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Design and dynamic evaluation for a linear ultrasonic stage using the thin-disc structure actuator
Available online at www.sciencedirect.com
Ultrasonics 47 (2007) 23–31 www.elsevier.com/locate/ultras
Design and dynamic evaluation for a linear ultrasonic stage using the thin-disc structure actuator Fuhliang Wen a
a,*
, C.-Y. Yen
b
Department of Mechanical and Computer-Aided Engineering, Graduate School of Automation and Mechatronics, St. John’s University, 499 Sec. 4 Tam King Road, Tamsui, Taipei 25135, Taiwan b Department of Electrical Engineering, National United University, Miaoli 360, Taiwan Received 21 May 2006; accepted 12 June 2007 Available online 1 July 2007
Abstract The design of a novel, single-axis ultrasonic actuating stage has been proposed. It consists of a movable plate, an edge-driving ultrasonic actuator as an actuating device, and a magnetic Magi encoder as a position sensor. The stage is impelled using a friction-contact mechanism by the ultrasonic actuator with long distance movement. Very high actuating and braking abilities are obtained. The stable and precise positioning control of the stage was achieved by using a neural-fuzzy controller. This simple and inexpensive structure of the single-axis stage demonstrates that the mechanical design of ultrasonic actuating concept could be done flexibly according to the requirements for various applications. Ó 2007 Elsevier B.V. All rights reserved. PACS: 43.38.Fx Keywords: Edge-driving actuator; Ultrasonic actuating stage; Piezoceramic; Friction contact; Laser-Doppler measurement; Performance evaluation
1. Introduction There are some inherent features in a conventional linear stage, such as (i) the gear backlash existing in transmission mechanism using a screw rod, (ii) the stick-slip phenomenon due to friction among mechanical elements, (iii) because of thermal dissipation for direct-converse piezoelectric effect during PZT ceramic driving; the positioning error exists in the heat effect zone. Therefore, for the submicron- or nano-order positioning capability, all factors (i.e. structure stability, fiction contact, thermal dissipation, vibration, and assembling error) shall be counted in the design of a linear stage. The previous designs for the linear ultrasonic stages are made of piezoelectric bulky materials or piezoelectric *
Corresponding author. Tel.: +886 2 28013131x6717; fax: +886 2 28013143. E-mail address: [email protected] (F. Wen). 0041-624X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2007.06.005
stacked discs [1–5]. Their actuators are primarily composed of the piezoelectric ceramics of zirconium–titanium–acid– lead (PZT) materials (called piezoceramic). In this study, the novel configuration of a thin-disc piezoceramic ultrasonic actuating linear stage is developed, in which the actuator is a piezoceramic membrane bonded on a metal sheet structure. When an AC power is applied to a piezoceramic, the piezoceramic and its bonded metal sheet will be forced to generate a mechanically extended–shrunk phenomenon [6,7]. Energy is transferred in wave-like forms. By applying the constraints of specific geometry positions on a metal sheet, various behaviors of flexural waves have been formed at different directions [8–10]. The piezoceramic can work within an ultrasonic frequency with the amplitude of several micrometers, which is controllable by input voltages. Therefore, it can be used as a driving actuator for a compact stage. The ultrasonic actuator has an alternative extended– shrunk motion through the AC power. By various
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F. Wen, C.-Y. Yen / Ultrasonics 47 (2007) 23–31
mechanical designs and different driving frequencies, linear motions in specific directions are controlled. Under the vibration of the ultrasonic frequency, an enlarger displacement velocity, up to several centimeters per second, is generated for driving precise devices such as the positioning of an X–Y platform. Meanwhile, the ultrasonic actuator has the following features: small volume, light weight, low noise, high speed, high retaining force, quick response, and no electromagnetic interference. Each of its advantages can be utilized in different products. This simple and inexpensive structure of a linear stage demonstrates that the mechanical design of the actuator and the slider could be done separately and flexibly according to the requirements for various applications. Following the driving frequency of a single-phase AC power, the slider is moved by the actuator with maximum linear speeds of 20 cm/s under rated operation using a friction-contact mechanism. Based on the unique features of the ultrasonic actuator in terms of quick response and a high braking ability, the multi-frequency driving circuit (MFDC) was designed for multi-resonant-mode operation [1,2]. A modern closed loop servo control, neural-fuzzy control, is used as a positioning tracker. The neural-fuzzy scheme does not need an exact mathematic model and has been successfully applied. Higher precision position control for a piezoceramic ultrasonic stage depends on mechanical design and servo control of a very precise and adequate metrology. This paper proposes the design of a compensator to deal with a contact-driving ultrasonic linear stage. The performance and effectiveness of the proposed controller is demonstrated by the command input of the step signals.
Piezoceramic actuator design FEM analysis
Preload adjustment
Experiment Tuning Statistics and Evaluation YES
2. The design for a large-movement, single-axis linear ultrasonic actuating stage In this study, the design of the major components for a linear stage consists of: a foundation, a platform, a linear sliding rail, a preload adjuster, an ultrasonic actuator, a sensing set of the magnetic belt, and a recorder. The piezoceramic actuator is fixed to a normal preload mechanism, as shown in Fig. 1a. The designed preload is conformed to the movable actuator and the normal direction of slider motion may contact at anytime. Also, a good insulation must be assuredly placed between the fixing stainless plate and the piezoceramic. Its major purpose is to keep the wire of the driving power from causing a short when it is connected. A general design philosophy was adopted, as shown in Fig. 1b, which reduced repeatable and nonrepeatable errors and maximized the probability of success. Linear motion errors have to be measured and evaluated in terms of preload adjustment. The successful control of an ultrasonic actuating stage (containing a movable part and the actuator) depends on the interaction of all elements that compose the system and its environment. The thin-disc structure of this ultrasonic actuating component includes: (1) the membrane of piezoceramics; (2) the elastic metal sheet of nickel alloy; (3) the covered with its
Platform fabrication and assembly
NO Prototype
Fig. 1. Schematic prototype of a linear stage: (a) exploded view of an ultrasonic actuating stage and (b) flow chart for prototype development.
