This paper provides a general framework for modeling bonded-type piezoelectric linear motors considering the stress transferred by adhesive layer. A three-dimensional static model of stator is first developed by the principle of minimum potential energy and finite element. The stress transferred by adhesive layer could be simulated and analyzed for arbitrary bonding conditions. Basing on the static stress-transfer analysis, a quasi-static stress acted to substrate by piezoelectric elements is assumed and integrated into the substrate dynamic model. A pure mechanical dynamic model is developed for the electromechanical coupling system of stator. Furthermore, the whole-machine dynamic model of motor is presented by incorporating the frictional contact force into the dynamic model of the stator and an analytical model of the mover. Finally, a bonded-type piezoelectric linear motor with V-shaped stator is investigated as an example for simulations and experiments. The methodology presented here for simulating the transferred load of adhesive layer in bonded-type piezoelectric motor as well as for estimating the vibration characteristics of stator and output performances of motor. It is believed that the proposed method would be helpful to design and manufacture the prototypes due to the wider applicability of allowing for irregular geometry and any bonding conditions.
AbuzaidAHrairiMDawoodMSIS (2017) Modeling approach to evaluating reduction in stress intensity factor in center-cracked plate with piezoelectric actuator patches. Journal of Intelligent Material Systems and Structures28: 1334–1345. DOI: 10.1177/1045389X16672562.
2.
AgrahariJKapuriaS (2016) Effects of adhesive, host plate, transducer and excitation parameters on time reversibility of ultrasonic lamb waves. Ultrasonics70: 147–157. DOI: 10.1016/j.ultras.2016.04.024.
3.
AndakhshidehARafieeRMalekiS (2019) 3D stress analysis of generally laminated piezoelectric plates with electromechanical coupling effects. Applied Mathematical Modelling74: 258–279. DOI: 10.1016/j.apm.2019.04.060.
BardinVVasilevV (2017) Combining measurement and control functions in the structure of a multilayer piezoelectric actuator of nano-and micro-motions. Measurement Techniques60: 711–716. DOI: 10.1007/s11018-017-1259-3.
6.
BolboriciVDawsonFPughM (2014) A finite volume method and experimental study of a stator of a piezoelectric traveling wave rotary ultrasonic motor. Ultrasonics54: 809–820. DOI: 10.1016/j.ultras.2013.10.005.
7.
CaiKTianYLiuX, et al. (2018) Modeling and controller design of a 6-dof precision positioning system. Mechanical Systems and Signal Processing104: 536–555. DOI: 10.1016/j.ymssp.2017.11.002.
8.
ChenXChenZLiX, et al. (2016) A spiral motion piezoelectric micromotor for autofocus and auto zoom in a medical endoscope. Applied Physics Letters108: 273–454. DOI: 10.1063/1.4941395.
9.
ChenPChenSGuoW, et al. (2018a) The interface behavior of a thin piezoelectric film bonded to a graded substrate. Mechanics of Materials127: 26–38. DOI:10.1016/j. mechmat.2018.08.009.
10.
ChenPChenSPengJ, et al. (2019b) The interface behavior of a thin film bonded imperfectly to a finite thickness gradient substrate. Engineering Fracture Mechanics217: 106529. DOI: 10.1016/j.engfracmech.2019.106529.
11.
ChenPChenSLiuH, et al. (2020b) The interface behavior of multiple piezoelectric films attaching to a finite-thickness gradient substrate. Journal of Applied Mechanics87: 011003. DOI: 10.1115/1.4044895.
12.
ChenPPengJLiH, et al. (2018b) The electromechanical behavior of a piezoelectric actuator bonded to a graded substrate including an adhesive layer. Mechanics of Materials123: 77–87. doi:10.1016/j.mechmat.2018.05.002.
13.
ChenNYanPOuyangJ (2019a) A generalized approach on bending and stress analysis of beams with piezoelectric material bonded. Sensors and Actuators, A: Physical290: 54–61. DOI: 10.1016/j.sna.2019.02.029.
14.
ChenJZhangCXuM, et al. (2015) Rhombic micro-displacement amplifier for piezoelectric actuator and its linear and hybrid model. Mechanical Systems and Signal Processing50–51: 580–593. DOI: 10.1016/j.ymssp.2014. 05.047.
15.
ChenNZhengJJiangX, et al. (2020a). Analysis and control of micro-stepping characteristics of ultrasonic motor. Frontiers of Mechanical Engineering15: 585–599. DOI: 10.1007/s11465-019-0577-3.
16.
CrawleyEFAndersonEH (1990) Detailed models of piezoceramic actuation of beams. Journal of Intelligent Material Systems and Structures1: 4–25. DOI: 10.1177/1045389X9000100102.
