Performance Analysis of a Travelling-Wave Ultrasonic Motor Under Impact Load

micromachines

Article Performance Analysis of a Travelling-Wave Ultrasonic Motor under Impact Load

Jiahan Huang 1 and Dong Sun 2,*

1 School of Mechatronics Engineering, Foshan University, Foshan 528225, China; [email protected] 2 School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China * Correspondence: [email protected]

Received: 24 June 2020; Accepted: 15 July 2020; Published: 16 July 2020

Abstract: With the increased application of ultrasonic motors, it is necessary to put forward higher demand for the adaptability to environment. Impact, as a type of extreme environment, is widespread in weapon systems, machinery and aerospace. However, there are few reports about the influence of impact on an ultrasonic motor. This article aimed to study the reasons for the performance degradation and failure mechanism of an ultrasonic motor in a shock environment. First, a finite element model is established to observe the dynamic response of ultrasonic motor in a shock environment. Meanwhile, the reasons of the performance degradation in the motor are discussed. An impact experiment is carried out to test the influence of impact on an ultrasonic motor, including the influence on the mechanical characteristic of an ultrasonic motor and the vibration characteristic of a stator. In addition, the protection effect of rubber on an ultrasonic motor in a shock environment is verified via an experimental method. This article reveals the failure mechanism of ultrasonic motors in a shock environment and provides a basis for the improvement of the anti-impact property of ultrasonic motors.

Keywords: shock environment; ultrasonic motor; dynamic response; mechanical characteristic

1. Introduction Over the past few decades, ultrasonic motors (USMs) based on the piezoelectric eﬀect have been developed well. There are many industrial applications, including micro-machine, information technology, surgery devices, ecological/energy areas, absolute gravimeter and nano-positioning stages [1–5]. There are numerous merits of USMs over electromagnetic motors, including low speed with high torque, a quick response, a wide velocity range and a high power/weight ratio [2–4,6]. The unique properties of USMs make it have a bright application prospect in extreme environments, such as space exploration [7,8]. A lot of research reports, mainly focusing on the application of USMs with ambient temperature changes and under vacuum, have been released [9–16]. In order to expand the application range of ultrasonic motors, some researchers start to turn their sights onto weapon systems, such as smart wings in airplanes [4], driving and anti-stealth technology [17] and a smart fuse safety system [18,19]. Impact, widespread in ammunition system, is an unavoidable destructive factor that needs to be considered. Many scholars have carried out a lot of research about various devices in a shock environment, such as the reliability of MEMS devices [20–22] and data recorders used in ammunition [23,24]. However, there are only a few research reports about the characteristic of an ultrasonic motor in a shock environment. Ren et al. tested the mechanical characteristic of ultrasonic motor after impact test, but there is a lack of analysis about the failure mechanism [25]. Our previous research established a model about the dynamic response of an ultrasonic motor in a shock environment based on the rigid plasticity model [26]. The model

Micromachines 2020, 11, 689; doi:10.3390/mi11070689 www.mdpi.com/journal/micromachines Micromachines 2020, 11, 689 2 of 14 reflects the dynamic process to a certain extent, but more accurate results are needed to analyze the characteristicMicromachines of an2020 ultrasonic, 11, x FOR PEER motor REVIEW in a shock environment. 2 of 13 This article aimed to study the reasons for the performance degradation and failure mechanism of an ultrasonicreflects motorthe dynamic in a shock process environment. to a certain extent, A finite but elementmore accurate model, results which are takes needed into to accountanalyze the material nonlinearity,characteristic is established. of an ultrasonic The motor dynamic in a shock response environment. of an ultrasonic motor in a shock environment This article aimed to study the reasons for the performance degradation and failure mechanism can be observed through transient solution. Meanwhile, the relationship between structural plastic of an ultrasonic motor in a shock environment. A finite element model, which takes into account deformationmaterial andnonlinearity, preload is established. obtained toThe explain dynami thec response performance of an ultrasonic degradation. motor Thein a mechanicalshock characteristicenvironment of an can ultrasonic be observed motor through after impacttransient is solution. tested. Moreover,Meanwhile, the the compensation relationship between gaskets are appliedstructural to recover plastic the deformation performance and of preload an ultrasonic is obtained motor. to explain Meanwhile, the performance the distortion degradation. of the vibrationThe characteristicmechanical of characteristic a stator after of impactan ultrasonic is discussed. motor after Finally,impact is the tested. protection Moreover, e fftheect compensation of rubber for an ultrasonicgaskets motor are applied in a shock to recover environment the performance is verified of an by ultrasonic experiment. motor. Meanwhile, the distortion of the vibration characteristic of a stator after impact is discussed. Finally, the protection effect of rubber 2. Structurefor an ultrasonic of an Ultrasonic motor in a Motor shock environment is verified by experiment.

The2. Structure typicalstructure of an Ultrasonic of a travelling-wave Motor ultrasonic motor is shown in Figure1a [ 27]. The ring- shaped stator with many teeth to enlarge the vibration amplitude is fixed on the base. The piezoelectric The typical structure of a travelling-wave ultrasonic motor is shown in Figure 1a [27]. The ring- wafershaped is affixed stator to thewith bottom many teeth surface to enlarge of the stator.the vibration A rotor amplitude is on the is topfixed of on stator. the base. The The cover is fixed onpiezoelectric the base. wafer The is bearing affixed to is the used bottom to improve surface of the the work stator. e Affi rotorciency is on by the reducing top of stator. friction The while operating.cover Thereis fixed is on preload the base. between The bearing the is stator used to and improve rotor the by applyingwork efficiency a gasket by reducing between friction rotor and bearing.while By operating. applying There electric is preload signal withbetween a frequency the stator and close rotor to theby applying resonance a gasket frequency between of rotor the stator, there isand a continuous bearing. By elliptical applying motionelectric insignal the topwith of a thefrequency stator. close This motionto the resonance is converted frequency to the of movement the of the rotorstator, throughthere is a thecontinuous friction elliptical between motion the stator in the and top rotorof the [stator.28]. This motion is converted to the movement of the rotor through the friction between the stator and rotor [28].

(a) Whole motor.

(b) Dimensions of the stator.

FigureFigure 1. Typical 1. Typical structure structure of of a a travelling travelling wave wave rotary rotary ultrasonic ultrasonic motor. motor. Micromachines 2020, 11, 689 3 of 14 Micromachines 2020, 11, x FOR PEER REVIEW 3 of 13

The operating mechanism of of an ultrasonic motor motor consists consists of of two two energy energy conversion processes: processes: One isis the the conversion conversion of electricalof electrical energy energy into mechanicalinto mechanical energy energy of high-frequency of high-frequency and micro-amplitude and micro- amplitudevibration in vibration stator through in stator the through inverse piezoelectric the inverse piezoelectric eﬀect of piezoelectric effect of materials. piezoelectric The materials. other converts The otherthe micro-vibration converts the micro-vibration of the stator into of the the macroscopic stator into the motion macroscopic of the rotor motion through of the the rotor friction through between the frictionthem. Afterbetween impact, them. the After damage impact, to thethe piezoelectricdamage to the wafer piezoelectric or stator, wafer including or stator, the fracture including of the fracturepiezoelectric of the wafer piezoelectric and the plastic wafer deformation and the ofplastic the stator, deformation may lead of to thethe incomplete stator, may vibration lead to mode the incompleteof the stator, vibration so that the mode input of power the stator, cannot sobe that converted the input into power high-frequency cannot be andconverted micro-amplitude into high- frequencyvibration of and the micro-amplitude stator eﬃciently. Onvibration the other of hand,the stat theor plastic efficiently. deformation On the ofother the rotorhand, or the stator plastic will deformationlead to a decrease of the in preload.rotor or Thestator analysis will oflead the to two a conventiondecrease in processes preload. in The a shock analysis environment of the two can conventionbe considered processes as the analysis in a shock of deformation environment of can the be structure considered and anti-impactas the analysis property of deformation of the stator of andthe structurepiezoelectric and wafer. anti-impact property of the stator and piezoelectric wafer.

