任意齿廓轮端面积的通用计算模型及验证

Unified Calculation Model and Its Verification of Gear Cross-section Area for Arbitrary Tooth Profile

为齿轮构建了适用于任意齿廓类型的轮端面积统一计算模型。首先,基于完全相同的两齿轮间的共轭关系,分析出轮端面积由节圆面积加上共轭面积减去最小顶隙面积三方面的计算组成;其次,依据共轭齿廓的几何关系,重点给出共轭面积最简单的无误差计算式和最小顶隙面积采用部分滚刀面积的简化计算方法;最后,对渐开线直齿轮进行实例计算与分析。结果表明,节圆面积远大于共轭面积和最小顶隙面积,但最小顶隙面积的计算方法决定了轮端面积的计算精度;计算误差仅为0.24%,可用于渐开线齿轮端面积的高精度计算;得出共轭面积公式可无误差地适用于任何类型的啮合齿廓和泵容积利用系数精确计算的重要结论。

To derive a unified calculation model for gear cross-section area suitable for arbitrary tooth profile.Firstly,based on the external conjugate relation between two identical gear,it is analyzed that cross-section area of gear is composed of pitch circle area,plus conjugated area,and minus minimum top gap area.Secondly,based on the geometric relationship of conjugate profile,the simplest calculation formula without error of the conjugated area and simplified calculating method of minimum top gap area adopts partial hob are given.Finally,example calculation and analysis of gear cross-section area with involute profile are carried out.All results show that the pitch circle area is much larger than conjugated area and minimum top gap area,but calculation method of minimum top gap area determined calculation accuracy of cross-section area,the theory error of gear cross-section area is 0.24%,which could be used in high precision calculation of gear cross-section area.It is concluded that the conjugated area formula is suitable for volume utilization coefficient calculation in arbitrary tooth profile without error for pump.