面齿轮传动整个啮合过程相对法曲率干涉检验的方法  

Checking method of relative normal curvature interference during entire meshing process of face-gear drive

作　　者：沈云波[1,2] 方宗德[2] 丁文强[1] 

机构地区：[1]中国航空动力机械研究所,湖南株洲412002 [2]西北工业大学机电学院,陕西西安710072

出　　处：《兰州理工大学学报》2013年第1期25-28,共4页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(50875211);陕西省自然科学基金(2012JM7003);陕西省教育厅基金(2010JK582)

摘　　要：两齿面在接触点处无曲率干涉才能正确啮合,由此提出一种面齿轮传动整个啮合过程的相对法曲率极值曲线曲率干涉检验的方法.建立两实体曲面干涉检验的物理模型,通过欧拉(Eurler)公式和Bertrand公式,导出曲面相对法曲率的数学解析式,对相对法曲率极值进行求解,分析两曲面在接触点无曲率干涉时相对法曲率极值的范围;建立面齿轮副的齿面方程,根据啮合原理,由插齿刀齿面的主曲率、主方向导出被展成面齿轮齿面的主曲率、主方向.通过计算机仿真得到面齿轮齿面的啮合印痕及各啮合位置相对法曲率的极值曲线,并对面齿轮传动在啮合点的曲率干涉情况进行分析.Proper meshing of two tooth surfaces with each other could be realized only when there was no curvature interference at their contacting points.Therefore,an inspection method was proposed for checking relative normal curvature interference of extrema curve during entire engagement process of face gear drive.A physical model was set up for checking the curvature interference of two substantial curved surfaces.Based on Euler and Bertrand equations,a mathematical analytical expression of relative normal curvature was derived for face gear drive and the extremum of the relative normal curvature was found and the extremum range of relative normal curvature was analyzed when there was no curvature interference of two curved surfaces with each other at their contacting points.The tooth surface equation of the face gear pair was set up and,according to the meshing theory,the principal curvatures and principal direction of the tooth surfaces of the generated gear were derived from those of the shaper.The meshing traces on tooth surface of face gear and extrema value of relative normal curvature at all meshing location were obtained by means of computer simulation and the situation of curvature interference at meshing point of the face gear drive was analyzed,also.

关 键 词：面齿轮 相对法曲率 诱导法曲率 干涉检验 

分 类 号：TH132[机械工程—机械制造及自动化]