Analytical modeling of spindle–tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF

Regenerative chatter is a well-known machining problem that results in unstable cutting process, poor surface quality and reduced material removal rate. This undesired self-excited vibration problem is one of the main obstacles in utilizing the total capacity of a machine tool in production. In order to obtain a chatter-free process on a machining center, stability diagrams can be used. Numerically or analytically, constructing the stability lobe diagram for a certain spindle–holder–tool combination implies knowing the system dynamics at the tool tip; i.e., the point frequency response function (FRF) that relates the dynamic displacement and force at that point. This study presents an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modification methods. The objective of the study is two fold. Firstly, it is aimed to develop a reliable mathematical model to predict tool point FRF in a machining center so that chatter stability analysis can be done, and secondly to make use of this model in studying the effects of individual bearing and contact parameters on tool point FRF so that better approaches can be found in predicting contact parameters from experimental measurements. The model can also be used to study the effects of several spindle, holder and tool parameters on chatter stability. In this paper, the mathematical model, as well as the details of obtaining the system component (spindle, holder and tool) dynamics and coupling them to obtain the tool point FRF are given. The model suggested is verified by comparing the natural frequencies of an example spindle–holder–tool assembly obtained from the model with those obtained from a finite element software. r 2006 Elsevier Ltd. All rights reserved.