Zhang Yifeng（張毅鋒）'Zhang Wu（張武）'Xiao Aiwu（肖愛武）' Zhu Meng（朱萌）'Pan Yunhua（潘云華）'Zhang Xiaoya（張小亞）

1.Xi′an Chuang Lian Ultrasonic Technology Co Ltd'Xi′an 710065'P.R.China；

2.School of Marine Science and Tchnology'Northwest Polytechnical University'Xi′an 710065'P.R.China；

3.Xi jing Electronic Corp'Xi′an 710065'P.R.China；

4.Xi′an Modern Control Technology Research Institute'Xi′an 710065'P.R.China

Influence of Friction Interface Contact on Ultrasonic Motor Efficiency Under Static Conditions

Zhang Yifeng（張毅鋒）1'2*'Zhang Wu（張武）1'Xiao Aiwu（肖愛武）3' Zhu Meng（朱萌）4'Pan Yunhua（潘云華）1'Zhang Xiaoya（張小亞）1

1.Xi′an Chuang Lian Ultrasonic Technology Co Ltd'Xi′an 710065'P.R.China；

2.School of Marine Science and Tchnology'Northwest Polytechnical University'Xi′an 710065'P.R.China；

3.Xi jing Electronic Corp'Xi′an 710065'P.R.China；

4.Xi′an Modern Control Technology Research Institute'Xi′an 710065'P.R.China

The friction interface matching plays a deterministic role in the motor efficiency'and the microcosmic contact status of friction interface should be investigated to improve the ultrasonic motor performance.The main purpose is to improve the effective output power of ultrasonic motor.Hence'one studies the contact condition of the friction interface of the ultrasonic motor'analyzes the micro condition of contact interface through finite element analysis'optimizes unreasonable structures'and compares the two different-structure ultrasonic motors through experiments.The results reflect the necessity of optimization.After optimization'the stator and rotor deform after pre-pressure and the contact interface of them full contact theoretically.When reaching heat balance the effective output of the motor is 37%'and the average effective output efficiency is 2.384 times higher than that of the unoptimized.It can be seen that the total consumption of the ultrasonic motor system decreases significantly. Therefore'when using in certain system the consumption taken from the system will decreases largely'especially in the system with a strict consumption control.

ultrasonic motor；friction interface；contact area；efficiency

0 Introduction

Ultrasonic motor is a new concept of microspecial motor'featuring small volume'light weight'compact structure'fast response'low noise and no electro-magnetic interference.As the actuator of a control system'it has a wide application prospect'and has been used in precision positioning field.With high-tech development'the application system has more strict requirements for control accuracy of the movement process. Improving speed stability is necessary for the ultrasonic motor to be widely used in precision control system.Traveling wave type rotary ultrasonic motor（TRUM）（hereinafter referred to as the ultrasonic motor）uses the converse piezoelectric effect of piezoelectric materials to activate vibration of the stator'and turns the micro-amplitude of the stator into rotary movement of the rotor' and exports power［1］.The speed stability of the ultrasonic motor is closely related to the contact interface of the stator and rotor.Kurosawa et al.［2-4］analyzed friction loss between the stator and rotor of the ultrasonic motor in 1988'and theoretically depicted the maximum input and output efficiency of the ultrasonic motor.Wallaschek［5］'Zhao et al.［6-7］and Xia et al.［8］qualitatively dissertated that there might be stick-slip on the stator and rotor contact interface'and analyzed the influence of tangential deformation. Storck et al.［9］also studied the influence of the tangential elasticity of the contact on electro-me-chanical performance of the ultrasonic motor. Maeno et al.［10-11］studied the function of pressure on the friction interface.With consideration of rotor inertia influence on interface'they computed the rotational speed-torque characteristic of the ultrasonic motor and motor performance parameters like energy loss and efficiency.In the condition of contact between flexible stator and rigid rotor'Zharii et al.［12-14］computed the speed and energy conversion efficiency of the ultrasonic motor'and also studied the stator and rotor smooth contact model and stick contact model for the ultrasonic motor.Duan et al.［15］established a complete 3-D model for piezoelectric ceramic and rotor coupling as well as stator and rotor contact interface of the ultrasonic motor.Ey using finite element software'Zhou et al.established a simplified finite element model which was used to analyze contact of the ultrasonic motor［16］'and simulated the influence of pre-pressure and the stator vibration amplitude on output performance of the ultrasonic motor［17］.Radi and Hami［18］conducted the dynamic contact model of stator and rotor contact interface of the ultrasonic motor by variational principle'and used the model into exploring the ineffective model of the ultrasonic motor.However'the above references do not mention the influence of the contact interface on the ultrasonic motor efficiency when the elastic stator and rotor are used under static conditions.Therefore'the structural improvement is presented for current USM-45 ultrasonic motor via redesign of some key parts as well as design of full contact of the stator and rotor contact interface.Some tests have also been conducted.The test results show that'the average output efficiency of improved ultrasonic motor is greatly increased'and the thermal loss rate is decreased by about 30%.