diameter of 24.5 mm sliver sol–gel membrane used as an electrode. The thin-disc structure is a piezoceramic membrane boned on a Ni-alloy sheet with its diameter 41 mm. Its total thickness is 0.23 mm and the thickness of the metal sheet is 0.10 mm, with its dimension specification as shown in Fig. 2a. The bonded structure of a smaller diameter PZT film adhered with the larger diameter Ni-alloy sheet, called a disk vibrator, has the capability of actuating in both the direction of the in-plane and the out-plane, depending on the location of the constraints and the amount. In this study, the multiple-resonant modes are performed by an external perturbation with a constraint technique on the metal sheet rather than cutting off the edge of a disk vibrator. The cutting edge method was also applied for application to an electromechanical filter as a communication frequency element [1]. This constraint technique is a completely different principle from a conventional multi-electrode ultrasonic motor. Using the controlled mode shapes in a single-phase driving power for one set of electrodes
F. Wen, C.-Y. Yen / Ultrasonics 47 (2007) 23–31
25
Fig. 2. (a) The thin-disc structure piezoceramics as an ultrasonic actuating component and (b) a vibration mode of three constraints using ANSYS simulation.
[8–10], a disk vibrator could possibly be expected to force the movable part in both directions of forward and backward as shown in Fig. 1a. For PZT thin-disc structure vibration in ultrasonic frequency, the piezoceramic acts as the driving source needed to generate the high frequency extended–shrunk motion of the metal sheet. The metal sheet plays the amplifier with vibrating magnitudes and constructs the desired mode shapes. The minimum deformation is located at the central portion, but larger deflection is located near the outer edge of the metal sheet. Contradictorily, the metal stiffness also constrains the piezoceramic, and limits the PZT dynamic response to electrical power. Only in suitable power entry matching resonance frequencies, the metal stiffness would be overcome by the piezoceramic to produce the optimal efficiency. Thus, the resonance deformation of a metal sheet always follows the flexural-like vibrating of the piezoceramic, called a mechanical flexural wave. The phenomenon exists especially in ultrasonic frequencies. Furthermore, if it is used as an actuator, we only need to
directly observe the resonant mode shapes. Then, the ultrasonic driving mechanism was roughly configured [8–10], as shown in Fig. 2b. Based on these concepts stated by flexural waves of the metal sheet, our lab has been developing some useful driving mechanisms for a DVD player tracking system, and a precise ultrasonic linear stage. In this study, a piezoceramic actuator is fixed to a normal preload mechanism, as shown in Fig. 3. The designed preload is conformed to the movable actuator and the normal direction of slider motion may cause contact at any time. Also, a good insulation must be assuredly placed between the fixing stainless plate and the piezoceramic. The major purpose of this insulation is to avoid the wire of the driving power from being shorted when a connection is made. When considering the precision in finishing and the balance of the mechanism, the sliding rail with rolling-balls under the linear guide (used in an optic positioner) is used as the linear movable component. The surface of the slider has been attached to the aluminum plate treated with positive electrode processing. This is to
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F. Wen, C.-Y. Yen / Ultrasonics 47 (2007) 23–31
A
Output
× 10
50Ω
100k
~
Function Generator
Input A
HSA 4011 Power Amplifier Output A
+
-
PZT Actuato r
AT0023
AC/DC
Linear stage Fig. 3. The assembly of normal preload adjustment and an ultrasonic actuator.
increase the friction between the actuator and the slider. Magnetic belts have been applied to the opposite end of the slider for sensing the position while measuring the slider motion via the magnetic encoder. The slider guide, as the platform, can carry the weight blocks and mark the home position. The proposed linear stage has a single-axis large-movement of 130 mm, but a tolerance for mechanical error within 1 lm. Fig. 4 shows the prototype of the ultrasonic actuating linear stage. 3. Characteristic measurement of the linear stage based on driving frequencies and various loadings The characteristic evaluation for the linear stage is via a laser-Doppler vibrometer (LDV) system. The frequency of the receiving wave would be shifted when the emitting wave source and/or the receiving object creates the relative motion. In other words, there are different frequencies occurring in the emitting wave source and the reflected wave source. The Doppler Effect demonstrates that the frequency of the receiving wave will turn higher than that of the emitting wave when both objects move gradually closer
OUTPUT RF INPUT
REFERENCE OUTPUT
Computer REFERENCE INPUT
RS-232
RF OUTPUT
Demodulation Unit
Oscilloscope
AC/DC INPUT
AT 3700
TDS 220 CH1
VEL [m/s/V]
Fig. 5. The experimental setup for a linear stage using the AT0023 laserDoppler system.
together. In contrast, when both objects are moving away from each other, the receiving frequency will record a lower wave than the original one. In this paper, using the LDV system, the characteristics among voltages onto piezoceramics, driving frequencies, and slider’s velocities are prospected, counting out the different weight loading. Thus, the features of the linear stage were evaluated for control purposes based on the measured configuration as shown in Fig. 5. 3.1. Measurement principle The measurement system consists of the AT300 LDV device, the AT 3700 demodulation unit for signal conditioning, and the TDS 220 oscilloscope for monitoring via hookup from the computer. The different driving frequencies and voltage levels could be tunable by the function generator. The AT0023 sensor head, manufactured by
Moving object Laser source fo Reflected light fr
θ1
Moving object velocity V1 Fig. 4. The prototype of an ultrasonic actuating linear stage.
Fig. 6. LDV measuring configuration.
