the design and characteristics of piezomotors using flexure-hinged displacement amplifiers

E L S E V I E R Robotics and Autonomous Systems 19 (1996) 189-197

Robotics and

Autonomous Systems

The design and characteristics of piezomotors using flexure-hinged displacement amplifiers

T i m K i n g *, We i X u Mechatronics Research Group, School of Manufacturing and Mechanical Engineering, The University of Birmingham, Edgbaston,

Birmingham, B15 2TT, UK

Abstract

Two prototype piezomotors are described in terms of their operational principles, design, construction and some operating characteristics. Both are driven by mechanically amplified piezoelectric stack type actuators. One is a harmonic piezomotor in which the mechanically amplified displacements are used as the wave generator of a harmonic gear drive. The other uses similar mechanical amplifiers to drive a roller clutch motion generator. The requirements for effective mechanical amplifiers are discussed and the performance advantages of piezomotors based on them outlined. It is concluded that such motors can offer useful possibilities for specialist mechatronic applications.

Keywords: Flexure hinges; Mechanical amplifier; Displacement amplifier; Piezoelectric motor; Harmonic drive; Harmonic motor; Roller clutch

1. Introduction

This paper describes the design and construction of two different piezomotors developed by the authors. Both employ flexure hinged mechanical displacement amplifiers to increase the output movement of stack- type piezoelectric actuators to enable them to be applied to rotational motion generating mechanisms. The first example is a harmonic piezomotor. The funda- mental principle of this kind of motor has been described by the authors in previous papers [3,13] and a completed motor design is presented here. The harmonic drive principle enables the production of an externally commutated motor which can be driven as a conventional stepping motor for open-loop applications and which yields a very fine rotational incre-

* Corresponding author. E-mail: [email protected].

ment. The use of piezoelectric stack actuators makes the motor power consumption almost zero in holding situations, which gives it an advantage over conventional electromagnetic motors in some applications.

The second prototype piezomotor presented is based on a roller clutch mechanism. Using one or more piezostack actuators and a roller clutch as the rotational motion converter, this motor has a very simple structure and requires only a single phase power input. To achieve effective movement of the motor using commercial tolerance roller c~utches, the output movement of the piezostack is magnified by a flexure- hinged displacement amplifier, as for the harmonic motor design. In order to investigate the characteristics of this motor, two different drive waveforms have been used in experimental tests. These were triangu- lar and sinusoidal waveforms. The output frequency of power supply is varied to alter the rotational speed

0921-8890/96/$15.00 g~ 1996 Elsevier Science B.V. All rights reserved PII S0921-8890(96)00046-2

190 T. King, W. Xu/Robotics and Autonomous Systems 19 (1996) 189-197

of the piezomotor, but the rotational increment is not constant and so this motor is not suitable for open- loop applications.

mechanical amplifiers, which are backlash-free. A comprehensive study of the performance of high mag- nifying ratio flexure-hinged amplifiers has thus been conducted.

2. Piezoelectric motors

Piezomotors, which use piezoelectric instead of electromagnetic driving mechanisms, are claimed to be capable of providing very high torque at low speeds and to allow very precise positioning [6]. The 'ultrasonic motor' was one of the first succes- ful forms using piezoelectric actuation. A number of designs have been reported using differing drive methods [15]. A motor, proposed and built in the USSR in 1978 by Vasiliev et al. [16], uses a Langevin vibrator. A travelling-wave principle has been used by AEG [7]. A 'fluid coupling' ultrasonic motor has been developed by Nakamura et al. [4]. Its rotational mechanism is similar to a stationary-wave ultrasonic motor and force transmission is by fluid coupling. The 'inchworm' mechanism was originally used by Burleigh Instruments for its patent linear piezoelectric Inchworm Motor. Based on this principle, high accuracy rotation has been achieved for different pro- poses such as semiconductor manufacturing [14] and surface finish metrology [11]. Positive drives have been provided by the 'cycloid piezomotor' [1] and 'harmonic piezomotor' [2] based on mechanical gear transmission mechanisms.

In summary, current piezomotor designs can be divided into two categories defined by the operation frequency of the piezoelectric actuator: resonant operation and non-resonant operation. Resonant operation piezomotors have advantages of high efficiency and, in some circumstances, high output torque. However, lack of speed and positioning control ability, and for some designs the requirement for multi-phase power input, are disadvantages of this kind of motor. The non-resonant operation piezomotor generally has a lower efficiency but can have other advantages, such as very precise positioning and open-loop speed control abilities.

