Machine tools mechatronic analysisR Maj, F Modica*, and G Bianchi

Institute of Industrial Technologies and Automation, National Research Council, Milan, Italy

The manuscript was received on 28 December 2004 and was accepted after revision for publication on 15 July 2005.

DOI: 10.1243/095440505X32733

Abstract: High-speed machine tools show close interaction between the dynamic behaviour ofthe mechanical structure, drives, and numerical control. In order to support the designer ofhigh-performance machines, a new analysis based on an integrated holistic mechatronicoptimization technique is proposed and compared with the traditional approach. The pro-posed approach is applied to a three-axis milling machine for dies and mould production.

Keywords: machine tools, dynamics, mechatronics

1 INTRODUCTION

The development of faster and faster machine toolsto reduce machining time and ensure the requiredprecision needs stiff but light mechanical structures,coupled with high bandwidth drives.

Classical machine tool design is composed byseparated optimization of the mechanical structure(optimizing static stiffness and dynamic behaviour)and control system (optimizing the performancemodelling the structure as lumped masses con-nected by springs). This approach is becoming lessand less effective because rigid transmissions andlight structures are usually used, therefore it isnecessary to consider also the distributed compli-ance of structures while evaluating the controlledsystem performance. Consequently it is essential tostudy the behaviour of the structure with the controlsystem active, using an integrated mechatronicapproach that considers the dynamic couplingbetween them [1].

To evaluate the accuracy of machines with highacceleration and light machining (for instancemilling machine for finishing moulds) it is useful tocarry out mechatronic simulations of movementswithout cutting forces (to avoid the complexity asso-ciated with the modelling of the cutting process), forexample carrying out circular trajectories as speci-fied in the standard ISO 230-4 [2].

In order to simulate the machine during motion itis necessary to describe in the model, in addition to

the mechanical structure, components includingmotors, sensors, drives, and control systems, thatallow and guide the motion. It is obvious that thecomplexity of this model can be very high, becauseit is necessary to reproduce correctly the characteris-tics of all components that can limit the machineperformances. This complexity can be dealt with bytwo approaches: either by constructing a reliablelibrary of models of components (leaning on univer-sities and research institutes), or by interacting withcomponent suppliers in order to construct modelswith their support or, even better, receive modelsdirectly from them.

A component for which the last approach is funda-mental is the numerical control (NC) controller,because it would be extremely complex to reproducecorrectly the modalities adopted in order to generatethe position references for the machine axis, startingfrom the part program in the ISO format. At this timesome producers of NC controls supply a softwarethat reproduces the calculation of this signal on aPC, with some limitation: NUM e FIDIA.

2 MECHANICAL STRUCTURE MODELLING

In machine tool design it is necessary to analyse themechanical structure, focusing on its inertia andcompliance. The most appropriate modelling tech-nique is the finite element analysis (FEA) [3]. Formachines with non-cartesian morphology (forinstance an anthropomorphic or parallel kinematicmanipulator), analysis demands also the solution ofcomplex kinematics, using multibody analysispackages [4].

*Corresponding author: Institute of Industrial Technologies

and Automation, National Research Council, Via delle

Magnolie, 4, Modugno, Bari 70026, Italy. email: f.modica

@itia.cnr.it

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SPECIAL ISSUE PAPER 345

In order to model realistically the structure usingFEA it is necessary to describe the frame throughelements that correctly represent the real space dis-tribution of stiffness, mass, and – eventually – thepresence of different materials. Using this approachthe finite element modelling (FEM) model hassystematically a very high number of degrees offreedom (DOF) and it can potentially describe thedeformation owing to any force system applied tothe nodes and is characterized by resonance fre-quencies that can be unimportant and invalid forthe model (for example, greater than 100 kHz).

To represent a complex structure with fewer DOF,it is possible to reduce the DOF based on the modalapproach: the first step of the procedure is todevelop a detailed FE model; the second step is thereduction that consists of maintaining the samegeometry, inertia, and stiffness of the completemodel, but it constrains the structure to move onlywith a linear combination of predefined deformedshapes Fi selected by the analyst. This approach isvery famous in literature and is also implementedin the best FEM softwares because it is used tomodel flexible bodies in multibody simulationpackages [5].

