Journal of Advances in Applied Mathematics

9

Authors: Huiliang Wang, Yangqi Cao

Based on the geometry theory and kinematics principle of gear form grinding machine, a mathematical model of gear form grinding machine vibration is established. Using the multiple scales method, the model is analyzed and solved, which provides a theoretical basis for the system study of the relationship between natural frequency and external excitation frequency. According to the theoretical analysis results, the test platform is set up on the YK7660 gear form grinding machine. By varying the parameters of grinding process, the data of vibration characteristics of gear form grinding is acquired and analyzed. The experimental results show that the change of grinding depth has great influence on the grinding force; meanwhile when the cutting depth is increased from 0.01mm to 0.02mm, the X axis vibration amplitude increases by 19% compared with the feed rate of the workpiece. The research of vibration characteristics of gear form grinding machine proves the validity of the grinding force derived by vibration theory, which provides the theoretical foundation for improving the accuracy of grinding gear in practical application.

18

Authors: Mohammed Harunor Rashid, Md. Zulfikar Ali, Alain Piétrus

Let X and Y be Banach spaces. Let be an open subset of X. Suppose that f : X ! Y is Fréchet differentiable in and F : X  2Y is set-valued mapping with closed graph. In the present paper, for solving the generalized equations 0 2 f(x) + F(x), an extended cubic method (ECM) is introduced and studied its convergence analysis. Indeed, we analyze semi-local and local convergence of the ECM.