F. Wen, C.-Y. Yen / Ultrasonics 47 (2007) 23–31
Graphtec Corp, Japan, with a built-in laser tube has the feature of an efficient laser light source and high sensitivity. The laser light is phase aligned resulting in its ideal feature for long distance measurement. The principle of the LDV system is the measurement of frequency changes caused by the Doppler Effect. Where the Doppler shifted frequency determines the ratio of the velocity to vibration [11], based on the theory of Eq. (1) and shown in Fig. 6. fD ¼ jfo fr j ¼
2v1 cos h1 ko
ð1Þ
27
where fD is the Doppler shift frequency, fo is the oscillation frequency of laser light, fr is the frequency of reflected light with Doppler shift, ko is the oscillation wavelength of laser light, v1 is the velocity of moving object, and h1 is the irradiation angle. 3.2. Dynamic characteristics In accordance to the various input signals which are relative to the frequency and voltage levels, the operating
Fig. 7. (a) The characteristic curves of velocity versus frequencies with free loading, (b) the characteristic curves of velocity versus frequencies with 250 g weight loading, (c) the characteristic curves of velocity versus frequencies with 500 g weight loading and (d) the characteristic curves of velocity versus frequencies with 1 kg weight loading.
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features of an ultrasonic actuating stage have to be evaluated. The experimental evaluation pertained to velocities based on free loading, 250 g, 500 g, and 1 kg weight loading, respectively. The emitting laser source is reflected by a small mirror, stuck on the head of a liner guide. Through the sensing head AT0023 hookup the demodulation unit AT3700, the accuracy velocity of the linear stage was acquired as shown in Fig. 7a–b with diverse weight loadings. There is a similar phenomenon in which the maximum forward speed of a linear stage is at a driving frequency of 73 kHz, but the maximum reverse speed near 85 kHz. The forward velocity is much faster than that of the backward velocity due to this mechanism’s limitation of an ultrasonic actuating linear stage. The higher input voltage level is much more powerful resulting in quicker motion. Otherwise, the minimum input voltage level shall be provided, usually above 3 V, due to the contact friction driving between the actuator and the slider.
Fig. 8. The damage of the piezoceramic and the wearing at the top edge of the metal sheet.
3.3. The damage and wearing phenomenon of the thin-disc ultrasonic vibrator The driving frequency in backward motion (that is 86 kHz) shows the shifting frequency dropping to lower ranges (about 85 kHz) as shown in Fig. 7a. One particular phenomenon in the linear stage is the disequilibrium of forward and backward motion as shown in all figures except Fig. 7d. The heavy weight loading could improve the equivalent velocity in both the movement directions. Added weight loading with the lower driving voltage, e.g. 5 V, did not appear to have enough electrical power needed to activate the slider and cause movement. Another big problem was the strain damage of the piezoceramics caused when the driving voltage was augmented, as shown in Fig. 8. However, the acceptable driving voltage shall be considered the impedance match for piezoceramics and the vibration amplitude induced from the metal deformation. There is a probability that damage could occur. Normally, the thinner metal sheet could offer the more activating vibration for mechanical driving power, but the capability of anti-wearing is also poor as shown in Fig. 8. 4. Experimental results and performance evaluation
the friction driving mechanism of a stage, there is deadzone phenomenon as obviously shown in Fig. 7. The critical input voltage and the driving frequency determine such nonlinear behaviors that the difficulties of control design are influenced by the minimum driving voltage and exact resonant frequency while the dead-zone is aggrandized. The response quality of the velocities depends on the moving speed of a stage based on the level of driving voltage and precise degree of the excited frequency for such a piezoceramic actuating stage. Visually, it has a tendency in the higher levels of the driving voltage to cause faster motion speed. Because of the inherent hysteresis in piezoelectric materials, there is a difference in linear positions while in ascending and descending voltages. The linear relationship between actuating voltages and displacements is no longer in existence. Thus, these hysteresis as shown in Fig. 9a and b shall be counted in the control design. Otherwise, the positioning accuracy is also an important factor relative to the design of control system. Fig. 9c illustrates the curve of the accumulated position error for a piezoceramic actuating stage. It has an estimated error about 2.8–3.2% under weight loading of 500 g.
4.1. Positioning evaluation 4.2. Positioning compensator The performance experiment for the linear stage is via the PC-base driving and control system. When the analog signals were sent out through the PC interface as the controlled voltage, the driving circuit amplified the signal. The stage moved in the forward or backward direction by the thin-disc ultrasonic actuator depending on the driving frequency. The displacement is monitored by HIWIN magnetic measurement system which is manufactured by HIWIN TECHNOLOGIES Corp. in Taiwan. Using the interface encoder to convert the voltage to a linear amount, the movement feature of the stage could be observed. For
The positioning compensator has applied the inverse recursive learning method of neural network to tune the output gain of fuzzy control in real-time. When the stage’s position error is converged on the specific value, the pulse corrector is ignited to suppress the error. In the design of the fuzzy controller, the Gaussian type membership function contains three displacement errors (x), three displacement error change rates (dx), and five outputs (y), where Gaussian membership function is Gaussian(x; c, r) = exp[0.5(x c/r)2], c denotes the center value of the
F. Wen, C.-Y. Yen / Ultrasonics 47 (2007) 23–31
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the direct tuning of output gain for fuzzy control. Thus, the transient response is improved while the movement direction and displacement amount are controlled. The block diagram illustrating the fuzzy-neural controller for output gain tuning is shown in Fig. 10a. For performance evaluation, the control inputs coming from the controller are implemented by Matlab/Simulink software via the AD/DA servo control card and inference. The pulse corrector or pulse generator categorizes the several small piece controllers, depending on error quantity, through the determination of error selectors as shown in Fig. 10b. The fuzzy controller, depending on the error amount of displacement, is divided into the number pieces of small controllers to perform the command via error selectors respectively. Because of the square signals of 0.3 Hz as control commands, an overshoot phenomenon instantly occurred during the switched pulse. The shape function became necessary to smooth the raised up command.
Fig. 9. Diagram (a) and (b) are the loops of hysteresis for the linear stage in forward and backward motions with weight loading of 500 g, respectively. (c) The accumulated position error for a pizeoceramic actuating stage with weight loading of 500 g.
membership function, and r denotes the width of membership function. Both optimal values of c and r could be obtained from trial and error via experiments. The control rule foundation is based on the relationship in the error amount and the error change rate of the stage’s displacement relative to control inputs. Applying the Min– Min–Max method for the Fuzzy inference mechanism and the center of gravity method for defuzzification, the diagram of the relationship curves for errors. Additionally, control inputs were calculated. During experimental testing, in order to reduce the CPU time consumption, the look-up table is built according to inference result. The Fuzzy function in the Matlab toolbox is also a solver used to directly gain the inference result. Since the output gain of the fuzzy control is designed for the steady-state properties of the stage, it is of poor efficiency in transient response. Therefore, the method of the inverse recursive neural network is introduced to perform
Fig. 10. (a) The block diagram of output gain tuning for a neural-fuzzy positioning compensator and (b) the block diagram of executable pulsed wave corrector by Matlab/Simulink software.
