面齿轮副扭转振动建模与分析
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摘要
面齿轮副在航空领域和汽车领域具有重要的应用前景。扭转振动问题是面齿轮副的核心问题之一。该文研究了面齿轮副扭转振动的建模与分析方法。建立了单输入单输出面齿轮副扭转振动模型,该模型包含非对称时变啮合刚度、间隙非线性、静态传动误差等因素。基于加载接触分析,提出面齿轮副扭转啮合刚度的计算方法,并对某型面齿轮副的非对称时变啮合刚度进行了计算。通过与Abaqus有限元动力学计算结果进行对比,验证了扭转振动模型的有效性。基于所建立的模型,分析了面齿轮副设计状态时的动态特性,研究了啮合刚度、啮合间隙、静态传动误差、扭矩波动等因素对面齿轮副动态特性的影响,以及面齿轮副蕴含的非线性动力学响应。结果表明:所提出的面齿轮副扭转振动建模方法是有效的,所建立的模型能够用于研究面齿轮副的啮合特性、动态特性,指导以及校核面齿轮副的设计。
Face-gear drives have great potential in the aviation and automotive industries.However,torsional vibrations are a key issue in face-gear pairs.This study focuses on modeling and analyses of the torsional vibrations in a face-gear pair.A torsional vibration model is given for a one-input,one-output face-gear drive with asymmetric time-varying mesh stiffness,backlash nonlinearity and static transmission errors.The torsional mesh stiffness of a face-gear pair is calculated from a loaded tooth contact analysis in a numerical example.The torsional vibration model is validated by comparing the responses with the dynamic responses predicted by Abaqus.The model is then used to analyze the dynamic behavior of a face-gear pair for the design conditions to investigate the effects of mesh stiffness,backlash,static transmission errors,and torque fluctuations on the dynamic characteristics of the face-gear pair and the nonlinear dynamic response.The results show that the model accurately predicts the face-gear pair torsional vibrations and can be used to study the mesh characteristics and the dynamic characteristics of face-gear pairs to guide the design of face-gear pairs.
Face-gear drives have great potential in the aviation and automotive industries.However,torsional vibrations are a key issue in face-gear pairs.This study focuses on modeling and analyses of the torsional vibrations in a face-gear pair.A torsional vibration model is given for a one-input,one-output face-gear drive with asymmetric time-varying mesh stiffness,backlash nonlinearity and static transmission errors.The torsional mesh stiffness of a face-gear pair is calculated from a loaded tooth contact analysis in a numerical example.The torsional vibration model is validated by comparing the responses with the dynamic responses predicted by Abaqus.The model is then used to analyze the dynamic behavior of a face-gear pair for the design conditions to investigate the effects of mesh stiffness,backlash,static transmission errors,and torque fluctuations on the dynamic characteristics of the face-gear pair and the nonlinear dynamic response.The results show that the model accurately predicts the face-gear pair torsional vibrations and can be used to study the mesh characteristics and the dynamic characteristics of face-gear pairs to guide the design of face-gear pairs.
引文
[1] KISSLING U,BEERMANN S.Face gears:Geometry and strength[J].Gear Technology,2007(1/2):54-61.
[2] BLOOMFIEID B.Designing face gears[J].Machine Design,1947,19:129-134.
[3] BILL R C. Advanced rotorcraft transmission program:NASA-TM-103276[R].Washington,DC,USA:NASA,1990.
[4] HEATH G F,BOSSLER R B JR.Advanced rotorcraft transmission(ART)program:NASA-CR-191057[R].Washington,DC,USA:NASA,1993.
[5] HEATH G F,FILLER R R,TAN J.Development of face gear technologyforindustrialandaerospacepower transmission:NASA/CR-2002-211320[R]. Washington,DC,USA:NASA,2002.
[6] LEWICKI D G,HEATH G F,FILLER R R,et al.RDS-21face-gear surface durability tests:NASA/TM-2007-214970[R].Washington,DC,USA:NASA,2007.
[7] BINNEY D A,VINAYAK H,GMIRYA Y,et al.Face gear transmission development program at Sikorsky Aircraft[C]//Proceedings of ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Chicago, USA,2003:307-313.
[8] HEATH G F,SLAUGHTER S C,FISHER D J,et al.Helical face gear development under the enhanced rotorcraft drive system program:NASA/TM-2011-217125[R].Washington,DC,USA:NASA,2011.
[9] CARUSO A,GORLA C.FACET:Face gears in aerospace transmissions[C]//Proceedings of the 25th European Rotorcraft Forum.Rome,Italy,1999.
