A study of a slim compact piezo inertia actuator

Pingping Sun, Haozhen Zhang, and Huan Yu

AFFILIATIONS School of Physics and Information Engineering,Jiangsu Second Normal University,Nanjing 211200,China

ABSTRACT Most previously reported inertia actuators suffer from the problems of low speed and large size.To overcome these shortcomings,this study proposes a slim compact piezo inertia actuator based on the principle of stick–slip drive.Actuated by the transverse motion of a cantilever beam forming part of a monolithic elastomer,this actuator achieves a high velocity.The construction and basic operating principle of the actuator are discussed in detail.Commercial finit element analysis software is employed to determine the appropriate geometry for the monolithic elastomer.To study the actuator’s mechanical characteristics,a prototype is fabricated and a series of experimental tests are performed.According to the results of these tests,the maximum velocity and maximum load force are about 24.03 mm/s and 1.96 N,respectively,and the minimum step size is about 0.47 μm.It is shown that the inertia actuator based on a monolithic elastomer with a cantilever beam not only has a slim compact structure,but also exhibits good output characteristics.

KEYWORDS Piezo actuator,Stick-slip,Monolithic elastomer,Cantilever beam,Transverse motion

I.INTRODUCTION

With advantages such as simple construction,absence of electromagnetic interference,and rapid responses,piezo actuators have attracted much attention from researchers worldwide.The structures and working modes of piezo actuators vary depending on the working mechanism.These actuators can be divided into four common types: standing wave actuators,travelling wave actuators,walking piezo actuators,and stick–slip piezo actuators.Each type has its pros and cons.Standing wave actuators have high output force,a compact structure,and high resolution,although their stroke is limited.1–3Travelling wave actuators have high output mechanical efficienc and rapid responses,but also suffer from problems such as heat loss and serious abrasion.4–6Walking piezo actuators operate at nonresonance frequencies and are characterized by excellent output mechanical characteristics and high resolution.7–9However,these actuators require complex control methods and structures.Piezo stick–slip actuators have the advantages of a simple structure,high resolution,and low power consumption,but problems such as low velocity and working noise remain.10,11Therefore,to overcome the existing shortcomings requires much work and further exploration.

In real-world applications,in particular,a micro locator is used in the driving mechanism of a micro-robot for precise positioning.12,13The micro locator has to meet the requirement of compact size.With its advantage of a simple structure,the piezo inertia actuator is a preferred choice to achieve high output performance with a compact structure.Therefore,this study focuses on the design and testing of a slim compact piezo inertia actuator.

In recent years,many piezo inertia actuators have been proposed for microprecision applications.For example,Zhanget al.14presented a triangular compliant actuator with a symmetricalstiffness flexibl hinged mechanism.The triangular compliant structure is connected to a piezo-stack with four linear-motion guiding flexur hinges.The actuator is rather large,but a stable velocity of 0.7 mm/s is achieved.Zhouet al.15designed an actuator with two flexur hinge mechanisms.Through cooperation between the two flexur hinge mechanisms,the actuator is able to achieve both high speed and high resolution.However,its structure is not sufficientl compact.Tanget al.16designed a novel actuator with a two-layer structure.In a new approach to achieving high speeds,a long driving lever is used to amplify the output displacement of the piezo-stack.The long driving lever is perpendicular to the piezo-stack,however,which results in the actuator having large external dimensions.

To produce an inertia actuator that is more compact and to balance output characteristics in terms of load,resolution,and motion speed,we machined a thin rectangular piece of metal by slow-feed electrical discharge machining to form a slim compact monolithic elastomer composed of two supporting parts,a mounting part,four elastic hinges,and a cantilever beam.Its overall dimensions are 32×14.5×3 mm3,and it is thus much smaller than previous actuators.

The remainder of this paper is organized as follows.Section II describes the mechanism construction,the operating principle,and a finit element analysis of the actuator.Section III describes the experimental system and the results obtained.Section IV gives a summary and conclusions.

