超声电机中压电材料的断裂失效研究
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摘要
本课题来源于国家自然科学基金项目《压电精密致动技术的基础研究》(项目编号:50735002)。
超声电机是一种基于压电效应和超声振动的高新技术产品。由于复杂的工作环境,超声电机中的压电陶瓷非常容易受到环境的影响而产生断裂失效,从而导致超声电机无法正常的工作。针对这一现象,本文通过简化超声电机定子为一弹性复合梁,研究环境对压电陶瓷断裂失效的影响,主要内容及成果如下:
综述了超声电机的发展历史,总结了现在超声电机工作中出现的断裂失效现象,并针对其工作的原理、结构和环境因素,提出了弹性复合梁的结构模型,确定了本课题的研究方向和内容;
分析指出了影响超声电机工作稳定性的原器件以及系统环节,介绍了压电陶瓷两种主要的失效类型:电致失效和多场耦合失效,并将两种主要的失效现象机械断裂失效和电击穿失效进行了对比分析。对含导通裂纹的各向同性电介质的临界击穿电场进行了推导。
对含预制裂纹的弹性复合梁进行了仿真计算,通过对不同位置预制裂纹的裂纹尖端应力分布的分析,得到极化区间内中间贯穿裂纹最易发生裂纹扩展。通过对压电陶瓷施加不同电压载荷、不同预载荷和温度载荷的弹性复合梁的仿真计算得到:电场增大促进裂纹的扩展,预载荷增大引起应变增大,促进了裂纹的扩展。而温度升高抑制裂纹的扩展。
在仿真计算的基础上对各个不同边界条件的压电陶瓷进行了J积分的计算,结果表明当电压载荷和预载荷增大时,J积分值不断增大;当温度载荷增大时,J积分值不断减小直至稳定。
最后,通过实验证实:电场载荷增大容易促进裂纹的扩展,预载荷增大引起裂纹应变减小,抑制了裂纹的扩展,施加的温度载荷越高裂纹越不容易发生扩展。
This project was granted by the project of the National Natural Science Foundation of China. (Contract No: 50735002).
Ultrasonic motor is a high-tech product based on the piezoelectric effect and ultrasonic vibration. Due to the complex service environment, cracking or fractures may often exist in piezoelectric ceramic of ultrasonic motor so that the ultrasonic motor can not work normally. In the present work, the stator of the ultrasonic motor was modeled as an elastic-composite beam, and then studies on the fracture and failure of the piezoelectric ceramic are made theoretically and experimentally. Main content and results are as follows:
The developing history of ultrasonic motor was summarized, and the fracture and failure phenomenon in the ultrasonic motor then was pointed out. According to the working principle structure of the ultrasonic motor and its working environment, the elastic-composite beam structure model was developed, and the following works were completed:
The devices and the other factors which influence the working stability of ultrasonic motor were pionted out. The main mechanism of failure and two main failure types were expounds. The two main failure phenomena (mechanical fracture failure and electric breakdown failure) were compared. Critical breakdown electric field was also derived.
Simulation calculation was done to the elastic-composite beam that contains a prefabricated crack. It is found, from the stress distribution at the crack tip in the samples with prefabricated cracks at different position, that the middle throughout crack is the easiest to propagate in the polarization interval. Through the simulation results for the piezoelectric ceramics under different voltage, preloading value and temperature applying at the elastic-composite beam,it is obtained that the electric field and preloading can promote the crack growth, while the temperature retard the crack growth.
J integral was made on the basis of simulation calculation of different boundary conditions for the piezoelectric ceramic.It is found that the J integral value increases constantly as the electric field and preloading value increases, but it constantly decrease and finally reaches a stability value as the temperature increases.
Eexperimental works about the faliue of piezoelectric materials with cracks are also conduceted, and it is found that increasing the electric field can promote the crack growth, and the decreasing of strain which causes by preloading restrain the crack gracks, while as the temperature becomes higher, the crack trends to close, which is consistent with the above theoretical predications.
