A new approach to stability analysis of variable speed machining systems |
| |
Authors: | Tsu-Chin Tsao Mark W McCarthy Shiv G Kapoor |
| |
Affiliation: | a Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Illinois, U.S.A. |
| |
Abstract: | This paper presents a new method for the stability analysis of variable speed machining systems. By using spindle angular position as the independent variable, the system dynamics are modeled as a linear periodic time-varying system with fixed delay. This representation is proven much easier to analyze and to numerically simulate than the time-varying delay representation, which traditionally uses the real-time as the independent variable. With a finite difference scheme, the infinite dimensional periodic time-varying system is approximated by a finite dimensional periodic time-varying discrete system, which in turn is converted to a time-invariant system by multiplying the time-varying state transition matrix over one period of speed variation. System-relative stability becomes tractable by spectral radius analysis. This approach makes possible the quantitative characterization of system stability as a function of variable speed profiles as well as other system parameters such as stiffness and damping of the cutting process and the tool/workpiece structure. Verifications for the face milling process by numerical simulation and experiment for both constant and variable speed are given. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|