2.1.Model Model Establishment Establishment As a a complex complex electromechanical electromechanical coupling coupling system, system, transient transient analysis analysis is necessary is necessary to observe to observe the dynamicthe dynamic response response of an of anultrasonic ultrasonic motor motor in ina ashock shock environment. environment. The The model model is is established established in Workbench 14.0. The key components that cannot be ignored are the stator, piezoelectric wafer and rotor. Instead, the base and cover cover can can be be ignored ignored be becausecause their strength is large enough to withstand impactimpact damage. damage. The The cover cover will will limit limit the the upward upward mo movementvement of ofthe the rotor rotor in a in shock a shock environment. environment. In orderIn order to show to show this this phenomenon phenomenon accurately, accurately, a limit a limit gasket gasket is set is on set the on thetop topof the of therotor rotor to limit to limit the upwardthe upward movement movement of the of therotor, rotor, as asshown shown in inFigure Figure 2.2 .To To reduce reduce the the amount of calculationcalculation andand computational complexity,complexity, the the mass mass of of the the shaft shaft in in the the simulation simulation was was equivalent equivalent to a to combination a combination of a ofbearing a bearing and and output output shaft. shaft.

Figure 2. FiniteFinite element element model.

Ultrasonic motormotor TRUM60,TRUM60, whichwhich means means the the diameter diameter of of the the stator stator is 60is mm,60 mm, is selected. is selected. The The key keydimensions dimensions of theof the stator stator (Figure (Figure1b) 1b) and and rotor rotor (Figure (Figure1c) are1c) are listed listed in Tablein Table1. Moreover,1. Moreover, it isit is significantsigniﬁcant to know the weight of the shaft, becaus becausee it it might increase the risk of rotor damage in a shock environment.

Table 1. Key parameters of a travelling-wave ultrasonic motor (unit: mm). Table 1. Key parameters of a travelling-wave ultrasonic motor (unit: mm).

Parameter ParameterValue Value Parameter Parameter Value Value rs1 rs1 9 9 rs2 rs2 16.5 16.5 r 22 r 30 rs3 s3 22 s4 rs4 30 hs1 2 hs2 2.5 hs1 2 hs2 2.5 hp 0.5 rc1 4 p c1 h rc2 0.5 11 rc3 r 27.5 4 rc2 rc4 11 29 hc1 rc3 4.5 27.5 rc4 hc2 29 2 weight of shaft hc1 23g 4.5 hc2 2 weight of shaft 23g Micromachines 2020, 11, x FOR PEER REVIEW 4 of 13 Micromachines 2020, 11, 689 4 of 14 There are several kinds of materials, including phosphor bronze for the stator, aluminum for the rotor, PZTThere-4 for are the several piezoelectric kinds of materials, wafer, and including structure phosphor steel bronzefor the for shaft. the stator, Structural aluminum deformation for the is whatrotor, we PZT-4are concerned for the piezoelectric about during wafer, andthe structureanalysis steelprocess, for the especially shaft. Structural in the deformation stator and isrotor. what The bilinearwe areisotropic concerned hardening about during model, the as analysis a classic process, elasto-plastic especially inmechanics the stator andmodel, rotor. is Thewidely bilinear used in engineeringisotropic research. hardening The model, mechanical as a classic property elasto-plastic of the mechanics material model, model is is widely shown used in inFigure engineering 3. Assume that research.the material The models mechanical of the property rotor ofand the stator material are modelbilinear is isotropic shown in Figurehardening3. Assume materials. that theAssume structuralmaterial steel models to be of an the isotropic rotor and statormaterial, are bilinearbecause isotropic the output hardening shaft materials.is strong Assumeenough structuralto withstand steel to be an isotropic material, because the output shaft is strong enough to withstand impact damage. impact damage. A piezoelectric wafer is a kind of anisotropic material. Compared to the whole USM, A piezoelectric wafer is a kind of anisotropic material. Compared to the whole USM, the volume and the volume and mass of a piezoelectric wafer can be neglected, so it has an extremely low impact on mass of a piezoelectric wafer can be neglected, so it has an extremely low impact on the dynamic the dynamiccharacteristics characteristics of a USM in of shock a USM environment. in shock Therefore,environment. to reduce Therefore, the amount to reduce of calculation the amount and of calculationcomputational and computational complexity, the complexity, piezoelectric ceramicthe piezoe is simpliﬁedlectric ceramic into an isotropicis simpli material.fied into Adhesive an isotropic material.and friction Adhesive material and are friction not taken material into consideration are not taken here. into The consideration key material parameters here. The are key shown material parametersin Table 2are. shown in Table 2.

FigureFigure 3. 3. BilinearBilinear isotropic isotropic hardeninghardening model. model.

Table 2. Material parameters. Table 2. Material parameters. Density Young’s Yield Tangent Material 3 Poisson’s Ratio Yield Tangent Density(kg/m ) ModulesYoung’s (Pa) Poisson's Strength (Pa) Modulus (Pa) Material Strength Modulus aluminum 27703 7.1 1010 0.33 2.8 108 5 108 (kg/m ) Modules(Pa)× Ratio × × phosphor bronze 8760 1.12 1011 0.33 4.4 10(Pa)8 1.15 10(Pa)9 × × × Piezoelectric wafer 7650 3.5 1010 10 0.31 *8 * 8 aluminum 2770 7.1× × 10 0.33 2.8 × 10 5 × 10 Structural steel 7850 2 1011 0.3 * * phosphor × 8760 1.12 × 1011 0.33 4.4 × 108 1.15 × 109 bronze PiezoelectricBesides, there are some contact and boundary conditions that need to be set. The grid of the contact area is made7650 to be high quality. 3.5 The× 1010 output shaft0.31 and rotor are bonded * together to replace * wafer the threaded connection. The displacement of the inner boundary of the stator is constrained to zero Structural at all degrees of freedom.7850 Assume that 2 the× 10 structure11 has experienced0.3 a half sine * shock acceleration, * whichsteel can be expressed as: ( a sin( π t), 0 t τ Besides, there are some contacta (andt) = boundary0 τ cond≤ itions≤ that need to be set. The grid(1) of the 0, t > τ contact area is made to be high quality. The output shaft and rotor are bonded together to replace the threadedwhere connection.a0 represents The the displacement amplitude of of shock the inner acceleration boundary and ofτ therepresents stator is the constrained pulse width to zero of at all degreesshock acceleration. of freedom. Assume that the structure has experienced a half sine shock acceleration, which3. Dynamiccan be expressed Responses as: of an Ultrasonic Motor π 3.1. Modal Analysis  ≤≤τ att0 sin( ),0 at()= τ (1) The ﬁnite element modal analysis of the whole structure is carried out. The results are shown  0,t >τ in Figure4. Because the direction of impact follows the Y axis, the mode shapes in the Y direction are selected. The frequency of ﬁrst modal (Figure4a) and sixth modal (Figure4b) is 860.47 Hz and where a0 represents the amplitude of shock acceleration and τ represents the pulse width of shock acceleration.

