考虑时变侧隙与时变轴承刚度的含质量偏心齿轮系统动力学分析

为了探究齿侧间隙与轴承刚度的时变特性对含质量偏心齿轮系统动态特性的影响,结合其耦合后的动力学模型,并利用龙格库塔(Runge-Kuta)算法,求解了时变侧隙和时变轴承刚度;根据不同偏心距,对齿轮系统进行了动态响应分析。首先,根据几何关系建立了因轴承变形引起的时变齿侧间隙模型,利用赫兹接触理论推导了滚动轴承时变轴承刚度公式;然后,基于时变齿隙与时变轴承刚度,建立了含齿面摩擦与质量偏心的六自由度直齿轮系统动力学模型;最后,分析了在不同偏心距下齿隙与轴承刚度的时变特性对齿轮系统动态响应的影响。研究结果表明:考虑齿隙和轴承刚度的时变特性后,动态传递误差幅值相比恒定齿隙和轴承刚度所对应幅值分别提高了16.46%、2.02%;偏心距从0 mm增加到0.5 mm及1 mm时,其对应系统的最大边频幅值从0μm增加到0.19μm和0.33μm;质量偏心会影响系统动态响应,且随偏心距的增大,其由稳定的周期运动变为有波动性的周期运动,波动幅度与偏心距成正相关;同时,质量偏心会导致系统出现边频,边频幅值随偏心距的增大而增大;因此,应将偏心距控制在合理范围内,以防其过大而引起齿轮系统发生不稳定现象。

A novel method to predict static transmission error for spur gear pair based on accuracy grade

This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modifications(PMs)are considered.For the prediction,a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented.Then,the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion.The prediction method is validated by comparison with the experimental results from the literature,and a set of cases are simulated to study the effects of MEs,AEs,TDs and PMs on the static transmission error.In addition,the time-varying backlash caused by both MEs and AEs,and the contact ratio under load conditions are also investigated.The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades.The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.