Virtual Machine Tool

Y. Altintas1 (1), C. Brecher2, M. Weck2 (1), S. Witt2 1Manufacturing Automation Laboratory-The University of British Columbia

Department of Mechanical Engineering, Vancouver, Canada 2Laboratory for Machine Tools and Production Engineering, Chair for Machine Tools

Aachen University of Technology, Aachen, Germany

Abstract This paper presents current state of Virtual Machine Tool Technology and related ongoing research chal-lenges. The structural analysis of machine tools using Finite Element models and their experimental cali-bration techniques are presented. The kinematic analysis and optimisation of machine tool elements are discussed with sample examples. The interaction between the control of the feed drives, cutting condi-tions and machine tool structure is presented. Multi-body dynamic models of the machine, which allow integrated simulation of machine kinematics, structural dynamics and control techniques, are discussed. The interaction between the machine tool, controller and cutting process disturbances are discussed with sample examples. The simulation of machining operation and its impact on the dynamics of the machine tool and CNC are elaborated. The paper presents both the summary of current and past research, as well as research challenges in order to realise a fully digitised model of the machine tool. Keywords: Simulation, Machine Tools, Virtual Prototype

1 INTRODUCTION The goal of present manufacturing technology is to pro-duce even the first part correctly in a shortest time and most cost effective way. Since the product complexities increase and the competitive product life cycle times are reduced, the realisation and testing of physical prototypes become major bottlenecks for the successful and eco-nomically advantageous production of modern machine tools [54], [114]. Presently, the machine tool builders can no longer afford the time- and cost-intensive manufacturing and testing of physical prototypes to detect weak spots and optimise

the design. Instead, the design processes of modern machine tools employ “virtual prototyping” technology to reduce the cost and time of hardware testing and iterative improvements of the physical prototype. The virtual pro-totype of a machine tool is a computer simulation model of the physical product that can be presented, analysed and tested like a real machine. Iterative changing of a virtual model of the machine tool during the design proc-ess and exercising design variations until the perform-ance requirements are achieved, reduce the whole prod-uct development time and cost significantly. The advan-tages and the potentials of time savings by virtual proto-types are illustrated in Figure 1.

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Figure 1: Comparison of the traditional design process and the design process with virtual prototypes.

If the possibility of comprehensive simulations during the entire design process is not available the optimisation of physical prototypes is often based on trial and error based on the past design experience, which leads to a costly and lengthy development process. In the virtual prototype approach, engineers are able to realistically simulate the kinematic, static and dynamic behaviour of the whole machine tool system including the cutting operations. Thus it is possible to quickly analyse multiple design variations until achieving an optimised prototype which satisfies the machining requirements in the best possible manner. The virtual design engineering is enabled by the use of high performance computer technology and software engineering tools. The virtual prototypes are not only helpful for the design process but also for the virtual initial start-up of the ma-chine tool or the simulation of the machining operations on the digital model of the machine tool. This paper presents the design, analysis, optimisation and operation of machine tools in a virtual environment. The paper is organised as follows: The concept of virtual machine tool design and testing is presented in Section 2. Finite Element, kinematics, structural analysis and optimi-sation of the machine tool elements are explained. The simulation model of the CNC system is presented in Sec-tion 3. Trajectory generation, axis control laws and tool path simulation with collision detection are discussed. The simulation of machining operations is given in Section 4. The predictions of cutting loads as well as the stress-temperature simulation in the chip and tool wedge are explained. Section 5 covers the integration of process and machine tool simulation, which is the ultimate goal in realising a complete digital model of the machine tool during machining of a part. The present research chal-lenges which has to be solved for the full realisation of virtual machine tool system are discussed in Section 6. The paper is concluded by assessing the effectiveness and future trends in “Virtual Machine Tool and Machining Systems”. 2 THE VIRTUAL MACHINE TOOL Modern machine tools are very complex mechatronical systems. The capability and efficiency of a machine tool are mainly determined by its kinematics, structural dy-namics, computer numerical control system and the ma-chining process as shown in Figure 2.