3. Dynamic Responses of an Ultrasonic Motor

3.1. Modal Analysis Micromachines 2020, 11, x FOR PEER REVIEW 5 of 13

Micromachines 2020, 11, 689 5 of 14 The finite element modal analysis of the whole structure is carried out. The results are shown in Figure 4. Because the direction of impact follows the Y axis, the mode shapes in the Y direction are selected.3349.4 Hz, The respectively. frequency of The first output modal shaft(Figure cannot 4a) and remain sixth stillmodal in (Figure a shock 4b) environment is 860.47 Hz considering and 3349.4 Hz,the structurerespectively. of an The ultrasonic output motor.shaft cannot The ﬁrst remain modal still with in aa frequency shock environment of 860.47 HZ considering is more easily the structurestimulated of in an a shockultrasonic environment. motor. The first modal with a frequency of 860.47 HZ is more easily stimulated in a shock environment.

(a) The first modal (b) The sixth modal

Figure 4. FirstFirst and and sixth sixth natural natural frequency frequency of an ultrasonic motor.

3.2. Dynamic Dynamic Response Response of of an Ultrasonic Motor By applying applying a a half half sine sine acceleration acceleration pulse pulse with with an an amplitude amplitude of of2000 2000 g and g and a pulse a pulse width width of 1.0 of 1.0ms, ms,transient transient simulation simulation has been has beendone. done. The dynamic The dynamic responses responses at different at diff timeserent are times listed are in listed Figure in 5.Figure The5 shaft. The moves shaft moves down downto the tomaximum, the maximum, as shown as shown in Figure in Figure 5a. Due5a. to Due the to elastic the elastic effect eofff theect structure,of the structure, the rotor the rebounds rotor rebounds and then and collides then collideswith the withlimit thegasket, limit as gasket, shown asin shownFigure 5b. in FigureThen, 5theb. wholeThen, thestructure whole structureturns into turns a complex into a complex transient transient vibration vibration state. Multiple state. Multiple collisions collisions between between rotor, statorrotor, statorand limit and limitgasket gasket result result in structural in structural instability, instability, especially especially in inthe the rotor. rotor. The The rotor rotor exhibits exhibits an unstable vibration state,state, asas shownshown in in Figure Figure5 c.5c. The The maximum maximum stress stress in in the the stator stator is 380is 380 MPa MPa at aat time a time of of0.8 0.8 ms ms during during the the whole whole process, process, as shown as shown in Figure in Fi5gured, which 5d, which is smaller is smaller than the than yield the stress. yield Itstress. means It meansthat there that is there no plastic is no deformation plastic deformation in the stator. in the Actually, stator. theActually, anti-impact the anti-impact property of property the stator of is the far statorgreater is than far the greater rotor becausethan the of therotor structure because diff erence.of the Figurestructure6 shows difference. the displacement-time Figure 6 shows curves the displacement-timeof the rotor and stator. curves Curves of the “max rotor inand rotor” stator. and Curv “mines in“max rotor” in rotor” refer to and the “min relative in rotor” displacement refer to thebetween relative the displacement upper surface between of the innerthe upper ring surfac and thee of bottom the inner surface ring and of the the outer bottom ring surface in the of rotor. the outerObviously, ring in there the rotor. is irreversible Obviously, plastic there deformation is irreversible in theplastic rotor. deformation Because the in innerthe rotor. boundary Because of the innerstator boundary is constrained, of the the stator curves is constrained, “max in stator” the curves and “min “max in stator”in stator” refer and to the“min displacement in stator” refer of the to theouter displacement edge of the bottomof the outer surface edge in of the the stator. bottom The su dynamicrface in responsethe stator. of The the dynamic structure response can be divided of the structureinto two parts:can be Period divided 1, theinto outer two parts: ring of Period rotor maintains1, the outer a stablering of ring, rotor and maintains the center a stable part movesring, and up theand center down part with moves the shaft; up and Period down 2, the with outer the ringshaft; of Pe theriod rotor 2, the is no outer longer ring stable, of thewhich rotor is leads no longer to the stable,result thatwhich “max leads in rotor”to the result and “min that in“max rotor” in graduallyrotor” and separate. “min in rotor” The peak gradually value ofseparate. the displacement The peak valuehas a timeof the delay displacement of 0.3 ms withhas a the time peak delay value of of0.3 the ms impact, with the as shownpeak value Figure of6 .the impact, as shown Figure 6.

(a) Rotor moves down to the maximum (b) Rotor rebounds and collides with the limit gasket Micromachines 2020, 11, x FOR PEER REVIEW 5 of 13

The finite element modal analysis of the whole structure is carried out. The results are shown in Figure 4. Because the direction of impact follows the Y axis, the mode shapes in the Y direction are selected. The frequency of first modal (Figure 4a) and sixth modal (Figure 4b) is 860.47 Hz and 3349.4 Hz, respectively. The output shaft cannot remain still in a shock environment considering the structure of an ultrasonic motor. The first modal with a frequency of 860.47 HZ is more easily stimulated in a shock environment.

(a) The first modal (b) The sixth modal

Figure 4. First and sixth natural frequency of an ultrasonic motor.

3.2. Dynamic Response of an Ultrasonic Motor By applying a half sine acceleration pulse with an amplitude of 2000 g and a pulse width of 1.0 ms, transient simulation has been done. The dynamic responses at different times are listed in Figure 5. The shaft moves down to the maximum, as shown in Figure 5a. Due to the elastic effect of the structure, the rotor rebounds and then collides with the limit gasket, as shown in Figure 5b. Then, the whole structure turns into a complex transient vibration state. Multiple collisions between rotor, stator and limit gasket result in structural instability, especially in the rotor. The rotor exhibits an unstable vibration state, as shown in Figure 5c. The maximum stress in the stator is 380 MPa at a time of 0.8 ms during the whole process, as shown in Figure 5d, which is smaller than the yield stress. It means that there is no plastic deformation in the stator. Actually, the anti-impact property of the stator is far greater than the rotor because of the structure difference. Figure 6 shows the displacement-time curves of the rotor and stator. Curves “max in rotor” and “min in rotor” refer to the relative displacement between the upper surface of the inner ring and the bottom surface of the outer ring in the rotor. Obviously, there is irreversible plastic deformation in the rotor. Because the inner boundary of the stator is constrained, the curves “max in stator” and “min in stator” refer to the displacement of the outer edge of the bottom surface in the stator. The dynamic response of the structure can be divided into two parts: Period 1, the outer ring of rotor maintains a stable ring, and the center part moves up and down with the shaft; Period 2, the outer ring of the rotor is no longer stable, which leads to the result that “max in rotor” and “min in rotor” gradually separate. The peak Micromachinesvalue of the2020 displacement, 11, 689 has a time delay of 0.3 ms with the peak value of the impact, as shown6 of 14 Figure 6.

