Key Engineering Materials Vol. 339 (2007) pp 195-199 online at http://www.scientific.net © (2007) Trans Tech Publications, Switzerland Online available since 2007/May/15
Design and Control of a Piezo-based Fast Tool Servo System for Precision Diamond Turning Y.H. Yang 1,a, S.J. Chen 1,b and K. Cheng 1,2,c 1
Precision Engineering Research Institute, Harbin Institute of Technology, China 2
Leeds Metropolitan University, UK
a
[email protected],
[email protected],
[email protected]
Keywords: Fast tool servo, Fuzzy PI control, Precision diamond turning
Abstract. A novel fast tool servo driven by piezoelectric actuator for precision diamond turning is designed in this paper. To overcome the inherent hysteresis and drift nonlinearity effect of the piezoelectric actuator, a closed-loop control system is established using strain gauge integrated in the actuator for position feedback, which has compact structure and can avoid interference in the machining. Furthermore, a fuzzy PI control algorithm is presented. It has not only the advantages of agility and adaptability of fuzzy control, but the characteristics of high accuracy of PI arithmetic. At last, experiments are carried out and the results show that the fuzzy PI control provides significantly better tracking accuracy and robustness against hysteresis and drift effects. Introduction Recently, fast tool servo has become an indispensable component in precision diamond turning machines to obtain higher positioning accuracy and bandwidth [1]. Various fast tool servo concepts have been presented in the past. Hara et al. presented a piezo driven fast tool servo to detect the initial contact between the tool and the workpiece [2]. Li et al. presented a piezoelectric fine positioning system for compensation of spindle errors in precision diamond turning [3]. Shamoto and Moriwaki designed various piezoelectric actuators to deliver long and continuous strokes in precision positioning as well as an actuator to deliver elliptical vibrations to diamond turning tool to reduce the chip-tool friction [4–6]. Kim developed a piezoelectric actuator to mount on a conventional lathe in order to control depth of cut precisely and compensate the waviness on the surface of the workpiece [7]. Most of these applications were for diamond turning where the cutting force disturbances were neglected, and the sensors were laser interferometer, grating ruler or capacitance micrometer, which are complex, costly, environment dependent and difficult to control. In this paper a fast tool servo driven by a piezoelectric actuator is presented. To correct the inherent hysteresis of piezoelectric actuators, fuzzy PI feedback control is implemented, which has not only the advantages of agility and adaptability of Fuzzy Control, but the characteristics of high accuracy of PI arithmetic [8]. The sensor used in this closed loop system is strain gauge integrated in the piezoelectric actuator, which has compact structure and can avoid interference in the machining. Design of fast tool servo The details of the FTS designed in this investigation are shown in Fig. 1. The FTS is composed of a main body base, a tool holder, a micro motion stage with two piezoelectric actuators, and a height adjusting mechanism with wedge block. A single diamond tool is mounted on the tool holder, which is bolted to the micro motion stage. The structure of the FTS makes for higher bandwidth because the mass of the moving body is small. The most important part of the FTS is the twodimensional micro motion stage, driven by two piezoelectric actuators. The configuration of the stage is shown in Fig. 2. The stage has the structure of a monolithic nested-loop type moving plates, in which each moving plate is guided by two four-link mechanisms. The four hinges of the four-link mechanism are implemented by four round-notched flexure hinges. Due to the nested-loop type structure, the moving plates are actuated independently each other by piezoelectric actuators so that All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.33-16/04/08,09:45:38)
196
Progress of Precision Engineering and Nano Technology
the stage can avoid coupled interference motions. To increase the motion range, a lever mechanism is applied. By experiment, the travel range of the stage is 25×20μm, and the first and second resonant frequency without the piezoelectric actuator is respectively 1375 Hz and 1500Hz. Inner plate Tool holder
Lever Fixed frame
Micro motion stage
Height adjusting mechanism
Flexure hinge Fig.1 Composing structure of fast tool servor
Outer plate
Fig.2 Structure of two-dimensional micro motion stage
Hardware design of closed-loop control system. In order to overcome the inherent hysteresis and drift nonlinearity effect of the piezoelectric actuator, a closed-loop control system is implemented. The system includes three elements: drive element, measuring element, and main control element, as shown in Fig.3.
Measuring Element A/D Main Control Element
Drive Element Piezo Actuator
Amplifier
D/A
Fig.3 System description The drive element, including D/A converter and the voltage amplifier, is used to drive the piezo actuator. The drive circuit is designed against the capacitive piezo, and has high resolution and stability. The analog signal, converted by 16-bit D/A converter, is transmitted to the power amplifier, and then drives the piezo actuator. The voltage scope of the drive element is 0-100V. For the motion measurement of the piezoelectric actuator, a strain gauge sensor is integrated in the piezoelectric actuator. Four resistive films, bonded to the PZT stack, form a Wheatstone bridge driven by a DC voltage (5 to 10 V). When the bridge resistance changes, the resulting voltage change converts into signal proportional to the displacement. The resolution of the sensor is better than 2 nm, the repeatability is to 0.1% of nominal displacement, and the bandwidth up to 5 kHz.