II.DESIGN AND ANALYSIS

A.Construction of the actuator

Figure 1 shows the detailed mechanical construction of the slim compact inertia actuator with dimensions of 32×14.5×3 mm3.The actuator is composed of a piezo-stack,a friction head,and a monolithic elastomer.The monolithic elastomer is a so-called “flexur hinge mechanism,”consisting of fiv main parts:supporting part A,supporting part B,a mounting part,elastic hinges,and a cantilever beam.The piezo-stack nests in the monolithic elastomer through mechanical capture.The friction head is glued to the top of the monolithic elastomer.A pair of parallel elastic hinges is mounted on each side of supporting part B.In the firs pair of elastic hinges,the two firs ends are connected to the mounting part on the left side of supporting part B,and the two second ends are connected to supporting parts A and B,respectively.In the other pair of elastic hinges,the two firs ends are connected to the cantilever beam on the right side of supporting part B,and the two second ends are connected to supporting parts A and B,respectively.The mounting part and the cantilever beam are separated by a slot.This design creates difference in structural stiffness between the two sides of the flexibl hinged mechanism.All parts except the piezo-stack and the friction head form a monolithic structure,which is made of AL7075 aluminum alloy.The friction head is made of a wear-resistant ZrO2ceramic.The respective material coefficient are listed in Table I.

FIG.1.Configuration of the actuator.

FIG.2.Configuration of linear motion stage.

TABLE I.Material constants.

The structure of the linear motion stage driven by the designed piezo inertia actuator is illustrated in Fig.2.The linear motion stage is composed of the actuator,a base,a slider,a preload screw,and two mounting screws.The normal force between the friction head and the slider can be changed through the preload screw,which is exposed to the bottom of the base.The value of the static friction coefficien between the friction head and the slider is 0.15.The two mounting screws are used to fi the actuator on the base.The slider,with a low coefficien of friction,has only one translational degree of freedom.

FIG.3.Deformation of the actuator.

As the piezo-stack receives power,it extends along its length.Owing to the difference in structural stiffness between the two sides of the actuator,supporting part A is subject to a certain deflectio motion toward the part with lower stiffness.The cantilever beam transfers this deflectio motion to the friction head to drive the slider and drives the friction head to move in both theyandzdirections,as shown in Fig.3.They-direction displacementUycorresponds to the transverse motion of the cantilever beam of the monolithic elastomer,which rubs on the slider and redirects the translational movement of the slider in theydirection.Thez-direction displacementUzcan be ignored in comparison with the largey-direction displacement.

B.Simulation of actuator

Commercial finit element analysis software is used to study the static deformation of the actuator.The material constants listed in Table I are used in the simulation.The simulation results are shown in Fig.4.The mounting part of the actuator remains absolutely fixe during the simulation.For a voltage of magnitude 100 V,the elongation displacement of the piezo-stack(an NEC AE0203D08H09DF)along its length is about 6.1 μm,and the displacements of the friction head in theyandzdirections are about 77.08 μm and 1.42 μm,respectively.In other words,the displacement of the piezo-stack serves to increase the displacement in theydirection of the cantilever beam.

FIG.4.FEM simulation of the flexible hinged mechanism:(a)y-direction displacement;(b)z-direction displacement.

FIG.5.Analysis of vibrational modes.

Generally,owing to the working characteristics of the piezostack,the driven frequency selected by the piezo-stack inertial actuator is in a low nonresonance frequency range.When the working frequency is close to the resonance frequency range,the inertial actuator generates self-excited vibrations,which affect the normal operation of the actuator.Therefore,it is necessary to perform a vibrational mode analysis of the actuator.In the frequency range below 1000 Hz,the actuator has a first-orde natural frequency of 772.9 Hz,as shown in Fig.5.At this frequency,the cantilever beam of the actuator vibrates back and forth along thexdirection,reducing the output mechanical characteristics of the actuator.Hence,the driving frequency of the actuator must be much less than the first-orde natural frequency.

C.Operating principles

Based on the “stick–slip” driving principle,a sawtooth-wave signal with a fixe degree of symmetry is applied to drive the actuator.The actuator operates in three steps over a full cycle,as shown in Fig.6.First[Fig.6(a)],the stage is at the original position without electrical input.Then[Fig.6(b)],from timet0tot1,the piezo-stack is subject to power excitation from a slow-ramp voltage signal,which pushes the monolithic elastomer to move forward in theydirection,with the mounting part remaining completely fixed The movement of the cantilever beam of the monolithic elastomer drives the friction head to stick to the slider,and the slider then shifts forward by a stepSFunder the static frictional force.This is the sticking process.Finally [Fig.6(c)],the voltage signal drops rapidly to zero from timet1tot2.The deformed monolithic elastomer,with the piezo-stack,contracts rapidly to its original position,which makes the friction head slide backward quickly,and the slider then shifts backward by a stepSBunder the sliding frictional force.This backward sliding distanceSBis smaller than the forward sticking distanceSFbecause of the inertia of the slider.This is the sliding process.Thus,the stepping displacement ΔSof the slider in a full cycle can be expressed as

Therefore,a “stick–slip” movement cycle of the piezo inertia actuator ends with a forward step.This is the so-called“stick–slip”process.

