Machine Tool Chatter and Surface Location Error in Milling Processes

Abstract

A two degree of freedom model of the milling process is investigated. The governing equation of motion is decomposed into two parts: an ordinary differential equation describing the periodic chatter-free motion of the tool and a delay-differential equation describing chatter. The stability chart is derived by using the semi-discretization method for the delay-differential equation corresponding to the chatter motion. The periodic chatter-free motion of the tool and the associated surface location error (SLE) are obtained by a conventional solution technique of ordinary differential equations. It is shown that the SLE is large at the spindle speeds where the ratio of the dominant frequency of the tool and the tooth passing frequency is an integer. This phenomenon is explained by the large amplitude of the periodic chatter-free motion of the tool at these resonant spindle speeds. It is shown that large stable depths of cut with a small SLE can still be attained close to the resonant spindle speeds by using the SLE diagrams associated with stability charts. The results are confirmed experimentally on a high-speed milling center.

Prediction of surface location error in milling considering the effects of uncertain factors

“…1, governing equation of cutter dynamics under dynamic milling force can be described as (Insperger et al, 2006;Ding et al, 2011Ding et al, , 2015 …”

“…Schmitz and Mann (2006) presented an analytical method to compute SLE based on frequency domain and harmonic balance analysis. Insperger et al (2006) decomposed the governing equation used to describe a typical milling process into two parts (ordinary differential equation part and delay-differential equation part) and obtained SLE by solving ordinary differential equations. Recently, Ding et al (2011Ding et al ( , 2015 generalized the fulldiscretization method and harmonic differential quadrature method to further improve efficiency of SLE prediction in milling.…”

Optimization rules for mill cutter and cutting parameters selection incorporating a control algorithm

“…The system is excited by the cutting force ( ) F t . Then, the equation of motion has the form [2,3] ( ) ( ) ( ) ( )…”

“…The milling cutting force is denoted by a tangential force proportional with the instantaneous chip thickness, and a radial force which is expressed in terms of the tangential force [2,3].…”

Dynamical changes during composite milling: recurrence and multiscale entropy analysis

“…Over the past years, its fast development gave way to a reliable high-speed cutting procedure. Consequently, elimina-tion and stabilization of the associated chatter oscillations have become a high interest in science and technology [1][2][3][4][5][6][7]. The plausible adaptive control concept, based on relatively short time series, is studied to gain deeper understanding.…”