Key Engineering Materials Vol. 339
197
Before transmitted to the main control element, the weak signal of the strain gauge must be amplified, filtered, and then be converted to digital signal by A/D converter card. The main control element, i.e. an industrial control computer, is used to send the drive signal and receive the measuring signal, and implement the closed control algorithm, which will be described in detail in the next section. Fuzzy PI Control and Testing For feedback control, a PI control algorithm is selected to offer excellent closed loop control performance along with good reduction in implementation time. In order to determine the proportional gain, kp, and the integral gain, ki, the fuzzy inference rule is adopted. The advantage of fuzzy control is that a mathematical model is not necessary. Fig. 4 shows the control block diagram for the feedback control of the FTS with Fuzzy PI controller. The fuzzy inference controller is twodimensional. The two inputs to the fuzzy controller are current error, e, and the change rate of error, ec, and the outputs are the correction factor of the parameters of PI controller, cp and, ci.
Fuzzy Inference Rule
PI Controller
High Voltage Amplifier
FTS
Fig.4 Block diagram of closed loop control of FTS Because the sensitivity of the proportional gain and integral gain to the error and the change rate of error is different, the membership function of them should be different. Basing on this idea, we convert the two-input two-output fuzzy inference controller to another two controllers, which have two-input and one-output. Fig. 5 shows the structure of the fuzzy inference controller. In fact, by the conversion, the coupling of the control parameters is neglected, so the solving process is simplified.
e d/dt d/dt
ec
Ep Fuzzy Quantization
Inference of Proportional Correction Factor
cp
ec
Ei Fuzzy Quantization
Inference of Integral Correction Factor
ci
Fig.5 Structure of fuzzy inference controller Suppose the normalized discourses universes of e and ec are {0, 1, 2, 3} and {0, 1, 2}, refer with E and EC respectively, the results of cp and ci are shown in Table 1 and Table 2, which are calculated by the fuzzy inference function. With the designed fuzzy PI control algorithm, we test the performance of the FTS. Fig.6 shows the step response of the closed system with 12 µm reference input without cutting. The rising time is about 0.02 s, the overshoot is below 2%, and the steady state error is below 10 nm. The tracking result for the 7.5 µm and 100 Hz sine wave input is illustrated in Fig. 7, which demonstrates that the tracking error of FTS is under a level of 20 nm in peak-to-valley, and is satisfactory for the requirement of ultra-precision machining.
198
Progress of Precision Engineering and Nano Technology
Table 1 Control of cp EC cp
-2
-1
0
1
2
-3 -2 -1 0 1 2 3
6 5 4 3 4 5 6
5 4 3 2 3 4 5
4 3 2 1 2 3 4
5 4 3 2 5 4 3
6 5 4 3 6 5 4
E
Table 2 Control of ci EC ci
-2
-1
0
1
2
-3 -2 -1 0 1 2 3
3 2 1 1 1 2 3
2 1 0 0 0 1 2
1 1 0 0 0 1 1
2 1 0 0 0 1 2
3 2 1 1 1 2 3
14 12 10 8 6 4 2 0.05
0.15 0.2 0.25 time(s) Fig.6 Step response of closed loop system Displacement (µm)
0
Error (nm)
Position (µm)
E
0.1
10 8 6 4 2 0 10
Reference Output
5
10
15
20
5
10 time (ms)
15
20
5 0 -5 -10 0
Fig.7 Tracking result of FTS for a sine wave
0.3
Key Engineering Materials Vol. 339
199
Summary A piezo-based two dimensional fast tool servo for precision turning has been presented. The compact design features the use of solid flexures to transmit motion from a piezo stack actuator to the turning tool assembly. The FTS has a total stroke of 25×20μm. To improve the positioning accuracy and the tracking performance, a closed control system has been established with a feedback signal from the strain gauge sensor integrated in the piezoelectric actuator, and a fuzzy PI control scheme has been implemented. The testing results demonstrate that a positioning accuracy of 10 nm has been achieved, and the FTS can follow the command input sine wave with amplitude of 7.5 µm and frequency up to 100 Hz effectively. References [1] H.S. Kim and E.J. Kim: Mach. Tools Manufact, Vol.43 (2003), pp.1177. [2] Y. Hara, S. Motonishi and K. Yoshida: Ann. CIRP, Vol. 39 (1990), pp.375. [3] C. Li, C. James and S. Li: Proc. ASME DSC, Vol.57 (1995) No.1, pp.567. [4] E. Shamoto and T. Moriwaki: Ann. CIRP, Vol.43 (1994), pp.35. [5] E. Shamoto and T. Moriwaki: Ann. CIRP, Vol.48 (1999), pp.441. [6] E. Shamoto, T. Yamaguchi and T. Moriwaki: Proc. 6th Int. Precision Engineering Seminar (1993), pp.1031. [7] J.D. Kim and D.S. Kim: Mach: Tools & Manufact., Vol.38 (1998), pp.1305. [8] J. Carvajal and G.R. Chen: Information Sciences, Vol.123 (2000), pp.249.