Non-resonant operation piezomotors, such as the harmonic piezomotor, require large displacement to be generated from the high force, but low displacement, output of the piezoelectric actuator. This is most practically achieved through the use of flexure-hinged

3. Design of flexure-hinged displacement amplifiers

To design a high gain, efficient, displacement amplifier, there are three main aspects that need to be considered. The first is the overall topology of the displacement amplifier. The second is the optimisation of the profile of its flexure hinges. The third is the selec- tion of the material of construction.

Flexure-hinged displacement amplifiers can be divided into two categories; precision oriented and displacement oriented, according to their application [17]. Piezomotor applications fall into the latter cate- gory. There are three basic varieties of flexure-hinged displacement amplifier topology which can be applied singly, or in combination to yield compound amplifiers [12]. These basic amplifying elements are the, simple lever, bridge and four-bar linkage amplifiers. Benefiting from a symmetrical structure, a bridge displacement amplifier has a high gain and linear output motion which can be used for precision oriented applications. The four-bar linkage flexure- hinged amplifier can provide some special output movements for both precision and high-displacement oriented applications. The simple lever flexure-hinged displacement amplifier can produce large output displacement and has the highest efficiency because it uses less hinges than the other two topologies [3]. Therefore, a flexure-hinged simple lever displacement amplifier has been selected for use in the prototype piezomotors described in this paper.

Once the topology of a flexure-hinged displacement amplifier is selected, the geometrical profile of the hinges will be a key factor in determining its performance. Fig. 1 shows a variety of hinge profiles which may be employed in flexure-hinged displacement amplifiers. The limiting cases are: at the left, a right-angle hinge profile and at the right, a right-circular one. In between there are various possibilities, of which two special cases are shown in the figure. These are elliptical and corner-filleted hinge profiles. The specific hinge profiles in these groups depend on the geomet-

T. King, W, Xu/Robotics and Autonomous Systems 19 (1996) 189-197 191

Circular Angle

Comer Filleted

Fig. t.

Deflection (l~rn) 140 t ~- - - - -

120 | \ - - '~l . . Comer-filleted too! ~ ' ~ ' ~ - / /

Elliptical --

2 0 ' 6 015 i 115 2 215 3 315 4 415 Ellipse Minor Axis or Radius of Comer Fillet (nun)

Fig. 2. Fig. 3.

ric parameters, i.e. the minor axis of the ellipse or the radius of the comer fillet.

The design theory for the fight circular profile flexure hinge was first introduced analytically for industrial applications in the mid-1960s [5]. In the 1970's, flexure-hinged mechanisms were used to magnify the displacement of piezoelectric actuators [8]. The performance of the right-circular hinge profile has been studied by both analytical and finite element methods [9] in terms of translation precision. However, there has been little work reported, using either analytical or FE methods, for other profiles, such as elliptical and comer-filleted de,;igns. FE methods have been employed by the authors for investigating performance of these profiles [17]. Fig. 2 shows a typical FE meshed hinge profile. Modelled hinges all have length 10 mm and centre thickness I mm.

One edge is restricted and a 10 N load applied to the other. The deflection at the point of loading is given in Fig. 3 for the two groups of hinges. When com- pared with 'equivalent' corner-filleted designs (where the radius of the corner fillet equals the minor axis length of the elliptic hinge) elliptical profile flexure hinges have higher stiffness. The fight circular hinge

profile has the highest stiffness. It should be avoided for use in amplifiers for piezomotors since it could re- duce the achievable displacement of the amplifier very significantly. The fight angle hinge, the other extreme case of the corner-filleted profile, has the lowest stiffness. However, from the points of view both of fatigue and manufacture, fight angle hinges are not a practical possibility.

There are two important considerations in selecting the material for displacement amplifier construction; maximum tensile stress and Young's modulus. To generate large output displacement high tensile stresses necessarily exist in the hinges of the amplifier. These stresses are a function not only of the input and output of the amplifier, but also the hinge profiles. Fig. 4 shows the FE results of maximum stress in the hinges for the two groups of hinge profiles investigated.

When the deflections of the hinges are the same (i.e. for equal amplifier output displacements), there is a general trend that the maximum stress in the hinges increases with increase of radius of corner-fillet or minor axis length of elliptic hinge profile.

Once the corner-fillet radius or minor axis length reduces to zero (the 'fight-angle' profile), the highest


Maximum Stress 8xl0~MPa

7

6,

5.

4. R=5 a=5

3.