超声电机是一种基于压电效应和超声振动的高新技术产品。由于复杂的工作环境,超声电机中的压电陶瓷非常容易受到环境的影响而产生断裂失效,从而导致超声电机无法正常的工作。针对这一现象,本文通过简化超声电机定子为一弹性复合梁,研究环境对压电陶瓷断裂失效的影响,主要内容及成果如下:
综述了超声电机的发展历史,总结了现在超声电机工作中出现的断裂失效现象,并针对其工作的原理、结构和环境因素,提出了弹性复合梁的结构模型,确定了本课题的研究方向和内容;
分析指出了影响超声电机工作稳定性的原器件以及系统环节,介绍了压电陶瓷两种主要的失效类型:电致失效和多场耦合失效,并将两种主要的失效现象机械断裂失效和电击穿失效进行了对比分析。对含导通裂纹的各向同性电介质的临界击穿电场进行了推导。
对含预制裂纹的弹性复合梁进行了仿真计算,通过对不同位置预制裂纹的裂纹尖端应力分布的分析,得到极化区间内中间贯穿裂纹最易发生裂纹扩展。通过对压电陶瓷施加不同电压载荷、不同预载荷和温度载荷的弹性复合梁的仿真计算得到:电场增大促进裂纹的扩展,预载荷增大引起应变增大,促进了裂纹的扩展。而温度升高抑制裂纹的扩展。
在仿真计算的基础上对各个不同边界条件的压电陶瓷进行了J积分的计算,结果表明当电压载荷和预载荷增大时,J积分值不断增大;当温度载荷增大时,J积分值不断减小直至稳定。
最后,通过实验证实:电场载荷增大容易促进裂纹的扩展,预载荷增大引起裂纹应变减小,抑制了裂纹的扩展,施加的温度载荷越高裂纹越不容易发生扩展。
This project was granted by the project of the National Natural Science Foundation of China. (Contract No: 50735002).
Ultrasonic motor is a high-tech product based on the piezoelectric effect and ultrasonic vibration. Due to the complex service environment, cracking or fractures may often exist in piezoelectric ceramic of ultrasonic motor so that the ultrasonic motor can not work normally. In the present work, the stator of the ultrasonic motor was modeled as an elastic-composite beam, and then studies on the fracture and failure of the piezoelectric ceramic are made theoretically and experimentally. Main content and results are as follows:
The developing history of ultrasonic motor was summarized, and the fracture and failure phenomenon in the ultrasonic motor then was pointed out. According to the working principle structure of the ultrasonic motor and its working environment, the elastic-composite beam structure model was developed, and the following works were completed:
The devices and the other factors which influence the working stability of ultrasonic motor were pionted out. The main mechanism of failure and two main failure types were expounds. The two main failure phenomena (mechanical fracture failure and electric breakdown failure) were compared. Critical breakdown electric field was also derived.
Simulation calculation was done to the elastic-composite beam that contains a prefabricated crack. It is found, from the stress distribution at the crack tip in the samples with prefabricated cracks at different position, that the middle throughout crack is the easiest to propagate in the polarization interval. Through the simulation results for the piezoelectric ceramics under different voltage, preloading value and temperature applying at the elastic-composite beam,it is obtained that the electric field and preloading can promote the crack growth, while the temperature retard the crack growth.
J integral was made on the basis of simulation calculation of different boundary conditions for the piezoelectric ceramic.It is found that the J integral value increases constantly as the electric field and preloading value increases, but it constantly decrease and finally reaches a stability value as the temperature increases.
Eexperimental works about the faliue of piezoelectric materials with cracks are also conduceted, and it is found that increasing the electric field can promote the crack growth, and the decreasing of strain which causes by preloading restrain the crack gracks, while as the temperature becomes higher, the crack trends to close, which is consistent with the above theoretical predications.
