渐开线斜齿轮传动摩擦动力学耦合研究
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摘要
综合考虑时变啮合刚度、轴承刚度以及摩擦力等对动力学行为的影响,基于载荷分担理论和动力学、弹流润滑理论,建立12自由度斜齿轮摩擦动力学模型。采用解耦方法求解该摩擦动力学模型,将动力学求解获得的动态轮齿作用力用于润滑分析中,而润滑分析获得的摩擦因数再次用于动力学分析计算中。通过实例研究了齿面摩擦学特性和动力学行为以及两者之间的耦合关系。研究表明:考虑耦合效应后的斜齿轮动态响应与定摩擦因数下的动态响应相比有较大不同,且时变摩擦力对垂直于啮合线方向的动态响应影响尤为显著;动态载荷等对斜齿轮润滑特性影响较大,转速接近共振转速时,动态载荷作用下的油膜厚度、油膜承载比例、油膜温升和摩擦因数分布规律与幅值与稳态载荷相比差异明显。动态载荷对斜齿轮润滑特性以及时变滑动摩擦力对动态响应的影响不可忽略。
A twelve-degree-of-freedom tribo-dynamics model for helical gear pair is proposed based on load sharing theory, dynamics and elastohydrodynamic lubrication theory. Time-varying mesh stiffness,bearing stiffness, as well as the friction force are considered when establishing the model. A decoupling method of dynamics and tribology is proposed to solve the lubrication and dynamics models simultaneously. In the iterative loop, the dynamic model predicted the dynamic tooth forces to be used in the lubrication model. In return, the gear lubrication model is provided the dynamic model with periodic friction coefficient. An example gear pair is analyzed using the proposed model and method to demonstrate this coupling relationship between tribological and dynamic behaviors.The results show that the helical gear's dynamic response with consideration of coupling effect is different from the dynamic response under the constant friction factor. Friction force has significant effect on dynamic response that's perpendicular to action line.Dynamic load offects lubrication property greatly. Moreover, when the working rotational speed is approaching the resonance speed,compared with steady load, the distribution and amplitude of oil film thickness, portion of load carried by film, film temperature rise and the friction coefficient the oil film thickness is quite different. The influence of dynamic load on helical gear's lubrication property can't be ignored, so does the influence of time-varying sliding friction on dynamic response.
A twelve-degree-of-freedom tribo-dynamics model for helical gear pair is proposed based on load sharing theory, dynamics and elastohydrodynamic lubrication theory. Time-varying mesh stiffness,bearing stiffness, as well as the friction force are considered when establishing the model. A decoupling method of dynamics and tribology is proposed to solve the lubrication and dynamics models simultaneously. In the iterative loop, the dynamic model predicted the dynamic tooth forces to be used in the lubrication model. In return, the gear lubrication model is provided the dynamic model with periodic friction coefficient. An example gear pair is analyzed using the proposed model and method to demonstrate this coupling relationship between tribological and dynamic behaviors.The results show that the helical gear's dynamic response with consideration of coupling effect is different from the dynamic response under the constant friction factor. Friction force has significant effect on dynamic response that's perpendicular to action line.Dynamic load offects lubrication property greatly. Moreover, when the working rotational speed is approaching the resonance speed,compared with steady load, the distribution and amplitude of oil film thickness, portion of load carried by film, film temperature rise and the friction coefficient the oil film thickness is quite different. The influence of dynamic load on helical gear's lubrication property can't be ignored, so does the influence of time-varying sliding friction on dynamic response.
引文
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[9]邹玉静,常德功.渐开线直齿轮的动力学与弹流润滑耦合[J].航空动力学报,2016,31(8):2010-2020.ZOU Yujing,CHANG Dechang.Study on coupling dynamics and elastohydrodynamic lubrication of spur gear[J].Journal of Aerospace Power,2016,31(8):2010-2020.
[10]CAI Y.Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon(a new stiffness function of helical involute tooth pair[J].Journal of Mechanical Design,1995,117(3):460-469.
[11]LITVIN F L.Gear geometry and applied theory[M].New Jersey:Prentice Hall,Englewood Cliffs,1994.
[12]XU H.Development of a generalized mechanical efficiency prediction methodology for gear pairs[D].Athens:Ohio State University,2005.