ProcessProcessProductProductrequirementsrequirements

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Figure 2: The mechatronic system “machine tool”. To ensure that the first physical prototype of the machine tool meets the requirements in the best possible way, it is essential that every design step is evaluated with simula-tions of the virtual prototype.

2.1 Integrated design of modern machine tools Initiated mainly by the automotive and aircraft industry, the development of modern software tools for the simula-tion of product properties has been enhanced significantly

in recent years [114]. Advanced software and hardware systems allow design engineers to evaluate and optimise critical product characteristics with virtual prototypes be-fore the first physical prototype is built. A wide range of software tools is available for the different design-stages of a machine tool [114], [124] as shown in Figure 3.

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Figure 3: Integrated development of modern machine tools with virtual prototypes.

Computer aided design and kinematics studies During the concept stage, simplified simulation models can be used to estimate the influence of general design parameters on the machine performance. The kinematic configuration or the geometry and widths of guideways can be given as examples for general design parameters. Especially the machine tools with parallel kinematics the kinematic behaviour needs to be simulated and optimised during the early design stage. The machine tools with complex kinematic configuration are much more sensitive to slight variations of geometric parameters than tradi-tional cartesian machine tools, and thus offer huge poten-tial for optimisation. The 3D-CAD-Model of the machine tool is exported to a kinematic analysis software environ-ment. The optimisation of the kinematic behaviour and the simulation with rigid multi-body simulation during the early design stages are illustrated in Sections 2.2 and 2.3. Finite-Element-Analysis The Finite-Element-Analysis (FEA) is used to calculate static stiffness or dynamic characteristics of the machine tool, e.g. natural-frequencies and mode shapes. Powerful optimisation methods, which are based on the Finite-Element-Method, are used effectively to find optimum design variants under given restrictions, e.g. the minimi-sation of masses of moving machine components or the maximisation of the static stiffness. The Finite-Element-Analysis as well as the application of structural optimisa-tion methods are discussed in Sections 2.4 and 2.5 . Coupled flexible Multi-Body-Simulation The development of high speed machine tools requires light-weight design in combination with sufficient stiffness of the structural components. Moreover, the machine control must be capable of dealing with the high-speed position changes at acceptable accuracy. Therefore, the interaction between structural dynamics and control loops must be considered during the design of modern machine tools. The coupled flexible multi-body simulation is illus-trated in Section 2.6.

Calibration of the Simulation Models To realise a good correlation between the results of measurements and Multi-Body-Simulation, the parame-ters of the simulation model, e. g. the damping and stiff-ness parameters of guiding systems and bearings, must be calibrated. Especially the correct prediction of damping parameters in machine tools is very difficult because of the dependency on a large number of different influences, e.g. the pre-load, temperatures, assembly conditions and many others. The calibration of simulation models with results of measurements are discussed in Section 2.7.

2.2 Optimisation of the kinematic behaviour During the early stages of the design process of machine tools the type of the kinematic as well as the desired workspace dimensions have to be defined. The efficiency of machine tools is basically determined by these charac-teristics. Especially machine tools with parallel kinematics are characterised by their non-linear transmission of movements and forces from joint- to task-space [106]. These transmission characteristics are influenced by the kinematic topology of the mechanism and its geometric configuration. Thus, the following two steps are most important during design [66]. • Determination of the appropriate kinematic topology • Determination of the right geometric dimensions The second step is most important since the performance is highly influenced by the geometric dimensions of a machine tool with parallel kinematics. A poor topology which is optimally designed may perform better than a mechanism with appropriate topology but poor design [66], [106]. The choice of the right dimensions for the design parame-ters with respect to a given application is a difficult task: • There are many performance values which have to

be taken into account and which are often antagonis-tic to the design parameters, i.e. kinematic stiffness vs. workspace.

• There is a nonlinear relation between design parame-ters and performance.

• Many performance values are of the type "best case - worst case" over an up to six-dimensional work-space.