FIG.6.Operating process of the linear piezo actuator over a full cycle.

III.EXPERIMENTS

A.Experimental system

FIG.7.Experimental setup for the actuator:(a)experimental system;(b)linear motion stage driven by the actuator.

FIG.8.Output displacement performances of the actuator:(a)22 Hz and 30 Hz;(b)a single step displacement.

FIG.9.Output displacement performance at different frequencies:(a)40-200 Hz;(b)200-600 Hz;(c)600-1000 Hz.

The actuator was fabricated by slow-feed electrical discharge machining,and its mechanical performance was studied using the experimental setup shown in Fig.7.The experimental system consisted of an amplifier a computer,a function signal generator,an oscilloscope,a laser sensor,and a controller,as shown in Fig.7(a).The function signal generator (SDG1005,SIGLENT Technologies Co.,Ltd.,China) generated a sawtooth voltage signal,which was amplifie by a power amplifie (E-501.00,PI Co.,Ltd.,Germany).An oscilloscope (ADS1042C,Atten Technologies Co.,Ltd.,China)was used to monitor changes in the amplitude and frequency of the driving sawtooth voltage signal.The displacement and velocity of the linear motion stage were measured by the laser sensor,with a repeat accuracy of 20 nm,together with the controller(LKH020/LK-G5001P,Keyence Co.,Osaka,Japan),with an optional resolution of 1 nm,and all the measurement data were collected by a computer.Figure 7(b)shows the linear motion stage driven by the actuator.The maximum static friction between the friction head and the slider was measured by pulling the slider with a mechanical tension meter.In this way,the normal force between the friction head and the slider could be obtained indirectly.The relationship between the maximum static friction and the normal force is

wheref,μ,andFare the maximum static friction,the static friction coefficient and the normal force,respectively.In the subsequent characteristic tests,the maximum static friction measured was about 3 N.Therefore,according to Eq.(2),the normal force can be indirectly calculated to be 20 N.

B.Output characteristics under various driving frequencies

Figures 8 and 9 show the output displacement performances within 0.4 s at different driving frequencies.The amplitude and the degree of symmetry of the sawtooth signal voltage are fixe at 100 V and 95%,respectively,in subsequent experiments.Figure 8(a)shows step displacement characteristics at 22 Hz and 30 Hz.Here,22 Hz is chosen as the lowest driving frequency because stable movement of the actuator is impossible at frequencies below 22 Hz.Every step displacement involves forward and backward motion.The forward displacementSFand backward displacementSBof the actuator can be clearly seen in the working cycles at 22 Hz and 30 Hz.Figure 8(b)is a detailed plot of the single step displacement outlined by the red dashed column in Fig.8(a).The forward displacementsSFat 22 Hz and 30 Hz are 22.90 μm and 13.37 μm,respectively,and the corresponding backward displacementsSBare 22.43 μm and 3.41 μm.According to Eq.(1),the step displacements at 22 Hz and 30 Hz are 0.47 μm and 9.96 μm,respectively.

Figures 9(a)–9(c)show the displacements of the actuator within 0.4 s at driving frequencies in the ranges of 40–200 Hz,200–600 Hz,and 600–1000 Hz.The output displacement curves show a linearly increasing trend with time.As the driving frequency increases to 600 Hz,the output displacement increases,but when the driving frequency exceeds 600 Hz,the output displacement decreases.The maximum output displacement is 9613.16 μm at 600 Hz.It can be noted that when the driving frequency is higher than 40 Hz,the backward displacement in every step of the actuator is suppressed.In other words,the stick–slip process no longer occurs,and the actuator enters a slip–slip process.Therefore,stable motion of the actuator can be achieved in the slip–slip process.

Table II shows the ratio of the backward displacement to the forward displacement in every step at various driving frequencies.This ratio can be calculated as follows:

TABLE II.Ratio β of backward displacement to forward displacement in every step at various driving frequencies.

Whenβis zero,the backward displacement in every step disappears in the slip–slip process.