[13]JOHNSON K L,GREENWOOD J A,POON S Y.Asimple theory of asperity contact in elastohydrodynamic lubrication[J].Wear,1972,19(1):91-108.
[14]GELINCK E R M,SCHIPPER D J.Deformation of rough line contacts[J].Journal of tribology,1999,121(3):449-454.
[15]GREENWOOD J A,TRIPP J H.The contact of two nominally flat rough surfaces[J].Proceedings of the Institution of Mechanical Engineers,1970,185(1):625-633.
[16]AKBARZADEH S,KHONSARI M M.Thermoelastohydrodynamic analysis of spur gears with consideration of surface roughness[J].Tribology Letters,2008,32(2):129-141.
[17]MOES H.Optimum similarity analysis with applications to elastohydrodynamic lubrication[J].Wear,1992,159(1):57-66.
[18]JANG J Y,KHONSARIL M M.Correction factor formula to predict the central and minimum film thickness for shear-thinning fluids in EHL[J].Journal of Tribology,2008,130(024501):1-4.
[19]HSU C H,LEE R T.An efficient algorithm for thermal elastohydrodynamic lubrication under rolling/sliding line contacts[J].Journal of tribology,1994,116(4):762-769.
[20]BAIR S,QURESHI F.The generalized newtonian fluid model and elastohydrodynamic film thickness[J].Journal of Tribology,2003,125:70-75
[21]BAIR S,VERGNE P,QUERRY M.A unified shear-thinning treatment of both film thickness and traction in EHD[J].Tribology Letters,2005,18(2):145-152
[22]BAIR S S.High pressure rheology for quantitative elastohydrodynamics[M].London:Elsevier,2007.
[23]YASUDA K Y,ARMSTRONG R C,COHEN R E.Shear flow properties of concentrated solutions of linear and star branched polystyrenes[J].Rheologica Acta,1981,20(2):163-178.
[24]DOOLITTLE A K.Studies in Newtonian Flow.II.The dependence of the viscosity of liquids on free-space[J].Journal of Applied Physics,2004,22(12):1471-1475.
[25]MASJEDI M,KHONSARI M M.Theoretical and experimental investigation of traction coefficient in line-contact EHL of rough surfaces[J].Tribology International,2014,70:179-189.
[26]JAEGER J C.Moving surfaces of heat and the temperature at sliding contacts[J].Proc.R.Soc.N.S.W.,1942,56:203-224.
[27]李朵朵.齿轮传动动态弹流润滑的数值计算模型研究[D].太原:太原理工大学,2004.LI Duoduo.A calculating model study for the elatohydrodynamic lubrication of the transmission of the gear in mesh[D].Taiyuan:Taiyuan University of Technology,2004.
[28]HE S,GUNDA R,SINGH R.Inclusion of sliding friction in contact dynamics model for helical gears[J].Journal of Mechanical Design,2007,129:1064-1075.
[29]ANURADHA P,KUMAR P.Effect of lubricant selection on EHL performance of involute spur gears[J].Tribology International,2012,50:82-90.
[2]潘晓东,刘祥环,黎超.纯电动汽车高速齿轮传动NVH性能优化研究[J].重庆理工大学学报,2017(11):25-31.PAN Xiaodong,LIU Xianghuan,LI Chun.Investigation on NVH performance optimization of BEV high speed gear transmission[J].Journal of Chongqing University of Technology,2017(11):25-31.
[3]BEILICKE R,BOBACH L,BARTEL D.Transient thermal elastohydrodynamic simulation of a DLC Coated helical gear pair considering limiting shear stress behavior of the lubricant[J].Tribology International,2016,97:136-150.
[4]LEE J,YOON M,BOO K,et al.Prediction of transmission error using dynamic analysis of a helical gear[J].Transactions of the Korean Society of Mechanical Engineers-A,2016,40(12):1005-1011.
[5]SAXENA A,PAREY A,CHOUKSEY M.Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects[J].Engineering Failure Analysis,2016,70:200-211.
[6]邹玉静,常德功.基于载荷分担理论的渐开线斜齿轮热混合弹流润滑分析[J].摩擦学学报,2015,5(4):495-504.ZOU Yujing,CHANG Degong.Mixed thermoelastohydrodynamic analysis of helical gears based on load sharing concept[J].Tribology,2015,5(4):495-504.
