Multipoint Constraints for Modeling of Machine Tool Dynamics

Abstract

The dynamic properties of machine tools are frequently calculated by means of finite-element (FE) models. Usually, in a first step, the structural components, such as machine bed, slides, columns, spindle housing, spindle, and work piece, are meshed. In a second step, these components are positioned relatively to each other and are connected by joints. Usually, the joints comprise a three-dimensional spring–damper element (SDE) and constraints that connect the SDE to adjacent structural components. Commercial FE programs do rarely offer insight into the underlying constraint equations. Rather, the constraints are realized by selecting the faces or nodes to connect and the type of constraint over a graphical user interface. Moreover, when insight into the underlying equations is offered, it is normally difficult to implement user-defined constraint equations. So far, literature lacks a coherent and in-depth description of constraints that are used for assembly of machine tool FE components. This drawback is addressed here. Different common constraints are revisited while particular focus is put on simulating moving machine axes. Common multipoint constraints (MPC) are supplemented by a shape function based node weighting. Thus, two new MPC are introduced, which improve model quality for ball screw joints (named node-to-beam (NB)-constraint) and linear guides (named RBE4-constraint). A three-axis milling machine serves as an application example for the different constraints. Simulation results are compared to experimentally derived results. Both, frequency response functions (FRF) and time-domain forced responses are considered. Showing reasonable correlation, the comparison of simulation and experiment indicates the validity of the constraints that have been introduced.

Development of a Modular Slotting Head With a Modified Rack-and-Pinion Transmission

“…The parameterization apparatus is also used in works [12,13], in which a comprehensive analysis of a modular modelling system was carried out using the example of the milling machine dynamics problem. Based on this analysis, methods to effectively integrate experimental and simulated models of machine, workpiece, and tool structures in different axis configurations are implemented.…”

Dynamic Modeling and Experimental Research on Position-dependent Behavior of Twin Ball Screw Feed System

“…The other way round, Spescha D et al [8][9] employed triangular interpolation based on Fourier series expansion, to introduce loads between moving interface of the feed axes of the machine tools. Brecher C et al [10][11] proposed rigid-body elements (RBE) that move with a component and search for the nearest node at the desired position. Law M [12][13] demonstrated Lagrange-multipliers method and penalty method to calculate the dynamic response of the reduced order model.…”

A novel identification technique of machine tool support stiffness under the variance of structural weight

“…Various studies have investigated the stiffness of joint units, including linear guideways, ball screws, and bearings, in the machine tool. Lin et al [10] developed a finite element (FE) model to discuss the effect of the preload of linear guideways on the dynamic stiffness of a spindle, Brecher et al [11] conducted a comprehensive study on joint constraints, and Ealo et al [12] examined the joint stiffness of linear guideways for the industrial milling machines. Support stiffness has a direct influence on the lowest frequency of a machine.…”