Since the performance characteristics vary within a work-space of complex shape a simple and unique perform-ance comparison of either parallel with serial kinematics or different parallel mechanisms becomes most difficult. To achieve an optimal kinematic configuration in a short time, the designer has to be supported by suitable analy-sis- and optimisation tools. A classical way of finding the required design parameters is to define a cost function, consisting of the weighted sum of the performance values as a function of the design parameters. A numerical procedure is then used to find the design parameters which minimise the cost-function with respect to an initial estimate. This strategy is limited by the definitions of the weight factors, e.g. in terms of priority [66]. In addition, finding the global optimum cannot be guaranteed due to the complexity of the optimisation problem. To avoid these limitations, different approaches have been proposed. The parameter space approach esti-mates all satisfying solutions within a multidimensional design-space for each performance requirement [65]. The intersections of these individual solutions contain the sets of design parameters which will meet all requirements.

Thus, the optimal solution is either chosen intuitively by the designer or estimated by the classical cost-function approach. An approach based on pareto-optimal design is proposed in [57], [112]. The idea is to estimate all sets of design parameters with genetic algorithms, in which the individ-ual performance values can only be maximised by a weakening of another performance requirement. Within the resulting sets of pareto-optimal design parameters, the optimal configuration for a given task can be chosen. The optimisation with the help of genetic algorithms is illustrated in Figure 4. The design parameters which were optimised are the dimensions of the platform, as well as the position of the joints at the machine bed under given restrictions [111].

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It can be observed, that the development of design tools for machine tools is still ongoing research. While tools for the performance analysis are widely established, the estimation of an optimal layout for a given application has to be automated to establish conceptual capabilities in terms of modularity and reconfigurability.

2.3 Simulation of rigid multi-body models During the early design stages the kinematic behaviour of the machine tool can be simulated with the multi-body simulation (MBS) as a rough estimation [113], [123] using rigid bodies. This kind of simulation enables the design engineer to make a first, quick prediction of the kinematic behaviour and estimations of the influence of parameter variations in the model, as, for example, the length of an actuator in machine tools with parallel kinematics [123]. Each individual element within the multi-body model con-sists of rigid bodies. In this context rigid bodies are parts that have mass and inertia properties but cannot deform. These rigid bodies can be imported from 3D-CAD-Models through interfaces using standard formats such as IGES, STEP, DXF/DWG and Parasolid or can even be gener-ated within the multi-body environment. Constraints de-fine how the parts are attached and how they move rela-tive to each other. Multi-body simulation tools usually provide a library of constraints including for example [64]: • Idealised joints that have a physical counterpart,

such as a revolute (hinge) or translational (sliding dovetail) joint.

• Joint primitives that place a restriction on relative motion, such as forced parallel movement of two parts.

• Motion generators that drive the model through a prescribed distance, velocity or acceleration profile as a function of time.

• Associative constraints that define how pairs of con-straints move, such as couplers or gears.

• Two-dimensional curve constraints that define how a point or curve moves along another curve.

Furthermore, forces that act on the model can be defined. These forces will affect part motion and reaction forces on constraints. Multi-body simulation tools provide libraries of forces that usually include: • Flexible connectors, such as spring-dampers and

bushings, which provide pre-defined, compliant force relationships.

• Special force elements that provide pre-defined forces that are commonly encountered.

• Applied forces that allow the writing of algorithms to represent a wide variety of different force relation-ships.

• Contact forces that specify how bodies react if they come in contact with each other while the model is in motion.

The analysis options in the established multi-body simula-tion systems consists of the following types [90]: • Assembly analysis • Kinematic analysis • Dynamic analysis • Inverse dynamic analysis • Static analysis In the assembly analysis, the MBS-software tries to as-semble the mechanism in the modelled configuration. This means that the underlying non-linear equation sys-tem is solved. If necessary, minor variations of the initial positions owing to the numerical precision of the input data are applied. This analysis step is carried out before each simulation. During a kinematic simulation, the position of all bodies of the mechanism is analysed depending on the time. Dur-ing such a simulation the movements of one or more bodies are described by a law of motion. This kind of analysis is used to simulate the reachable kinematic per-formance, e.g. the acceleration capability of the design over the complete workspace. The model of a machine tool with parallel kinematics and some results of such a kinematic simulation are shown in the following Figure 5.

