This paper was proceedings of Ninth World Congress of the Theory of Machines and Mechanisms (IFToMM) held in Politecnico di Milano, Italy, August 29/Spetember 2, 1995.
Development of precise rotating mechanism with fine motion stage
Takaaki OIWA, Shizuoka University, Hamamatsu 432 Japan
Katsumi KANEKO, Nagaoka University of Technology, Nagaoka 940-21 Japan
Akira KYUSOJIN, Nagaoka University of Technology, Nagaoka 940-21 Japan
Abstract: In this study, we made a new rotating mechanism with spindle error correction using specially-made fine motion stage. This stage with five-degrees-of-freedom except the rotation around Z-axis has high loading capacity and positioning accuracy. As a result, errors of the spindle mounted on the stage were decreased from 0.2 micro meter to 0.02 micro meter in the radial and axial directions within 1 rpm.
Keywords: Spindle motion error, Multi-degree-of-freedom mechanism, Fine motion mechanism, Piezoelectric actuator, Wedge mechanism
Introduction
Presently, it is impossible to obtain a rotating mechanism with nano-meter accuracies by using ball bearings or sliding bearings. Only we can establish it by using gas bearings. However, the stiffness lack of the gas bearings often becomes a serious problem. Thus, to improve the accuracy and the stiffness, some researchers made active controlled rotating mechanisms. Bifano et al.[1] carried out an experiment to control the radial runout of the ball bearing spindle by using piezoelectric actuators. Horikawa et al.[2], furthermore, developed an active air journal bearing which is capable of precisely controlling the radial axis position. In this study, we made a new rotating mechanism by using specially-made fine motion stage with multi-degrees-of-freedom except the rotation around Z-axis. This mechanism, consisting of the stage and the spindle separately, can adopt various spindle type.
Principle
The feedback controlled rotating mechanism consists of a high-rigidity multi-degree-of-freedom fine motion stage, a feedback control system for real-time error correction and a conventional ball bearing spindle. Figure 1 shows a conception of the rotating mechanism. The central processing unit measures runouts of the spindle and drives the fine motion stage to decrease the spindle runout. This stage needs a high positioning accuracy and a high loading capacity because the mechanical spindle mounted on the stage is heavy. In this paper, we reported correction results of the radial and axial runouts of the spindle.
High-rigidity fine motion stage
Figure 2 shows the principle of the fine motion stage. To make the stiffness of Z-direction high, we adopted a unique structure. Three wedge-shaped plates sandwich the multi-layered piezoelectric actuators. Therefore, all the mass provides a perpendicular load on the high mechanical strength actuators. Figure 2(a) represents a state when no voltage is applied. When all actuators extend the same length d0 (figure 2(b)), the top wedge plate or the stage lifts in only Z-direction. When the upper actuators contract and the lower actuators extend, the stage shifts in only X-direction (figure 2(c)). This stage can precisely move without friction because it has no sliding guide way.
Moreover, expansion and contraction of the actuators rotate the stage in b-direction around Y-axis as shown in figure 2(d). The rotation in b-direction, however, will cause simultaneously the translational displacement in X-direction, i.e. interference. Therefore, if we want to rotate the stage in only beta-direction, the stage must be shifted in -X-direction to compensate the displacement.
Expansion of all actuator lifts the stage in only Z-direction (figure 2(e)). If we prepare two of this X-Z-beta mechanism and stack them with phase difference of 90 degree, five-degree-of-freedom fine motion stage will be completed (see figure 3).
In this paper, we tentatively manufactured a three-degree-of-freedom stage or a X-Z-beta stage. Figure 4 shows a front cross-sectional view and a top view of the manufactured stage. To limit the height of the stage, only both ends of the plates were shaped to wedge. The multi-layered piezoelectric actuators were put in holders because the tensile strength and shearing strength of the actuators were considerably inferior to the compression strength. The holder consists of elastic hinges and a parallel link mechanism as the wedge plates move parallel (figure 5). We designed a wedge angle of 10 degree to improve the resolution of the X-direction positioning.
The actuator measures 5*5*9 mm long, and generates maximum force 385N and maximum elongation of 6.5 micro meter at applied voltage of 100V. Six holders were bolted between the wedge plates with three-point supports.
Control circuits
Figure 6 shows the block diagram of the control system. In general, the hysteresis between the elongation of the piezoelectric actuator and the applied voltage requires the compensation by feedback control. We measured the elongation by semiconductor strain gauges glued on the elastic hinge of the holder. The relationship between the strain and the elongation was linear with deviation within 0.02 micro meter. The proportional and integral feedback control was conducted on each of six piezo electric actuators. The settling time of positioning was 40 ms at 1 kHz sampling frequency.
Performance of fine motion stage
We drove the stage in X-, Z-, and beta-directions separately using above control system. The weight of 200N or 400N was placed on the stage. To measure the translational displacement and the rotation of the stage, noncontact capacitive gauges with a nominal resolution of 0.015 micro meter were installed on the stage.