引文
[1]赵淳生.超声电机技术和应用.北京:科学出版社,2007.9
[2] Hiroshi Hirata and Sadayuki Ueha, Characteristics Estimation of a Traveling Wave Type Ultrasonic Motor, IEEE. Transactions on Ultrasonics,Ferroelectricsand Frequency Control, July 1993, 40(4): 402-406
[3] Y. Tomikawa, T. Takano, C. Kusakabe. Manabu Aoyagi and Seiji Hirose, Development of Ultrasonic Motors, 9th Smart Actuator Symposium at ICAT The Pennsylvania State University, 1994, 4:1-11
[4]李朝东,赵淳生.超声马达在日本的开发与应用.振动、测试与诊断,1996,16(2):1-6
[5]赵淳生,熊振华.国内压电超声马达研究的现状和发展.振动、测试与诊断,1997, 17(2): 1-7
[6]赵淳生.对发展我国超声电机技术的若干建议.全国第三届超声波电机理论和应用技术研讨会,中国·杭州,2005, 5:12-14
[7] Sounkalo Dembéléand Karima Rochdi,A three DOF linear ultrasonic motor for transport and micropositioning , Sensors and Actuators A. Physical (In Press), Available online 22 September 2005
[8] J. Satonobu, N. Torii, K. Nakamura and S. Ueha. Construction of Megatorque Hybrid Transducer Type Ultrasonic Motor. Jpn. J. Appl. Phys, 1996, 35:5038-5041
[9]金龙,朱美玲,赵淳生.国外超声马达的发展与应用.振动、测试与诊断,1996, 16(1):1-7
[10]陈明,陈新业,姜开利,周铁英.超声波马达的应用.应用声学,2000, 19(4):38-43
[11]陈超.旋转型行波超声电机理论模型的研究.江苏:南京航空航天大学博士学位论文,2006
[12] Pak Y E. Linear electro-elastic fracture mechanics of piezoelectric materials. Int. J. Fract, 1992, 54:79-100
[13] Pak Y E. Crack extension force in a piezoelectric material. J. Appl. Mech,1990, 57: 647-653
[14] Wang T.. Analysis of strip electric saturation model of crack problem in piezoelectric materials.Int. J. Solids Struct, 2000, 37:6031-6049
[15] Suo Z. Models for breakdown-resistant dielectric and ferroelectric ceramics. J Mech Phys Solids, 1993, 41: 55–76
[16] Deeg W F.The analysis of dislocation, crack and inclusion problems in piezoelectric solids. PhD Thesis, Stanford University,1980
[17] Parton V Z. Fracture mechanics of piezoelectric materials. Acta Astronaut, 1976, 3:671-683
[18]方岱宁,刘金喜.压电与铁电体的断裂力学.北京:清华大学出版社,2008
[19] Zhang T Y, Zhao M H and Tong P. Fracture of piezoelectric ceramics. Adv. Appl. Mech. 2001, 38:147-289
[20] Zhang T.Y,Qian C.F,Tong Pin.Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material .Int. J. Solids Struct,1998, 35:2121-2149
[21] Zhang T.Y, Tong Pin. Fracture mechanics for a mode 1II crack in a piezoelectric material .Int. J.Solids Struct,1995, 33:343-359
[22] Gao C.F, Wang M.Z. An easy method for calculation the energy release rate of cracked piezoelectric media. Mechanics Research Communications,1999, 26:433-436
[23] Gao C.F, Zhao M.h,Pin Tong, Zhang T.Y.The energy release rate&the J-integral of an electrically insulated crack in a piezoelectric material. International Journal of Engineering Science,2004, 42:2175-2192
[24]程锦泉,张统一,王彪,杜善义.电场对PZT-复合材料层合板破坏强度影响的实验研究.复合材料学报,2001,18(3):97-100.
[25]杨卫.力电失效学.北京:清华大学出版社,2001.02
[26]陆永根.超声电机可靠性和预载荷自动调节装置的研究.博士后研究工作报告,2004.
[27]杨刚,岳振星,李龙土.压电陶瓷场致疲劳特性与机理研究.无机材料学报,2007,22(1):1-6
[28]丁洪志.材料退化失效的微观统计理论:从固体断裂到电介质击穿.北京:北京理工大学博士学位论文.1995
[29] Chan K H. Hagood N W. Modeling of nonlinear piezoceramics for structural actuation. Smart Structures and Materials 1994: Smart Structures and Intelligent Systems, Ed. by Hagood N W,Proc of SPIE,1994, 2190: 194-205
[30] Hwang S C, Lynch C S, McMeeking R M. Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metall. Mater, 1995, 43:2073-2084
[31] Hwang S C, McMeeking R M. A finite element model of ferroelastic polycrystals. Int. J. Solids Struct,1999, 36:1541-1556
[32] Freeman A R and Joshi S P. Numerical modeling of PZT nonlinear electromechanical behavior. Smart Structures and Materials 1996: Mathematics and Controls in Smart Structures, Ed. By Varadan V V and Chandra J, Proc of SP1E,1996, 2715: 602-613
