Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations

Abstract

This paper presents a general, integrated model of the spindle bearing and machine tool system, consisting of a rotating shaft, tool holder, angular contact ball bearings, housing, and the machine tool mounting. The model allows virtual cutting of a work material with the numerical model of the spindle during the design stage. The proposed model predicts bearing stiffness, mode shapes, frequency response function (FRF), static and dynamic deflections along the cutter and spindle shaft, as well as contact forces on the bearings with simulated cutting forces before physically building and testing the spindles. The proposed models are verified experimentally by conducting comprehensive tests on an instrumented-industrial spindle. The study shows that the accuracy of predicting the performance of the spindles require integrated modeling of all spindle elements and mounting on the machine tool. The operating conditions of the spindle, such as bearing preload, spindle speeds, cutting conditions and work material properties affect the frequency and amplitude of vibrations during machining.

Introduction

The successful application of high-speed machining technology is highly dependent on spindles operating free of chatter vibration without overloading the angular contact ball bearings. Unless avoided, vibration instability in the metal-cutting process leads to premature failure of the spindle bearings [1]. The spindle, tool-holder, and tool are the main sources of chatter vibrations on high-speed machines. The objective of the design engineer is to predict the cutting performance of the spindle during the design stage by relying on engineering model of the process and system dynamics.

Early spindle research focused mainly on static and quasi-static analysis, whereas current research is extended to optimal design by using dynamic analysis. Ruhl et al. [2] is one of the earliest researchers to use the finite element (FE) method for modeling of rotor systems. His model includes translational inertia and bending stiffness but neglects rotational inertia, gyroscopic moments, shear deformation, and axial load. Nelson [3] used the Timoshenko beam theory to establish shape functions and formulate system matrices, including the effects of rotary inertia, gyroscopic moments, shear deformation, and axial load.

In the past, little research has been conducted to model the coupling of bearings and spindles. The effects of preload and spindle speeds on bearing stiffness and the dynamics of the spindle system are seldom studied. Wardle et al. [4] presented a very simplified model for describing the dynamics of a spindle-bearing system with a constant preload. The theoretical maximum operating speed of the spindle system is increased by maintaining a constant preload, but Wardle neglected the softening of bearing stiffness due to rotational speeds. Chen et al. [5] built a model for determining the response of a spindle-bearing system at high speeds with an analytical method. His model considers the spindle as a uniform Euler–Bernoulli beam supported by a pair of angular contact bearings. Using Jones’ [6] bearing model, Chen analyzed the dynamic behavior of the spindle around the trivial equilibrium configuration with zero end loads. Only the axial preload is considered in this model. First, the Newton–Raphson iteration method is used to calculate the bearing stiffness matrix at a given spindle speed, then the dynamic behavior is computed at this speed using the obtained bearing stiffness. Li and Shin [7] presented a coupled spindle-bearing model that includes thermal effects to predict the bearing stiffness and natural frequencies of the spindle system, using DeMul's bearing model. The bearing configuration, however, is limited to several cases and the gyroscopic effect is not included.

All of the above models predict the natural vibration and frequency response for a specific spindle design, and consider only the spindle shaft and bearings. The effects of the machine tool on the spindle dynamics are neglected. Neither centrifugal force nor gyroscopic effect is included in modeling the spindle shaft. The contact forces on bearing balls and the time response of the spindle-bearing system under dynamic cutting forces have not been reported in the literature.

In this paper, a general method is presented for modeling the spindle machine tool system, which consists of the cutter, tool-holder, spindle shaft, bearings, housing, and the machine tool. A simplified model, representing the dynamics of the whole machine tool without the spindle, is developed by means of experimental modal analysis which needs to be done only once for every machine tool. The model of the whole machine tool system is then created by coupling the spindle model developed by the authors [8], [9] with the simplified model of the machine tool without the spindle. The assembly of the spindle unit and spindle head is modeled through contact springs. The proposed method is validated by performing frequency response and cutting tests.