The maximum movements of the stage depend on the load. In this stage, the maximum movements were 3 mcro meter in X-direction, 12 micro meter in Z-direction and 12" in beta-direction with 400 N load. Figure 7(a) shows positioning deviations delta-X, delta-Y and delta-Z, and roll delta-alpha, pitch delta-beta and yaw delta-gamma when driven over a X-travel of plus or minus1.5 micrometer. These deviations are caused by the error of the expansion and the contraction of each actuators. The positioning error and the motion error were less than plus or minus 0.01 micrometer and plus or minus 0.02". When the load was 0 N and 400 N, similar results were obtained. Figure 7(b) shows the motion error when the stage lifts over a Z-travel distance of ±6 mm. Moreover, figure 7(c) shows the motion error when the stage tilts in beta-direction over a rotating angle of plus or minus 3". As before, the rotation b causes the interference in X-direction. However, the compensation of X-displacement enables the stage to rotate around a center having a given height. Summarizing the experimental results, the positioning error and the motion error of this stage were less than plus or minus 0.01 micrometer and plus or minus 0.02".
Figure 8 shows the positioning error in X-direction at 0N, 200N and 400N load. Straight lines in the figure represent the regression lines. The increase of the load slightly decreases the displacement, because the load alters the coefficient between the strain and the displacement of the holder. However we can compensate the decrease of the displacement by calibration of the coefficient because the alteration of the coefficient is very small.
Figure 9(a) shows 1 micrometer step response in X-directions. During X-positioning, considerable interferences in other direction occurred owing to the expansion and contraction velocity difference of each actuators. The velocity difference was due to the hysteresis between the elongation of the actuator and the applied voltage. In particular, the speed difference will be produced certainly when driving in X-direction of this stage. Thus, the decrease of the interference will require adopting the velocity feedback control to unify the velocities of each actuators.
Figure 9(b) and (c) show that slight interference was observed in 1 micrometer and 1" step responses in Z- and beta-directions. Moreover, no interference occurred in 0.1 micrometer and 0.1" step response because the velocity difference is small at short positioning travel.
Figure 10 shows step positioning responses in X-, Z- and beta-directions. We used the capacitive gauge and an analog lowpass filter with cut-off frequency of 20Hz. The figure shows that the step positioning resolutions were less than 10 nm and 0.01" even if 200N weight was placed on the stage. Consequently, this stage is suitable for the motion error correction of the spindle.
Results of corrections of spindle errors
To achieve the purpose mentioned in the introduction, we conducted the motion error correction of the spindle. Figure 11 shows an experimental apparatus for correcting the spindle error. The turn table using bearing steel balls is mounted on the fine motion stage. The radial and axial runouts of the turn table were approximately 0.2 micrometer. The turn table has a weight of approximately 400N, and was rotated at 1 rpm by a DC motor and a belt. A 1024 pulse/revolution incremental encoder was used to trigger data collection. A 12.7mm (0.5 in.) diameter master ball was rested on the spindle face. Two noncontacting capacitive gaging systems detected radial and axial runouts of the spindle. The personal computer employing an Intel i486-25 micro processor, drove the stage to decrease the radial runout of the master ball.
First, the turn table was rotated at 1 rpm; sampling rate of 1024/rev. Figure 12 shows radial runouts before correction and after correction. The correction diminished the runout except high order harmonics of the runout. In this paper, feedback control with A/D and D/A converters was conducted by software. Therefore, the high order harmonics cannot be decreased because execution of the software and conversions in the converters require much more time.
Second, figure 13 shows radial runouts when rotating at 0.25 rpm; sampling rate of 4096/rev. As a result, all runouts of the spindle diminished to plus or minus 0.02 mm. Figure 14 shows that axial runout also diminished to plus or minus 0.02 mm.
Conclusions
To develop a precise rotating mechanism satisfying the accuracy less than 0.1 micrometer, we controlled the attitude of the spindle by using a high-rigidity fine motion stage. The maximum movements of the stage were 3 micrometer in X-direction, 12 micrometer in Z-direction and 12" in beta-direction under 400 N load. The positioning resolutions in the translational and rotational directions were less than 0.01 micrometer and 0.01" respectively. The positioning errors and the motion error were less than plus or minus 0.01 micrometer and plus or minus 0.02" under 400 N load. Thus, this stage was useful for positioning heavy mechanism e.g. the spindle within the limited travel. The feedback control system using a master ball diminished the radial and axial runouts of the turn table installed on the stage from 0.2 micrometer to plus or minus 0.02 micrometer at 0.25 rpm.
References
[1] T. G. Bifano and T. A. Dow: Real time control of spindle runout, Opt. Eng., 24, 5(1985)888.
[2] O. Horikawa and A. Shimokohbe: An active air journal bearing - control of radial axis motion and stiffness, JSME Int. J., Ser. III, 33, 1(1990)55.