to compensate for the eccentricity by manually adjusting the ball-screw driving mechanism to move the rotary table or the workpiece. Various probes with different measurement ranges and resolutions are selected for different measurement precision requirements. In general, the probe with the smaller measurement range can provide higher resolution but a small offset between the probe and workpiece is required. The selection of a proper probe is
Corresponding author. Tel.: +886-5-6335195; fax: +886-5-6331211. E-mail address: [email protected] (W.-Y. Jywe).
0890-6955/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2003.10.025
always determined by the eccentricity between the centerline of the workpiece and the rotary table, and the measuring range of the probe. Although manual adjustment can compensate for rough eccentricity, the compensated values cannot achieve the micrometer level and may often result in the worst results. Piezoelectric actuators have been widely used as actuators to produce the microdisplacement [1–3]. Jouaneh and colleagues [4] employed a piezoelectric actuator to provide a single axis movement for a laser welding application. James Li and Li [5] improved workpiece roundness by using a piezoelectric micropositioning controller. Moreover, high precision micropositioners are required to provide the motion in nanometer scales using piezoelectric devices [6,7]. In this paper, the design development of an automaticadjustment four-degrees-of-freedom microstage for the compensation of eccentricity during the roundness measurement is described. Four piezoelectric actuators were set up on the same plane to minimize the effect of the abbe’s offset and were used as the drivers to move and rotate the stage. Two of them provide the translational displacement and the others provide the
366
C.H. Liu, W.-Y. Jywe / International Journal of Machine Tools & Manufacture 44 (2004) 365–371
rotational displacement. This microstage was used as an automatic eccentricity compensation mechanism to improve the precision of a roundness machine. It can easily be fixed on the table of any roundness test machine and the four-degrees-of-motion (two-translational displacement and two-rotational displacement) can automatically compensate for the x- and y-axial eccentricity and rotate the rotary table (or the central line of a cylindrical workpiece) to meet the horizontal (or vertical) level. 2. Design of the four-degrees-of-freedom microstage A schematic of the tower fixture base of the microstage is shown in Fig. 1. Four piezoelectric actuators are set on the same plane to minimize the thickness of this compensator and provide two-translational and two-rotational motions. These piezoelectric actuators are driven by an amplifier (0–1000 DCV), which is controlled by a PC with a D/A interface card. Fig. 2 shows the assembled structure of the microstage and Fig. 3 shows two structures, the upper cover and the lower fixture base, of the microstage. As shown in Fig. 3, the main parts in microstage are composed of four piezoelectric actuators, a double T-slot with two slide blocks, two angular offset blocks, one master ball on the lower fixture and two master balls on the upper cover. The actuators, named piezo 1 and piezo 4, elongate/shorten their lengths to provide the x- and
Fig. 1. cover.
The structure of the microstage mechanism without upper
Fig. 2.
The assembly diagram of the compensator mechanism.
y-translational motion. A double T-slot block with two slide blocks, shown in Figs. 3 and 4, is designed to avoid the effect of shear stress between the piezo 1 and piezo 4 actuators. Piezo 1 and piezo 4 actuators are connected with two slide blocks, respectively. When the piezo 1 elongates/shortens its length, the slide block will avoid the effect of shear stress on piezo 4. A master ball is machined on the top of the T-slot block and is well assembled with a ball socket machined on the upper cover. The actuators change their lengths to move the master ball of the T-slot block and transfer the translational movements to the upper cover. The actuators, named piezo 2 and piezo 3, elongate/shorten their lengths to provide the angular motion about xand y-axis. Two other designed master balls, machined on the upper cover which is in good contact with the two angular offset motion blocks on the lower fixture base, ensure the transfer of translational motion to rotational motion from the lower fixture base to the upper cover. Fig. 5 shows the angular error compensation method on piezo 3 side, and the same occurs on the piezo 2 side. The actuators change their lengths to move two angular offset motion blocks and the motion is transferred to the upper cover via the master ball to provide x- and y-rotational motion. By the movement described above, the upper cover of the microstage
C.H. Liu, W.-Y. Jywe / International Journal of Machine Tools & Manufacture 44 (2004) 365–371
Fig. 3.
