考虑齿顶修形和时变中心距的渐开线直齿轮振动特性研究  

Vibration characteristic analysis of spur gears with tip relief and time-varying center distance

作　　者：王成[1] 刘辉[2] 张晨 邹天刚[1] WANG Cheng;LIU Hui;ZHANG Chen;ZOU Tian-gang(Key Laboratory of Vehicle Transmission,China North Vehicle Research Institute,Beijing 100072,China;School of Mechanical and Vehicular Engineering,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]中国北方车辆研究所车辆传动重点实验室,北京100072 [2]北京理工大学机械与车辆学院,北京100081

出　　处：《振动工程学报》2019年第1期128-139,共12页Journal of Vibration Engineering

摘　　要：针对渐开线直齿轮,考虑时变中心距推导了动态啮合角、动态间隙的解析表达式,考虑时变转速、时变中心距和齿顶修形,并采用解析方法得到了齿轮的动态啮合刚度,在此基础上建立了齿轮啮合模型。考虑几何偏心、齿向偏载力矩和陀螺力矩,建立了单级齿轮传动系统10自由度横-扭-摆耦合非线性动力学模型。将非线性动力学模型和齿轮啮合模型进行耦合计算,对比分析了转速和扭矩对不同修形齿轮振动特性的影响。结果表明:当转速超过某临界值,短修形齿轮的振动载荷大于无修形齿轮,而长修形齿轮不存在临界转速;随着扭矩的增加,无修形齿轮的啮合力峰峰值呈线性比例增加,短修形齿轮和长修形齿轮的啮合力峰峰值近似呈先减小后增大的趋势变化,说明在某扭矩下修形齿轮的振动载荷最小,且长修形对应的扭矩大于短修形;短修形和长修形齿轮均存在临界扭矩,当扭矩小于该临界值时,修形齿轮的振动载荷大于无修形齿轮,且长修形对应临界扭矩小于短修形。For spur gears,the analytic formulas of dynamic pressure angle and backlash are derived with considering the time-varying center distance.Taking into account the time-varying rotational speed,time-varying center distance and tip relief,we calculated the dynamic mesh stiffness with the analytic method.Thus,the gear mesh dynamic model is established.In consideration of the geometry eccentricity,gyroscopic effect and load distribution factor along the tooth width,a 10-DOF lateral-torsional-rocking coupled nonlinear dynamic model of a spur gear system was established.The nonlinear dynamic model and the gear mesh dynamic model are coupled.Comparison analysis on the vibration characteristic with different speeds and torques are carried out.The results show that when the speed exceeds certain value,the dynamic load for the short tip relief are bigger than the non-modification gear,while the long tip relief do not have critical speed.With the increase of the torque,the variation trend of the dynamic load will increase proportionally for the non-modification gear,while increase at first and then decrease for the long and short tip relief,and so an optimal amount of torque exists to acheive a minimum dynamic load factor.There exist critical torques for both long and short tip relief such that when the torque is smaller than these critical value,the dynamic load of modification gear are bigger than the non-modification gear,and the value for the long tip relief are bigger than the short tip relief.

关 键 词：机械振动 渐开线直齿轮 齿顶修形 振动特性 啮合刚度 

分 类 号：TH113.1[机械工程—机械设计及理论] TH132.413