17.
CrawleyEFde LuisJ (1987) Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal25: 1373–1385. DOI: 10.2514/3.9792.
18.
DengYZhaoGYiX, et al. (2019) Contact modeling and input-voltage-region based parametric identification for speed control of a standing wave linear ultrasonic motor. Sensors and Actuators, A: Physical295: 456–468. DOI: 10.1016/j.sna.2019.06.016.
19.
FanPLiCYuanT (2018) New design of piezoelectric plate-type vibrator based on quasi-traveling wave. Journal of the Brazilian Society of Mechanical Sciences and Engineering40: 176. DOI:10.1007/s40430-018-1110-z.
20.
GaoXYangJWuJ, et al. (2020) Piezoelectric actuators and motors: Materials, designs, and applications. Advanced Materials Technologies5: 1900716. DOI: 10.1002/admt.201900716.
21.
GlushkovEGlushkovaNKvashaO, et al. (2007) Integral equation based modeling of the interaction between piezoelectric patch actuators and an elastic substrate. Smart Materials and Structures16: 650–664. DOI: 10 .1088/0964-1726/16/3/012.
22.
GuoWChenPYuL, et al. (2020) Numerical analysis of the strength and interfacial behaviour of adhesively bonded joints with varying bondline thicknesses. International Journal of Adhesion and Adhesives98: 102553. DOI: 10.1016/j.ijadhadh.2020.102553.
23.
HeYYaoZDaiS, et al. (2019) Hybrid simulation for dynamic responses and performance estimation of linear ultrasonic motors. International Journal of Mechanical Sciences153–154: 219–229. DOI: 10.1016/j.ijmecsci.2019.01.041.
24.
HwangHNasserJSodanoH (2019) Piezoelectric stack actuator for measurement of interfacial shear strength at high strain rates. Experimental Mechanics59: 979–990. DOI: 10.1007/s11340-019-00502-6.
25.
ImSAtluriS (1989) Effects of a piezo-actuator on a finitely deformed beam subjected to general loading. AIAA Journal27: 1801–1807. DOI: 10.2514/3.10337
26.
ItoSTroppmairSLindnerB, et al. (2019) Long-range fast nanopositioner using nonlinearities of hybrid reluctance actuator for energy efficiency. IEEE Transactions on Industrial Electronics66: 3051–3059. DOI: 10.1109/TIE.2018.2842735.
27.
JinCWangX (2011) Analytical modelling of the electromechanical behaviour of surface-bonded piezoelectric actuators including the adhesive layer. Engineering Fracture Mechanics78: 2547–2562. DOI: 10.1016/j.engfracmech.2011.06.014.
28.
KapuriaSAgrahariJ (2016) Two dimensional shear lag solution for stress transfer between rectangular piezoelectric wafer transducer and orthotropic host plate. European Journal of Mechanics, A/Solids55: 181–191. DOI: 10.1016/j.euromechsol.2015.09.003.
29.
KirillovaESeemannWShevtsovaM (2019) The influence of an adhesive layer on the interaction between a piezo-actuator and an elastic 3d-layer and on the excited wave fields. Materials Physics and Mechanics42: 40–53. DOI: 10.18720/MPM.4212019\5.
30.
KohKHKobayashiTHsiaoFL, et al. (2010) Characterization of piezoelectric pzt beam actuators for driving 2d scanning micromirrors. Sensors and Actuators, A: Physical162: 336–347. DOI: 10.1016/j.sna.2010.04.021.
31.
KohnkeP (2013) Ansys Mechanical Apdl Theory Reference. Canonsburg, PA: ANSYS Inc.
32.
LiGPatelNAHagemeisterJ, et al. (2020) Body-mounted robotic assistant for mri-guided low back pain injection. International Journal of Computer Assisted Radiology and Surgery15: 321–331. DOI: 10.1007/s11548-019-02080-3.
33.
LiXChenZYaoZ (2019) Contact analysis and performance evaluation of standing-wave linear ultrasonic motors via a physics-based contact model. Smart Materials and Structures28: 015032. DOI: 10.1088/1361-665X/aaf11a.
34.
LiXYaoZ (2018) Analytical modeling and experimental validation of a v-shaped piezoelectric transducer with a flexible joint for generating an elliptical motion. Precision Engineering52: 55–63. DOI: 10.1016/j.precisioneng.2017.11.004.
35.
LiuYYangXChenW, et al. (2016) A bonded-type piezoelectric actuator using the first and second bending vibration modes. IEEE Transactions on Industrial Electronics63: 1676–1683. DOI: 10.1109/TIE.2015.2492942.