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Furthermore, the shut down switch was added onto the controller to avoid any tiny vibrations that could cause displacement errors. 5. Discussion Fig. 11 displays the characteristics of control inputs, position tracking, or position errors, and the driving voltages with weight loading of 500 g respectively. Obviously, the piezoceramic stage has the capability to fellow the control commands reaching the specific position, but there was an inevitable error during the position tracking. One of the possible reasons for the position error is that it was induced by the friction-contact-driving mechanism between the ultrasonic actuator and the slider. Therefore, if one would
like to eliminate such an error, the stage shall be redesigned or modified in the transmission mechanism. Due to the friction-contact-driving, there are nonlinear dynamic behaviors like dead zone or hysteresis apparently, especially in lower input voltage (within 1.5 V) onto piezoceramics. Fortunately, the neural-fuzzy strategy, in our design for the controller, can successfully overcome the nonlinear dynamic behavior. Because of this success, the design’s position tracking ability performs well for the stage as shown in Fig. 11. Before the pulse corrector was added to the neural-fuzzy controller, the driving voltages were always sent to the actuator resulting that the positioning track was unable to be converged as the desired signal of command inputs. Now, the pulse corrector offers the instant response to cut off the driving voltage when the desired position is reached. These results, shown in Fig. 11c, demonstrate the intermittent signals of tracking command for driving voltages. Otherwise, due to the lack of continuous supplied driving voltages, the thermal dissipation could be minimized as possible for piezoceramic excitation. Since the direction and velocity of linear motion is controlled by the specific driving frequency and voltage, the design of the positioning compensator has been implemented for the novel ultrasonic actuating linear stage. Based on the recognition of nonlinear behaviors relative to the contact-transfer driving force, the neural-fuzzy method, without the exact mathematical model of the linear stage, is employed to complete the tracking performance. The pulse corrector is a very helpful assisting device added on the controller to reduce the oscillation time and immediately converge towards the system’s stability. The experimental characteristics have demonstrated that the positioning accuracy could be reached and low thermal dissipation could be obtained due to discontinuous electrical power coming into the piezoceramics. 6. Conclusion
Fig. 11. The position characteristics of a linear stage with 500 g weight loading: (a) control inputs and position tracking, (b) position tracking errors and (c) driving voltage onto the piezoceramic.
The stage with long distance movement is evaluated by using a LVD measurement system. The experimental results have demonstrated that the friction-contact ultrasonic actuating mechanism could reach very high actuating and braking abilities. Thus, the mechanical design and control involving four fundamental tasks has been achieved: (a) positioning motion was proposed using a linear platform supported by bearings of a rail guide ensuring kinematical movement; (b) thermal drifts were avoided due to point contact by the use of ultrasonic friction driving actuator, and the temperature control was unnecessary; (c) dynamic decoupling has been achieved between the actuator and the slider to avoid parasitic movements and (d) natural resonant frequencies of the whole system indicate a preponderance of vibration modes of the friction drive, because of ultrasonic operation of actuator (above 65 kHz). It is obvious that the mechanical design has been achieved with high quality and the ultrasonic actuating
F. Wen, C.-Y. Yen / Ultrasonics 47 (2007) 23–31
stage will follow the control commands for high performances. Also, its running accuracy and positioning precision are predictable. These concepts of mechanism design can be used in lithography positioning equipment, medical focusing instrument, and tracking devices of hard disk drives and/ or optic disk drives. Furthermore, the cost of this structure is low and has a preferred efficiency. Acknowledgement The authors thank the financial support of the National Science Council of the Taiwan government and Grant Number: NSC-93-2212-E-129-007. References [1] S. Ueha, Y. Tomikawa, M. Kurosawa, N. Nakamura, Ultrasonic Motors Theory and Applications, Oxford Publications, Clarendon Press, Oxford, 1993. [2] K. Uchino, Piezoelectric Actuators and Ultrasonic Motors, Kluwer Academic Publishers, Boston, 1997.
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[3] T. Sashida, Takashi Kenjo, An Introduction to Ultrasonic Motors, Clarendon Press, Oxford, 1993. [4] S.H. Chang, C.K. Tseng, H.C. Chien, An ultra-precision XYhz piezomicropositioner – Part I: design and analysis, IEEE Trans. Ultrason. Ferr. 46 (4) (1999) 897–905. [5] S.H. Chang, C.K. Tseng, H.C. Chien, An ultra-precision XYhz piezomicropositioner – Part II: experiment and performance, IEEE Trans. Ultrason. Ferr. 46 (4) (1999) 906–912. [6] N. Lamberti, A. Iula, M. Pappalardo, A piezoelectric motor using flexural vibration of a thin piezoelectric membrane, IEEE Trans. Ultrason. Ferr. 45 (1) (1998) 23–29. [7] R. Carotenuto, N. Lamberti, A. Iula, M. Pappalardo, A new low voltage piezoelectric micromotor based on stator precessional motion, IEEE Trans. Ultrason. Ferr. 45 (5) (1998) 1427–1434. [8] F.L. Wen, C.Y. Yen, M.S. Ouyang, Thin-disk piezoceramic ultrasonic motor. Part I: design and performance evaluation, Ultrasonics 41 (6) (2003) 437–450. [9] C.Y. Yen, F.L. Wen, M.S. Ouyang, Thin-disc piezoceramic ultrasonic motor. Part II: system construction and control, Ultrasonics 41 (6) (2003) 451–463. [10] F.L. Wen, S.C. Mou, M.S. Ouyang, Design and construction of a shaft-driving type piezoceramic ultrasonic motor, Ultrasonics 43 (1) (2004) 35–47. [11] Theory, characteristics, and sample measurements with a laserDoppler vibrometer, in: Work Shop for Vibration Measurement, Sanlien Technology Corp., 2003.