[33]李君余.行波型旋转超声波电机的建模与仿真.华侨大学硕士学位论文,2005年6月
[34] ANSYS入门手册.美国ANSYS公司北京办事处,1998
[35] ANSYS动力分析指南.美国ANSYS北京办事处,1998
[36]李小兵,田莳,赵建伟.热压与常压烧结PZN-PZT陶瓷的温度稳定性.压电与声光,2003,24(4):287-290
[37]于健.压电材料断裂行为的数值模拟.西南交通大学硕士学位论文,2006年4月
[38]许煜寰.铁电与压电材料.北京:科学出版社,1978.07
[39]王自强.压电材料裂纹顶端条状电饱和区模型的力学分析.力学学报,1999, 31: 311-319
[40]王保林.压电材料及其结构的断裂力学.北京:国防工业出版社.2003
[41] Park S B, Sun C T. Fracture criteria for piezoelectric ceramics. J. Amen Ceram. Soc, 1995, 78: 1475-1480
[42] Kamlah M, Tsakmakis C. Phenomenological modeling of the nonlinear electro-mechanical coupling in ferroelectrics. Int. J. Solids Struct, 1999, 36: 669-695
[43] Joshi S P. Nonlinear constitutive relations for piezoelectric materials. Smart Mater. Struct, 1992, 1:80-83
[44] Hom C L, Shankar N. A fully coupled constitutive model for electrostrictive ceramic materials. J.Intelligent Mater. Sys. Struct, 1994, 5:795-801
[45] Ghandi K.M, Hagood N .W.Nonlinear finite element modeling of phase transition in electric-mechanically coupled material. Smart Structures and Materials 1996: Mathematics and Controls in Smart Structures, Ed by Varadan V V, Chandra J, Proc of SPIE, 1996, 2715: 121-140
[46] Kim S J. A simple continuum model for polarization levels in ferroelectrics. Smart Mater. Struct.1998, 7:572-579
[47] Ghandi K M. Nonlinear Modeling and Characterization Techniques for Phase Transitions in Electro-Mechanically Coupled Devices. PhD Thesis, MIT, Cambridge, MA, 1998
[48] Zhu T, Yang W. Crack kinking in a piezoelectric solid. Int. J. Solids Struct,1999, 36:5013-5027
[49] Yang S, Yuan F G. Kinked crack in anisotropic bodies. Int. J. Solids Struct,2000, 37:6635-6682
[50]宋启明,李国成.三维J积分在ANSYS中的计算.石油化工设设备,2006, 35(2):76- 78
[51]刘金依,薛河.平面界面裂纹J积分的研究.机械设计,2002(12):20- 22
[52]张朝晖.ANSYS 12.0结构分析工程应用实例解析(第三版).北京:机械工业出版社.2010
[53] Kumar S, Singh R N. Energy release rate and crack propagation in piezoelectric materials. Part I: Mechanical/electrical load; Part II: Combined mechanical and electrical loads. Acta Mater, 1997, 45:849-868
[54] McMeeking R M. Crack tip energy release rate for a piezoelectric compact tension specimen. Engng. Fract. Mech, 1999, 64:217-244
[2] Hiroshi Hirata and Sadayuki Ueha, Characteristics Estimation of a Traveling Wave Type Ultrasonic Motor, IEEE. Transactions on Ultrasonics,Ferroelectricsand Frequency Control, July 1993, 40(4): 402-406
[3] Y. Tomikawa, T. Takano, C. Kusakabe. Manabu Aoyagi and Seiji Hirose, Development of Ultrasonic Motors, 9th Smart Actuator Symposium at ICAT The Pennsylvania State University, 1994, 4:1-11
[4]李朝东,赵淳生.超声马达在日本的开发与应用.振动、测试与诊断,1996,16(2):1-6
[5]赵淳生,熊振华.国内压电超声马达研究的现状和发展.振动、测试与诊断,1997, 17(2): 1-7
[6]赵淳生.对发展我国超声电机技术的若干建议.全国第三届超声波电机理论和应用技术研讨会,中国·杭州,2005, 5:12-14
[7] Sounkalo Dembéléand Karima Rochdi,A three DOF linear ultrasonic motor for transport and micropositioning , Sensors and Actuators A. Physical (In Press), Available online 22 September 2005
[8] J. Satonobu, N. Torii, K. Nakamura and S. Ueha. Construction of Megatorque Hybrid Transducer Type Ultrasonic Motor. Jpn. J. Appl. Phys, 1996, 35:5038-5041
[9]金龙,朱美玲,赵淳生.国外超声马达的发展与应用.振动、测试与诊断,1996, 16(1):1-7
[10]陈明,陈新业,姜开利,周铁英.超声波马达的应用.应用声学,2000, 19(4):38-43
[11]陈超.旋转型行波超声电机理论模型的研究.江苏:南京航空航天大学博士学位论文,2006
[12] Pak Y E. Linear electro-elastic fracture mechanics of piezoelectric materials. Int. J. Fract, 1992, 54:79-100
[13] Pak Y E. Crack extension force in a piezoelectric material. J. Appl. Mech,1990, 57: 647-653