[7]LI S,ANISETTI A.A tribo-dynamic contact fatigue model for spur gear pairs[J].International Journal of Fatigue,2017,98:81-91.
[8]苑士华,董辉立,胡纪滨,等.考虑油膜润滑作用的渐开线齿轮动载荷分析[J].机械工程学报,2012,48(19):10-16.YUAN Shihua,DONG Huili,HU Jibin,et al.Dynamic loading analysis of involute gears considering lubrication performance[J].Journal of Mechanical Engineering,2012,48(19):10-16.
[9]邹玉静,常德功.渐开线直齿轮的动力学与弹流润滑耦合[J].航空动力学报,2016,31(8):2010-2020.ZOU Yujing,CHANG Dechang.Study on coupling dynamics and elastohydrodynamic lubrication of spur gear[J].Journal of Aerospace Power,2016,31(8):2010-2020.
[10]CAI Y.Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon(a new stiffness function of helical involute tooth pair[J].Journal of Mechanical Design,1995,117(3):460-469.
[11]LITVIN F L.Gear geometry and applied theory[M].New Jersey:Prentice Hall,Englewood Cliffs,1994.
[12]XU H.Development of a generalized mechanical efficiency prediction methodology for gear pairs[D].Athens:Ohio State University,2005.
[13]JOHNSON K L,GREENWOOD J A,POON S Y.Asimple theory of asperity contact in elastohydrodynamic lubrication[J].Wear,1972,19(1):91-108.
[14]GELINCK E R M,SCHIPPER D J.Deformation of rough line contacts[J].Journal of tribology,1999,121(3):449-454.
[15]GREENWOOD J A,TRIPP J H.The contact of two nominally flat rough surfaces[J].Proceedings of the Institution of Mechanical Engineers,1970,185(1):625-633.
[16]AKBARZADEH S,KHONSARI M M.Thermoelastohydrodynamic analysis of spur gears with consideration of surface roughness[J].Tribology Letters,2008,32(2):129-141.
[17]MOES H.Optimum similarity analysis with applications to elastohydrodynamic lubrication[J].Wear,1992,159(1):57-66.
[18]JANG J Y,KHONSARIL M M.Correction factor formula to predict the central and minimum film thickness for shear-thinning fluids in EHL[J].Journal of Tribology,2008,130(024501):1-4.
[19]HSU C H,LEE R T.An efficient algorithm for thermal elastohydrodynamic lubrication under rolling/sliding line contacts[J].Journal of tribology,1994,116(4):762-769.
[20]BAIR S,QURESHI F.The generalized newtonian fluid model and elastohydrodynamic film thickness[J].Journal of Tribology,2003,125:70-75
[21]BAIR S,VERGNE P,QUERRY M.A unified shear-thinning treatment of both film thickness and traction in EHD[J].Tribology Letters,2005,18(2):145-152
[22]BAIR S S.High pressure rheology for quantitative elastohydrodynamics[M].London:Elsevier,2007.
[23]YASUDA K Y,ARMSTRONG R C,COHEN R E.Shear flow properties of concentrated solutions of linear and star branched polystyrenes[J].Rheologica Acta,1981,20(2):163-178.
[24]DOOLITTLE A K.Studies in Newtonian Flow.II.The dependence of the viscosity of liquids on free-space[J].Journal of Applied Physics,2004,22(12):1471-1475.
[25]MASJEDI M,KHONSARI M M.Theoretical and experimental investigation of traction coefficient in line-contact EHL of rough surfaces[J].Tribology International,2014,70:179-189.
[26]JAEGER J C.Moving surfaces of heat and the temperature at sliding contacts[J].Proc.R.Soc.N.S.W.,1942,56:203-224.
[27]李朵朵.齿轮传动动态弹流润滑的数值计算模型研究[D].太原:太原理工大学,2004.LI Duoduo.A calculating model study for the elatohydrodynamic lubrication of the transmission of the gear in mesh[D].Taiyuan:Taiyuan University of Technology,2004.
[28]HE S,GUNDA R,SINGH R.Inclusion of sliding friction in contact dynamics model for helical gears[J].Journal of Mechanical Design,2007,129:1064-1075.
[29]ANURADHA P,KUMAR P.Effect of lubricant selection on EHL performance of involute spur gears[J].Tribology International,2012,50:82-90.