中文摘要：

以一批装配间隙符合正态分布的单对直齿轮副传动系统为例,对具有随机装配侧隙的齿轮副系统动力学行为特征进行分析。基于非线性系统动力学的分析方法,建立考虑随机装配侧隙的单对齿轮副系统动力学模型。利用分岔图及最大Lyapunov指数等对考虑随机装配侧隙的齿轮副系统动力学性态进行分析。在分析中引入系统失稳指数和临界方差的概念,通过数值方法系统分析失稳指数与侧隙方差、侧隙均值与临界方差的关系,结果发现,减小侧隙并不是提高系统动力稳定性的唯一途径,即便选择较大侧隙,只要匹配合适的临界方差,也能确保齿轮系统动力学性态的稳定,从而为齿轮传动系统设计中的精度等级的确定、齿轮加工方法的选择及齿轮副的安装精度等提供了理论依据。

英文摘要：

One set of one-stage gear pair,whose assembling backlash meets normal distribution,is taken as an example,and the dynamic analysis of a set of gear pair with stochastic assembling backlash is presented. Based on nonlinear dynamic theories,the nonlinear dynamic model of the gear pair with stochastic assembling backlash is established. The bifurcation diagram and the maximum Lyapunov index of the gear system with stochastic assembling backlash are presented. The chaos index and critical variance are introduced in the analysis. The relationship between the instability index and variance of assembling backlash,and the relationship between the mean value and critical variance of assembling backlash are discussed. It shows that the dynamic stability of the system can be achieved not only by minimizing the backlash,but also by well matched mean value of the backlash and its variation,which provides theoretical basis for determination of precision level in the design of gear system,selection of machining method,and mounting precision of gear pair.