对数螺旋线齿锥齿轮齿面的形成及传动原理(Ⅰ)

Gearing theory and tooth area’s formation of logarithmic spiral bevel gear(Ⅰ)

提出了一种新型锥齿轮-对数螺旋线齿锥齿轮传动形式,并以基曲线和基曲面滚动原理为基础,结合对数螺旋线极坐标方程,分析了对数螺旋线以及对数螺旋线齿锥齿轮齿面的形成过程,建立其了齿面方程。结果表明:对数螺旋线齿锥齿轮传动作为一种新型的锥齿轮传动形式在几何理论上可行。其齿面的形成过程及方程的确定为进一步分析研究建立该种齿轮传动的啮合方程、共轭齿面方程奠定了数学基础,为研究这种新的锥齿轮传动形式的传动原理提供了理论上的保证。

New logarithmic spiral transmission form of bevel gear is presented. The formation of tooth face is analyzed based on the theory of original curve and area as well as the logarithmic spiral polar coordinates equation. Tooth area＇s equation is set up after analyzing the formation of the logarithmic spiral and the tooth area of logarithmic spiral bevel gear. The results show that a new bevel gear transmission form, logarithmic spiral gear tooth bevel gear transmission, is feasible in geometry theory.A mathematic foundation is laid for further study and establishment of gearing equation and conjugate profiles equation of gear transmission. It making theoretical guantee for researching the new fundamentals of transmission of bevel gear transmission form.