Micromachines 2020, 11, x FOR PEER REVIEW 6 of 13

Micromachines 2020, 11, x FOR PEER REVIEW 6 of 13 (a) Rotor moves down to the maximum (b) Rotor rebounds and collides with the limit gasket

(c) Rotor exhibits an unstable vibration state (d) The maximum stress in the stator (c) Rotor exhibits an unstable vibration state (d) The maximum stress in the stator Figure 5. Dynamic response of an ultrasonic motor and stress distribution in a stator. FigureFigure 5. 5.Dynamic Dynamic response response of of an an ultrasonic ultrasonic motor moto andr and stress stress distribution distribution in in a a stator. stator.

Figure 6. Simulated displacement—time curves of a rotor and a stator. Figure 6. Simulated displacement-–time curves of a rotor and a stator. 3.3. Dynamic ResponseFigure of an 6. Ultrasonic Simulated Motor displacement-–time in a Shock Environment curves of a withrotor a and Diﬀ aerent stator. Amplitude and 3.3.Pulse Dynamic Width Response of an Ultrasonic Motor in a Shock Environment with a Different Amplitude and Pulse3.3. Width Dynamic Response of an Ultrasonic Motor in a Shock Environment with a Different Amplitude and Dynamic responses do not only depend on the amplitude of shock acceleration but also the Pulse Width pulseDynamic width. responses Compared do not with only the depend stator, on the the rotor amp withlitude lower of shock strength acceleration is easier but to also distort. the pulse Hence, width.the dynamicComparedDynamic response responseswith the of the stator,do rotornot onlythe is what rotordepend concernswith on thelower us. amp Figurestrengthlitude7 aof shows isshock easier theacceleration to results distort. of but theHence, also maximum the the pulse dynamicrelativewidth. response displacement–timeCompared of the with rotor the curves is stator, what of the concernsthe rotor rotor under us.with Figure an lo impactwer 7a strengthshows of 1000 the g,is 1500easierresults g, 2000toof distort.the g, 2500maximum Hence, g, 3000 the g, relativeanddynamic3250 displacement–time g response with a pulse of the widthcurves rotor of of 1is the ms. what rotor Apparently, concerns under an theus. impact deformationFigure of 7a1000 shows increasesg, 1500 the g, results with2000 theg, of 2500 increase the g, maximum 3000 in the g, andamplitude.relative 3250 g displacement–time with While a pulse the impact width curves exceedsof 1 ms. of 3000 Apparently,the rotor g, the under center the andeformation part impact of the of rotor1000increases g, collides 1500 with g, with 2000the theincrease g, 2500 stator g,in and 3000 thebounces amplitude.g, and 3250 back. While g Itwith will the a result pulse impact in width anexceeds earlier of 1 3000ms. rebound Apparently, g, the time center and the part a deformation shorter of the pulse rotor increases width. collides Figure withwith 7 thetheb shows increasestator the in andresults bouncesthe amplitude. of displacement–timeback. It While will result the impact in curves an earlier exceeds of the rebound rotor 3000 underg, time the anandcenter impact a shorter part of of 2000pulse the grotor width. with collides a Figure pulse with width 7b shows the of stator 0.25, the0.5, resultsand 1, bounces 2, of and displacement–time 4 ms.back. Impact It will withresult curves a pulsein an of earlier width the rotor ofrebound 0.5 under ms time and an 1andimpact ms a will shorter of cause 2000g pulse maximum with width. a pulse displacement Figure width 7b ofshows in 0.25,the 0.5, results 1, 2, andof displacement–time 4 ms. Impact with curves a pulse of the width rotor ofunder 0.5 msan impactand 1 ofms 2000g will withcause a maximumpulse width of displacement0.25, 0.5, in1, the2, androtor. 4 Pulsems. Impact widths with of 0.5 a andpulse 1 mswidth correspond of 0.5 ms to theand frequencies 1 ms will 1000cause and maximum 500 Hz, whichdisplacement are closest in the to rotor.the first Pulse modal widths frequency of 0.5 and of 860.471 ms correspond Hz among toall the the frequencies pulse widths 1000 listed and 500 above.Hz, This which phenomenon are closest is to consistent the first withmodal the frequency results of of the 860.47 modal Hz analysis. among all the pulse widths listed above. This phenomenon is consistent with the results of the modal analysis. Micromachines 2020, 11, 689 7 of 14

the rotor. Pulse widths of 0.5 and 1 ms correspond to the frequencies 1000 and 500 Hz, which are closest to the ﬁrst modal frequency of 860.47 Hz among all the pulse widths listed above. This phenomenon is Micromachinesconsistent with20202020,, 1111 the,, xx FOR resultsFOR PEERPEER of REVIEWREVIEW the modal analysis. 77 ofof 1313

0.25ms0.25ms 0.5ms0.5ms 0.50.5 1ms1ms 2ms2ms 4ms4ms 0.00.0

-0.5-0.5

-1.0-1.0 Relative displacement/mm Relative displacement/mm -1.5-1.5

012345012345 Time/msTime/ms ((aa)) displacement–timedisplacement–time curvescurves withwith differentdifferent amplitudeamplitude ( (bb)) displacement–timedisplacement–time curvescurves withwith differentdifferent pulsepulse widthwidth

FigureFigure 7. 7. SimulatedSimulatedSimulated displacement–timedisplacement–time displacement–time curvescurves curves ofof aa of rotorrotor a rotor underunder under impactimpact impact withwith with aa differentdifferent a diﬀerent amplitudeamplitude amplitude andand duration.and duration.

3.4.3.4. Relationship Relationship between between Plastic Plastic Deformation Deformation in in Rotor Rotor and and Preload Preload TheThe micro-vibration micro-vibration of of the the stator stator can can be be transferred transferred into into the the macroscopic macroscopic motion motion of of the the rotor rotor throughthroughthrough thethe the friction friction betweenbetweenbetween them. them.them. The TheThe preload preloadpreload between betweenbetween stator statorstator and andand rotor rotorrotor is produced isis producedproduced through throughthrough a gasket aa gasketbetween between the rotor the androtor bearing. and bearing. Based Based on finite on fi elementnite element calculation, calculation, the preload the preload is 229.71N is 229.71N while whilethe thickness the thickness of gasket of gasket is 0.3 is mm. 0.3 mm. Many Many theoretical theoreticalretical and andand experimental experimentalexperimental results resultsresults have havehave proved provedproved that thatthat the thethepreload preloadpreload is significant isis significantsignificant to thetoto thethe performance performanceperformance of motorofof momotortor [29 [29,30].,[29,30].30]. Obviously, Obviously,Obviously, the thethe plastic plasticplastic deformation deformationdeformation of theofof rotor will lead to a decrease in preload. Assume that sinkage in the center of rotor is d after impact, thethe rotorrotor willwill leadlead toto aa decreasedecrease inin preload.preload. AsAssumesume thatthat sinkagesinkage inin thethe centercenter ofof rotorrotorc isis dcc afterafter impact,impact,as shown asas shownshown in Figure inin FigureFigure8a. By 8a.8a. applying ByBy applyingapplying a static aa staticstatic acceleration accelerationacceleration that thatthat will willwill result resultresult in plastic inin plasticplastic deformation deformationdeformation in the rotor, the relationship between deformation d and preload under the premise of a gasket with a inin thethe rotor,rotor, thethe relationshiprelationship betweenbetween deformationdeformation cdcc andand preloadpreload underunder thethe premisepremise ofof aa gasketgasket withwith aconstant constant thicknessthickness ofof 0.30.3 mmmm isis obtained,obtained, as shown inin FigureFigure 88b.8b.b. Obviously,Obviously, there there isis aa relationshiprelationship between d and the preload. The polynomial fitted formula is: between dcc candand thethe preload.preload. TheThe polynomialpolynomial fittedfitted formulaformula is:is:

