精密钢球传动耦合热弹性半解析接触模型及其接触特征
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摘要
在修正精密钢球传动受力模型和相对滑动模型基础上,建立精密钢球传动啮合副耦合热弹性半解析接触模型。采用热源法推导啮合副接触温升的半解析式,并利用影响系数法计算考虑耦合热弹性影响的啮合刚度和啮合副变形。为提高模型的计算效率,给出了对应公式的离散卷积形式。深入分析精密钢球传动的耦合热弹性接触特征,并通过对比分析验证半解析模型的可行性。结果表明:中心盘外侧齿面上的接触温升相对最高,行星盘内侧齿面上的接触温升相对最低;啮合副耦合热弹性接触模型计算的啮合副变形和啮合刚度要大于Hertz接触模型的计算结果。研究结果可为考虑热特性的精密钢球传动动力学特性的研究以及实际工程应用提供一定的理论依据。
Based on the modified model of the force and the relative slide for the precision ball transmission,a coupled thermoelastic semi-analytical contact model of meshing pair is established.The semi-analytical formula of the contact temperature rise of meshing pair is deduced by using the heat source method,and the influence coefficient method is adopted to compute the meshing stiffness and the deformation of meshing pair which considering the effect of coupled thermoelasticity.In order to improve the computational efficiency,the discrete convolution forms of related expressions are also derived.The coupled thermoelastic contact characteristics for precision ball transmission are analyzed deeply,and the comparative analysis approach is used for verifying the availability of the semi-analytical model.The results indicate that the contact temperature rise of the outer tooth surface of the central disc is relatively high,and it is relatively low on the inner surface of the planetary disc;the meshing stiffness and the deformation calculated by the coupled thermoelastic model are larger than those of the Hertz contact model.Therefore,the research results can provide some theoretical foundation for the study of dynamic characteristics of precision ball transmission considering thermal properties and the practical engineering application.
Based on the modified model of the force and the relative slide for the precision ball transmission,a coupled thermoelastic semi-analytical contact model of meshing pair is established.The semi-analytical formula of the contact temperature rise of meshing pair is deduced by using the heat source method,and the influence coefficient method is adopted to compute the meshing stiffness and the deformation of meshing pair which considering the effect of coupled thermoelasticity.In order to improve the computational efficiency,the discrete convolution forms of related expressions are also derived.The coupled thermoelastic contact characteristics for precision ball transmission are analyzed deeply,and the comparative analysis approach is used for verifying the availability of the semi-analytical model.The results indicate that the contact temperature rise of the outer tooth surface of the central disc is relatively high,and it is relatively low on the inner surface of the planetary disc;the meshing stiffness and the deformation calculated by the coupled thermoelastic model are larger than those of the Hertz contact model.Therefore,the research results can provide some theoretical foundation for the study of dynamic characteristics of precision ball transmission considering thermal properties and the practical engineering application.
引文
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[19]李晓滨,丁桦,唐正友.GCr15轴承钢连铸过程中热物性参数的研究[J].材料与冶金学报,2010,9(4):241-244.LI Xiaobin,DING Hua,TANG Zhengyou.Study of thermo-physical properties for GCr15 bearing steel in continuous casting[J].Journal of Materials and Metallurgy,2010,9(4):241-245.
[20]TIAN X,KENNEDY F E.Maximum and average flash temperatures in sliding contacts[J].Journal of Tribology,1994,116(1):167-174.
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[2]安子军.摆线钢球行星传动研究[D].秦皇岛:燕山大学,2000.AN Zijun.The research for cycloid steel ball planetary transmission[D].Qinhuangdao:Yanshan University,2000.
[3]张鹏,安子军,杨作梅.摆线钢球行星传动啮合副非线性力学性能研究[J].工程力学,2010,27(3):186-192.ZHANG Peng,AN Zijun,YANG Zuomei.Research on nonlinear mechanical properties for engagement pair of cycloid ball planetary transmission[J].Engineering Mechanics,2010,27(3):186-192.
[4]杨荣刚,安子军,段丽英.摆线钢球行星传动自由振动分析[J].中国机械工程,2016,27(14):1883-1891.YANG Ronggang,AN Zijun,DUAN Liying.Analysis of free vibration of cycloid ball planetary transmission[J].China Mechanical Engineering,2016,27(14):1883-1891.