Results of a Positioning OperationResults of a Positioning Operation

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In this example the multi-body model is used to simulate the dependency between reachable acceleration and necessary jerk setting for positioning operations of the kinematics [112]. In the dynamic analysis, the position of all bodies of the mechanism is determined as a result of time-dependent forces applied from outside. Generally, kinematic con-straints are replaced by flexible connectors like 3-dimensional spring-damper-elements. With the help of this analysis the simulation of expected load histories of machine components can be estimated for the dimension-ing [20], [90], [76], [108]. During the analysis of inverse dynamics, the motion pat-tern of one or more bodies is specified and the drive and the internal forces of the joints and flexible connectors are calculated. This kind of simulation is especially useful for the dimensioning of the drive systems during the early design stages. The static calculation is traced back to a dynamic calcula-tion where the MBS-system determines the state of equi-librium [64], [90]. The multi-body simulation provides an easy way to ana-lyse the kinematic behaviour over the complete work-space of a machine tool as well as to determine load histories of components or joints [64], [90], [123]. In addi-tion, it helps to choose proper elements or detect weak spots of a machine tool in the early design stages. How-ever, the flexibility and strain of single machine parts cannot be considered with the pure multi-body simulation using rigid body models [113], [64].

2.4 Finite Element Analysis of machine tools After the concept of the machine tool and the dimensions of the kinematics have been defined the structural behav-iour has to be analysed and optimised [64], [113], [124]. The structural behaviour under static, dynamic and ther-mal loads is evaluated to derive an optimal machine de-sign with respect to minimum structure mass and highest machining precision. The Finite-Element-Analysis (FEA) is an established tool to evaluate the properties mentioned above. It is applica-ble for single components such as columns or spindle housings as well as for complete machine tools. The most common types of the Finite-Element-Analysis for structural problems are illustrated in Figure 6. Apart from these analysis types the Finite-Element-Analysis is also applicable for other physical problems, e.g. in hy-draulic, electromagnetic and casting simulations.

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Figure 6: Analysis types of the Finite-Element-Analysis. For structural problems the types of analysis can be di-vided into three groups as depicted below: namely the linear and non-linear static analysis, the dynamic analysis and the thermal analysis [30].

A static analysis calculates the effects of steady load conditions on a structure, while ignoring inertia and damp-ing effects caused by time-varying loads. A static analysis can, however, include steady inertia loads (such as grav-ity and rotational velocity), and time-varying loads that can be approximated as static equivalent loads. Static analysis is used to determine the displacements, stresses, strains, and forces in structures or components caused by loads that do not induce significant inertia and damping effects. Steady load and response conditions are assumed in static analysis; i.e., the loads and the structure’s response are assumed to vary slowly with time. A static analysis can be either linear or non-linear. The linear static approach is selected when small, elastic deformations occur on the structure. In general, the analysis refers to the classical calculation of elasticity problems that can also be described analytically in the case of very simple structures. In this context buckling problems can be analysed that match the classical Euler solution. In non-linear analysis different types of non-linearity are allowed such as large deformations, plasticity (non-linear material properties), creep, stress stiffening, contact (gap) elements or hyperelastic elements. Contrary to the static case, the dynamic analysis allows the examination of a structure with respect to time-varying effects. For machine tools the most important aspect is the analysis of normal mode dynamics to determine the vibration characteristics (natural frequencies and mode shapes) of a structure or a machine component in the frequency domain, as well as analysis of time domain response of the machine [30]. Apart from the mechanical aspects the influence of heat sources on the machine’s structure is another most rele-vant topic that can be examined using the thermal Finite-Element-Analysis. In most cases the basis for thermal analysis is a heat balance equation obtained from the principle of the conservation of energy. In a thermal simu-lation the three primary modes of heat transfer can be considered: conduction, convection and radiation. For machine tools the most important results in a Finite-Element-Analysis are [20]: • Deformations, e.g. deflection of the tool centre point