1 Average Effective OutPut Efficiency of Ultrasonic Motor ProPerty

The average effective output efficiency of the ultrasonic motor is mainly determined by the stator and rotor friction interface and stator structure（mainly elastomer）.The stator and rotor of the ultrasonic motor contact directly'they are driven by friction.Generally'alternating voltage is applied on the piezoelectric ceramic element stuck to the stator of the ultrasonic motor'capable of activating mechanical vibration of the stator.The vibration is turned into orientation movement of rotor by the stator and rotor contact friction. Hence'two-energy conversion process exists in the ultrasonic motor.The electro-mechanical energy conversion between the piezoelectric ceramic and stator is fulfilled by converse piezoelectric effect.If the lag effect of the piezoelectric ceramic and elastomer is ignored'the rotor free vibration and electro-mechanical energy conversion of piezoelectric ceramic are linearly reversible.Reversely' electric energy is generated.Eased on the above' although the ultrasonic motor is driven by friction'the motor must have greater energy loss. With friction making the motor be heated'the temperature is increasing higher'leading the motor output power to be increasingly smaller. When the ultrasonic motor reaches thermal balance'its effective output power also reaches balance.Therefore'the friction interface matching plays a deterministic role in the motor efficiency' and the microcosmic contact status of friction interface must be studied to improve the ultrasonic motor performance.Curves of torque and rotational speed'and efficiency and torque are as shown in Eig.1.

In the meantime'the elastomer structure has great effect on effective output efficiency of the ultrasonic motor.Eig.2 shows a common elastomer structure.A is the total thickness of the elastomer'and E the base thickness of the elastomer.The base thickness of the elastomer has obvious effect on the dynamics of the stator'directly influencing modal frequency and modal amplitude as well as working current of the motor.The base thickness is bigger'the stator rigidity increases' the same-order modal frequency increases'the working current of the motor increases greatly' the motor heating gradient increases'and the power loss decreases.The base thickness is smaller'the stator rigidity decreases'the same-order modal frequency decreases'the motor output moment decreases while the working current of the motor is decreasing.Therefore'it is not proper to change the elastomer base thickness.If it is required to change'overall evaluation and optimization with more complicated process must be conducted.

Eig.2 Elastomer structure

In conclusion'research on the average effective output power of the ultrasonic motor is actually the research on the stator-rotor friction interface contact and rotor base thickness.The paper mainly presents the research on the stator and rotor friction interface contact'optimization design for the stator and rotor friction interface for improvement of the average effective output power of the ultrasonic motor.

2 Stator and Rotor Friction Interface of Ultrasonic Motor Analysis

2.1 Stator and rotor friction interface

The contact model is Hertz contact model. Although stator and rotor contact of the traveling wave ultrasonic motor is not fully the same as general Hertz contact'the Hertz contact theory can better solve the contact friction problem of the traveling wave ultrasonic motor'the torque mathematics model is built.

There are the following hypotheses as per actual working status of the motor:

（1）The materials of the stator and rotor of the traveling wave ultrasonic motor are all elastomer；

（2）The traveling wave surface of the stator and the stator and rotor contact are smooth；

（3）The stator and rotor surfaces are not fully closely contacted；

（4）The stator and rotor of the traveling wave ultrasonic motor do not have relative movement；

（5）The contact of the stator and rotor of the traveling wave ultrasonic motor at the traveling wave peak is curvature cylinder surface contact.

