斜齿轮由于具有传动平稳等众多优点，在高速重载场合广泛应用。斜齿轮副在啮合时，不可避免地受到摩擦力影响。因此在计算斜齿轮副的时变啮合刚度时，有必要将齿面摩擦计入其中。先通过切片法将斜齿轮切成直齿轮微元薄片，再根据能量法计算微元薄片的啮合刚度，最后沿齿宽方向进行积分累加，获取斜齿轮副精准时变啮合刚度。研究斜齿轮副时变啮合刚度在零摩擦、定摩擦和时变摩擦作用下的变化规律，揭示时变摩擦作用下齿面粗糙度、转矩、转速、齿宽等参数对斜齿轮副时变啮合刚度的作用机理。研究结果表明：在摩擦力的作用下，斜齿轮副时变啮合刚度会发生变化；定摩擦作用下，斜齿轮副的时变啮合刚度会减小，且定摩擦因数越大，时变啮合刚度越小；时变摩擦作用下，斜齿轮副的时变啮合刚度会随齿面粗糙度增大而减小，分别随输入转矩、转速和齿宽的增大而增大。
Helical gears are widely used in high-speed and heavy-duty situations due to their smooth transmission and many other advantages. When helical gear pair meshing, it is inevitablely affected by friction, so it is necessary to take tooth surface friction into account when calculating the time-varying meshing stiffness(TVMS) of helical gear pair. Firstly, the helical gear is cut into micro-element slices of spur gear by the slicing method, and then the meshing stiffness of micro-element slices is calculated by the energy method. Finally, the accurate TVMS of helical gear pair is obtained by integral accumulation along the tooth width direction. The change rule of TVMS of helical gear pair under zero friction, constant friction, and time-varying friction is studied. The action mechanism of tooth surface roughness, torque, speed, tooth width, and other parameters on TVMS of helical gear pair under time-varying friction are revealed. The results show that the TVMS of helical gear pair will change under the action of friction; Under constant friction, the TVMS of helical gear pair will decrease, and the greater the constant friction coefficient, the smaller TVMS; Under the action of time-varying friction, the TVMS of helical gear pair will decrease with the increase of tooth surface roughness, increase with the increase of input torque, speed, and tooth width, respectively.
[1] 马辉, 逄旭, 宋溶泽, 等. 基于改进能量法的直齿轮时变啮合刚度计算[J]. 东北大学学报(自然科学版), 2014, 35(6): 863-866,884. DOI:10.3969/j.issn. 1005-3026.2014.06.023.
[2] Chen Z G, Shao Y M. Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth[J]. Engineering Failure Analysis, 2011, 18(8): 2149-2164. DOI:10.1016/j. engfailanal.2011.07.006.
[3] Gu X, Velex P, Sainsot P, et al. Analytical investigations on the mesh stiffness function of solid spur and helical gears[J]. Journal of Mechanical Design, 2015, 137(6): 063301. DOI:10.1115/1. 4030272.
[4] 莫帅, 岳宗享, 冯志友, 等. 面齿轮分汇流系统动力学均载特性研究[J]. 华中科技大学学报(自然科学版), 2020, 48(2): 23-28. DOI:10.13245/j.hust. 200205.
[5] Mo S, Zhang T, Jin G G, et al. Analytical investigation on load sharing characteristics of herringbone planetary gear train with flexible support and floating sun gear[J]. Mechanism and Machine Theory, 2020, 144: 103670. DOI:10. 1016/j.mechmachtheory.2019.103670.
[6] Wan Z G, Cao H R, Zi Y Y, et al. Mesh stiffness calculation using an accumulated integral potential energy method and dynamic analysis of helical gears[J]. Mechanism and Machine Theory, 2015, 92: 447-463. DOI:10.1016/j.mechmachtheory.2015.06. 011.
[7] 刘文, 李锐, 张晋红, 等. 斜齿轮时变啮合刚度算法修正及影响因素研究[J]. 湖南大学学报(自然科学版), 2018, 45(2): 1-10. DOI:10.16339/j.cnki. hdxbzkb.2018.02.01.
[8] 林腾蛟, 赵子瑞, 江飞洋, 等. 考虑温度效应的斜齿轮时变啮合刚度解析算法[J]. 湖南大学学报(自然科学版), 2020, 47(2):6-13. DOI:10.16339/j.cnki. hdxbzkb.2020.02.002.
[9] 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. DOI:10.1016/j.engfailanal.2016.09.003.
[10] 黄康, 汪涛, 熊杨寿, 等. 计及摩擦影响的直齿轮时变啮合刚度计算方法[J]. 应用力学学报, 2017, 34(3): 564-569. DOI:10.11776/cjam.34.03.B046.
[11] 杨勇, 王家序, 周青华, 等. 考虑摩擦的磨损和修形齿轮啮合刚度计算[J]. 工程科学与技术, 2018, 50(2): 212-219. DOI:10.15961/j.jsuese.201700574.
[12] 邹玉静, 庞峰, 樊智敏. 渐开线斜齿轮传动摩擦动力学耦合研究[J]. 机械工程学报, 2019, 55(3): 109-119. DOI:10.3901/JME.2019.03.109.
[13] 李飞, 袁茹, 朱慧玲, 等. 计及齿面摩擦的弧齿锥齿轮动态特性[J]. 航空动力学报, 2020, 35(8): 1687-1694. DOI:10.13224/j.cnki.jasp.2020.08.013.
[14] Ma H, Feng M J, Li Z W, et al. Time-varying mesh characteristics of a spur gear pair considering the tip-fillet and friction[J]. Meccanica, 2017, 52(7): 1695-1709. DOI:10.1007/s11012-016-0502-3.
[15] Han L, Xu L X, Qi H J. Influences of friction and mesh misalignment on time-varying mesh stiffness of helical gears[J]. Journal of Mechanical Science and Technology, 2017, 31(7): 3121-3130. DOI:10.1007/s12206-017-0602-6.
[16] Sainsot and P, Velex P, Duverger O. Contribution of gear body to tooth deflections： a new bidimensional analytical formula[J]. Journal of Mechanical Design, 2004, 126(4): 748-752. DOI:10.1115/1.1758252.
[17] Xu H, Kahraman A, Anderson N E, et al. Prediction of mechanical efficiency of parallel-axis gear pairs[J]. Journal of Mechanical Design, 2007, 129(1): 58-68. DOI:10.1115/1.2359478.
[18] 熊杨寿, 韩广志, 黄康, 等. 考虑时变摩擦系数的微线段齿轮系统动态特性分析[J]. 机械工程学报,2021, 57(19): 113-127. DOI:10.3901/JME.2021.19.113.
