General expression of pressure angle and principal curvature of globoidal indexing cam mechanism

7th Global Conference on Materials Science and Engineering

工业技术（总论）;材料科学

Li, J.^1 ; Rao, X.^1 ; Tang, M.^1 ; Li, Y.J.^2

School of Mechanical Engineering, Chengdu University, Chengdu

610106, China^1

School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta

GA

30332, United States^2

关键词: Analytic expressions;    Design and manufactures;    Globoidal indexing cam;    Homogeneous coordinates;    Mathematical expressions;    Matrix transformation;    Method of modeling;    Principal curvature;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/474/1/012019/pdf
DOI  :  10.1088/1757-899X/474/1/012019

来源: IOP

【 摘 要 】

Given the lack of general mathematical model for the parameters of the globoidal indexing cam (GIC) mechanism, a method of modeling the contour for the GIC based on the unified mathematical expression is proposed by applying the envelope theory and the matrix transformation of the homogeneous coordinates. Taking the globoidal cams with cylindrical, conical, and hyperbolic meshing turret-rollers as the research object, a unified mathematical model of profile model for the GIC is derived. On this foundation, the general analytic expression of pressure angle and principal curvature is further obtained, which provides a theoretical basis for the precise design and manufacture of the GIC and provides a mathematical basis for the fatigue strength analysis of the GIC material.