222 yddypreload=−229.60= 229.60 813.92813.92dc ++ 163.93163.93d (2)(2)(2) preloadpreload − ccccc wherewhere yypreloadpreloadpreload isis isthethe the preload,preload, preload, dddcc cisisis thethe the deformationdeformation deformation of of thethe rotor.rotor.rotor. ItItIt is isis necessary necessarynecessary to toto recover recoverrecover the thethe preload preloadpreload via viaadding adding the the thickness thickness of the of gasketthe gasket to restore to restore the performance thethe performanceperformance of the ofof motor. thethe motor.motor. The thickness TheThe thicknessthickness that ensures thatthat ensuresensuresthe preload thethe recoverpreloadpreload to recoverrecover the initial toto valuethethe initialinitial is called valuevalue “compensation”, isis calledcalled “compensation”,“compensation”, and the relationship andand thethe between relationshiprelationshipdc and betweencompensation dcc andand is compensationcompensation calculated by isis the calculatedcalculated ﬁnite element byby thethe method, finitefinite elementelement as shown method,method, in Figure asas8 shownshownb. The polynomialinin FigureFigure 8b.8b. ﬁtting TheThe polynomialformula is: fitting formula is: 4 2 ycompensation = 1.76 −10−4242− + 1.08dc 0.234d (3) ydd=×+1.76 10× 1.08 − 0.234− c (3)(3) compensationcompensation cccc where ycompensation is the thickness of the compensation gasket and dc is the deformation of the rotor. where yycompensationcompensation isis thethe thicknessthickness ofof thethe compensationcompensation gasketgasket andand ddcc isis thethe deformationdeformation ofof thethe rotor.rotor.

(a)(a) TheThe diagramdiagram ofof rotor’srotor’s deformationdeformation

Figure 8. Cont. Micromachines 2020, 11, x FOR PEER REVIEW 8 of 13 MicromachinesMicromachines2020 2020, 11, 11, 689, x FOR PEER REVIEW 88 of of 14 13

250 0.4 250 0.4 Preload Preload Compensation 200 Compensation 200 0.3 0.3 150 150 0.2 0.2

Preload/N 100

0.1 Compensation/mm 50 0.1 Compensation/mm 50

0 0.0 0.000 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Deformation d /mm Deformationc d /mm c (b) The preload and compensation versus deformation (b) The preload and compensation versus deformation FigureFigure 8. 8. RelationshipRelationship between between deformation deformation again again preload preload and and compensation. compensation. Figure 8. Relationship between deformation again preload and compensation. 4.4. Experiments Experiments 4. Experiments ThreeThree substantially substantially identical identical ultrasonic ultrasonic motors motors (TRUM60) (TRUM60) are are chosen chosen to to test test the the performance performance Three substantially identical ultrasonic motors (TRUM60) are chosen to test the performance changechange after after impact impact test. test. Ultrasonic Ultrasonic motors motors are are fixe fixedd on on the the fixture. fixture. The The fixture fixture is is fixed fixed on on a aMachete Machete change after impact test. Ultrasonic motors are fixed on the fixture. The fixture is fixed on a Machete hammerhammer to to carry carry out out the the impact impact test. test. The The half-sine half-sine acceleration acceleration pulse pulse induced induced by by the the Machete Machete hammer hammer hammer to carry out the impact test. The half-sine acceleration pulse induced by the Machete hammer isis obtained obtained by by free free falling falling on on the the cushion, cushion, and and th thee half-sine half-sine accelerations accelerations with with a adifferent different amplitude amplitude is obtained by free falling on the cushion, and the half-sine accelerations with a different amplitude cancan be be obtained obtained by by adjusting adjusting the the height height of of the the hammer hammer and and the the thickness thickness of of the the cushion. cushion. The The whole whole can be obtained by adjusting the height of the hammer and the thickness of the cushion. The whole USMUSM is is fixed fixed on on the the hammer hammer through through the the clamp clamp devi device,ce, and and the the shock shock acceleration acceleration is is applied applied to to the the USM is fixed on the hammer through the clamp device, and the shock acceleration is applied to the wholewhole USM. USM. The The schematic schematic diagram diagram of of the the shock shock experiment experiment is is shown shown in in Figure Figure 9a.9a. A A data data acquisition acquisition whole USM. The schematic diagram of the shock experiment is shown in Figure 9a. A data acquisition systemsystem is is adopted adopted to to capture capture the the acceleration acceleration data. data. The The impact impact test test platform platform is shown is shown in Figure in Figure 9b. 9Ab. system is adopted to capture the acceleration data. The impact test platform is shown in Figure 9b. A mechanicalA mechanical characteristic characteristic test test platform platform is set is set up up to totest test the the performance performance of of the the ultrasonic ultrasonic motor motor after after mechanical characteristic test platform is set up to test the performance of the ultrasonic motor after impact,impact, as as shown shown in inFigure Figure 9c.9 c.The The speed speed of motors of motors is measured is measured under under different di fferent loads loadsutilizing utilizing a non- a impact, as shown in Figure 9c. The speed of motors is measured under different loads utilizing a non- contactnon-contact laser velocity laser velocity meter. meter. contact laser velocity meter.

(a) Schematic diagram of an impact test platform. (a) Schematic diagram of an impact test platform.

Figure 9. Cont. Micromachines 2020, 11, x FOR PEER REVIEW 9 of 13

Micromachines 2020, 11, 689 9 of 14 Micromachines 2020, 11, x FOR PEER REVIEW 9 of 13 (b) Impact test platform for an ultrasonic motor. (c) Performance test platform for an ultrasonic motor

Figure 9. Experiment test platform.

