一种新的渐开线直齿圆柱齿轮传动理论重合度算法

摘要

理论重合度随中心距和啮合角的变化而变化,其经典计算公式没能完全反映该关系.在当今计算机普及的时代,计算公式的精确性要求优先于简单性要求,因此有必要对其进行补正.基于余弦定理,推导了渐开线直齿圆柱齿轮传动时的理论重合度计算公式,并进行了实例计算.该公式表明,对于特定的一对渐开线直齿圆柱齿轮传动,其理论重合度只与啮合角有关.基于该公式,方便地写出了变位齿轮传动、斜齿轮传动的重合度计算公式.斜齿圆柱齿轮各圆柱面上的螺旋角均为齿面发生线与齿轮圆柱面母线的夹角.补正了斜齿圆柱轮传动因逐渐进入和退出啮合而增加在重合度.%The theoretic contact ratio is changed with the change of width between centers and engaging angle.However,its classics design formula can not reflect the relation wholly. Nowadays, the precision of design formula is more important than the simplification because of the popular of computer,therefore it is necessary to supplement the formula,Based on the cosine theorem,a theoretic contact ratio design formula for the involute spur cylindrical gearing is deduced,which indicates that the theoretic contact ratio has only care about the engaging angle for special involute spur gearing.Based on the proposed design formula, the contact ratio formula for profile shifted gearing and helical gearing are written conveniently.All helix angles in each cylindrical surface of bevel cylinder gear are equal to the included angle between the tooth surface generating line and the generatrix of gear base cylinder, which compensates the contact ratio increased as the bevel cylindrical gearing enters into or and secedes meshing.