,

1

0

R=5 _ ~ a = 0

a=0.5

in Hinges R=0.5 R=0

R = 5 ~ _ ~ • LOad=iON

. 41, Load=10N

a=0.5 Elliptic Hinges a - r n i n o r ax is I~ Load=40N

R=0 R-Radius • Load=30N

• Load=10N

I l I I I I

0 10 20 30 40 50 Deflection of Flexure Hinges

Fig. 4.

60xl0-2mm

flexibility is achieved, however, the disadvantage of this profile is the existence of high stress concentra- tions which make this an impractical option. Fig, 4 also shows that elliptical profile hinges have a better performance than corner-filleted ones, especially around the point where the minor axis length is equal to 1/20 of the hinge length. This ratio is thus recommended for the design of hinges for large output displacement applications.

Use of high Young's modulus material has been reported for achieving high overall amplifier efficiency [10]. However, the high output displacement required for our motor applications cannot be achieved due to the drawback of the flexure hinges consuming more energy when the amplifier is made from high Young's modulus material. For such a material, large deflection of the hinges also implies that large tensile stresses will be generated around the hinge area. This limits the attractiveness of using high Young's modulus materials for high gain displacement amplifiers. However, there is a limitation in using low Young's modulus material too [10], since strain energy losses in the structure have a detrimental effect on efficiency. Stiffness matching between the piezostack and the structure is also a factor to be considered. As an engineering compromise, titanium has been selected as an appropriate material for the construc-

tion of displacement amplifiers used by the authors. The amplifiers were constructed in monolithic form by wire electro-discharge machining (EDM) using a Charmilles Technologies ROBOFIL 200 CNC machine. The use of a fine wire electrode (0.25 mm) provides freedom to produce a wide range of hinge profiles and allows them to be machined without significantly stressing the structure; an important con- sideration in view of the small feature dimensions involved. Fig. 5 shows an enlarged view of hinges produced by this method.

Although the harmonic drive and roller clutch piezomotors, discussed in this paper, have completely different structures and operation principles, they have similar requirements for their driving elements. Based on the above discussion, a displacement amplifier has, therefore, been designed to suit both motors.

In order to achieve as large an output displacement as possible, a large input displacement is required. Therefore two PI P842.10 stack-type piezoactuators, each 18 mm long and 5 x 5 mm in cross-section, were used in series. These provide a total maximum input displacement of 301.~m(at 100 V) for the displacement amplifier. Fig. 6 shows a drawing of the displacement amplifier. It can produce 0.49 mm and 0.41 mm output displacement under 1N and 2N output load, respec- tively.

T. King, W. Xu/Robotics and Autonomous Systems 19 (1996) 189-197 193

Fig. 5.

15.50 : 5.GO

_ , _ 7.(]0

67.00 I 25.00

Fig. 6.

LI2..___O0

W3.0

4. Piezomotor topologies and operation principles

Two different motor principles, a harmonic drive and a roller clutch piezomotor, have been designed by the authors.

4.1. Harmonic piezomotor

The harmonic piezomotor consists of displacement generating and motion converting parts. The displacement generating part is made from a group of piezostacks and attached flexure-hinged displacement amplifiers. They produce both displacement and force for the motion converting part. The motion converting part is constructed by adapting the gears of a harmonic drive. It converts the linear movement of the first part into rotational movement of the motor. Unlike the de-

sign of conventional harmonic drives where rotational wave generators are used, the harmonic drive for our piezomotor uses a radial spokes wave generator in which the rotational wave on the flexspline is generated by the appropriate movement of the spokes. The shape of the flexspline depends on the number of si- multaneously energised piezoactuators. Fig. 7 shows a photograph of the prototype harmonic piezomotor.

FE analysis of flexure splines with and without teeth shows that the presence of the teeth does not affect the deformation significantly [ 13]. A simple analytical design formula was, therefore, used to give an acceptable design approximation for the flexure spline thickness.

The maximum required deflection of the flexure spline of the harmonic drive is equal to its tooth height plus the necessary clearance. From the configuration of the Davall circular spline used, which had a module


Fig. 7.

of 2.06, the maximum displacement requirement for the wave generator is found to be 0.41 mm. Consider- ing the clearance requirement, the total deformation of the flexure spline is taken to be around 0.45 mm. This was confirmed by comparison with the Davall DDC- 650 'Duodrive' (from which the components were de- rived) which has a wave generator displacement of approximately 0.46 mm.

As stated above the displacement amplifier has been designed to be able to provide around 2N output force at the required displacement. With a flexure spline thickness of 0.3 mm, less than 1N force is required to deform the flexure spline, leaving over 1N force to generate rotational torque. Output torque, can, therefore, be estimated to be around 0.064 Nm.

