螺旋锥齿轮传动系统的时变参数调制及分析方法  

Time-varying Parameter Modulation and Analysis Method of Spiral Bevel Gear Transmission System

作　　者：冯美君 苏国营[2] FENG Meijun1 , SU Guoying2(1. AECC Harbin Dong＇an Engine Co. , Ltd. , Harbin 150000, China; 2. School of Mechanical Engineering＆ Automation, Beihang University, Beijing 100191, Chin)

机构地区：[1]中国航发哈尔滨东安发动机有限公司,黑龙江哈尔滨150000 [2]北京航空航天大学机械工程及自动化学院,北京100191

出　　处：《新技术新工艺》2018年第5期32-35,共4页New Technology & New Process

摘　　要：针对含摩擦、传动误差等强迫外激励和油膜挤压、时变啮合刚度等内激励的螺旋锥齿轮传动系统的动力学问题,提出了一种用于非线性动力学系统的时变参数连续阶跃调制和分析方法。通过对周期矩阵序列的傅里叶级数的展开和矩阵指数函数的Lagrange-Sylvester定理变换,获得了只依赖于状态转移矩阵的瞬态响应和稳态响应的伪闭合解;在规定频谱内,对含有无限多频率成分的时变参数进行连续阶跃调制,避免了周期分段法计算状态转移矩阵造成的失真解;以含不规律时变参数的二自由度HillMeissner方程为例,验证了该数学分析方法的正确性和稳定性,为今后多自由度强参数激励方程的动态特性研究提供了思路。In order to solve the dynamic problem of spiral bevel gear drive system considering forced outside incentives such as friction and transmission error, as well as inside incentives such as oil film extrusion and time varying meshing stiff hess, a method for time varying parameter continuous step modulation and analysis method for nonlinear dynamical systems is proposed. By expansion of the Fourier series of periodic matrix sequences and Lagrange Sylvester theorem transformation of matrix exponential function, pseudo closed solutions of response of transient and steady state who only depend on the state transition matrix are obtained, time varying parameter is continuous step modulation within the prescribed spectrum and distortion solution cased by periodic segmentation algorithm is avoided, the two degree of freedom Hill Meissner equa tion is taken as an example to verify the correctness and stability of the mathematical analysis method, which provides a new idea for the research of dynamic characteristics of strong parametric excitation equations with many degree of freedom from nOW on.

关 键 词：螺旋锥齿轮 时变参数 阶跃调制 傅里叶级数 瞬态响应 稳态响应 

分 类 号：TN761[电子电信—电路与系统]