36.
LuoQTongL (2002a) Exact static solutions to piezoelectric smart beams including peel stresses i: Theoretical formulation. International Journal of Solids and Structures39: 4677–4695. DOI: 10.1016/S0020-7683(02)00383-9.
37.
LuoQTongL (2002b) Exact static solutions to piezoelectric smart beams including peel stresses. ii. Numerical results, comparison and discussion. International Journal of Solids and Structures39, 4697–4722. DOI: 10.1016/S0020-7683(02)00384-0.
38.
MoharanaSBhallaS (2015) Influence of adhesive bond layer on power and energy transduction efficiency of piezoimpedance transducer. Journal of Intelligent Material Systems and Structures26: 247–259. DOI: 10.1177/1045389X14523858.
39.
RenWYangMChenL, et al. (2020) Mechanical optimization of a novel hollow traveling wave rotary ultrasonic motor. Journal of Intelligent Material Systems and Structures31: 1091–1100. DOI: 10.1177/1045389X20910263.
40.
Renteria MarquezIBolboriciV (2017) A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method. Ultrasonics77: 69–78. DOI: 10.1016/j.ultras.2017.01.019.
41.
Renteria-MarquezIRenteria-MarquezATsengB (2018) A novel contact model of piezoelectric traveling wave rotary ultrasonic motors with the finite volume method. Ultrasonics90: 5–17. DOI: 10.1016/j.ultras.2018.06.004.
TanoueYMoritaT (2020) Opposing preloads type ultrasonic linear motor with quadruped stator. Sensors and Actuators, A: Physical301: 111764. DOI: 10.1016/j.sna.2019.111764.
44.
TianXLiuYDengJ, et al. (2020) A review on piezoelectric ultrasonic motors for the past decade: Classification, operating principle, performance, and future work perspectives. Sensors and Actuators, A: Physical306: 111971. DOI: 10.1016/j.sna.2020.111971.
45.
TzouHTsengC (1990) Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems. A piezoelectric finite element approach. Journal of Sound and Vibration138: 17–34. DOI: 10.1016/0022-460X(90)90701-Z.
46.
WangGShenRGuoJ (2006) Adhensive technology and its effects on performances of stator of ultrasonic motor. Jixie Gongcheng Xuebao/Chinese Journal of Mechanical Engineering42: 91–96. DOI: 10.3901/JME.2006.09.091.
47.
WangJLuDJinF, et al. (2013a) Accuracy of the half-power bandwidth method with a third-order correction for estimating damping in multi-dof systems. Earthquake Engineering and Engineering Vibration12: 33–38. DOI: 10.1007/s11803-013-0149-1.
48.
WangLBaiRXChenH (2013b) Analytical modeling of the interface crack between a piezoelectric actuator and an elastic substrate considering shear effects. International Journal of Mechanical Sciences66: 141–148. DOI: 10.1016/j.ijmecsci.2012.11.002.
49.
WangLHofmannVBaiF, et al. (2018a) Systematic electromechanical transfer matrix model of a novel sandwiched type flexural piezoelectric transducer. International Journal of Mechanical Sciences138–139: 229–243. DOI: 10.1016/j.ijmecsci.2018.02.012.
50.
WangLQuanQXueK, et al. (2018b) Development of a three-dof piezoelectric actuator using a thin cross-beam vibrator. International Journal of Mechanical Sciences149: 54–61. DOI: 10.1016/j.ijmecsci.2018.09.039.
51.
WangSRongWWangL, et al. (2019) A survey of piezoelectric actuators with long working stroke in recent years: Classifications, principles, connections and distinctions. Mechanical Systems and Signal Processing123: 591–605. DOI: 10.1016/j.ymssp.2019.01.033.
52.
WilsonEL (2002) Three-dimensional static and dynamic analysis of structures. In: Wilson EL (ed) Computers and Structures. Berkeley, California, USA: Computers and Structures, Inc.
53.
YousefsaniSTahaniM (2018) Edge effects in adhesively bonded composite joints integrated with piezoelectric patches. Composite Structures200: 187–194. DOI: 10.1016/j.compstruct.2018.05.071.
54.
ZhaoC (2011) Ultrasonic Motors: Technologies and Applications. Springer Heidelberg Dordrecht, London, New York: Springer Science & Business Media. doi:10.1007/978-3-642-15305-1.
55.
ZhuCChuXYuanS, et al. (2016) Development of an ultrasonic linear motor with ultra-positioning capability and four driving feet. Ultrasonics72: 66–72. DOI: 10.1016/j.ultras.2016.07.010.