Photograph of the upper cover and lower fixture base of the four-degrees-of-freedom microstage.
carries the workpiece to do the four-degrees-of-motion. Because of the effect of abbe’s offset, the design of the four-degrees-of-freedom microstage was arranged in a single layer plane to reduce the height and weight of the total measuring device. In the actual application, this compensator mechanism (four-degrees-of-freedom microstage) is easily fixed on the top of a rotary table and can be applied to most types of roundness test machines. 3. The relation between the microstage and rotary table Fig. 6 shows the error components of a rotary table without consideration of the abbe’s offset. There are three linear positioning errors: x-axis (dx ðhÞ), y-axis (dy ðhÞ) and z-axis (dz ðhÞ) and angular errors ex ðhÞ, ey ðhÞ and ez ðhÞ. For the compensation of eccentricity of a
roundness test machine, the positioning errors in the x-axis (dx ðhÞ) and y-axis (dy ðhÞ) and the angular errors (ex ðhÞ and ey ðhÞ) have to be considered. Let the {T}-coordinate system be embedded in the center of the rotary table of the roundness test machine and the {C}-coordinate system be embedded in the center of the cover of the microstage. The relation between the {T}- and {C}-coordinate systems is shown Fig. 7. Let pm be the vector of the elongational displacement of the piezoelectric actuator, i.e. pm ¼ ½ p1 p4 p2 p3 T . Let xm ¼ ½ xm ym be the translational value and am ¼ ½ am bm be the tilt error along the x- and the y-axes, respectively, in the {C}-coordinate system. Then, the relation between pm, xm and am can be shown as follows:
xm ym
1 ¼ 0
0 1
p3 tanw1 l1 p tanw 4 2 bm ¼ tan1 l2
am ¼ tan1
Fig. 4.
367
Photograph of the double T-slot block.
p1 p4
ð1Þ ð2Þ ð3Þ
Fig. 5. The angular error compensation method on piezo 3 side.
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and the designed parameters in this paper are w1 ¼ w2 ¼ 45
v
l1 ¼ l2 h ¼ 0; the relation between pm, x and a is x 1 0 p1 ¼ y 0 1 p4 p 3 a ¼ tan1 l1 p4 b ¼ tan1 l1 Fig. 6. The error components of a rotary table.
ð5Þ ð6Þ ð7Þ
4. The performance test of the microstage 4.1. Drift (repeatability) test results of the microstage
As shown in Fig. 5 where wi (i ¼ 1 2) is the angle of angular offset motion blocks, li (i ¼ 1 2) is the distance between the centers of two balls. Suppose x ¼ ½ x y is the eccentricity value and a ¼ ½ a b is the tilt error in the {T}-coordinate system. As shown in Fig. 7, the relation of coordinate transformation between x and xm can be obtained as x cosh sinh xm ¼~ r0 þ ð4Þ y ym sinh cosh where h is the angle orientation between the {T}-coordinate system and {C}-coordinate system. The vector ~ r0 ¼ ½xC ; yC is the position vector between points T and C in {T}-coordinate system. Because the eccentricity value obtained is in the {T}-coordinate system
Fig. 7. Relation between the {T}- and {C}-coordinate system.
It is of importance to calibrate the performance of the microstage before it is employed for any application. Therefore, a laser interferometer (HP5529) was set up to check the drift of the microstage. The variation output was monitored and the results are shown in Fig. 8. It was found that the actuator of the microstage needed at least 15 min to warm up. After warming up, the drift could be maintained at less than 0.2 lm in the x-axis, y-axis or z-axis. Thus, the drift (repeatability) test results prove the effectiveness of the application of the microstage for eccentricity compensation in a roundness test. 4.2. Calibration of the microstage The microstage was calibrated with the HP5529A laser interferometer throughout its possible working ranges and applied input voltages. The input voltage was set from 0 to 700 V. The output in each of the axes of the microstage was at a range of about 0–53 lm. Fig. 9 shows the calibrated results in the x-axis. It was found that the hysteresis effect, which occurs while
Fig. 8. Drift test for piezoelectric actuator of the compensator mechanism.
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369
applied without any problem. To obtain high precision measurement results, probes with smallest possible working range are generally employed. A probe with a long working range was employed for an initial test to obtain the eccentricity between the center of the workpiece and the center of the rotary table of the roundness test machine. Then, the microstage, set on the top of the rotary table, was employed to compensate for the eccentricity. The flowchart of the compensation procedure is shown in Fig. 11. The small movements in the x-axis and y-axis and two rotational angles are of micrometer dimension, which cannot be executed by a general Fig. 9.