(TCP) under process loads, deflection of guideways, reaction forces, e.g. forces in bearings or guiding-systems

• Linear normal modes of vibration • Flexibility frequency response (with limitation) • Stress distribution, e.g. in highly loaded tool inter-

faces under additional rotational loads • Temperature distribution, thermal fluxes and resulting

deformations The detailed procedure of a Finite-Element-Analysis for machine tools according to Figure 7 is exemplified in the following. For the effective use of simulations during the design process Finite-Element programs are often integrated into CAD-systems or provide standard interfaces, such as IGES, STEP or Parasolid in order to transfer existing geometry models. In a first step it is necessary to prepare the CAD model for the following Finite-Element-Analysis (pre-processing). Geometric details, such as chamfers, small holes and radii that only have a local influence on the structural behaviour are neglected. After simplifying the geometry,

the geometric model is split into surface patches (parti-tions). By this, a complex structure is fractionalised into simple base geometry elements that allow easy meshing.

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Figure 7: Steps of a FEA-Analysis of a machine tool. Next, the prepared geometric structure is reproduced by finite elements. Depending on the simulation problem and the desired calculation accuracy, the FEA programs offer a variety of different elements that are specific to the analysis (static, dynamic, thermal). The finite elements are connected by nodes that make up the complete finite element mesh. Each element type contains information on its degree-of-freedom set (e.g. translational, rotational, thermal), its material properties and its spacial orientation (1D-, 2D-, 3D-element types). Thin-walled structural components of machine tools, like columns or machine beds, are usually meshed with shell-elements (2D-element types). The wall thickness of the structure is contained as a physical property of each ele-ment. Compact parts are typically meshed with solid ele-ments (3D-element types) [30]. Semi-automatic mesh generators are widely used in prac-tise, helping the engineer to reduce the model generation effort. In the semi-automatic meshing process, also called mapped meshing, regular FEA meshes made of quadri-lateral or hexahedral elements are generated. These kind of FEA meshes are distinguished by balanced element proportions and smooth dimensional transitions. On the contrary, with fully automatic meshing methods, only the generation of irregular FEA meshes is possible, which in general provide lower calculation accuracy com-pared to the mapped meshes. While the real structure components of machine tools are commonly connected by guidance systems and drives, e.g. ball-screws, the meshed structural components are connected using spring elements with corresponding stiffness values. These spring elements represent the connection stiffness of real machine components with adequate accuracy. They may also contain local damping properties, if those are needed for direct dynamic calcula-tions and if they are known for the corresponding machine component. Finally, boundary and load conditions are added to fully describe the simulation model. Boundary conditions are applied to give specified displacements and to describe symmetry conditions. The boundary conditions are de-fined by fixing the various translational and, rotational degrees of freedom, or by constrained mesh’s nodes. Loads are added to describe the machine tool loading scenarios such as machining forces or heated motors.

Therefore, loads can be of a structural (forces), thermal (heat sources) or fluid (pressures) nature. For machine tools the static and dynamic behaviour is of major interest, as illustrated in Figure 7. In post-processing, the calculation results can be reviewed and load cases of different operating conditions can be super-imposed. While displaying the calculation results (e.g. static, dynamic) in the post-processing program, the ma-chine model can be examined with respect to displace-ments, stresses, reaction forces, mode shapes or natural frequencies, which allows the designer to evaluate the machine properties in the design phase. Albertz [1] and Schneider [87] presented applications of the Finite-Element-Analysis for the simulation of the static and the dynamic behaviour of machining centres during the design process. Zatarain [134] used a FE-Model with movable joints be-tween the structural components for a modular synthesis of the static and dynamic behaviour of machine tools at several positions in the workspace. Groche [46] used Finite-Element-Analysis for the optimi-sation of a forming press under dynamic loads. The industrial application of Finite-Element-Analysis as a tool for computer aided engineering is illustrated by many different examples [20], [76], [125], [108]. However a single analysis of the actual state of a ma-chine tool (analysis of weak spots) during the design process is usually of little help. Rather, in most cases, continuous improvements to the design are necessary in order to improve the static and dynamic behaviour of suboptimal components, to reduce masses of moving parts. These improvements of the machine performance can be achieved cost-effectively by the use of modern optimisa-tion methods based on the Finite-Element-Method. These methods will be explained and discussed in the next sec-tion.