4.1. Mechanical Characteristic Test and Result Analysis Different acceleration amplitudes of 1630, 1865 and 2320g are applied to three motors numbering 1 to 3, respectively. The original mechanical characteristic of the motors is shown in Figure 10. After impact, ultrasonic motor 1 can work normally, but the output performance degrades. Performance degradation in motor 2 is more apparent and there is noise “sha-sha” while operating. Motor 3 cannot work while powered. The output shaft can rotate freely, which means that the preload disappears and the motor has no self-locking ability. The mechanical characteristic of motors after impact is shown in Figure 10. Obviously,(b) Impact test the platform central for anpart ultrasonic of the motor. rotor is sunken, (c) Performanceand the depth test platform of sinking for an ultrasonicis measured motor and listed in Table 3. The theoretical preloadFigureFigure 9. after 9.ExperimentExperiment impact test based test platform. platform. on Equation (2) is listed in Table 3. The compensation is carried out to restore preload. The theoretical compensation thickness is based on 4.1.Equation4.1. Mechanical Mechanical (3), Characteristicand Characteristic the actual Test thickness Test and and Result Result of Analysisthe Analysis compensation gaskets is listed in Table 3. The actual compensation thicknesses are obtained through debugging when ultrasonic motors are at optimal DifferentDiﬀerent acceleration acceleration amplitudes amplitudes of of1630, 1630, 1865 1865 and and 2320g 2320g are are applied applied to tothree three motors motors numbering numbering performance levels. There is a difference between theoretical and actual compensation. Different 1 to1 to3, respectively. 3, respectively. The Theoriginal original mechanical mechanical characteristic characteristic of the ofmotors the motors is shown is shownin Figure in 10. Figure After 10 . thickness gaskets are used in debugging. The voids between gaskets lead to the increase in total impact,After impact,ultrasonic ultrasonic motor motor1 can work 1 can worknormally, normally, but the but output the output performance performance degrades. degrades. Performance Performance thickness, which means the decrease in actual thickness. degradationdegradation in inmotor motor 2 is 2 more is more apparent apparent and and there there is isnoise noise “sha-sha” “sha-sha” while while operating. operating. Motor Motor 3 cannot 3 cannot Moreover, the performance of motors after compensation is tested, as shown in Figure 10. It is workwork while while powered. powered. The The output output shaft shaft can can rotate rotate freely, whichwhich meansmeans that that the the preload preload disappears disappears and obvious that the mechanical characteristic will be restored with the application of the compensation andthe the motor motor has has no self-lockingno self-locking ability. ability. The The mechanical mechan characteristicical characteristic of motors of motors after after impact impact is shown is gasket. However, the performance will never be restored to original state. It will always degrade shownin Figure in Figure 10. 10. irreversibly. The reasons behind this need more analysis. Obviously, the central part of the rotor is sunken, and the depth of sinking is measured and 140 listed in Table 3. The theoretical preload after impact based on Equation motor1 (2) is listed in Table 3. The motor2 compensation is carried out to restore preload. The theoretical compensation motor3 thickness is based on 120 motor1 after shock Equation (3), and the actual thickness of the compensation gaskets motor2 is after listed shock in Table 3. The actual compensation thicknesses are obtained through debugging when motor1 ultrasonic after compensation motors are at optimal 100 motor2 after compensation performance levels. There is a difference between theoretical and motor3 actual after compensation compensation. Different thickness gaskets are used in debugging. The voids between gaskets lead to the increase in total thickness, which means 80the decrease in actual thickness. Moreover, the performance of motors after compensation is tested, as shown in Figure 10. It is obvious that the mechanical60 characteristic will be restored with the application of the compensation gasket. However, the speed/ r/min Rotate performance will never be restored to original state. It will always degrade irreversibly. The reasons40 behind this need more analysis. 140 motor1 20 motor2 motor3 120 motor1 after shock motor2 after shock 0 motor1 after compensation 100 0.0 0.2 0.4 0.6 motor2 after compensation 0.8 motor3 after compensation Torque/N·m FigureFigure 8010. 10. PerformancePerformance of of motors motors before before an andd after after impact impact and and compensation. compensation.

Obviously, the central part of the rotor is sunken, and the depth of sinking is measured and 60 listed in Table3. The theoretical preload after impact based on Equation (2) is listed in Table3. Rotate speed/ r/min Rotate The compensation is carried out to restore preload. The theoretical compensation thickness is based 40 on Equation (3), and the actual thickness of the compensation gaskets is listed in Table3. The actual compensation thicknesses are obtained through debugging when ultrasonic motors are at optimal 20 performance levels. There is a diﬀerence between theoretical and actual compensation. Diﬀerent thickness gaskets are used in debugging. The voids between gaskets lead to the increase in total thickness, which means0 the decrease in actual thickness. 0.0 0.2 0.4 0.6 0.8 Torque/N·m Figure 10. Performance of motors before and after impact and compensation. Micromachines 2020, 11, 689 10 of 14

Table 3. Deformation dc of a rotor and compensation thickness.

Deformation Theoretical Preload Theoretical Actual Number d (mm) after Impact(N) Compensation (mm) Compensation (mm) Micromachines 2020,c 11, x FOR PEER REVIEW 10 of 13 1 0.1 149.8 0.106 0.1 2 0.2Table 3. Deformation 73.4 dc of a rotor and compensation 0.207 thickness. 0.15 3 0.55 0 0.523 0.45 Theoretical Actual Deformation dc Theoretical Preload Number Compensation Compensation Moreover, the(mm) performance of motorsafter Impact(N) after compensation is tested, as shown in Figure 10. It is (mm) (mm) obvious that the mechanical characteristic will be restored with the application of the compensation 1 0.1 149.8 0.106 0.1 gasket. However, the performance will never be restored to original state. It will always degrade 2 0.2 73.4 0.207 0.15 irreversibly. The reasons behind this need more analysis. 3 0.55 0 0.523 0.45 4.2. Anti-Impact Property of Stator 4.2. Anti-Impact Property of Stator In order to test the anti-impact property of stators, motors 1 and 2 are subjected to a higher impact load ofIn 9718.3order to and test 3582.6 the anti-impact g, respectively. property Obviously, of stator thes, motors two motors 1 and cannot 2 are subjected operate normally. to a higher There impact is noload obvious of 9718.3 damage and 3582.6 in the stators.g, respectively. The vibration Obviou characteristicsly, the two of motors the stators cannot after operate impact normally. is measured There by ais laser no Dopplerobvious vibrometerdamage in systemthe stat (PSV-300F-B).ors. The vibration The vibration characteristic shapes of of statorthe stators 1 and after 2 are relativelyimpact is complete,measured as by shown a laser in Doppler Figures 11vibrometer and 12. However, system (PSV the vibration-300F-B). The shape vibration of stator shapes 2 is far of better stator than 1 and that 2 ofare stator relatively 1. The complete, crest heights as shown in these in Figure two stators 11 and are Figure both inconsistent, 12. However, but the the vibration inconsistence shape of is morestator apparent2 is far better in stator than 1. that Besides of stator that, 1. there The iscrest a wave heig discontinuityhts in these two in statorstators 1. are The both inconsistent inconsistent, crests but show the thatinconsistence the stator is presents more apparent a state of in twisted stator 1. vibration, Besides that, which there means is a thatwave the discontinuity stator is no longerin stator a stable1. The ring.inconsistent This will crests lead show to inhomogeneous that the stator contact presents between a state the of statortwisted and vibration, rotor; thus, which the means output that torque the andstator speed is no of longer the USM a stable are severelyring. This weakened. will lead to The inhomogeneous small distortions contact in the between vibration the characteristicstator and rotor; of statorsthus, the are output part of torque the reasons and speed behind of the the performance USM are severely degradation weakened. after theThe compensation small distortions described in the invibration previous characteristic section. of stators are part of the reasons behind the performance degradation after the compensation described in previous section.

(a)Phase A with frequency 39.766 kHz (b) Phase B with frequency 39.836 kHz

FigureFigure 11. 11.Vibration Vibration characteristic characteristic of of stator stator 1. 1

(a) Phase A with frequency 40.328 kHz (b) Phase B with frequency 40.328 kHz Micromachines 2020, 11, x FOR PEER REVIEW 10 of 13

Table 3. Deformation dc of a rotor and compensation thickness.

