二级齿轮非线性动态特性同伦摄动法分析  

The homotopy analysis for the nonlinear dynamics of a multi-mesh gear train

作　　者：荀超 吴海轩 王云龙 XUN Chao;WU Haixuan;WANG Yunlong(School of Mechanical Engineering,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院机械工程学院,南京211167

出　　处：《振动与冲击》2024年第8期89-97,108,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(52105191);南京工程学院科研启动基金(YKJ201951)。

摘　　要：考虑时变啮合刚度、脱齿、各级齿轮啮合间的耦合关系,建立了二级齿轮传动机构的刚柔混合模型,采用同伦超越摄动法分析了机构的非线性动态特性,得到了二级齿轮机构主共振、超谐共振和亚谐共振的频响表达式。与多尺度法不同,同伦法的分析精度不受脱齿程度的影响。与数值积分结果的对比表明,在脱齿率达到30%以上时,同伦法较多尺度法具有明显的计算精度优势。该研究为复杂齿轮传动机构的非线性动态特性分析提供了更为精确的理论分析方法。The nonlinearity in a multi-mesh gear train due to the periodically time-varying mesh stiffness,contact loss,and the couplings between multi-mesh stiffnesses were considered.The nonlinear oscillation was investigated by the homotopy analysis method(HAM).And closed-form approximations for the primary resonance,sub-harmonic resonance,and super-harmonic resonance were obtained.In contrast to the method of multi-scale(MMS),the HAM is independent of the contact loss ratio.Results indicate that with large contact loss ratios over 30%,the amplitude-frequency curves obtained by HAM agree better with the numerical integration(NI)results than those obtained by the MMS.This study lays a higher accurate foundation for more complex nonlinear dynamic analysis of gear sets.

关 键 词：多级齿轮 同伦摄动法 脱齿 非线性动态特性 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3