Eig.3 is the contact model of the iso-curvature radius cylinder and the elatomer plane.It is assumed that'the stator is a iso-curvature radius cylinder at the traveling wave peak'the rotor is a elastic plane'and the rotor contacts the stator within the area with the width of a under pressure action.The contact width a［19-21］is

where D is the cylinder diameter'FNthe pressure applied on the rotor（at each peak）'i.e.pre-pressure'and CEa parameter related to material characteristic that can be expressed by

where E1and E2are elastic moduli of materials of the stator and rotor'respectively；γ1andγ2the Poisson ratios of materials of the stator and rotor' respectively.

Eig.3 Hertz contact model

The locked rotor torque of the motor M［22］iswhereμdis the friction coefficient'and r the average radius of the rotor.

The effective output power of the motor Poutputis

Erom Eqs.（1'3'4）'the relationship between the contact area and effective output power can be obtained

The variables in Eq.（5）are n0and a'the other paramenters can be marked as constant Z

Then Eq.（5）can be simplified as

Erom Eq.（7）'we can obtain the conclusion that'when the rotating speed of the motor is not changed'the output power of the motor is directly proportional to the square of the stator and rotor contact width.The wider the contact width is'the bigger the contact area is'and vice versa.

2.2 Stator and rotor contact model of ultrasonic motor

The structure of the traveling wave ultrasonic motor is shown in Eig.4.Eirstly'the elastomer is fixed on the motor base'then the rotor is placed on the elastomer'the circular disk at the rotor center is used to apply pre-pressure.To make the traveling wave ultrasonic motor output great moment'great axial pre-pressure is usually applied between the stator and rotor.In the mean time' the pre-pressure can make the stator and rotor bend in radial.

It is found that'because of radial bending' the actual stator and rotor contact area decreases greatly'and pressure is not evenly distributed. The stator and rotor contact is rapidly worn and heat loss power is sharply increased'leading to very low ultrasonic motor efficiency'as shown in Eig.5.

Eig.4 Stator and rotor coordination section of ultrasonic motor

Eig.5 Stator and rotor radial bending effect

2.3 Simulation analysis

2.3.1 Euilding finite element model

The finite element model is built by means of AEAQUS［23］.Since the rotor and stator model is equally divided into three parts along the circumference'the finite element model is only for the 1/3 part of the model（Eig.6）.In the model'the inner circular ring at the base of the stator is taken as the rigid body'the Kulun friction coeficient of the stator and rotor is 0.2'the prepressure is 160 N'i.e.about 1 MPa pressure intensity is applied onto the disk at the rotor center.

2.3.2 Model analysis

Eig.6 Einite element analysis model of USM45 ultrasonic motor

Eig.7 USM45 stator finite element analysis of displacement

The whole analysis result is shown in Eig.7. In Eig.7'it is found that'the displacement of the rotor outer edge is up（positive value）'and the displacement of the stator outer edge is down（negative value）'at this time'there is gap at the contact between the stator outer edge and rotor outer edge.That is'the stator and rotor contact width is not the whole rotor contact surface'is a part of the rotor contact surface.Check the displacement diagrams respectively'as shown in Eigs.8'9.In the diagrams'XIA-1 is the simulation data of the stator'and SHANG-1 the simulation data of the rotor.Draw the curvesby the data'as shown in Eig.10.It is shown that'the 2 mm length of rotor radial contact is actually inner 0.3 mm contact with an area of 42.96 mm2' and outer ring width is 1.7 mm'being separated' with an area of 252.61 mm2.The contact acreage of the stator and rotor is only 14.5%of the theoretical contact acreage'which makes the pressure of the contact acreage too high and increases the inner cycling stress of the friction materials'and finally makes rapid wear of the friction materials and heat of the moter.At this time'the heat energy loss of the motor is increased to 3 times as much as the theoretical heat energy loss'making the effective output power of the motor decreases greatly.

2.4 Structure oPtimization

Eig.8 Stator displacement before optimization

Eig.9 Rotor displacement before optimization

Eig.10 Displacements of stator and rotor contacting ring surface in pre-pressure status

The data shown in Eig.10 are the reference for the stator and rotor structure optimization. The optimization idea is to make the two curves in Eig.10 approach to coincide.Where s is the displacement.Therefore'deformation displacements of the stator and rotor are approximately the same'and the actual contact area is close to the theoretical contact area.According to the data analysis in Table 1'after deformation'the displacement of the inner rotor is 0.001 968 mm more than that of the inner stator'and the displacement of the outer rotor is 0.012 071 3 mmless than that of the outer elastomer.The inner displacement difference value is only 1/6 of the outer one.The optimization neglects the inner displacement difference value'focusing on the outer displacement difference value.

