基于时变啮合刚度的修形齿轮承载接触分析  

Loaded Tooth Contact Analysis of Involute Spur Gear with Profile Modification Based on Time-Varying Meshing Stiffness

作　　者：王浩 韩振华 周酝晨 石万凯[3] 单文桃 曹忠亮 WANG Hao;HAN Zhenhua;ZHOU Yunchen;SHI Wankai;SHAN Wentao;CAO Zhongliang(School of Mechanical Engineering,Jiangsu University of Technology,Changzhou 213001,China;Nan-jing Huaqin Light Sound Technology Co.,Ltd.,Nanjing 210034,China;不详)

机构地区：[1]江苏理工学院机械工程学院,常州213001 [2]南京华秦光声科技有限责任公司,南京210034 [3]重庆大学机械传动国家重点实验室,重庆400044

出　　处：《组合机床与自动化加工技术》2024年第4期181-186,192,共7页Modular Machine Tool & Automatic Manufacturing Technique

基　　金：国家自然科学基金项目(52005229);江苏省自然科学基金项目(BK20201055);江苏省青蓝工程中青年学术带头人项目(KYQ20004);常州市领军型创新人才引进培育项目(CQ20210119);江苏理工学院研究生实践创新计划项目(XSJCX22_37)。

摘　　要：为了解决传统齿轮承载接触分析力学解析方法难以考虑齿廓修形的问题,以齿廓修形渐开线直齿轮为研究对象,基于时变啮合刚度,提出了一种齿轮承载情况下齿间载荷分配系数与齿面接触应力解析算法。通过对比齿轮承载接触时接触点在啮合线方向的变形量与修形量,提出修形齿轮单双齿啮合状态判定方法,并计算不同状态下的啮合刚度;推导修形齿轮的啮合力、刚度与变形的力学关系,建立各啮合齿对的齿间载荷分配系数计算模型,应用赫兹接触理论求解齿面接触应力;分别在不同修形高度、修形曲线与配对齿数情况下,计算分析多种齿廓修形算例的齿间载荷分配系数与齿面接触应力。结果表明,解析算法求解的齿间载荷分布系数、齿面接触应力及相应单双齿啮合区间与有限元结果相一致,相对误差较小,证明了该算法有较高的精度与稳定性,为齿廓修形齿轮承载接触分析提供一种高效便捷的新方法。In order to address the challenge of traditional mechanical analytical methods in loaded tooth contact analysis faced difficulties in considering gear profile modifications.Based on time-varying mesh stiffness,an analytical algorithm for load distribution factors and tooth surface contact stress under load conditions is proposed,and involute spur gears are taken as the research object.Comparing the deformation amount with the modification amount during loaded tooth contact,a method for determining the single or double-tooth engagement state of modified gears is proposed.The meshing stiffness is then calculated for different engagement states.Additionally,the mechanical relationships among meshing force,stiffness,and deformation for modified gears are derived.A calculation model for load distribution factors for each engaged pair is established,and Hertz contact theory is applied to solve tooth surface contact stress.Subse-quently,various examples of gear profile modifications are analyzed under different modification heights,modification curves,and paired tooth numbers,calculating load distribution factors and tooth surface contact stress.The results indicate that the load distribution factors and tooth surface contact stress obtained by the analytical algorithm are consistent with finite element results,and the relative error is small,thereby proving that the algorithm has high precision and stability.Therefore,this method provides an efficient and convenient new approach for loaded tooth contact analysis after profile modifications.

关 键 词：齿轮承载接触分析 时变啮合刚度 齿廓修形 载荷分配 接触应力 

分 类 号：TH16[机械工程—机械制造及自动化] TG506[金属学及工艺—金属切削加工及机床]