外文翻譯--評(píng)價(jià)機(jī)床設(shè)計(jì)的建模方法(英文）

1、Precision Engineering 34 (2010) 399–407Contents lists available at ScienceDirectPrecision Engineeringjournal homepage: www.elsevier.com/locate/precisionEvaluation of modelling approaches for machine tool designDaisuke Ko

2、no a,?, Thomas Lorenzer b, Sascha Weikert c, Konrad Wegener ca Dept. of Micro Engineering, Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japanb Inspire AG, Tannenstrasse 3,

3、 8092, Zurich, Switzerlandc Institute for Machine Tools and Manufacturing (IWF), ETH Zurich, Tannenstrasse 3, 8092, Zurich, Switzerlanda r t i c l e i n f oArticle history:Received 12 February 2009Received in revised for

4、m 8 June 2009Accepted 16 September 2009Available online 23 September 2009Keywords:Rigid body simulationFinite element methodModal analysisMachine tool designa b s t r a c tIn order to evaluate the configuration of machin

5、e tools, the IWF Axis Construction Kit (ACK) has beendeveloped. This paper describes the evaluation of this approach. The ACK supports rigid body simulationsand simple elastic body simulations. The ACK is compared with c

6、ommercial FEM software to investigateits usability and reliability. Required time was compared in modelling of a machine tool. The ACK needed30% of the total required time for the FEM because of its modularity in machine

7、 modelling. Then, inorder to investigate the reliability of the ACK, static and dynamic simulations of both approaches werecompared with each other and with analytical calculations on basic beam models. The result showed

8、that the ACK provided equivalent results to the FEM. Static and dynamic simulations were also comparedwith measurements on an actual machine tool. The ACK obtained almost equivalent results to the FEM.Almost all lower st

9、ructural mode shapes and their natural frequencies could be reproduced with the ACKwhen crucial parts were modelled using elastic bodies.© 2009 Elsevier Inc. All rights reserved.1. IntroductionRecently, dynamic erro

10、rs of machine tools such as vibration areone of the crucial problems in high precision machining. Sincedynamic properties of machines are greatly influenced by themachine configuration, the configuration should be evalua

11、ted veryearly in the design phase. However, only few manufacturers useevaluation tools in order to check configuration variants. For thisreason, a lack of reliable and effortless simulation software can bestated. Simulat

12、ion methods for machine tools can roughly be clas-sified into two groups: one is the finite element method (FEM) andthe other is the rigid multi-body simulation (MBS) [1].In industrial use, the FEM is popular and widely

13、used. Severalstudies have been carried out, modelling machine components withthe FEM. Zaeh and Oertli have developed a model for ball screwdrives by the cross coupling between axial and torsional degreesof freedom [2]. A

14、ltintas and Cao have developed a FEM model ofspindles composed of nonlinear models of shafts and bearings [3,4].Reliable results can be obtained with the FEM. Furthermore, theFEM is useful in the design process because m

15、any FEM softwarepackages have useful interfaces to 3D CAD systems.However, the FEM needs much calculation effort to modelthe whole structure of a machine because of its large number ofdegrees of freedom (nDOF). In commer

16、cial 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

17、 representguideways or ballscrews, and detailed modelling in a certain levelis required to avoid the interference between components. In orderto reduce nDOF, the machine has been divided into subcomponentsor modules, and

18、 these modules have been coupled with boundaryconditions [5–8]. Also in the simulations of positioning system withflexture hinges, hinges are modelled as a simple beam element toreduce nDOF [9].Compared to the FEM, nDOF

19、can be significantly reduced whenusing the MBS. Especially in the early design stage, the MBS isan appropriate tool to obtain quick and rough predictions of themachine behaviour [1]. Teeuwsen et al. developed a motion er

20、rormodel of CMM with the MBS [10]. Tool motions in the time domainand modal characteristics have been simulated by the MBS also formachine tools [11,12]. In recent years, the MBS has been used forreal time simulation of

21、motion errors [13]. The MBS and the FEMwere combined to acquire more reliable results in dynamic analy-ses [14]. Although these studies have shown the advantage of theMBS, there are only few practical software packages t

22、hat focus onthe construction of machine tools.As can be seen in the use of the FEM, a combination of 3D CADand commercial MBS software is used to analyse the motion of aparallel kinematic machine tool [15]. This method i

23、s practical. How-ever, commercial software packages generally need more effort tomodel a specific machine, since they are designed for all-purpose.In order to evaluate the configuration of machine tools, the AxisConstruc