Ultrasonics 47 (2007) 23–31 www.elsevier.com/locate/ultras
Design and dynamic evaluation for a linear ultrasonic stage using the thin-disc structure actuator Fuhliang Wen a
a,*
, C.-Y. Yen
b
Department of Mechanical and Computer-Aided Engineering, Graduate School of Automation and Mechatronics, St. John’s University, 499 Sec. 4 Tam King Road, Tamsui, Taipei 25135, Taiwan b Department of Electrical Engineering, National United University, Miaoli 360, Taiwan Received 21 May 2006; accepted 12 June 2007 Available online 1 July 2007
Abstract The design of a novel, single-axis ultrasonic actuating stage has been proposed. It consists of a movable plate, an edge-driving ultrasonic actuator as an actuating device, and a magnetic Magi encoder as a position sensor. The stage is impelled using a friction-contact mechanism by the ultrasonic actuator with long distance movement. Very high actuating and braking abilities are obtained. The stable and precise positioning control of the stage was achieved by using a neural-fuzzy controller. This simple and inexpensive structure of the single-axis stage demonstrates that the mechanical design of ultrasonic actuating concept could be done flexibly according to the requirements for various applications. Ó 2007 Elsevier B.V. All rights reserved. PACS: 43.38.Fx Keywords: Edge-driving actuator; Ultrasonic actuating stage; Piezoceramic; Friction contact; Laser-Doppler measurement; Performance evaluation
1. Introduction There are some inherent features in a conventional linear stage, such as (i) the gear backlash existing in transmission mechanism using a screw rod, (ii) the stick-slip phenomenon due to friction among mechanical elements, (iii) because of thermal dissipation for direct-converse piezoelectric effect during PZT ceramic driving; the positioning error exists in the heat effect zone. Therefore, for the submicron- or nano-order positioning capability, all factors (i.e. structure stability, fiction contact, thermal dissipation, vibration, and assembling error) shall be counted in the design of a linear stage. The previous designs for the linear ultrasonic stages are made of piezoelectric bulky materials or piezoelectric *
Corresponding author. Tel.: +886 2 28013131x6717; fax: +886 2 28013143. E-mail address: [email protected] (F. Wen). 0041-624X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2007.06.005
stacked discs [1–5]. Their actuators are primarily composed of the piezoelectric ceramics of zirconium–titanium–acid– lead (PZT) materials (called piezoceramic). In this study, the novel configuration of a thin-disc piezoceramic ultrasonic actuating linear stage is developed, in which the actuator is a piezoceramic membrane bonded on a metal sheet structure. When an AC power is applied to a piezoceramic, the piezoceramic and its bonded metal sheet will be forced to generate a mechanically extended–shrunk phenomenon [6,7]. Energy is transferred in wave-like forms. By applying the constraints of specific geometry positions on a metal sheet, various behaviors of flexural waves have been formed at different directions [8–10]. The piezoceramic can work within an ultrasonic frequency with the amplitude of several micrometers, which is controllable by input voltages. Therefore, it can be used as a driving actuator for a compact stage. The ultrasonic actuator has an alternative extended– shrunk motion through the AC power. By various
24
F. Wen, C.-Y. Yen / Ultrasonics 47 (2007) 23–31
mechanical designs and different driving frequencies, linear motions in specific directions are controlled. Under the vibration of the ultrasonic frequency, an enlarger displacement velocity, up to several centimeters per second, is generated for driving precise devices such as the positioning of an X–Y platform. Meanwhile, the ultrasonic actuator has the following features: small volume, light weight, low noise, high speed, high retaining force, quick response, and no electromagnetic interference. Each of its advantages can be utilized in different products. This simple and inexpensive structure of a linear stage demonstrates that the mechanical design of the actuator and the slider could be done separately and flexibly according to the requirements for various applications. Following the driving frequency of a single-phase AC power, the slider is moved by the actuator with maximum linear speeds of 20 cm/s under rated operation using a friction-contact mechanism. Based on the unique features of the ultrasonic actuator in terms of quick response and a high braking ability, the multi-frequency driving circuit (MFDC) was designed for multi-resonant-mode operation [1,2]. A modern closed loop servo control, neural-fuzzy control, is used as a positioning tracker. The neural-fuzzy scheme does not need an exact mathematic model and has been successfully applied. Higher precision position control for a piezoceramic ultrasonic stage depends on mechanical design and servo control of a very precise and adequate metrology. This paper proposes the design of a compensator to deal with a contact-driving ultrasonic linear stage. The performance and effectiveness of the proposed controller is demonstrated by the command input of the step signals.
Piezoceramic actuator design FEM analysis
Preload adjustment
Experiment Tuning Statistics and Evaluation YES
2. The design for a large-movement, single-axis linear ultrasonic actuating stage In this study, the design of the major components for a linear stage consists of: a foundation, a platform, a linear sliding rail, a preload adjuster, an ultrasonic actuator, a sensing set of the magnetic belt, and a recorder. The piezoceramic actuator is fixed to a normal preload mechanism, as shown in Fig. 1a. The designed preload is conformed to the movable actuator and the normal direction of slider motion may contact at anytime. Also, a good insulation must be assuredly placed between the fixing stainless plate and the piezoceramic. Its major purpose is to keep the wire of the driving power from causing a short when it is connected. A general design philosophy was adopted, as shown in Fig. 1b, which reduced repeatable and nonrepeatable errors and maximized the probability of success. Linear motion errors have to be measured and evaluated in terms of preload adjustment. The successful control of an ultrasonic actuating stage (containing a movable part and the actuator) depends on the interaction of all elements that compose the system and its environment. The thin-disc structure of this ultrasonic actuating component includes: (1) the membrane of piezoceramics; (2) the elastic metal sheet of nickel alloy; (3) the covered with its
Platform fabrication and assembly
NO Prototype
Fig. 1. Schematic prototype of a linear stage: (a) exploded view of an ultrasonic actuating stage and (b) flow chart for prototype development.