[5]聂松辉,李鸿,颜彧.摆线钢球减速器振动分析[J].机械设计与研究,2014,30(2):56-59.NIE Songhui,LI Hong,YAN Yu.The vibration analysis of the cycloid steel ball reducer[J].Machine Design and Research,2014,30(2):56-59.
[6]HONG Cheng,AN Zijun.Research on instantaneous contact temperature rising of constantly no clearance precision steel ball transmission[C]//Advanced Information Technology,Electronic and Automation Control Conference,December19-20,2015,Chongqing,China.IEEE,2016:39-43.
[7]王海侠.精密钢球传动啮合副摩擦性能研究[D].秦皇岛:燕山大学,2014.WANG Haixia.Study on friction performance of engagement pair of precision ball drive[D].Qinhuangdao:Yanshan University,2014.
[8]孙鹏飞,安子军,刘向辉.精密钢球传动减速机构的瞬时接触热特性分析[J].中国机械工程,2017,28(9):1009-1015.SUN Pengfei,AN Zijun,LIU Xianghui.Analysis on instantaneous contact thermal characteristics of reducing mechanisms for precision ball transmissions[J].China Mechanical Engineering,2017,28(9):1009-1015.
[9]洪诚,安子军,夏婧琪,等.实时无隙钢球精密传动啮合副本体温度场分析[J].机械强度,2017,39(6):1391-1397.HONG Cheng,AN Zijun,XIA Jingqi,et al.Analysis of bulk temperature field of constantly no clearance precision steel ball transmission[J].Journal of Mechanical Strength,2017,39(6):1391-1397.
[10]安子军,杨荣刚,宜亚丽.精密钢球传动啮合法向力与弹性回差[J].机械工程学报,2016,52(9):42-48.AN Zijun,YANG Ronggang,YI Yali.Engagement normal force and elastic backlash of precision ball transmission[J].Journal of Mechanical Engineering,2016,52(9):42-48.
[11]宜亚丽,安子军,王海侠.无隙钢球精密传动啮合副滑动特性研究[J].中国机械工程,2014,25(23):3206-3211.YI Yali,AN Zijun,WANG Haixia.Research on sliding property of no-backlash ball precision transmission meshing pair[J].China Mechanical Engineering,2014,25(23):3206-3211.
[12]BUCKINGHAM.Analytical mechanics of gears[D].New York:Dover,1949.
[13]JOHNSON K L.Contact mechanics[D].London:Cambridge University Press,1985.
[14]JAEGER J C.Moving sources of heat and the temperature at sliding contacts[J].J.and Proc.Roy.Soc.,1942,76:203-224.
[15]KUO W,LIN J.General temperature rise solution for a moving plane heat source problem in surface grinding[J].Int.J.Adv.Manuf.Technol.,2006,31(3-4):268-277.
[16]BLOK H.Theoretical study of temperature rise at surfaces of actual contact under oiliness lubricating condition[C]//Proceeding of the Institute of mechanical engineers general discussion of lubrication.London:Institute of Mechanical Engineers,1937:222-235.
[17]BARBER J R.Distortion of the semi-infinite solid due to transient surface hearting[J].Int.J.Mech.Sci.,1972,14(6):377-393.
[18]LIU S B,WANG Q.A three-dimensional thermomechanical model of contact between non-conforming rough surfaces[J].Journal of Tribology,2001,123(1):17-26.
[19]李晓滨,丁桦,唐正友.GCr15轴承钢连铸过程中热物性参数的研究[J].材料与冶金学报,2010,9(4):241-244.LI Xiaobin,DING Hua,TANG Zhengyou.Study of thermo-physical properties for GCr15 bearing steel in continuous casting[J].Journal of Materials and Metallurgy,2010,9(4):241-245.
[20]TIAN X,KENNEDY F E.Maximum and average flash temperatures in sliding contacts[J].Journal of Tribology,1994,116(1):167-174.
[21]李维特,黄保海,毕仲波.热应力理论分析及应用[D].北京:中国电力出版社,2004.LI Weite,HUANG Baohai,BI Zhongbo.Thermal stress theory analysis and aplication[D].Beijing:China Electric Power Press,2004.