[10]PENG X L,ZHANG L,FANG Z D.Manufacturing process for a face gear drive with local bearing contact and controllable unloaded meshing performance based on ease-off surface modification[J].Journal of Mechanical Design,2016,138(4):043302.
[11]WANG Y Z,HOU L W,LAN Z,et al.Precision milling method for face-gear by disk cutter[J].The International Journal of Advanced Manufacturing Technology,2017,89(5-8):1545-1558.
[12]LIN C, CAO X J, FAN Y, et al. Pitch deviation measurement and analysis of curve-face gear pair[J],Measurement,2016,81:95-101.
[13]CHEN S Y,TANG J Y,CHEN W T,et al.Nonlinear dynamic characteristic of a face gear drive with effect of modification[J].Meccanica,2014,49(5):1023-1037.
[14]HU Z H,TANG J Y,CHEN S Y,et al.Effect of mesh stiffness on the dynamic response of face gear transmission system[J]. JournalofMechanicalDesign, 2013,135(7):071005.
[15]HU Z H, TANG J Y,CHEN S Y,et al. Coupled translation-rotation vibration and dynamic analysis of face geared rotor system[J].Journal of Sound and Vibration,2015,351:282-298.
[16]杨振,王三民,范叶森,等.正交面齿轮传动系统分岔特性[J].哈尔滨工业大学学报,2011,43(3):107-110.YANG Z, WANG S M,FAN Y S,et al.Bifurcation characteristics of face-gear transmission system[J].Journal of Harbin Institute of Technology,2011,43(3):107-110.(in Chinese)
[17]林腾蛟,冉雄涛.正交面齿轮传动非线性振动特性分析[J].振动与冲击,2012,31(2):25-31.LIN T J,RAN X T.Nonlinear vibration characteristic analysis of face-gear drive[J].Journal of Vibration and Shock,2012,31(2):25-31.(in Chinese)
[18]李晓贞,朱如鹏,李政民卿,等.非正交面齿轮传动系统的耦合振动分析[J].中南大学学报(自然科学版),2013,44(6):2274-2280.LI X Z,ZHU R P,LI Z M Q,et al.Analysis of coupled vibration of face gear drive with non-orthogonal intersection[J].Journal of Central South University(Science and Technology),2013,44(6):2274-2280.(in Chinese)
[19]勒广虎,朱如鹏,鲍和云.正交面齿轮传动系统的非线性振动特性[J].中南大学学报(自然科学版),2010,41(5):1807-1813.JIN G H,ZHU R P,BAO H Y.Nonlinear dynamical characteristics of face gear transmission system[J].Journal of Central South University(Science and Technology),2010,41(5):1807-1813.(in Chinese)
[20]TANG J Y, HU Z H,CHEN S Y,et al.Effects of directional rotation radius and transmission error on the dynamic characteristics of face gear transmission system[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science, 2014,228(7):1108-1118.
[21]LITVIN F L,FUENTES A.Gear geometry and applied theory[M]. 2nd ed. New York, USA:Cambridge University Press,2004.
[22]KUANG J H,LIN A D.Theoretical aspects of torque responses in spur gearing due to mesh stiffness variation[J].MechanicalSystemsandSignalProcessing, 2003,17(2):255-271.
[23]THEODOSSIADES S,NATSIAVAS S.Non-linear dynamics of gear-pair systems with periodic stiffness and backlash[J].Journal of Sound and Vibration,2000,229(2):287-310.
[24]HE S,GUNDA R,SINGH R.Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness[J].Journal of Sound and Vibration, 2007,301(3-5):927-949.
[25]PADMANABHAN C,BARLOW R C,ROOK T E,et al.Computational issues associated with gear rattle analysis[J].Journal of Mechanical Design,1995,117(1):185-192.
[26]BARTHOD M,HAYNE B,TBEC J L,et al.Experimental study of gear rattle excited by a multi-harmonic excitation[J].Applied Acoustics,2007,68(9):1003-1025.
[2] BLOOMFIEID B.Designing face gears[J].Machine Design,1947,19:129-134.
[3] BILL R C. Advanced rotorcraft transmission program:NASA-TM-103276[R].Washington,DC,USA:NASA,1990.
[4] HEATH G F,BOSSLER R B JR.Advanced rotorcraft transmission(ART)program:NASA-CR-191057[R].Washington,DC,USA:NASA,1993.
[5] HEATH G F,FILLER R R,TAN J.Development of face gear technologyforindustrialandaerospacepower transmission:NASA/CR-2002-211320[R]. Washington,DC,USA:NASA,2002.
[6] LEWICKI D G,HEATH G F,FILLER R R,et al.RDS-21face-gear surface durability tests:NASA/TM-2007-214970[R].Washington,DC,USA:NASA,2007.