[14] Wang T.. Analysis of strip electric saturation model of crack problem in piezoelectric materials.Int. J. Solids Struct, 2000, 37:6031-6049
[15] Suo Z. Models for breakdown-resistant dielectric and ferroelectric ceramics. J Mech Phys Solids, 1993, 41: 55–76
[16] Deeg W F.The analysis of dislocation, crack and inclusion problems in piezoelectric solids. PhD Thesis, Stanford University,1980
[17] Parton V Z. Fracture mechanics of piezoelectric materials. Acta Astronaut, 1976, 3:671-683
[18]方岱宁,刘金喜.压电与铁电体的断裂力学.北京:清华大学出版社,2008
[19] Zhang T Y, Zhao M H and Tong P. Fracture of piezoelectric ceramics. Adv. Appl. Mech. 2001, 38:147-289
[20] Zhang T.Y,Qian C.F,Tong Pin.Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material .Int. J. Solids Struct,1998, 35:2121-2149
[21] Zhang T.Y, Tong Pin. Fracture mechanics for a mode 1II crack in a piezoelectric material .Int. J.Solids Struct,1995, 33:343-359
[22] Gao C.F, Wang M.Z. An easy method for calculation the energy release rate of cracked piezoelectric media. Mechanics Research Communications,1999, 26:433-436
[23] Gao C.F, Zhao M.h,Pin Tong, Zhang T.Y.The energy release rate&the J-integral of an electrically insulated crack in a piezoelectric material. International Journal of Engineering Science,2004, 42:2175-2192
[24]程锦泉,张统一,王彪,杜善义.电场对PZT-复合材料层合板破坏强度影响的实验研究.复合材料学报,2001,18(3):97-100.
[25]杨卫.力电失效学.北京:清华大学出版社,2001.02
[26]陆永根.超声电机可靠性和预载荷自动调节装置的研究.博士后研究工作报告,2004.
[27]杨刚,岳振星,李龙土.压电陶瓷场致疲劳特性与机理研究.无机材料学报,2007,22(1):1-6
[28]丁洪志.材料退化失效的微观统计理论:从固体断裂到电介质击穿.北京:北京理工大学博士学位论文.1995
[29] Chan K H. Hagood N W. Modeling of nonlinear piezoceramics for structural actuation. Smart Structures and Materials 1994: Smart Structures and Intelligent Systems, Ed. by Hagood N W,Proc of SPIE,1994, 2190: 194-205
[30] Hwang S C, Lynch C S, McMeeking R M. Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metall. Mater, 1995, 43:2073-2084
[31] Hwang S C, McMeeking R M. A finite element model of ferroelastic polycrystals. Int. J. Solids Struct,1999, 36:1541-1556
[32] Freeman A R and Joshi S P. Numerical modeling of PZT nonlinear electromechanical behavior. Smart Structures and Materials 1996: Mathematics and Controls in Smart Structures, Ed. By Varadan V V and Chandra J, Proc of SP1E,1996, 2715: 602-613
[33]李君余.行波型旋转超声波电机的建模与仿真.华侨大学硕士学位论文,2005年6月
[34] ANSYS入门手册.美国ANSYS公司北京办事处,1998
[35] ANSYS动力分析指南.美国ANSYS北京办事处,1998
[36]李小兵,田莳,赵建伟.热压与常压烧结PZN-PZT陶瓷的温度稳定性.压电与声光,2003,24(4):287-290
[37]于健.压电材料断裂行为的数值模拟.西南交通大学硕士学位论文,2006年4月
[38]许煜寰.铁电与压电材料.北京:科学出版社,1978.07
[39]王自强.压电材料裂纹顶端条状电饱和区模型的力学分析.力学学报,1999, 31: 311-319
[40]王保林.压电材料及其结构的断裂力学.北京:国防工业出版社.2003
[41] Park S B, Sun C T. Fracture criteria for piezoelectric ceramics. J. Amen Ceram. Soc, 1995, 78: 1475-1480
[42] Kamlah M, Tsakmakis C. Phenomenological modeling of the nonlinear electro-mechanical coupling in ferroelectrics. Int. J. Solids Struct, 1999, 36: 669-695
[43] Joshi S P. Nonlinear constitutive relations for piezoelectric materials. Smart Mater. Struct, 1992, 1:80-83
[44] Hom C L, Shankar N. A fully coupled constitutive model for electrostrictive ceramic materials. J.Intelligent Mater. Sys. Struct, 1994, 5:795-801
[45] Ghandi K.M, Hagood N .W.Nonlinear finite element modeling of phase transition in electric-mechanically coupled material. Smart Structures and Materials 1996: Mathematics and Controls in Smart Structures, Ed by Varadan V V, Chandra J, Proc of SPIE, 1996, 2715: 121-140
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