齿侧间隙非线性函数拟合阶次的选取研究

Study on selection of fitting order of gear backlash nonlinearity

针对齿侧间隙非线性函数拟合阶次的选取问题,以斜齿轮传动系统为例,对齿轮系统进行了理论建模、仿真分析,并对实际齿轮系统进行了实验研究。首先,采用集中质量法建立了考虑轴向振动的齿轮非线性系统模型,并对数学模型进行了无量纲化,对齿侧间隙函数分别进行了无拟合、4阶拟合和8阶拟合处理;然后,采用Runge-Kutta数值积分法进行了数值仿真分析,得到了齿轮系统x、y、z三个方向的幅值-频率比响应曲线图,研究了拟合阶次对系统x、y、z三个方向动态特性的影响;最后,进行了齿轮系统动态测试,得到了齿轮系统x、y、z三个方向的振动响应图,根据仿真与实验结果得出了结论。研究结果表明:不同处理方式下的齿轮系统振动响应在z向的差异较大,拟合阶次的选取应重点考虑z向;在x、y方向,齿侧间隙非线性4阶拟合函数会提前改变齿面接触状态且共振振幅分别增大1倍和1/3倍;对于多间隙的齿轮非线性系统,对齿侧间隙进行无拟合处理,可能导致计算困难和结果不准确;在固有频率附近,对齿侧间隙进行4阶拟合处理能够最大程度弥补其他非线性因素带来的影响;在其他频率范围,对齿侧间隙进行8阶拟合处理会更接近真实齿轮系统。齿侧间隙非线性函数的拟合处理在提高了计算效率的同时,也提高了模型的准确性。

Aiming at the problem of difficulty in selecting the fitting order of gear backlash nonlinearity,a comprehensive study of the helical gear system was executed by theoretical modeling and simulation,and the actual gear system was explored by experimental test.Firstly,a nonlinear gear system was established with the axial vibration under consideration by Runge-Kutta integration method and the mathematical model was dimensionless,the gear backlash was respectively treated with no fitting,4th order fitting and 8th order fitting.Secondly,the amplitude-frequency response ratio curves of gear system in x,y and z directions were obtained,and the effects of fitting order on the dynamic characteristics in x,y and z directions were explored.Finally,the dynamic tests of the gear system were carried out,the vibration response diagram of the gear system in x,y and z directions was obtained,and the conclusion was drawn with the simulation results.The results indicate that the vibration response of the gear system of the differences is big in the z axis,the selection of fitting order should focus on z axis.The nonlinear fourth-order fitting function of the backlash nonlinearity changing the contact state of the tooth surface in advance,which also respectively increase the resonance amplitude significantly in x and y axis by 1 time and 1/3 times.For multi-clearance gear nonlinear systems,the non-fitting of the clearances may lead to computational difficulties and inaccurate results.The fourth fitting processing of tooth backlash can make up for the influences of other nonlinear factors to the greatest extent close-by inherent frequency.In other frequency ranges,the dynamic response of the gear system with the eighth fitting function of the tooth backlash is close to the reality.The fitting processing of nonlinear function of tooth backlash can not only improve the calculation efficiency,but also improve the accuracy of the model.