diameter of 24.5 mm sliver sol–gel membrane used as an electrode. The thin-disc structure is a piezoceramic membrane boned on a Ni-alloy sheet with its diameter 41 mm. Its total thickness is 0.23 mm and the thickness of the metal sheet is 0.10 mm, with its dimension specification as shown in Fig. 2a. The bonded structure of a smaller diameter PZT film adhered with the larger diameter Ni-alloy sheet, called a disk vibrator, has the capability of actuating in both the direction of the in-plane and the out-plane, depending on the location of the constraints and the amount. In this study, the multiple-resonant modes are performed by an external perturbation with a constraint technique on the metal sheet rather than cutting off the edge of a disk vibrator. The cutting edge method was also applied for application to an electromechanical filter as a communication frequency element [1]. This constraint technique is a completely different principle from a conventional multi-electrode ultrasonic motor. Using the controlled mode shapes in a single-phase driving power for one set of electrodes
F. Wen, C.-Y. Yen / Ultrasonics 47 (2007) 23–31
25
Fig. 2. (a) The thin-disc structure piezoceramics as an ultrasonic actuating component and (b) a vibration mode of three constraints using ANSYS simulation.
[8–10], a disk vibrator could possibly be expected to force the movable part in both directions of forward and backward as shown in Fig. 1a. For PZT thin-disc structure vibration in ultrasonic frequency, the piezoceramic acts as the driving source needed to generate the high frequency extended–shrunk motion of the metal sheet. The metal sheet plays the amplifier with vibrating magnitudes and constructs the desired mode shapes. The minimum deformation is located at the central portion, but larger deflection is located near the outer edge of the metal sheet. Contradictorily, the metal stiffness also constrains the piezoceramic, and limits the PZT dynamic response to electrical power. Only in suitable power entry matching resonance frequencies, the metal stiffness would be overcome by the piezoceramic to produce the optimal efficiency. Thus, the resonance deformation of a metal sheet always follows the flexural-like vibrating of the piezoceramic, called a mechanical flexural wave. The phenomenon exists especially in ultrasonic frequencies. Furthermore, if it is used as an actuator, we only need to
directly observe the resonant mode shapes. Then, the ultrasonic driving mechanism was roughly configured [8–10], as shown in Fig. 2b. Based on these concepts stated by flexural waves of the metal sheet, our lab has been developing some useful driving mechanisms for a DVD player tracking system, and a precise ultrasonic linear stage. In this study, a piezoceramic actuator is fixed to a normal preload mechanism, as shown in Fig. 3. The designed preload is conformed to the movable actuator and the normal direction of slider motion may cause contact at any time. Also, a good insulation must be assuredly placed between the fixing stainless plate and the piezoceramic. The major purpose of this insulation is to avoid the wire of the driving power from being shorted when a connection is made. When considering the precision in finishing and the balance of the mechanism, the sliding rail with rolling-balls under the linear guide (used in an optic positioner) is used as the linear movable component. The surface of the slider has been attached to the aluminum plate treated with positive electrode processing. This is to
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A
Output
× 10
50Ω
100k
~
Function Generator
Input A
HSA 4011 Power Amplifier Output A
+
-
PZT Actuato r
AT0023
AC/DC
Linear stage Fig. 3. The assembly of normal preload adjustment and an ultrasonic actuator.
increase the friction between the actuator and the slider. Magnetic belts have been applied to the opposite end of the slider for sensing the position while measuring the slider motion via the magnetic encoder. The slider guide, as the platform, can carry the weight blocks and mark the home position. The proposed linear stage has a single-axis large-movement of 130 mm, but a tolerance for mechanical error within 1 lm. Fig. 4 shows the prototype of the ultrasonic actuating linear stage. 3. Characteristic measurement of the linear stage based on driving frequencies and various loadings The characteristic evaluation for the linear stage is via a laser-Doppler vibrometer (LDV) system. The frequency of the receiving wave would be shifted when the emitting wave source and/or the receiving object creates the relative motion. In other words, there are different frequencies occurring in the emitting wave source and the reflected wave source. The Doppler Effect demonstrates that the frequency of the receiving wave will turn higher than that of the emitting wave when both objects move gradually closer
OUTPUT RF INPUT
REFERENCE OUTPUT
Computer REFERENCE INPUT
RS-232
RF OUTPUT
Demodulation Unit
Oscilloscope
AC/DC INPUT
AT 3700
TDS 220 CH1
VEL [m/s/V]
Fig. 5. The experimental setup for a linear stage using the AT0023 laserDoppler system.
together. In contrast, when both objects are moving away from each other, the receiving frequency will record a lower wave than the original one. In this paper, using the LDV system, the characteristics among voltages onto piezoceramics, driving frequencies, and slider’s velocities are prospected, counting out the different weight loading. Thus, the features of the linear stage were evaluated for control purposes based on the measured configuration as shown in Fig. 5. 3.1. Measurement principle The measurement system consists of the AT300 LDV device, the AT 3700 demodulation unit for signal conditioning, and the TDS 220 oscilloscope for monitoring via hookup from the computer. The different driving frequencies and voltage levels could be tunable by the function generator. The AT0023 sensor head, manufactured by
Moving object Laser source fo Reflected light fr
θ1
Moving object velocity V1 Fig. 4. The prototype of an ultrasonic actuating linear stage.
Fig. 6. LDV measuring configuration.
