Stability Analysis of Milling Via the Differential Quadrature Method

Author:

Ding Ye1,Zhu LiMin2,Zhang XiaoJian,Ding Han3

Affiliation:

1. e-mail:

2. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

3. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

Abstract

This paper presents a time-domain semi-analytical method for stability analysis of milling in the framework of the differential quadrature method. The governing equation of milling processes taking into account the regenerative effect is formulated as a linear periodic delayed differential equation (DDE) in state space form. The tooth passing period is first separated as the free vibration duration and the forced vibration duration. As for the free vibration duration, the analytical solution is available. As for the forced vibration duration, this time interval is discretized by sampling grid points. Then, the differential quadrature method is employed to approximate the time derivative of the state function at a sampling grid point within the forced vibration duration by a weighted linear sum of the function values over the whole sampling grid points. The Lagrange polynomial based algorithm (LPBA) and trigonometric functions based algorithm (TFBA) are employed to obtain the weight coefficients. Thereafter, the DDE on the forced vibration duration is discretized as a series of algebraic equations. By combining the analytical solution of the free vibration duration and the algebraic equations of the forced vibration duration, Floquet transition matrix can be constructed to determine the milling stability according to Floquet theory. Simulation results and experimentally validated examples are utilized to demonstrate the effectiveness and accuracy of the proposed approach.

Publisher

ASME International

Subject

Industrial and Manufacturing Engineering,Computer Science Applications,Mechanical Engineering,Control and Systems Engineering

Reference49 articles.

1. Analytical Models for High Performance Milling. Part I: Cutting Forces, Structural Deformations and Tolerance Integrity;Int. J. Mach. Tools Manuf.,2006

2. Analytical Models for High Performance Milling. Part II: Process Dynamics and Stability;Int. J. Mach. Tools Manuf.,2006

3. Chatter Stability of Metal Cutting and Grinding;CIRP Ann.—Manuf. Technol.,2004

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