Table 1 DisPlacement data of stator and rotor contacting ring surface in Pre-Pressure status

In new structure'with consideration of the friction surface of the rotor being stuck with friction slice'so only the stator structure is optimized.The original design is that the friction surface of the stator is a parallel surface.Now the friction surface of the stator is designed into a conical surface with an outside displacement difference from the inner to the outer'to counteract the outer displacement difference while the stator and rotor deforming.The converted angle is about 0.2°.Therefore'in elatomer structure design'the tooth surface of the elatomer is designed as taper and the conical degree is 0.2°' which makes the two curves shown in Eig.7 approach to coincide'structure before and after contrast is shown in Eig.11.

Eig.11 Stator structure

Draw a 3-D mathematic model again as per the optimized structure'and analysis by AEAQUS.The friction coefficient and pre-pressure are set the same as those before optimization.The analysis results are shown in Eigs.12' 13.XIA-1 is the stator simulation data'SHANG-1 is the rotor simulation data.Concrete analysis data are shown in Table 2.Draw the curves by means of the analysis data of Table 2'as shown in Eig.14.It is found that'the deformation amount of the rotor is basic the same from the inner ring contacting to the outer ring contacting'and the changing magnitude is 10—14 mm'which can be neglected during actual machining and grinding. According to the displacement data of the rotor contacting the ring surface'it is found that the down displacement of the outer ring is more than that of the inner ring.It is obtained by calculation that'the deformation angle for ring surface contacting is about 0.194°'which approaches to the converted angle in stator optimization design'i.e. the contact surface of stator is approximately parallel to the fixed bottom after stator deformation. Additionally'on the basis of the deformation data in Eig.14'it is found that'the deformation displacement values of the nodes corresponding to the inner stator and rotor of the ring surface of the contract circle are-5.43×10-2and-5.66× 10-2'respectively'the difference is 1.7μm.The nodes can be considered as deformation coincidence.

Table 2 DisPlacement data of stator and rotor contacting ring surface in Pre-Pressure status after oPtimization

Eig.12 Stator displacement after optimization

Eig.13 Rotor displacement after optimization

Eig.14 Displacements of stator and rotor contacting ring surface in pre-pressure status after optimization

Therefore'it is concluded that'after optimization'when the stator and rotor are deformed in pre-pressure status'the stator and rotor contact surface fully contacts in a theoretical manner.

3 ExPeriment

3.1 ExPerimental facilities

Magtrol power analyzer is used'including electric analyzer and motor test system.Electric analyzer includes Dynamom Etermodel:DSP6001 and Power analyzer model:6510S（Eigs.15'16）.

Eig.15 Electric analyzer

Eig.16 Motor test system

3.2 ExPerimental law

Conduct machining as per the optimized stator'and assemble into a motor to do the performance experiment.The experimental law is as follows:

Set the input voltage as U=24 V'the environmental temperature 21℃'the start rotating speedτ=115 r/min'and the start pre-pressure 0.5 N·m'the experimental law is tested once every 5 min.The data to be tested include current I'rotating speed r'temperature t'and locked rotor torque M.Moreover'test the data for twostructure motors before and after optimization' and test the data for one-hour motor running. There are 13 groups of data in total'as shown in Tables 3'4'respectively.

Table 3 Motor test data before oPtimization

3.3 Result analysis

3.3.1 Easic curve analysis

It is shown in Tables 3'4 that'the tempera ture at which the motor reaches heat balance be-fore optimization is 80℃'and is 57℃after optimization.Eefore optimization'the null running current of the motor for each test is average 1.6 times as much as the post-optimization one.After optimization'the locked rotor torque of the motor for each test is average 1.5 times as much as the pre-optimization one.Eecause the locked rotor torque M and the current I are percentile data' when draw curves as per the data in Tables 3'4' the locked rotor torque M and the current I are magnified 100 times'the tested 4 types of parameters can be used for drawing in a same curve graph'as shown in Eigs.17'18.