In view of the difficulty of manufacturing the required small module gears, the gear parts of the prototype harmonic piezomotor were re-manufactured from a production series Davall DDC-650 'Duodrive'. The thickness of the flexspline gear was reduced to 0.3 mm. The circular spline was machined to be supported by

a large diameter ball-race. It works as the rotating element of the motor.

4.2. Roller clutch piezomotor

The operating principle of a roller clutch is similar to a ratchet mechanism. Based on this principle, the roller clutch piezomotor drives the clutch element directly with circumferencially arranged piezoactuators. The tangential push of the piezoactuators yields rotation of the cam coupled to a shaft. In order to achieve continuous rotation, two identical or similar sized roller clutches are required. One is used to generate forward movement as described above (the 'driving clutch'). The other is used to prevent backward rotation of the shaft when the piezoactuators return to their start positions for the next stroke (the 'stopping clutch'), it allows the motor shaft to rotate when the actuators push the first roller clutch but locks backward rotation of the shaft. The motor can provide two kinds of torque: static (holding) torque and dynamic


Fig. 8.

(rotational) torque. The holding torque of the motor is produced by the stopping clutch. However, the dynamic torque or rotational torque depends on the push- ing force generated by the displacement amplifier. This will provide stepped motion with some backlash and only unidirectional rotation. Nevertheless, relatively high speed in comparison with other piezomotors, and good efficiency are possible.

The prototype motor consists of a pair of displacement amplifiers driven by two piezostack actuators. They are arranged symmetrically on opposite sides of a driving cam. The linkage between the displacement amplifier and cam is via an adjustable point contact. The driving clutch is a press fit in the cam. An HFL0408KF roller clutch is used for the driving clutch with a HF0306KF for the stopping clutch element. The clutching direction of the driving clutch is same as the rotational direction of motor shaft, and vice versa for the stopping clutch. The stopping clutch is held by the frame of the motor. Fig. 8 shows the prototype motor.

Rotational Speed (Rev, qVlin) 350, 300, 250, 200 150 100 50 . 0 ~ ,.i_a: •

0

Sine • Triangle

|

5'0 1oo l;o Exciting Frequency (Hz)

Fig. 9.

4.3. Characteristics of the roller clutch piezomotor

To investigate the performance of the motor, two different input waveforms were used; sine and triangle waves. The differing input waveforms affect the performance of the displacement amplifier, and hence the motor. The experimental data in Fig. 9 were measured by increasing driving frequency from 5 to 150 Hz. The


Rotational Speed (Rev/s)

n

O[]

Input Frequency (Hz)

[] 150

• 100

• 80

• 50

• 30

[]

l i * • n . R

m [] [] " A I I , I t l -- " " -.

0 0.01 0.02 0.03 Output Torque (Nm)

Fig. 10.

[] I

0.04

graph shows the characteristics of the rotational speed against excitation frequency of the motor in the no load condition.

The results in Fig. 9 indicate that the same excitation frequency with different wave shapes yields different rotational speeds. The sine input has a slightly higher no load rotational speed than the triangle one.

Figure 10 gives the experimentally determined rotational speed vs. output torque characteristic for a sine wave input. It shows that increasing the output torque reduces the output speed. Similar results were obtained with the triangle wave shapes.

5. Discussion and conclusions

Piezomotors are a new generation of torque generating device driven by piezoelectric actuators. Many different approaches have been used or proposed for converting linear displacement of the piezoelectric material into rotational movement. The harmonic drive is one such mechanism possessing several advantages. By comparison with existing motors driven by mutual actions of electrical current and magnetic field, this kind of motor offers excellent controllability and high efficiency in some operating conditions. It may be of particular interest in applications where its low magnetic field production is an advantage. Where operating cycles include long standstill periods, the ability of the motor to sustain a static torque with virtually

zero power expenditure may be useful. The design has many of the advantages of a stepping motor with fine positional resolution.

A roller clutch piezomotor has also been built and tested. The motor was operated with variable excitation frequency and with different excitation waveforms to investigate its characteristics. The rotational speed of the motor increases with the applied frequency. However, the slope of the speed vs frequency curve is affected by the excitation wave shape. The advantages of this motor are its single phase drive, wide speed range, useful output torque and simple structure which could be rendered appropriate for mass production. The main disadvantages are that rotation is possible in only one direction and there is a small stepped backlash during the rotation of the motor.

For both the harmonic and the roller clutch piezomotor, generation of significant displacements is crucial. Therefore, the development of large displacement piezoelectric ceramics and design of efficient displacement amplifiers is vital to the future development of piezomotors.

