A Stability Algorithm for a Special Case of the Milling Process: Contribution to Machine Tool Chatter Research—6

Abstract

In an effort to determine the stability of the milling process, and due to the complexity of its describing equation, a special case of this equation is considered. In this way, it is possible to isolate and study its salient characteristics. Moreover, the simplified equation is representative of a machining operation on which experimental data can be obtained. This special case is described by a linear differential equation with periodic coefficients. A computer algorithm is developed for determining the stability of this equation. To demonstrate the use of the algorithm on an example whose solution is known, the classical Mathieu equation is studied. Also, experimental results on an actual machining operation described by this type of equation are compared to the results found using the stability algorithm. As a result of this work, some knowledge about the stability solution of the general milling process is obtained.