To model machine tools it is convenient to use anapproach that combines both deformed static anddynamic analysis (i.e. the Craig Bampton approach)[6] in order to represent both the local structurecompliance (important in modelling the connectionbetween actuators and mechanical structure) and itsdynamic global behaviour.

It is always critical to model the energy dissipationwithin the structure and in the moving contacts: it ispossible to use viscous friction, hysteretic friction orstatic friction types, but often the data are not veryprecise. In general, for structures built with tradi-tional materials, such as welded steel and cast iron,a uniform value of modal damping is assumed, forexample around 3–4 per cent.

3 DRIVE MODELLING

The dynamic performances of the machine dependon the characteristics of the main components thatrealize the movement of the axis (the model dependson the problem that is to be analysed):

(a) electric motor connected to the drive powersection: saturation owing to the current limit,non-linearity of torque/force in function ofposition and current;

(b) position sensor: measurement resolution, inter-polation error inside the grid step, reversal error;

(c) regulators: architecture of the current and speedregulators, sampling time, digital filters;

(d) numerical control: generation strategy of posi-tion references (limitation of acceleration andjerk by the look-ahead function), structure ofthe position regulator (and speed feedforward).

The introduction of these components, with theirlimitations, can help to obtain an understanding ofthe contribution of each component on the limita-tion in reachable bandwidth.

The resultant regulator model is non-linear and itsstability depends not only on the tuning parameters,but also on the specific input signal. It is importantthat the simulations can show the effect of theselection of more or less ‘expensive’ components,to support the designer in this choice. In thedevelopment of these models the collaboration ofthe suppliers is fundamental. Figure 1 shows themodel of the Siemens 611D drive realized in theMatlab/Simulink environment with the indicationssupplied by the handbook (i.e. [7]).

4 SOFTWARE FOR THE VIRTUALPROTOTYPING OF MACHINE TOOLS

A fully integrated mechatronic simulation imposesseveral requirements on the modelling software. Itmust be able to:

(a) model distributed compliance of the mechanicalstructure (using FEA), represented with areduced number of DOF (‘super elements’);

(b) model structural damping, including materialproperties (specific damping);

(c) join structural modules representing movingcontact on flexible bodies [8];

(d) model static and dynamic friction in thecontacts [9];

(e) create an open system that allows the userseasily to add non-linear models (for instancesensors and motors, etc.);

(f) represent continuous and discreet time model ofregulators (current, speed, and position loops);

(g) emulate the numerical control for the correctedgeneration of the position references of con-trolled axes.

A fully integrated mechatronic simulation is oftennot required, and it is possible to focus on particularaspects that require only some of the above-mentioned capabilities.

The mechatronic simulation is currently techni-cally feasible, alone or in combination, by commer-cial packages for FEA simulation, multibodysystems simulation or control systems design.Several solutions are possible: data or linearizedmodels of the structural components are exchangedbetween various softwares; a single software package

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Fig.1

Modelofindustrialdrive

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that models both mechanical objects and controlcomponents; two softwares specialized respectivelyin mechanical modelling and in control modellinginteracting during simulation.

5 ANALYSIS METHODS ANDEXEMPLIFICATION

Mechatronic simulation can perform several ana-lyses, some of which are possible using a classicalapproach (i.e. static deformation, normal modes).Others are possible only with a mechatronicapproach (regulator tuning, complex modes withactive control, dynamic response of the controlledsystem, simulation of a part program execution).

To demonstrate the issues previously outlined, themechatronic analysis is adopted of a millingmachine with three linear motor axes (shown inFig. 2). This is a common morphology for a millingmachine, but it is not a real machine in order toavoid incurring incomprehensible problems ofconfidentiality. The goal of the present study is notto achieve particularly high performances, but todemonstrate how mechatronic analysis can supportdesigners in their work, highlighting the limits ofmechanical structures. The effect of friction on theguides is neglected to avoid a too complex model,as this is not the aim of this article.