Figure 10 shows the variation of the step displacement with driving frequency.As the driving frequency increases,the average step displacement firs sharply rises,then fluctuate in a stable manner,and eventually decreases linearly.Once the frequency exceeds 600 Hz,the output performance of the actuator decreases within the natural frequency range.It is easy to understand from the modal analysis results in Sec.II that the performance of the actuator is mainly affected by the first-orde inherent vibration.The average step displacement is about 37.5 μm at 600 Hz.The velocity of the slider,V,is the product of the step displacement ΔSand the corresponding driving frequencyf:

The maximum velocity of the slider is 24.03 mm/s at 600 Hz.

C.Output characteristics under various driving voltages

Figure 11 illustrates the variation of the step displacement with voltage.The frequency is fixe at 600 Hz in these experiments.According to Eq.(4),as the driving voltage increases,theoutput average step displacement increases,increasing the velocity of the slider.Therefore,the values of the voltage and frequency are significan factors affecting the output performance of the actuator.

FIG.10.Variation of step displacement and velocity with driving frequency.

FIG.11.Variation of the step displacement and velocity with voltage.

D.Load characteristics

Figure 12 shows the relationship between the external load and the velocity.The values of the voltage and frequency are fixe at 100 V and 600 Hz,respectively,in subsequent experiments.The velocity of the actuator decreases from 24.03 mm/s to 0.21 mm/s as the external load increases from 0 g to 200 g.When the external load is above 200 g,the velocity of the slider suddenly drops to zero.The load force is the product of the external load and the gravitational acceleration.The maximum load force is about 1.96 N.

Motor efficienc refers to the ratio of the converted mechanical kinetic energy to the electrical energy lost by the motor.This efficiencηis expressed as

wherePoutandPinare the mechanical kinetic energy and the electrical energy input,respectively,mandgare the value of the load and the gravitational acceleration,respectively,andUandIare DC voltage and current,respectively,with values of 12 V and 0.1 A.It is worth noting that the maximum efficienc of the actuator is 0.85%,and the corresponding load and speed are 100 g and 10.23 mm/s,respectively.

FIG.12.Relationship between external load and velocity.

FIG.13.Variation of output performance with normal force.

E.Output characteristics under various normal forces

All of the above output characteristics were determined under a pre-pressure of 20 N.This subsection further explores the impactof different normal forces on the output performance of the actuator.The driving voltage and frequency are again fixe at 100 V and 600 Hz,respectively.Figure 13 shows the variation of the output performance with the normal force.As the normal force increases,the maximum speed and maximum load firs increase and then decrease.When the normal force increases to 20 N,the actuator reaches its highest speed and maximum load capacity.Therefore,the optimal normal force between the friction head and the slider is about 20 N.

TABLE III.Comparison with other actuators.

F.Comparison and discussion

In Table III,the slim compact piezo inertial motor designed in this study is compared with a variety of other piezo inertia actuators in terms of maximum speed,resolution,load and structural size.It is observed that the actuator designed here has been greatly improved in speed,load,and structure size,reflectin its high volume energy density.It is especially suitable for small applications such as micro-robot joint drives,focusing in micro-imaging,and consumer electronics products.

IV.CONCLUSIONS

A slim compact piezo inertia actuator based on transverse motion has been designed and fabricated.Compared with existing actuators,this one has a slim compact structure and a higher velocity.Experimental results indicate that the maximum velocity is around 24.03 mm/s when the voltage and frequency are 100 V and 600 Hz,respectively,and the maximum load force is about 1.96 N.The minimum step size is about 0.47 μm when the voltage and frequency are 100 V and 22 Hz,respectively.Thus,the use of a monolithic elastomer with a cantilever beam in this actuator design increases the piezo-stack’s displacement and the velocity of the actuator.

The results of this study demonstrate that the design of a piezo inertia actuator using a monolithic elastomer with a cantilever beam is feasible and is appropriate as a basis for further development of piezo inertia actuators with high velocities and compact structures.Potential directions for future study include(i)examination of the relationship between the output characteristics of the actuator and the coefficien of friction and(ii)further reductions in size.

ACKNOWLEDGMENTS

This work was supported by a Specialized Research Fund(Grant No.923801).The authors are grateful to Xingxing Zhu,Xuguang Zhu,Yan Zhu,Yue Zhu,and Suhong Miao for their help.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflict to disclose.

DATA AVAILABILITY

The data that support the finding of this study are available from the corresponding author upon reasonable request.