考虑摩擦的磨损和修形齿轮啮合刚度计算
Stiffness Calculation Considering Friction for a Spur Gear Pair with Tooth Wear and Profile Modification
作者：杨勇(四川大学 空天科学与工程学院, 四川 成都 610065)；王家序(四川大学 空天科学与工程学院, 四川 成都 610065;重庆大学 机械传动国家重点实验室, 重庆 400044)；周青华(四川大学 空天科学与工程学院, 四川 成都 610065)；李文广(四川大学 空天科学与工程学院, 四川 成都 610065)；熊林冬(洪都航空工业集团有限责任公司 综合采购部, 江西 南昌 330024)
Author：YANG Yong(School of Aeronautics and Astronautics,Sichuan Univ.,Chengdu 610065,China)；WANG Jiaxu(School of Aeronautics and Astronautics,Sichuan Univ.,Chengdu 610065,China;State Key Lab. of Mechanical Transmissions,Chongqing Univ.,Chongqing 400044,China)；ZHOU Qinghua(School of Aeronautics and Astronautics,Sichuan Univ.,Chengdu 610065,China)；LI Wenguang(School of Aeronautics and Astronautics,Sichuan Univ.,Chengdu 610065,China)；XIONG Lindong(AVIC Jiangxi Hongdu Aviation Industry Group Corp. Ltd.,Nanchang 330024,China)
收稿日期：2017-07-19 年卷（期）页码：2018,50(2):212-219
期刊名称：工程科学与技术
Journal Name：Advanced Engineering Sciences
关键字：啮合刚度;摩擦;齿轮磨损;齿廓修形;传动误差
Key words：mesh stiffness;friction;tooth wear;tooth profile modification;transmission error
基金项目：国家高技术研究发展计划资助项目（2015AA043001）
中文摘要
时变啮合刚度是齿轮传动系统主要动态激励源之一，研究齿面偏差和齿间滑动摩擦对齿轮啮合刚度的影响，对准确获得齿轮系统动态特性具有重要意义。基于改进的能量法，提出了一个考虑齿面滑动摩擦的直齿轮啮合刚度的完整求解模型。根据加工刀具齿廓参数方程能够求得齿轮渐开线齿廓和过渡曲线的参数方程，并能体现刀具圆角半径对过渡曲线的影响。量化磨损或修形齿轮的齿面偏差并加之于齿廓参数方程，可得出该齿轮单齿对啮合刚度。通过齿形误差带来的齿间间隙和齿间加载变形量之间的协调关系，可求解出齿轮副在双齿啮合区的总刚度。分析了加工刀具圆角半径和齿间滑动摩擦力对齿轮啮合刚度的影响。研究了磨损齿轮的磨损量、修形齿轮的修形长度和外载荷大小对齿轮啮合刚度、齿间载荷分配系数以及传递误差的影响。结果表明：加工刀具圆角半径越大单齿对啮合刚度越高；摩擦力使啮入阶段齿对啮合刚度增大、啮出阶段齿对啮合刚度减小，摩擦系数越大刚度变化量越大；齿面非均匀磨损量会显著降低双齿啮合区刚度并降低重合度，轻载条件下尤为严重；修形齿轮载荷大于修形设计载荷值时，修形效果不明显，而载荷小于修形设计载荷值时，可能出现刚度不足、重合度减小和加载传动误差显著增大等问题。
英文摘要
Time varying mesh stiffness is one of the main reasons leading to the vibration in a gear transmission system.In order to obtain more accurate dynamic characteristics of gear systems,it is important to investigate the influence of sliding friction and tooth deviation of a gear pair on mesh stiffness.A complete mesh stiffness model was proposed base on the improved energy method with consideration of sliding friction.According to parameter equations of cutting tool tooth flank,the parameter equations of both involute tooth profile and transition curve of gears can be obtained.The presented model considered the influence of wear and profile modification on mesh stiffness by utilizing parameter equations of gear tooth flank and the total mesh stiffness of two meshing gear pairs was obtained by the relationship of tooth clearances derived from tooth deviations and deformation under loading.The influence of tool fillet radius and sliding friction on gear meshing stiffness was analyzed.The total mesh stiffness,load sharing ratio between two meshing tooth pairs and loaded static transmission errors of wear gears and profile modification gears under different loading conditions were investigated.Numerical simulations showed that mesh stiffness decreases with the decrease of tool tip fillet radius.Sliding friction between meshing gear teeth increases the meshing stiffness during the access process but decreases it during the recess process,and the greater the friction,the greater the amount of change in stiffness.Especially under light loading condition,nonuniform wear of tooth profile induces remarkable mesh stiffness reduction and contact ratio decrement.When the load is greater than the profile modification design load,the benefits of modification are not obvious.If the load is lighter than the profile modification design load,the following problems may arise,such as a lack of mesh stiffness,a decrease in contact ratio and a significant increment of loaded static transmission.
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