The FE model, represented in Fig. 2, has 3272nodes and 5303 elements. In the reduction sevenstatic modes are considered: four due to relativedisplacements between the motors’ primary windingand secondary winding (three axes, one of them isgantry) and three related to tool displacements inthree directions (x y z). A further 47 dynamic modes(calculated with locked motors and locked tools) areadded to the previous ones: the resultant structuralmodel has 54 DOF (starting from a model withapproximately 18 000 DOF). A uniform modal damp-ing of 2 per cent is assigned to the structure (thisvalue is very low and, therefore, precautionary).To study the behaviour of the machine in variouspositions of the workspace it is necessary to com-pute the reduced model ([AiBiCiDi] matrix seti ¼ 1 � k) corresponding to the position Pi. To ana-lyse the mechatronic model with the machine inthe Pn workspace position it is sufficient to set thecorresponding [AnBnCnDn] matrix in the assembledmodel (Fig. 2).

The mechatronic model will be used to analyse:

(a) regulator tuning: analysing the influence of themechanical structure and regulator functional-ities;

(b) machining capability: estimating the maxi-mum depth of chip based on cutting processstability;

(c) simulation of part program execution: trajectoryerrors identifying the contribution of structuredeformation and drive performances.

An important step in the analysis (as with thestart-up of a real machine tool) is the tuning of regu-lators. For this reason it is attempted to reproduce insimulation the functionalities of the real system, todefine both the parameters and the test modalities(time and frequency responses). The first step con-sists of estimating the frequency response functions(FRFs) of the structure (Fig. 3 shows the FRF of thereconstructed velocity from the measure of the posi-tion sensor). As in the real machine, the commonprocedure for tuning regulators is to apply the Bodestability criterion, to obtain the regulator parametersshown in Table 1.

In this phase of calibration the gains are maxi-mized (in order to maximize the disturbance rejec-tion), taking into account that a lightly dampedmachine will be driven with a more regular signal,to reduce the jerk and therefore increase the execu-tion times.

By means of routines developed by ITIA-CNR it ispossible to analyse and visualize the mode shapesof the machine with controlled axes. This is useful,for example, to estimate if any modes can be activelydamped by the regulators. In Fig. 4, mode A pro-vokes deformations on the supports and on theguideways, with a limited axis movement and there-fore the resultant damping is low; mode B provokesaxes movement that will be strongly dampened bythe regulators.

The dynamics of the machine can also be analysedby examining the steady state oscillations of thestructure, caused by the sinusoidal input signal(also called running modes). Typical cases are thedeformation resulting from external forces or froman axis position command.

A classic stability criterion of the cutting process(see [10]) is used as a machine performance indica-tor. This criterion estimates the maximum depth ofchip [blim (mm)] as a function of the minimum ofthe real part of the FRFtool/tool(v) of the dynamicscompliance at the tool

blim ¼ 1

2minvðrealPartFRFtool=toolðvÞÞkCFCð1Þ

where FRF [displacement(mm)/force(N)] isestimated on the tool, kCFC(N/mm2) is the cuttingforce coefficient, that is a function of theworkpiece material, of the geometry of the cuttingtool and of the chip thickness. The formula is auseful qualitative indicator (a more detailedanalysis must take into account direction of theforces generated by the cutting process and therespective dynamic compliance in all three

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Fig.2

Mechatronic

simulationofathree-axismillingmachine

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directions). This analysis quantifies the machiningcapability of the machine in various directions and,moreover, supplies useful information on whichmodes limit performance.

The mechatronic model has also been studiedby estimating the dynamic stiffness at the tool.Figure 5 shows a Nyquist diagram of the FRF (displa-cement tool)/(force on tool), in the y direction, andthe different conditions performed during drive tun-ing, including a locked motor, normally consideredin the structure design. The maximum cutting depthcorresponds to the minimum of the real part, asindicated by the cross in this figure. The large differ-ence between the blim evaluated with locked motorsand blim evaluated with controlled axes, highlightsthe usefulness of mechatronic analysis.

The next criterion of evaluation consists of simu-lating the part program execution. The simulationallows an estimation of the trajectory error, usingboth position sensors and effective tool position(which includes deformations of the structure).Figure 6 shows the displacement, suitably amplified,between the demanded trajectory (see part program)

and the reconstruction of the position measured bythe sensors. As expected, the larger error is in thezone of larger curvature.