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Graphtec Corp, Japan, with a built-in laser tube has the feature of an efficient laser light source and high sensitivity. The laser light is phase aligned resulting in its ideal feature for long distance measurement. The principle of the LDV system is the measurement of frequency changes caused by the Doppler Effect. Where the Doppler shifted frequency determines the ratio of the velocity to vibration [11], based on the theory of Eq. (1) and shown in Fig. 6. fD ¼ jfo fr j ¼
2v1 cos h1 ko
ð1Þ
27
where fD is the Doppler shift frequency, fo is the oscillation frequency of laser light, fr is the frequency of reflected light with Doppler shift, ko is the oscillation wavelength of laser light, v1 is the velocity of moving object, and h1 is the irradiation angle. 3.2. Dynamic characteristics In accordance to the various input signals which are relative to the frequency and voltage levels, the operating
Fig. 7. (a) The characteristic curves of velocity versus frequencies with free loading, (b) the characteristic curves of velocity versus frequencies with 250 g weight loading, (c) the characteristic curves of velocity versus frequencies with 500 g weight loading and (d) the characteristic curves of velocity versus frequencies with 1 kg weight loading.
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features of an ultrasonic actuating stage have to be evaluated. The experimental evaluation pertained to velocities based on free loading, 250 g, 500 g, and 1 kg weight loading, respectively. The emitting laser source is reflected by a small mirror, stuck on the head of a liner guide. Through the sensing head AT0023 hookup the demodulation unit AT3700, the accuracy velocity of the linear stage was acquired as shown in Fig. 7a–b with diverse weight loadings. There is a similar phenomenon in which the maximum forward speed of a linear stage is at a driving frequency of 73 kHz, but the maximum reverse speed near 85 kHz. The forward velocity is much faster than that of the backward velocity due to this mechanism’s limitation of an ultrasonic actuating linear stage. The higher input voltage level is much more powerful resulting in quicker motion. Otherwise, the minimum input voltage level shall be provided, usually above 3 V, due to the contact friction driving between the actuator and the slider.
Fig. 8. The damage of the piezoceramic and the wearing at the top edge of the metal sheet.
3.3. The damage and wearing phenomenon of the thin-disc ultrasonic vibrator The driving frequency in backward motion (that is 86 kHz) shows the shifting frequency dropping to lower ranges (about 85 kHz) as shown in Fig. 7a. One particular phenomenon in the linear stage is the disequilibrium of forward and backward motion as shown in all figures except Fig. 7d. The heavy weight loading could improve the equivalent velocity in both the movement directions. Added weight loading with the lower driving voltage, e.g. 5 V, did not appear to have enough electrical power needed to activate the slider and cause movement. Another big problem was the strain damage of the piezoceramics caused when the driving voltage was augmented, as shown in Fig. 8. However, the acceptable driving voltage shall be considered the impedance match for piezoceramics and the vibration amplitude induced from the metal deformation. There is a probability that damage could occur. Normally, the thinner metal sheet could offer the more activating vibration for mechanical driving power, but the capability of anti-wearing is also poor as shown in Fig. 8. 4. Experimental results and performance evaluation
the friction driving mechanism of a stage, there is deadzone phenomenon as obviously shown in Fig. 7. The critical input voltage and the driving frequency determine such nonlinear behaviors that the difficulties of control design are influenced by the minimum driving voltage and exact resonant frequency while the dead-zone is aggrandized. The response quality of the velocities depends on the moving speed of a stage based on the level of driving voltage and precise degree of the excited frequency for such a piezoceramic actuating stage. Visually, it has a tendency in the higher levels of the driving voltage to cause faster motion speed. Because of the inherent hysteresis in piezoelectric materials, there is a difference in linear positions while in ascending and descending voltages. The linear relationship between actuating voltages and displacements is no longer in existence. Thus, these hysteresis as shown in Fig. 9a and b shall be counted in the control design. Otherwise, the positioning accuracy is also an important factor relative to the design of control system. Fig. 9c illustrates the curve of the accumulated position error for a piezoceramic actuating stage. It has an estimated error about 2.8–3.2% under weight loading of 500 g.
4.1. Positioning evaluation 4.2. Positioning compensator The performance experiment for the linear stage is via the PC-base driving and control system. When the analog signals were sent out through the PC interface as the controlled voltage, the driving circuit amplified the signal. The stage moved in the forward or backward direction by the thin-disc ultrasonic actuator depending on the driving frequency. The displacement is monitored by HIWIN magnetic measurement system which is manufactured by HIWIN TECHNOLOGIES Corp. in Taiwan. Using the interface encoder to convert the voltage to a linear amount, the movement feature of the stage could be observed. For
The positioning compensator has applied the inverse recursive learning method of neural network to tune the output gain of fuzzy control in real-time. When the stage’s position error is converged on the specific value, the pulse corrector is ignited to suppress the error. In the design of the fuzzy controller, the Gaussian type membership function contains three displacement errors (x), three displacement error change rates (dx), and five outputs (y), where Gaussian membership function is Gaussian(x; c, r) = exp[0.5(x c/r)2], c denotes the center value of the
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the direct tuning of output gain for fuzzy control. Thus, the transient response is improved while the movement direction and displacement amount are controlled. The block diagram illustrating the fuzzy-neural controller for output gain tuning is shown in Fig. 10a. For performance evaluation, the control inputs coming from the controller are implemented by Matlab/Simulink software via the AD/DA servo control card and inference. The pulse corrector or pulse generator categorizes the several small piece controllers, depending on error quantity, through the determination of error selectors as shown in Fig. 10b. The fuzzy controller, depending on the error amount of displacement, is divided into the number pieces of small controllers to perform the command via error selectors respectively. Because of the square signals of 0.3 Hz as control commands, an overshoot phenomenon instantly occurred during the switched pulse. The shape function became necessary to smooth the raised up command.
Fig. 9. Diagram (a) and (b) are the loops of hysteresis for the linear stage in forward and backward motions with weight loading of 500 g, respectively. (c) The accumulated position error for a pizeoceramic actuating stage with weight loading of 500 g.
membership function, and r denotes the width of membership function. Both optimal values of c and r could be obtained from trial and error via experiments. The control rule foundation is based on the relationship in the error amount and the error change rate of the stage’s displacement relative to control inputs. Applying the Min– Min–Max method for the Fuzzy inference mechanism and the center of gravity method for defuzzification, the diagram of the relationship curves for errors. Additionally, control inputs were calculated. During experimental testing, in order to reduce the CPU time consumption, the look-up table is built according to inference result. The Fuzzy function in the Matlab toolbox is also a solver used to directly gain the inference result. Since the output gain of the fuzzy control is designed for the steady-state properties of the stage, it is of poor efficiency in transient response. Therefore, the method of the inverse recursive neural network is introduced to perform
Fig. 10. (a) The block diagram of output gain tuning for a neural-fuzzy positioning compensator and (b) the block diagram of executable pulsed wave corrector by Matlab/Simulink software.