Table 4 Motor test data after oPtimization

Eig.17 Pre-optimization motor parameter-time

3.3.2 Ultrasonic motor efficiency analysis

The total power consumption of the ultrasonic motor consists of the power consumption of the motor-driven controller and the power consumption of the motor.The motor power consumption includes the motor effective output power consumption and the motor heating power consumption

Eig.18 Post-optimization motor parameter-time

In test'the input voltage of the motor is 24 V'the motor current changes with time.The solvable motor power changing with time is the total power consumption of the motor.There are two calculation schemes for the power consumption of the ultrasonic motor-driven controller. The first is adding power consumption of each element/device.The second one is testing the controlling circuit board bus over current of the ultrasonic motor driver in the case of voltage for the fixed value'and then multiplying the current by the voltage.Here'the second scheme is adopted' the tested overcurrent of the circuit board is 5 m A'then the power consumption of the driver circuit board is

The output power of the ultrasonic motor is

where M is the locked rotor torque of the motor' ωthe no-load angular speed of the motor'and n0the on-load rotating speed of the motor.

The effective output power of the motor is

The Ptotal'Pmotor'Pdrive'Pheatandηcan be calculated by Eqs.（8—12）.

According to Tables 3'4'calculate corresponding parameters shown in Tables 5'6.Thendraw each power curve as per Tables 5'6'as shown in Eigs.19'20.After optimization'the efficiency comparison result is shown in Eig.21.It is known that'before optimization'the highest effective output efficiency of the motor is only 0.224'when heat balance is reached'the effective output efficiency of the motor is only 0.151'and the average effective output efficiency is 0.172' and the loss efficiency by motor heating rises to 0.84 after heat balance from the start 0.765.After optimization'the effective output efficiency of the motor is increased greatly with the highest value of 0.561'and it is about 0.37 after heat balance'the average output efficiency is 0.41. Meanwhile'the motor heating loss efficiency is decreased greatly'rising to 0.613 from 0.422 with the average value of 0.575.Additionally'itis also found that'the total power of the motor decreases greatly.The total power of the motor before optimization is 12.8 W in average'and it is only 7.38 W after optimization.That is to say' when the ultrasonic motor is used in a system' the power consumption of a whole system decreases greatly'being very important for application in a system with strict control for power consumption.

Table 5 Power and efficiency of motor before oPtimization

Table 6 Power and efficiency of motor after oPtimization

Eig.20 Motor power after optimization

Eig.21 Motor efficiency before and after optimization

4 Conclusions

Eefore optimization'the contact area of stator and rotor is only 14.5%of theoretical area' and it makes the pressure of contact area too bigand enlarges the inner stress of friction material which makes rapid wear of it and heat of the motor'at last the effective output power of the motor is only 17%.After optimization'the stator and rotor deform after pre-pressure and the contact interface of both approaches theoretically full contact.When reaching heat balance the effective output of the motor is 37%'and the average effective output efficiency is 2.384 times compared with the one which has not been optimized.

Meanwhile'the heat loss of motor deceases greatly'which comes from 10.48 W before optimization to 4.31 W after optimization'and according to the total power'the efficiency of heat loss decreases 30%after optimization.Moreover' the motor total power decreases greatly'which comes from 12.8 W the average before optimization to 7.38 W after it and is 58%of the one before optimization.It can be seen that the total consumption of the ultrasonic motor system decreases greatly'in other words'when using in certain system'the consumption will decreases greatly'especially in the system which has strict consumption control.

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（Executive editor:Xu Chengting）

TM383 Document code:A Article ID:1005-1120（2015）02-0163-11

*CorresPonding author:Zhang Yifeng'Senior Engineer'E-mail:no_bestzhyf@163.com.

How to cite this article:Zhang Yifeng'Zhang Wu'Xiao Aiwu'et al.Influence of friction interface contact on ultrasonic motor efficiency under static conditions［J］.Trans.Nanjing U.Aero.Asrto.'2015'32（2）:163-173.

http://dx.doi.org/10.16356/j.1005-1120.2015.02.163

（Received 10 January 2015；revised 26 January 2015；accepted 28 Eebruary 2015）