2.5 Optimisation of structural components In machine tool design, optimisation offers the possibility of improving different properties of the design by using numerical optimisation [20], [84], [89], [91], [114], [124]. The numerical optimisation of structural components is generally based on the Finite-Element-Method and can thus easily be integrated in the design process [89]. De-pending on the necessary level of detail, different meth-ods are used to find or improve the design of structural components of machine tools. The topology optimisation is used to define the best mate-rial distribution in a given design space. Thus this method is mainly used in the early design stages supporting the engineer in finding a design concept with regard to given demands [79], [84], [87], [91], [92]. As a result of this optimisation an optimal material distribution in the given design space is calculated. For the design of machine tools this method is often used to determine the design of machine beds or columns in terms of light weight design. Some examples and applications of the topology optimi-sation will be discussed in Section 2.5.1. The parameter optimisation is used for the optimisation of more detailed designs of machine tools. This numerical method is used to optimise parameters of Finite-Elements (2D-element types) considering different constraints, e.g. maximal allowed deformation [13], [89], [113], [124]. A typical application is the optimisation of the wall thickness of machine beds or columns for machine tools. Generally the overall weight of the structural components is mini-mised with regard to a desired static stiffness at the tool

centre point. The application of the parameter optimisa-tion will be illustrated in Section 2.5.2. The following Figure 8 illustrates the most common meth-ods for structural optimisation.

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Figure 8: Methods of structural optimisation. The topography as well as the shape optimisation are of secondary importance for the design and optimisation of structural components for machine tools.

2.5.1 Topology Optimisation The topology optimisation supports the designer in the task of finding a preliminary rough design based on mini-mum design specifications, wherein the mass of the com-ponent is distributed with load-orientation in the solution space [69], [79], [84], [91], [123]. The topology optimisation requires no design plan as an initial solution. Starting from the available design space and the requirements for the component, a basic design of the component is determined. The objective of a topol-ogy optimisation mostly lies in designing the component with a minimum mass with simultaneous adherence to the boundary conditions, such as stiffness specifications. Moreover, some topology optimisation systems allow the formulation of reference stress and natural frequencies as goal and restriction functions [89]. The topology of a com-ponent created in this way must finally be smoothed and transformed into a CAD model to be able to reuse it [13], [113]. Hessel [50], [113] developed an approach to transfer the results of a topology optimisation back to the CAD-based design process. The mesh of the optimisation result is transferred into a surface model consisting of NURBS-surfaces and standard geometry. These models can be exported in a standard format, like STEP or IGES, and can thus be used for the detail design-engineering work. Fleischer et al. [44], [70], [92], [124] developed an ap-proach for the topology optimisation of structural compo-nents which is called “coupled hybrid multi-body simula-tion with topology optimisation” (HMBS-TO). This soft-ware environment uses the multi-body simulation to cal-culate the loads and the FEA-software in combination with the optimisation software. The advantage of this approach is the automatic load and inertia update which guarantees a fully automated optimisation loop [70]. The workflow for the new dynamic topology optimisation is illustrated in the following Figure 9. After the preparation of the flexible bodies, a modal re-duction has to be carried out to reduce the degrees of freedom of the hybrid multi-body simulation model. This can be achieved by means of computing the Craig-Bampton modes [31], which are described in detail in Section 2.6.3.2.

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The third step is the setup of the HMBS model and the definition of imposed motions and load cases [44], [70], [123]. The resulting forces of the MBS simulations are exported, as are component deformations and stresses. This loop (steps 2-5) is repeated until the topology optimi-sation finishes with a design proposal (step 6) which fulfils the desired objectives.