24、tion Kit (ACK) has been developed at the IWF (ETH Zurich,Institute for Machine Tools and Manufacturing) [16]. Fundamental0141-6359/$ – see front matter © 2009 Elsevier Inc. All rights reserved.doi:10.1016/j.precisio

25、neng.2009.09.003D. Kono et al. / Precision Engineering 34 (2010) 399–407 401Rigid (R): This is the basic model. All bodies are rigid. The machinebase, the columns, and the Y-base are rigidly coupled. (The modelis describ

26、ed in the first paragraph.)Bolts elastic (BE): The machine base and the columns are elasticallycoupled.Columns elastic (CE): The columns are elastic and segmented inthe Z-direction.Y-base elastic (YE): The Y-base is elas

27、tic and segmented in theY-direction.Y-base and columns elastic (YCE): The Y-base as well as thecolumns is elastic.The initial model parameters are identified in the followingprocedure: the dimensions of bodies are determ

28、ined from their out-ward forms, and the densities are adjusted so that the masses agreeto the design value. The stiffness of the guideways of Y- and Z-axesare derived from their catalogue specifications. The stiffness of

29、 airsprings, drives and the X-guideway are identified experimentally.In order to confirm the reliability of the approach when param-eters are properly selected, these parameters are tuned using theresult of the experimen

30、tal modal analysis described in Section 4.2.The modified parameters are the stiffness in the Z-direction of theY-guideway, the stiffness of the Y-drive and the thickness of thecolumns and the Y-base. In BE, the stiffness

31、 in the Z-direction ofthe couplings between the machine base and the columns is deter-mined also from the result of the modal analysis. Because this paperfocuses on static displacements and natural frequencies with modes

32、hapes, damping has not to been taken into account.2.3. Modelling with commercial FEM softwareThe machine is also modelled with a commercial FEM softwarepackage, Ansys Workbench, similarly as mentioned in Section 2.2.Bond

33、ed contacts are used to group the bodies. The rigidity or theelasticity of bodies is determined by the behaviour of surface nodes.Bodies are meshed automatically under default settings. With theFEM, reference surfaces ar

34、e required to couple components. How-ever, the reference surfaces affect the behaviour of elastic bodies. Inorder to suppress this influence, reference surfaces are minimisedusing the extrusion with the thickness of 1 ?m

35、 so that only actualcontacted areas become the reference.2.4. Comparison in required time for the ACK and a commercialFEMThe time required for simulations with the ACK and the FEM iscompared. The evaluation is carried ou

36、t in modelling, modal anal-ysis and the modification of the thickness of the columns afterthe analysis on R. The operator has all the model parameters athand and has developed the same model several times with bothsoftwa

37、re. With the FEM, modelling of the extrusion for the refer-ence surface is omitted to investigate the time in the equivalentoperations to ACK.The comparison of the required time is shown in Fig. 4. It isobserved that the

38、 ACK needs only 30% of the total required time forthe FEM. Direct 3D modelling and module coupling system mainlycontribute to this time reduction. Comparing the time required forthe modification, the ACK needs 25% of the

39、 time for the FEM.3. Fundamental evaluation on basic componentsIn order to evaluate the accuracy of elastic body simulationsby the ACK, simulation results are compared with those by the FEMand with analytical calculation

40、s in basic simulations. In elastic bodysimulations, the number of degrees of freedom (nDOF) of modelshas a large influence. Therefore, simulations are conducted withFig. 4. Comparison of required time with the ACK and a

41、commercial FEM.various nDOF to clarify this effect. The simulation of displacementsdue to static forces and the modal analysis are carried out on acantilever and a beam fixed on both sides. In this paper, nDOF withthe AC

42、K and the FEM are calculated as follows:nDOFACK = 6 × me (1)nDOFFEM = 3 × mn (2)where me is the number of elements (segmented bodies) and mn isthe number of nodes. For example with the FEM, nDOF of a singleelem

43、ent is 60 with a 20-node solid element composed of 8 cor-ner and 12 midside nodes. When elements are connected, nDOF ofnodes shared on boundaries decreases.3.1. Cantilever beamFig. 5 shows a cantilever used in the calcul

44、ation. l, h and t rep-resent the width, the height and the thickness of the cantilever,respectively. In static analyses, forces are applied at the load point,which is on the center of the top surface. The cantilever is s

45、eg-mented in the Z-direction with the ACK. In order to compare theACK and the FEM in the similar nDOF, the cantilever is modelledwithout midside nodes with the FEM. The physical parameters areFig. 5. Cantilever used in t