By means of linearized models of the mechanicalstructure, the rigid body component of the motioncan be distinguished from the contribution ofstructural flexibility (this task is not easily feasiblewith complete original FEM model simulation).Moreover, an animation can show the movementof the machine during the execution of the trajec-tory. This option may be used, for instance, to visua-lize the movement of the machine with differentamplification of the motion amplitude owing tothe rigid component and flexible modes. Theanalysis of the movie and associated data, canhelp the designer to comprehend the dynamicbehaviour of the machine under operating condi-tions, from which good indications can be obtainedof any required modification to the mechanicalstructure.

6 METHODOLOGY EXTENSION ANDAPPLICATION: THE MECOMAT PROJECT

Analysis methods previously discussed were appliedand extended in a European project: the MECOMAT(MEchatronic COmpiler of MAchine Tool) project,briefly presented here. The objective of theMECOMAT project was the development of an inte-grated computer aided design/computer aided engi-neering (CAD/CAE) tool for the mechatronic designand the optimization of machine tool performance,

Table 1 Regulator parameters after tuning

Kv Jerk Velocity loop Position loop

Axis [(m/min)/mm] m/s3 �3 dB �45� �3 dB �45�

X 2.5 200 33 Hz 28 Hz 28 Hz 13 HzY 2.5 200 23 Hz 15 Hz 18 Hz 7.5 HzZ 4 200 33 Hz 24 Hz 21 Hz 8.8 Hz

Mode A: 51 hz, damping 2.3% Mode B: 59 hz, damping 39%

Fig. 4 Modes with different damping owing to controlled axis

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which provided a new integrated design methodol-ogy that took into account a mechatronic analysisclose to that presented in this paper.

The mechatronic optimization methodology isdivided into two parts: conceptual analysis andpreliminary analysis. The conceptual analysis isperformed using a rigid body structure model,

whose main goal is to reach the optimal layout ofthe machine, taking into account performancesof motion unit, general objectives, and userspecifications.

The preliminary analysis is performed usingapproximated models: parametric and/or homo-geneous materials, structural component library,axes, guideways and sensors model library, and con-trols and regulators model library. The main goal is

Fig. 6 Trajectory error from simulation

Fig. 7 Mechatronic optimization process

Fig. 5 Dynamic compliance on tool during a progressiveclosing of loops. (A) open loop, (I) locked motor,(H) all loops closed

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to optimize structural dimensions, axes and guide-way parameters (such as stiffness, inertia, etc.), con-trol design, and tuning.

The MECOMAT modules support the develop-ment of a new machine tool, see Fig. 7. Layoutdesign supports the user in the definition of themachine architecture starting from the user specifi-cations. A motion unit selection is provided accord-ing to the machine performance requirements,taken into account during the layout optimizationprocess. Once the global architecture of the machineis defined, using the parametric models library forstructural components, axes sensors, etc, a preli-minary analysis is performed in order to optimize(separately but in sequence):

(a) structure (dimensions, thickness and number ofribs), axes (performances requirement, andchoice), guideway (stiffness and supports) etc.

(b) control design and tuning.

These two optimization processes are under a glo-bal mechatronic optimization process that can driveobjectives of the inner optimization.

7 CONCLUSIONS

The use of mechatronic simulation is needed moreand more to support the design of high-performancemachine tools. Today it is possible quickly todevelop a model that permits the analysis of the tightconnection between the dynamics of the mechanicalstructure and its control system. To be able to usethis approach in an industrial environment profit-ably it is necessary to have some fundamental soft-ware (these have been rapidly developed in thisdirection in the recent years, because of the general-ized diffusion of the mechatronic simulation),appropriate models of commercial components(particularly if developed with the suppliers’ sup-port), and an improved mechatronic culture.

Mechatronic analysis can assist the designerto comprehend the dynamic behaviour of themachine under operating conditions, obtaining a

good indication of the modification of the mechani-cal structure and the best choice of components.

ACKNOWLEDGEMENTS

The authors greatly acknowledge the support fromthe European Commission Growth projectMECOMAT: ‘Mechatronic Compiler for MachineTools design’. Contract No. G1RD-2000-00357. Pro-ject funded by the European Community under the‘Competitive and Sustainable Growth’ Programme(1998–2002).

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