Theoretical Actual Deformation dc Theoretical Preload Number Compensation Compensation (mm) after Impact(N) (mm) (mm) 1 0.1 149.8 0.106 0.1 2 0.2 73.4 0.207 0.15 3 0.55 0 0.523 0.45

4.2. Anti-Impact Property of Stator In order to test the anti-impact property of stators, motors 1 and 2 are subjected to a higher impact load of 9718.3 and 3582.6 g, respectively. Obviously, the two motors cannot operate normally. There is no obvious damage in the stators. The vibration characteristic of the stators after impact is measured by a laser Doppler vibrometer system (PSV-300F-B). The vibration shapes of stator 1 and 2 are relatively complete, as shown in Figure 11 and Figure 12. However, the vibration shape of stator 2 is far better than that of stator 1. The crest heights in these two stators are both inconsistent, but the inconsistence is more apparent in stator 1. Besides that, there is a wave discontinuity in stator 1. The inconsistent crests show that the stator presents a state of twisted vibration, which means that the stator is no longer a stable ring. This will lead to inhomogeneous contact between the stator and rotor; thus, the output torque and speed of the USM are severely weakened. The small distortions in the vibration characteristic of stators are part of the reasons behind the performance degradation after the compensation described in previous section.

(a)Phase A with frequency 39.766 kHz (b) Phase B with frequency 39.836 kHz Micromachines 2020, 11, 689 11 of 14 Figure 11. Vibration characteristic of stator 1

Micromachines 2020, 11, x FOR PEER REVIEW 11 of 14

Figure 12. Vibration characteristic of stator 2. (a) Phase A with frequency 40.328 kHz (b) Phase B with frequency 40.328 kHz In order to ensure the performanceFigure 12. Vibrationof ultrason characteristicic motor of stator in shock 2. environment, the protection device is necessary. Rubber, which can effectively reduce the impact amplitude and increase the In order to ensure the performance of ultrasonic motor in shock environment, the protection impact pulse width, is widely used in vibration and impact buffering devices because of its excellent device is necessary. Rubber, which can eﬀectively reduce the impact amplitude and increase the impact propertypulse and width,its cheap is widely price. used A in sh vibrationock experiment and impact buis ﬀcarriedering devices out with because the of protection its excellentproperty of rubber. The impact loadsand its are cheap 3090, price. 3035, A shock and experiment 2980 g. The is carried ultrason out withic motors the protection used in of rubber.the experiment The impact loadsare the three motors arethat 3090, have 3035, been and 2980adjusted g. The ultrasonicafter the motors previous used inexperiment. the experiment The are therubber three motorsused thatduring the experimenthave is been shown adjusted in Figure after the 13. previous The mechanical experiment. characteristic The rubber used of during the ultrasonic the experiment motor is shown is tested after in Figure 13. The mechanical characteristic of the ultrasonic motor is tested after impact with the impact with the protection of rubber. The experiment results show that the performance of the protection of rubber. The experiment results show that the performance of the ultrasonic motor drops ultrasonicslightly motor compared drops slightly with that compared has no protection with method,that has as no shown protection in Figure method, 14. Obviously, as shown rubber in can Figure 14. Obviously,protect rubber the motors can protect in a shock the environment motors in toa someshock extent. environment to some extent.

Figure Figure13. Ultrasonic 13. Ultrasonic motor motor with with (right) (right) and and withoutwithout (left) (left) the the protection protection of rubber. of rubber.

Figure 14. Performance of motors with the protection of rubber.

5. Conclusion In this article, a typical structure of a travelling-wave ultrasonic motor is proposed and the influence of shock acceleration on an ultrasonic motor is investigated. A theoretical model is established to observe the dynamic response of an ultrasonic motor in a shock environment based on the finite element method. Meanwhile, a relationship between plastic deformation in the rotor and Micromachines 2020, 11, x FOR PEER REVIEW 11 of 14

Figure 12. Vibration characteristic of stator 2.

In order to ensure the performance of ultrasonic motor in shock environment, the protection device is necessary. Rubber, which can effectively reduce the impact amplitude and increase the impact pulse width, is widely used in vibration and impact buffering devices because of its excellent property and its cheap price. A shock experiment is carried out with the protection of rubber. The impact loads are 3090, 3035, and 2980 g. The ultrasonic motors used in the experiment are the three motors that have been adjusted after the previous experiment. The rubber used during the experiment is shown in Figure 13. The mechanical characteristic of the ultrasonic motor is tested after impact with the protection of rubber. The experiment results show that the performance of the ultrasonic motor drops slightly compared with that has no protection method, as shown in Figure 14. Obviously, rubber can protect the motors in a shock environment to some extent.

Micromachines 2020, 11, 689 12 of 14 Figure 13. Ultrasonic motor with (right) and without (left) the protection of rubber.

FigureFigure 14. 14. PerformancePerformance of of motors motors with with the the protection protection of of rubber. rubber.

5.5. Conclusion Conclusions InIn this this article,article, aa typical typical structure structure of aof travelling-wave a travelling-wave ultrasonic ultrasonic motor motor is proposed is proposed and the influenceand the influenceof shock accelerationof shock acceleration on an ultrasonic on an motorultrasonic is investigated. motor is investigated. A theoretical A model theoretical is established model is to establishedobserve the to dynamic observe response the dynamic of an response ultrasonic of motor an ultrasonic in a shock motor environment in a shock based environment on the finite based element on themethod. finite element Meanwhile, method. a relationship Meanwhile, between a relationship plastic deformation between plastic in the deformation rotor and preload in the isrotor obtained. and After that, an impact experiment is carried out to test the influence of a shock environment on an ultrasonic motor, including the influence on the mechanical characteristic of motors and the vibration characteristic of stators. Moreover, the compensation gasket is applied to recover the performance of motors. Finally, the protection effect of rubber on an ultrasonic motor in a shock environment is verified by experiments. The meaningful results are summarized in the following. The deformation of structure does not only depend on the amplitude of shock acceleration but also the pulse width. The distortion of the rotor is smaller while the shock frequency is far away from the resonant frequency. This means that the influence of shock acceleration on an ultrasonic motor can be reduced by changing the impact pulse width besides reducing impact amplitude. The preload decreases while the deformation of the rotor increases. It will result in the performance degradation of the motor. The preload can be recovered by adding an extra gasket. The relationships between the deformation of the rotor and preload as well as compensation thickness are obtained, respectively. The experiment results also show that the mechanical characteristic can be recovered by applying an extra gasket. A shock environment will lead to the small distortion of the vibration characteristic of a stator, including the inconsistent crest heights and wave discontinuity. This is part of the reason that leads to irreversible damage to the ultrasonic motors. As a typical cushioning material, rubber can protect an ultrasonic motor in a shock environment efficiently. A protection device is necessary when an ultrasonic motor is applied in a shock environment.

