机床齿轮副机械效率计算方程组

A Group Equations for Calculating the Machinery Efficiency of the Gear pair in the Machine Tool Gearing

至今大部分技术人员依然根据机械设计手册提供的数值或数值范围来确定各种齿轮副的效率。这里对机床渐开线直齿圆柱齿轮机构正确安装条件下其齿轮副所传递的有效功与齿间滑动摩擦系数等有关参数之关系展开了系统的分析及研究 ,并推导出一组可直接确定齿轮副效率数值的计算方程组。由该方程组显示的严密数学关系可知 ,齿轮副效率不仅直接与齿间滑动摩擦系数有关 ,而且还受主动轮及从动轮的齿数、齿顶高系数及分度圆压力角等参数变化的影响。

Up to now most machinery engineers and technicians have determined the machinery efficiencies of various gear pairs by means of selecting data which are thought reasonable from numericals or numerical ranges provided by relative machine design handbooks.The author of this article has made systematical analyses and researches on the relationships between the effective work transfered by the gear pair in the machine tool involute spur gearing and the sliding friction between teeth, and derived a group of equations by which the machinery efficiency of the gear pair is able to be calculated directly.The complex and strict mathematical relationships shown in the group of equations indicates that the machinery efficient of the gear pair not only is relative to the coefficient of sliding friction between teeth directly, but also is affected by changes of such parameters as tooth numbers of the driving and driven gears, the addendum coefficient, the pressure angle on the pitch circle, and so on.