Calibration results for the microstage.
sampling the same nominal target at different sampling directions, causes a dead zone in the output. The data of the relative results can be recorded in the database for the compensation of eccentricity for an open loop control system. 4.3. Loading test of the microstage For the application of the compensation of eccentricity on a roundness test, the loading capability of the microstage should be at a range of the weight of a general tested part. Thus, a loading performance test was carried out. Four test parts, weighing from 2 to 10 kg, were loaded on the microstage within a range of 100– 900 V driving force. The average results of the loading tests for several runs in the x-axis were shown in Fig. 10. The data of the relative results can be recorded in the database for the compensation of eccentricity. 5. Experimental tests for the compensation of eccentricity in a roundness test In the actual application, the compensation microstage is set on the rotary table. For most types of roundness test machines, this mechanism can be
Fig. 10. The loading test result of the compensator mechanism.
Fig. 11. The flowchart of the compensation procedure for eccentricity.
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ball-screw driving mechanism like the manual adjustment mechanism. 5.1. Off-line error separation calculation method As shown in Fig. 12, a simple measurement device is set up to measure the error components of the rotary table. A position sensitivity detector with an associated fixture is set on the rotary table while a laser diode is set on its top, supported by a fixture. During the test, the quadrant sensor is carried with the rotary table. The unideal movement of the rotary table makes the laser diode project the laser light on different positions of the quadrant sensor. Thus, the quadrant sensor can collect the movement by outputting the 2-D positioning signal. The obtained error components of the rotary table can be further used to separate the error components obtained via real workpiece measurement. As seen in Fig. 12, in order to obtain the same error signals of the rotary spindle from a position sensitivity detector and probe, the heights h1 and h2 should be the same. This off-line method can be employed for the error separation of the workpiece and rotary spindle if good repeatability of the rotary table is found. The data sampled by the probe can be expressed by the following equation: Sp ðhÞ ¼ Ec ðhÞ þ Ew ðhÞ þ Er ðhÞ þ Eabbe ðhÞ
ð8Þ
where Sp(h) is the sampled data of the probe, ec(h) is the eccentricity between the workpiece and the rotary table, ew(h) is the error produced by the rotary table (obtained via a quadrant sensor), er(h) is the error of the workpiece, eabbe(h) is the error due to abbe’s offset. The sampled data of the probe can be obtained via A/D card and computer. The eccentricity between the centerline of the workpiece and the centerline of the rotary table can be analyzed by the minimum zone technique provided by Jywe et al. [8]. The rotary table error can be pre-measured via the quadrant sensor outputs.
The error due to abbe’s offset is normally not considered for this application because only out-of-roundness is under consideration (the radius error is not considered). The out-of-roundness is defined as the minimum error band between the maximum and minimum circles, of which sampled data are included. The radius error is defined as the error between the nominal radius and the analyzed radius by the least square fitting or minimum zone technique. In this application, due to the rotary table, errors were pre-measured via the quadrant sensor outputs, the individual errors of the workpiece can be separated from the total sampled data. 5.2. The experimental results of the test First of all, the microstage was used to adjust the horizontal level of the table using the tilt angle compensation. The tilt angle compensation can also be used to compensate the centerline of the workpiece, especially for cylindricity measurement. Then, a round part was set on the stage. A probe with a long working range was selected for an initial test. The measurement result is shown in Fig. 13(a). A large eccentricity (5 lm, 32 lm) was obtained. After compensating the eccentricity using the microstage, a high precision probe with a small working range was selected for more precise measurement. The measurement result is shown in Fig. 13(b). The eccentricity (1.2 lm, 2.8 lm) shows a sufficient improvement using the microstage. Fig. 14 shows the measuring result of rotary table errors using a laser diode and a position sensitivity detector. For the off-line error separation method, the rotary table errors (Fig. 14, obtained from the position sensitivity detector) can be separated from the measurement result (Fig. 13, obtained from probe) to obtain the real error of the workpiece. Fig. 15 shows the final result with the roundness of workpiece being 6.7 lm.
6. Conclusion
Fig. 12. The set up to measure the error of the rotary table.
In the roundness measurement, the difficulty of microadjustment at micrometer level is overcome in this paper by the designed automatic adjustment microstage. The four-degrees-of-motion (two-translational displacement and two-rotational displacement) can automatically compensate for the x- and y-axial eccentricity and rotate the rotary table or the central line of a cylindrical workpiece to meet the horizontal or vertical level. The automatic adjustment microstage can replace manual adjustment mechanism (the ballscrew driving mechanism) and can be applied to most roundness measurement machines.
C.H. Liu, W.-Y. Jywe / International Journal of Machine Tools & Manufacture 44 (2004) 365–371
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Fig. 15. Roundness test result using the off-line error separation method.
Acknowledgements The work was supported by the National Science Council, Taiwan, Republic of China (Number NSC-892212-E-150-037).
References
Fig. 13. Roundness measurement result.
Fig. 14. Spindle error measured using a laser diode and a position sensitivity detector.
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