Computing method for induced curvature parameters based on normal vector of instantaneous contact line and its application to Hindley worm pair

作者：Zhao, Yaping^*; Zhang, Yimin

来源：Advances in Mechanical Engineering, 2017, 9(10): 1687814017721884.

DOI：10.1177/1687814017721884

• Normal vector of instantaneous contact line
• induced normal curvature
• induced geodesic torsion
• line-conjugate surfaces
• Hindley worm drive

The main objective of this article is to propose a practical methodology to compute the induced curvature parameters for a line-conjugated tooth surface couple based on the normal vector of its instantaneous contact line. The computing formulae in different form are thus suggested for the preceding normal vector in order for convenient use. Based on this, the formulae for the induced curvature parameters are accordingly given out. Compared to the previous work, the deducing process is more rigorous and more laconic, and the obtained results are more practical. Concurrently, different deducing techniques are provided, and this is beneficial for the development of the meshing theory for gear drives. The theory and method presented are applied to the modified Hindley worm drive, and its basic and important equations are attained. The concrete numerical example is a type I drive, whose conjugate zone is divided into two parts. In one part, the value of the induced principal curvature is much smaller than that in the other one. The biggest induced principal curvature comes into view about at the inlet portion of the worm, and certainly the highest contact stress between the teeth will happen consistently at that position.

• 出版日期2017-10-23
• 单位东北大学