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Furthermore, the shut down switch was added onto the controller to avoid any tiny vibrations that could cause displacement errors. 5. Discussion Fig. 11 displays the characteristics of control inputs, position tracking, or position errors, and the driving voltages with weight loading of 500 g respectively. Obviously, the piezoceramic stage has the capability to fellow the control commands reaching the specific position, but there was an inevitable error during the position tracking. One of the possible reasons for the position error is that it was induced by the friction-contact-driving mechanism between the ultrasonic actuator and the slider. Therefore, if one would
like to eliminate such an error, the stage shall be redesigned or modified in the transmission mechanism. Due to the friction-contact-driving, there are nonlinear dynamic behaviors like dead zone or hysteresis apparently, especially in lower input voltage (within 1.5 V) onto piezoceramics. Fortunately, the neural-fuzzy strategy, in our design for the controller, can successfully overcome the nonlinear dynamic behavior. Because of this success, the design’s position tracking ability performs well for the stage as shown in Fig. 11. Before the pulse corrector was added to the neural-fuzzy controller, the driving voltages were always sent to the actuator resulting that the positioning track was unable to be converged as the desired signal of command inputs. Now, the pulse corrector offers the instant response to cut off the driving voltage when the desired position is reached. These results, shown in Fig. 11c, demonstrate the intermittent signals of tracking command for driving voltages. Otherwise, due to the lack of continuous supplied driving voltages, the thermal dissipation could be minimized as possible for piezoceramic excitation. Since the direction and velocity of linear motion is controlled by the specific driving frequency and voltage, the design of the positioning compensator has been implemented for the novel ultrasonic actuating linear stage. Based on the recognition of nonlinear behaviors relative to the contact-transfer driving force, the neural-fuzzy method, without the exact mathematical model of the linear stage, is employed to complete the tracking performance. The pulse corrector is a very helpful assisting device added on the controller to reduce the oscillation time and immediately converge towards the system’s stability. The experimental characteristics have demonstrated that the positioning accuracy could be reached and low thermal dissipation could be obtained due to discontinuous electrical power coming into the piezoceramics. 6. Conclusion
Fig. 11. The position characteristics of a linear stage with 500 g weight loading: (a) control inputs and position tracking, (b) position tracking errors and (c) driving voltage onto the piezoceramic.
The stage with long distance movement is evaluated by using a LVD measurement system. The experimental results have demonstrated that the friction-contact ultrasonic actuating mechanism could reach very high actuating and braking abilities. Thus, the mechanical design and control involving four fundamental tasks has been achieved: (a) positioning motion was proposed using a linear platform supported by bearings of a rail guide ensuring kinematical movement; (b) thermal drifts were avoided due to point contact by the use of ultrasonic friction driving actuator, and the temperature control was unnecessary; (c) dynamic decoupling has been achieved between the actuator and the slider to avoid parasitic movements and (d) natural resonant frequencies of the whole system indicate a preponderance of vibration modes of the friction drive, because of ultrasonic operation of actuator (above 65 kHz). It is obvious that the mechanical design has been achieved with high quality and the ultrasonic actuating
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stage will follow the control commands for high performances. Also, its running accuracy and positioning precision are predictable. These concepts of mechanism design can be used in lithography positioning equipment, medical focusing instrument, and tracking devices of hard disk drives and/ or optic disk drives. Furthermore, the cost of this structure is low and has a preferred efficiency. Acknowledgement The authors thank the financial support of the National Science Council of the Taiwan government and Grant Number: NSC-93-2212-E-129-007. References [1] S. Ueha, Y. Tomikawa, M. Kurosawa, N. Nakamura, Ultrasonic Motors Theory and Applications, Oxford Publications, Clarendon Press, Oxford, 1993. [2] K. Uchino, Piezoelectric Actuators and Ultrasonic Motors, Kluwer Academic Publishers, Boston, 1997.
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[3] T. Sashida, Takashi Kenjo, An Introduction to Ultrasonic Motors, Clarendon Press, Oxford, 1993. [4] S.H. Chang, C.K. Tseng, H.C. Chien, An ultra-precision XYhz piezomicropositioner – Part I: design and analysis, IEEE Trans. Ultrason. Ferr. 46 (4) (1999) 897–905. [5] S.H. Chang, C.K. Tseng, H.C. Chien, An ultra-precision XYhz piezomicropositioner – Part II: experiment and performance, IEEE Trans. Ultrason. Ferr. 46 (4) (1999) 906–912. [6] N. Lamberti, A. Iula, M. Pappalardo, A piezoelectric motor using flexural vibration of a thin piezoelectric membrane, IEEE Trans. Ultrason. Ferr. 45 (1) (1998) 23–29. [7] R. Carotenuto, N. Lamberti, A. Iula, M. Pappalardo, A new low voltage piezoelectric micromotor based on stator precessional motion, IEEE Trans. Ultrason. Ferr. 45 (5) (1998) 1427–1434. [8] F.L. Wen, C.Y. Yen, M.S. Ouyang, Thin-disk piezoceramic ultrasonic motor. Part I: design and performance evaluation, Ultrasonics 41 (6) (2003) 437–450. [9] C.Y. Yen, F.L. Wen, M.S. Ouyang, Thin-disc piezoceramic ultrasonic motor. Part II: system construction and control, Ultrasonics 41 (6) (2003) 451–463. [10] F.L. Wen, S.C. Mou, M.S. Ouyang, Design and construction of a shaft-driving type piezoceramic ultrasonic motor, Ultrasonics 43 (1) (2004) 35–47. [11] Theory, characteristics, and sample measurements with a laserDoppler vibrometer, in: Work Shop for Vibration Measurement, Sanlien Technology Corp., 2003.