[7] BINNEY D A,VINAYAK H,GMIRYA Y,et al.Face gear transmission development program at Sikorsky Aircraft[C]//Proceedings of ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Chicago, USA,2003:307-313.
[8] HEATH G F,SLAUGHTER S C,FISHER D J,et al.Helical face gear development under the enhanced rotorcraft drive system program:NASA/TM-2011-217125[R].Washington,DC,USA:NASA,2011.
[9] CARUSO A,GORLA C.FACET:Face gears in aerospace transmissions[C]//Proceedings of the 25th European Rotorcraft Forum.Rome,Italy,1999.
[10]PENG X L,ZHANG L,FANG Z D.Manufacturing process for a face gear drive with local bearing contact and controllable unloaded meshing performance based on ease-off surface modification[J].Journal of Mechanical Design,2016,138(4):043302.
[11]WANG Y Z,HOU L W,LAN Z,et al.Precision milling method for face-gear by disk cutter[J].The International Journal of Advanced Manufacturing Technology,2017,89(5-8):1545-1558.
[12]LIN C, CAO X J, FAN Y, et al. Pitch deviation measurement and analysis of curve-face gear pair[J],Measurement,2016,81:95-101.
[13]CHEN S Y,TANG J Y,CHEN W T,et al.Nonlinear dynamic characteristic of a face gear drive with effect of modification[J].Meccanica,2014,49(5):1023-1037.
[14]HU Z H,TANG J Y,CHEN S Y,et al.Effect of mesh stiffness on the dynamic response of face gear transmission system[J]. JournalofMechanicalDesign, 2013,135(7):071005.
[15]HU Z H, TANG J Y,CHEN S Y,et al. Coupled translation-rotation vibration and dynamic analysis of face geared rotor system[J].Journal of Sound and Vibration,2015,351:282-298.
[16]杨振,王三民,范叶森,等.正交面齿轮传动系统分岔特性[J].哈尔滨工业大学学报,2011,43(3):107-110.YANG Z, WANG S M,FAN Y S,et al.Bifurcation characteristics of face-gear transmission system[J].Journal of Harbin Institute of Technology,2011,43(3):107-110.(in Chinese)
[17]林腾蛟,冉雄涛.正交面齿轮传动非线性振动特性分析[J].振动与冲击,2012,31(2):25-31.LIN T J,RAN X T.Nonlinear vibration characteristic analysis of face-gear drive[J].Journal of Vibration and Shock,2012,31(2):25-31.(in Chinese)
[18]李晓贞,朱如鹏,李政民卿,等.非正交面齿轮传动系统的耦合振动分析[J].中南大学学报(自然科学版),2013,44(6):2274-2280.LI X Z,ZHU R P,LI Z M Q,et al.Analysis of coupled vibration of face gear drive with non-orthogonal intersection[J].Journal of Central South University(Science and Technology),2013,44(6):2274-2280.(in Chinese)
[19]勒广虎,朱如鹏,鲍和云.正交面齿轮传动系统的非线性振动特性[J].中南大学学报(自然科学版),2010,41(5):1807-1813.JIN G H,ZHU R P,BAO H Y.Nonlinear dynamical characteristics of face gear transmission system[J].Journal of Central South University(Science and Technology),2010,41(5):1807-1813.(in Chinese)
[20]TANG J Y, HU Z H,CHEN S Y,et al.Effects of directional rotation radius and transmission error on the dynamic characteristics of face gear transmission system[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science, 2014,228(7):1108-1118.
[21]LITVIN F L,FUENTES A.Gear geometry and applied theory[M]. 2nd ed. New York, USA:Cambridge University Press,2004.
[22]KUANG J H,LIN A D.Theoretical aspects of torque responses in spur gearing due to mesh stiffness variation[J].MechanicalSystemsandSignalProcessing, 2003,17(2):255-271.
[23]THEODOSSIADES S,NATSIAVAS S.Non-linear dynamics of gear-pair systems with periodic stiffness and backlash[J].Journal of Sound and Vibration,2000,229(2):287-310.
[24]HE S,GUNDA R,SINGH R.Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness[J].Journal of Sound and Vibration, 2007,301(3-5):927-949.
[25]PADMANABHAN C,BARLOW R C,ROOK T E,et al.Computational issues associated with gear rattle analysis[J].Journal of Mechanical Design,1995,117(1):185-192.
[26]BARTHOD M,HAYNE B,TBEC J L,et al.Experimental study of gear rattle excited by a multi-harmonic excitation[J].Applied Acoustics,2007,68(9):1003-1025.