考虑弹性误差的渐开线圆柱齿轮半解析接触模型与传动精度分析  

Semi-analytical contact model and transmission accuracy analysis of involute cylindrical gear considering elastic error

作　　者：肖康 张楚 董惠敏[1] 毛范海[1] XIAO Kang;ZHANG Chu;DONG Huimin;MAO Fanhai(School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China;Naval Architecture and Ocean Engineering College,Dalian Maritime University,Dalian 116026,China)

机构地区：[1]大连理工大学机械工程学院,辽宁大连116024 [2]大连海事大学船舶与海洋工程学院,辽宁大连116026

出　　处：《工程设计学报》2024年第1期91-97,共7页Chinese Journal of Engineering Design

基　　金：国家自然科学基金资助项目(52175045)。

摘　　要：在弹性和误差作用下,齿轮接触的高效、精准建模是研究齿轮传动精度的重要基础。为准确分析渐开线圆柱齿轮的弹性和误差对传动精度的影响,提出了一种考虑弹性误差的齿轮半解析接触模型。以渐开线斜齿圆柱齿轮为例,首先,结合齿轮的齿面方程与齿廓误差建立误差齿面模型,得到了误差齿面方程。然后,将解析法和有限元法相结合,建立了弹性误差作用下的齿轮半解析接触模型,并推导了其变形协调方程和力平衡方程。最后,建立齿轮的完整和局部有限元模型,通过提取接触齿面的柔度矩阵来计算齿轮的传动误差。应用所构建的半解析模型分析了齿廓误差和弹性变形对齿轮传动精度的影响规律,并与有限元仿真结果进行对比,验证了该半解析模型的高效性和精准性。研究结果可为渐开线圆柱齿轮在工程中的应用提供理论指导。Under the action of elasticity and errors,the efficient and precise modeling of gear contact is a crucial foundation for studying the transmission accuracy of gears.In order to accurately analyze the influence of elasticity and errors on the transmission accuracy of involute cylindrical gears,a semi-analytical contact model for gears considering elastic error is proposed.Taking the involute helical cylindrical gear as an example,firstly,the error tooth surface model of gear was established by combining the tooth surface equation and the tooth profile error,and the error tooth surface equation was obtained.Then,the semi-analytical contact model of gear under the action of elastic error was established by combining analytical method and finite element method,and the deformation coordination equation and force balance equation were derived.Finally,the complete and local finite element model of the gear was conducted,and the transmission error of the gear was calculated by extracting the compliance matrix of the contact tooth surface.The influence of the tooth profile error and elastic deformation on the transmission accuracy of gear was analyzed by using the semi-analytical model,and compared with the finite element simulation results,which verified the efficiency and accuracy of the semi-analytical model.The research results can provide theoretical guidance for the application of involute cylindrical gears in engineering.

关 键 词：渐开线圆柱齿轮 弹性误差 半解析模型 传动误差 

分 类 号：TH132.4[机械工程—机械制造及自动化]