Precision Engineering 34 (2010) 399–407
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Precision Engineering
journal homepage: www.elsevier.com/locate/precision
Evaluation of modelling approaches for machine tool design
Daisuke Kono
a,∗
, Thomas Lorenzer
b
, Sascha Weikert
c
, Konrad Wegener
c
a
Dept. of Micro Engineering, Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan
b
Inspire AG, Tannenstrasse 3, 8092, Zurich, Switzerland
c
Institute for Machine Tools and Manufacturing (IWF), ETH Zurich, Tannenstrasse 3, 8092, Zurich, Switzerland
article info
Article history:
Received 12 February 2009
Received in revised form 8 June 2009
Accepted 16 September 2009
Available online 23 September 2009
Keywords:
Rigid body simulation
Finite element method
Modal analysis
Machine tool design
abstract
In order to evaluate the configuration of machine tools, the IWF Axis Construction Kit (ACK) has been
developed. This paper describes the evaluation of this approach. The ACK supports rigid body simulations
and simple elastic body simulations. The ACK is compared with commercial FEM software to investigate
its usability and reliability. Required time was compared in modelling of a machine tool. The ACK needed
30% of the total required time for the FEM because of its modularity in machine modelling. Then, in
order to investigate the reliability of the ACK, static and dynamic simulations of both approaches were
compared with each other and with analytical calculations on basic beam models. The result showed
that the ACK provided equivalent results to the FEM. Static and dynamic simulations were also compared
with measurements on an actual machine tool. The ACK obtained almost equivalent results to the FEM.
Almost all lower structural mode shapes and their natural frequencies could be reproduced with the ACK
when crucial parts were modelled using elastic bodies.
© 2009 Elsevier Inc. All rights reserved.
1. Introduction
Recently, dynamic errors of machine tools such as vibration are
one of the crucial problems in high precision machining. Since
dynamic properties of machines are greatly influenced by the
machine configuration, the configuration should be evaluated very
early in the design phase. However, only few manufacturers use
evaluation tools in order to check configuration variants. For this
reason, a lack of reliable and effortless simulation software can be
stated. Simulation methods for machine tools can roughly be clas-
sified into two groups: one is the finite element method (FEM) and
the other is the rigid multi-body simulation (MBS) [1].
In industrial use, the FEM is popular and widely used. Several
studies have been carried out, modelling machine componentswith
the FEM. Zaeh and Oertli have developed a model for ball screw
drives by the cross coupling between axial and torsional degrees
of freedom [2]. Altintas and Cao have developed a FEM model of
spindles composed of nonlinear models of shafts and bearings [3,4].
Reliable results can be obtained with the FEM. Furthermore, the
FEM is useful in the design process because many FEM software
packages have useful interfaces to 3D CAD systems.
However, the FEM needs much calculation effort to model
the whole structure of a machine because of its large number of
degrees of freedom (nDOF). In commercial software, coupling set-
∗
Corresponding author. Tel.: +81 75 753 5226; fax: +81 75 753 5226.
E-mail address: Daisuke.Kono@t02.mbox.media.kyoto-u.ac.jp (D. Kono).
tings between assembled parts are often not practical to represent
guideways or ballscrews, and detailed modelling in a certain level
is required to avoid the interference between components. In order
to reduce nDOF, the machine has been divided into subcomponents
or modules, and these modules have been coupled with boundary
conditions [5–8]. Also in the simulations of positioning system with
flexture hinges, hinges are modelled as a simple beam element to
reduce nDOF [9].
Compared to the FEM, nDOF can be significantly reduced when
using the MBS. Especially in the early design stage, the MBS is
an appropriate tool to obtain quick and rough predictions of the
machine behaviour [1]. Teeuwsen et al. developed a motion error
model of CMM with the MBS [10]. Tool motions in the time domain
and modal characteristics have been simulated by the MBS also for
machine tools [11,12]. In recent years, the MBS has been used for
real time simulation of motion errors [13]. The MBS and the FEM
were combined to acquire more reliable results in dynamic analy-
ses [14]. Although these studies have shown the advantage of the
MBS, there are only few practical software packages that focus on
the construction of machine tools.
As can be seen in the use of the FEM, a combination of 3D CAD
and commercial MBS software is used to analyse the motion of a
parallel kinematic machine tool [15]. This method is practical. How-
ever, commercial software packages generally need more effort to
model a specific machine, since they are designed for all-purpose.
In order to evaluate the configuration of machine tools, the Axis
Construction Kit (ACK) has been developed at the IWF (ETH Zurich,
Institute for Machine Tools and Manufacturing) [16]. Fundamental
0141-6359/$ – see front matter © 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.precisioneng.2009.09.003