Author Contributions: Conceptualization, D.S. and J.H.; methodology, D.S.; software, J.H.; validation, J.H. and D.S.; formal analysis, D.S.; investigation, J.H.; resources, D.S.; data curation, J.H.; writing—original draft preparation, J.H.; writing—review and editing, J.H.; visualization, D.S.; supervision, D.S.; project administration, D.S.; funding acquisition, J.H. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Natural Science Foundation of China, grant number 51805277 and the Research Projects of Universities Guangdong Province, grant number 2018KZDXM074. Micromachines 2020, 11, 689 13 of 14

Acknowledgments: This work is supported by the National Natural Science Foundation of China (grant number 51805277) and the Research Projects of Universities Guangdong Province(2018KZDXM074). Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Xu, D.; Liu, Y.; Liu, J.; Yang, X.; Chen, W. Developments of a piezoelectric actuator with nano-positioning ability operated in bending modes. Ceram. Int. 2017, 43, S21–S26. [CrossRef] 2. Uchino, K. Piezoelectric ultrasonic motors: Overview. Smart Mater. Struct. 1998, 7, 273. [CrossRef] 3. Uchino, K.; Cagatay, S.; Koc, B.; Dong, S.; Bouchilloux, P.; Strauss, M. Micro piezoelectric ultrasonic motors. J. Electroceramics 2004, 13, 393–401. [CrossRef] 4. Uchino, K. Piezoelectric actuators 2006. J. Electroceramics 2008, 20, 301–311. [CrossRef] 5. Jian, Y.; Yao, Z.; Silberschmidt, V.V. Linear ultrasonic motor for absolute gravimeter. Ultrasonics 2017, 77, 88–94. [CrossRef] 6. Díaz-Molina, A.; Ruiz-Díez, V.; Hernando-García, J.; Ababneh, A.; Seidel, H.; Sánchez-Rojas, J.L. Generation of Linear Traveling Waves in Piezoelectric Plates in Air and Liquid. Micromachines (Basel) 2019, 10, 283. 7. Kubota, T.; Tada, K.; Kunii, Y. Smart manipulator actuated by Ultra-Sonic Motors for lunar exploration. In Proceedings of the IEEE International Conference on Robotics and Automation, Pasadena, CA, USA, 19–23 May 2008; pp. 3576–3581. 8. Das, H.; Bao, X.; Bar-Cohen, Y.; Bonitz, R.; Lindemann, R.A.; Maimone, M.; Voorhees, C.J. Robot manipulator technologies for planetary exploration. In Proceedings of the Smart Structures and Materials 1999: Smart Structures and Integrated Systems, Newport Beach, CA, USA, 9 June 1999; International Society for Optics and Photonics: Bellingham, WA, USA, 1999; Volume 3668, pp. 175–183. 9. Liu, Y.; Shi, S.; Wang, D.; Chen, W.; Xu, D. Research on the Thermal Characteristics of Bending Hybrid Piezoelectric Actuators under Different Exciting Methods. Ceram. Int. 2017, 43, s15–s20. [CrossRef] 10. Morita, T.; Takahashi, S.; Asama, H.; Niino, T. Rotational feedthrough using an ultrasonic motor and its performance in ultra high vacuum conditions. Vacuum 2003, 70, 53–57. [CrossRef] 11. Sanguinetti, B.; Varcoe, B.T.H. Use of a piezoelectric SQUIGGLE motor for positioning at 6 K in a cryostat. Cryogenics 2006, 46, 694–696. [CrossRef] 12. Yamada, Y.; Morizono, T.; Sato, S.; Shimohira, T.; Umetani, Y.; Yoshida, T.; Aoki, S. Proposal of a SkilMate finger for EVA gloves. In Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea, 21–26 May 2001; Volume 2, pp. 1406–1412. 13. Yamaguchi, D.; Kanda, T.; Suzumori, K. Bolt-clamped Langevin-type transducer for ultrasonic motor used at ultralow temperature. J. Adv. Mech. Des. Syst. Manuf. 2012, 6, 104–112. [CrossRef] 14. Qu, H.; Wen, Z.; Qu, J.; Song, B. Study on effects of ultrasonic vibration on sliding friction properties of PTFE composites/phosphor bronze under vacuum. Vacuum 2019, 7, 164. 15. Song, F.H.; Yang, Z.H.; Zhao, G.; Wang, Q.; Zhang, X.; Wang, T. Tribological performance of filled PTFE-based friction material for ultrasonic motor under different temperature and vacuum degrees. J. Appl. Polym. Sci. 2017, 39, 45358. 16. Lee, D.; Lee, S.; Kim, W. Precise contour motion of XY stage driven by ultrasonic linear motors in a high vacuum environment. Int. J. Precis. Eng. Manuf. 2016, 17, 293–301. 17. El Diwiny, M.; Abou El Magd, G. Implementation of anti stealth technology for safe operation of unmanned aerial vehicle. In Proceedings of the IEEE Digital Avionics Systems Conference, Colorado Springs, CO, USA, 5–9 October 2014; pp. 7E2-1–7E2-12. 18. Tang, Y.J.; Yang, Z.; Wang, X.J.; Wang, J. Research on the Piezoelectric Ultrasonic Actuator Applied to SFSS. In Proceedings of the ASME 2015 International Mechanical Engineering Congress and Exposition, Houston, TX, USA, 13–19 November 2015; p. V04BT04A048. 19. Tang, Y.; Yang, Z.; Wang, X.; Wang, J. Research on the piezoelectric ultrasonic actuator applied to smart fuze safety system. Int. J. Appl. Electromagn. Mech. 2017, 53, 1–11. [CrossRef] 20. Tanner, D.M.; Walraven, J.A.; Helgesen, K.; Irwin, L.W.; Brown, F.; Smith, N.F.; Masters, N. MEMS reliability in shock environments. In Proceedings of the IEEE Reliability Physics Symposium, San Jose, CA, USA, 10–13 April 2000; pp. 129–138. Micromachines 2020, 11, 689 14 of 14

21. Sundaram, S.; Tormen, M.; Timotijevic, B.; Lockhart, R.; Overstolz, T.; Stanley, R.P.; Shea, H.R. Vibration and shock reliability of MEMS: Modeling and experimental validation. J. Micromech. Microeng. 2011, 21, 045022. [CrossRef] 22. Srikar, V.T.; Senturia, S.D. The reliability of microelectromechanical systems (MEMS) in shock environments. J. Microelectromech. Syst. 2002, 11, 206–214. [CrossRef] 23. Forrestal, M.J.; Frew, D.J.; Hickerson, J.P.; Rohwer, T.A. Penetration of concrete targets with deceleration-time measurements. Int. J. Impact Eng. 2003, 28, 479–497. [CrossRef] 24. Booker, P.M.; Cargile, J.D.; Kistler, B.L.; La Saponara, V. Investigation on the response of segmented concrete targets to projectile impacts. Int. J. Impact Eng. 2009, 36, 926–939. [CrossRef] 25. Ren, J.; Chen, C.; Zhou, J. Research on the overload characteristic of Traveling Wave Type Rotary Ultrasonic Motor. In Proceedings of the IEEE Piezoelectricity, Acoustic Waves and Device Applications (SPAWDA), Changsha, China, 25–27 October 2013; pp. 1–4. 26. Sun, D.; Wang, X.J.; Chen, C.; Wang, J.; Liu, Y.F. Dynamic Response Mechanism of Rotary Type Ultrasonic Motor Under High Impact Load. In Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition, Phoenix, AZ, USA, 11–17 November 2016; American Society of Mechanical Engineers: New York, NY, USA, 2016; p. V04AT05A026. 27. Lu, X.; Hu, J.; Zhao, C. Analyses of the temperature ﬁeld of traveling-wave rotary ultrasonic motors. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2011, 58, 2708–2719. [CrossRef] 28. Bekiroglu, E. Ultrasonic motors: Their models, drives, controls and applications. J. Electroceramics 2008, 20, 277–286. [CrossRef] 29. Frangi, A.; Corigliano, A.; Binci, M.; Faure, P. Finite element modelling of a rotating piezoelectric ultrasonic motor. Ultrasonics 2005, 43, 747–755. [CrossRef][PubMed] 30. Hagood, N.W.; McFarland, A.J. Modeling of a piezoelectric rotary ultrasonic motor. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 1995, 42, 210–224. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).