Acknowledgements

The authors wish to thank Davall Ltd. who provided a DDC-650 'Duodrive' which was used in the construction of the Harmonic Piezomotor.


References

[1] I. Hayashi, N. Iwatsuki, M. Kawai, J. Shibata and T. Kitagawa, Development of a piezoelectric cycloid motor, Mechatronics 2 (5) (1992) 433 A.A.A..

[2] M. Ishida, T. Hori and J. Hamaguchi, Principle and operation of the new type motor consisted of piezo-electric device and strain wave gearing, Trans. Inst. Electr. Eng. Japan D (Japan) I10-D (12) (1990) 1247-1256.

[3] T. King, W. Xu and J. Thornley, A piezoelectric harmonic motor, in: Makra and Penney, eds., Mechatronics, The Basis of New Industrial Development ISBN 1-85312- 367- 6, (Computational Mechanics Press, 1994) 411-417.

[4] K. Nakamura, T. Ira, M. Kurosawa and S. Ueha, A trial construction of an ultrasonic motor with fluid coupling, Japanese Journal of Applied Physics 29 (1) (1990) L160- L161.

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[6] U. Schaaf, Pushy motors, lEE Review (1995) 105-108. [7] G. Schadebrodt and B. Salomon, The piezo travelling wave

motor, Design Engineering (1991) (Jan.) 36-38. [8] EE. Scire and E.C. Teague, Piezodriven 50 - ~m range

stage with subnanometer resolution, Rev. Sci. Instrum. 49 (1978) 1735-1740.

[9] S.T. Smith, D.G. Chetwynd and D.K. Bowen, Design and assessment of monolithic high precision translation mechanisms, Journal of Physics E 20 (1987) 977-983.

[10] J. Thornley, Methods of application of piezoelectric multilayer actuato~rs to high-speed clutching, using displacement amplification, Ph.D. Thesis, Loughborough University of Technology, 1993.

[11] J. Thornley, T. King and M.E. Preston, A piezoelectrically controlled rotary micropositioner for applications in surface finish metrology, IFToMM-jc Int. Symp. on Theory of Machines and Mechanisms, Nagoya, Japan, (September 1992).

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[14] T. Tojo and K. Sugihara, Piezoelectric-driven turntable with high positioning accuracy (first report), JSPE-53-06, (1987) 879-884.

[15] Y. Tomikawa, T. Ogasawara and T. Takano, Ultrasonic motors-constructions/ characteristics/ applications, Ferroelectrics 91 (1989) 163-178.

[16] P.E. Vasiliev et al., UK Patent Application, GB 2020857 A (1978).

[17] W. XU and T. King, Application of flexure-hinges to displacement amplifiers for piezo-actuators, ASPE Annual Meeting, Cincinnate, OH (October 1994) 258-261.

Tim King received his first degree in Mechanical Engineering from King's College London and his MDes (RCA) in Industrial Design (Engineering) from the Royal College of Art. His Ph.D. studies in surface metrology brought him into contact with mini- computers and early microprocessors and led to his appointment to the De- partment of Mechanical Engineering at Loughborough University in 1981, to develop microprocessor applica-

tions in mechanical engineering. In 1992 he was appointed to the Chair of Mechanical Engineering at The University of Birmingham, where he now heads the Mechatronics Research Group. His current research includes microprocessor and DSP based systems for computer-visual inspection and control of deformable patterned materials, development of ultra high- speed piezoelectric actuators and motors, calibration techniques for surface metrology and CMM applications. He is a Fellow of both the IEE and the IMechE, a Member of the IEEE and the author of 100 journal and conference papers.

Wei Xu received his first degree in material science at Tshinghua Univer- sity of PR China in 1983. He then worked as an assistant materials engi- neer in the Chemical Machinery Fac- tory of Beijing Chemical Corporation. He joined Beijing Institute of Technol- ogy in 1986. He received a fellowship from the International Atomic Energy Agency, in 1988, and took on-the-job training in the UK, returning to China in 1989, where he then worked as a

nuclear safety inspector at the National Nuclear Safety Admin- istration of Science & Technology Committee. In 1992, he received an ORS award from the UK CVCP and started Ph.D. research in mechatronics at the University of Birmingham, UK. He gained his Ph.D. in April 1996 for his work on piezoelectric actuators and motors and is now doing research in advanced tools for minimal access surgery at the University of Dundee, UK.

the design and characteristics of piezomotors using flexure-hinged displacement amplifiers

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