斜齿轮时变啮合刚度算法修正及影响因素研究  

Study on Correction Algorithm of Time-varying Mesh Stiffness of Helical Gears and Its Influencing Factors

作　　者：刘文[1] 李锐 张晋红[1,2] 林腾蛟 杨云[1] LIU Wen;LI Rui;ZHANG Jinhong;LIN Tengjiao;YANG Yun(The State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China;Chongqing BOE Optoelectronics Technology CO., LTD, Chongqing 400714, China)

机构地区：[1]重庆大学机械传动国家重点实验室,重庆400044 [2]重庆京东方光电科技有限公司,重庆400714

出　　处：《湖南大学学报（自然科学版）》2018年第2期1-10,共10页Journal of Hunan University:Natural Sciences

基　　金：国家科技支撑计划资助项目(2015BAF06B02);国家自然科学基金资助项目(51175524)~~

摘　　要：针对势能法计算斜齿轮时变啮合刚度精度不足问题,提出一种刚度修正算法.考虑端面重合度大于或小于轴向重合度两种情况下单齿接触线长度的不同表达形式,建立齿根圆与基圆不重合时的变截面悬臂梁模型,采用切片法和积分思想推导并计算了斜齿轮啮合刚度,通过与ISO算法和有限元法对比分析,验证了该修正算法的可行性.在此基础上,探讨了螺旋角、模数、齿数、齿宽和压力角等参数对啮合刚度的影响.计算与分析表明,啮入段的相对时间与端面重合度和轴向重合度大小及比重有关;齿轮基本参数的变化引起重合度和单齿啮合刚度的改变,进而影响综合啮合刚度波动值和均值;当端面重合度或轴向重合度在整数附近时,啮合刚度波动值较小,而总重合度在整数附近时,啮合刚度波动值较大.与传统势能法相比,修正算法提高了斜齿轮时变啮合刚度的计算精度,在斜齿轮刚度激励的准确计算方面具有较强的实用性.Due to the inaccuracy of potential energy method in calculation of time-varying mesh stiffness of helical gears,a stiffness correction algorithm was proposed.Considering the different expressions for the length of contact lines of single tooth on two kinds of situations in which the transverse contact ratio is greater or less than the overlap ratio,a non-uniform cantilever beam model was established when root circle and base circle misaligned,and then the mesh stiffness of helical gears was derived and calculated by using slice-integral method.By comparing with ISO standard and finite element method,the feasibility of the proposed correction algorithm was verified.Meanwhile,a parametric study was conducted to investigate the effects of various parameters,such as helix angle,normal module,tooth number,face width and normal pressure angle on the behavior of mesh stiffness.The calculation and analysis indicate that the relative time of the engaging-in section is related to the proportion values of transverse contact ratio and overlap ratio.Variation of gear parameters affects the fluctuation value of total mesh stiffness and average mesh stiffness by changing the contact ratios and single mesh stiffness.In addition,the fluctuation is little when the transverse contact ratio or overlap ratio is close to an integer,while it fluctuates more intensively when the total contact ratio is close to an integer.Compared with the traditional potential energy method,the precision of correction algorithm in calculating time-varying mesh stiffness of helical gears is obviously improved.It has relatively better practicability in the accurate calculation of stiffness excitation of helical gears.

关 键 词：势能法 斜齿轮 时变啮合刚度 重合度 

分 类 号：TH132.41[机械工程—机械制造及自动化]