2.5.2 Parameter Optimisation Parameter optimisation tools are used to find optimum sets of structural parameters by using the Finite-Element-Analysis [13], [89], [113]. These optimisation tools are used after the rough dimensions of the components are defined. Different parameters of the draft designs can be optimised under different constraints such as: • wall thickness values of shell elements for models of

structural components • cross-sections of beam elements for models of

frameworks • fibre orientation angles of shell elements for models

of light-weight design The parameter optimisation is a useful tool for the design engineer to meet the demands of light weight design especially for moving parts of highly dynamic machine tools. The results of such an optimisation of a High-Performance-Cutting (HPC) machine tool are presented in Figure 10.

1

34

2

5

6

xy

z

7

1 vertical table - bottom2 vertical table - top3 pallet carrier4 pallete5 column6 head Sprint Z37 fixation

Optimisation of a Milling Machine

optimisation of the design

comparison of different design-versions

consequently realisation of light weight design parameter optimisation of the wall thickness

by the use of Finite-Element-Analysis

0

20

40

60

80

100

120

140

over-all mass 1. eigenfrequency

perc

ent [

%]

020406080

100120140160180

over-all mass 1. eigenfrequency

perc

ent [

%]

optimisation table

optimisation columnStart designOptimised design

Start designOptimised design

Figure 10: Parameter optimisation of a machining centre.

The over-all weight of the structural components could be reduced significantly by maintaining a constant static stiffness at the tool centre point [22]. During the optimisa-

tion the thickness of each wall of the structural compo-nents was defined as a design parameter which could be varied within limits. The optimisation led to a noticeable improvement of the dynamic behaviour resulting in a significant increase of the first natural-frequency.

2.6 Coupled Simulation of structural dynamics and control loops of machine tools

Generally, the requirements on modern highly dynamic machine tools can be summarised as follows [21], [22], [116]: • high static and dynamic stiffness to ensure high ac-

curacy of the finished workpieces • high dynamic properties of the feed drives to realise

highly dynamic positioning operations and move-ments to decrease the processing time of each work-piece

• low path deflection during the chip removal These ambitious demands on machine tools can only be fulfilled employing small moving masses with sufficient static and dynamic stiffness of the structural components as well as high adjustable controller parameters of the drives [22], [116]. This leads to interactions between structural dynamics and feed drive controls. Natural fre-quencies of the feed drives are coupled with lower natural frequencies of the machine structure. To avoid instabili-ties the control parameters have to be reduced, whereby the bandwidth of the feed axes decreases. This leads to a limitation of the productivity of the machine tool. Despite these known interactions the dimensioning of the feed drives and the design of the structural components of the machine tool nowadays still take place decoupled from each other. Different approaches are known to simulate these interac-tions during the early design stage of the machine tool [33], [48], [80], [81], [116], [131]. Figure 11 illustrates the most common approaches for the coupled simulation of structural dynamics and control loops used today.

Replacing Models

Co-Simulation

redu

ced

mod

el

of th

e m

echa

nic

[M];

[K];

[C]

Digital Block-Simulation (DBS)

Coupled flexible Multi-Body SimulationCoupled rigid Multi-Body Simulation (MBS)

- -s

--

posi

tion,

vel

ocity

forc

es

DBS

MBS

FEA

- -s

--

m red k red

C red

Finite Element Analysis (FEA)

DBS

redu

ced

mod

elof

the

driv

esm

red,

k red

, cre

d

- -s

--

PT2

interface

interface

- -s

--

posi

tion,

vel

ocity

forc

es

DBS

interface

interface

MBS

Figure 11: Methods of coupled simulation of structural

dynamics and control loops.

The different approaches can be classified as the simula-tion with replaced models and the co-simulation of the dynamic behaviour. The simulation with replaced models uses either analogue models of the control loop for the FEA-Model of the structure or analogue models of the mechanics for the simulation of the control loop [48].

In the context of the co-simulation, two independent simu-lation environments, one for the control loops and one for the machine structure, are coupled via interfaces during the simulation [33], [48], [73], [131]. Within the research project MECOMAT (FP5 Growth Programme of the European Union) [103] an computer aided engineering tool was developed for the mechatronic design of machine tools, which supports the conceptual design as well as the detailed verification. The different approaches will be explained with some examples within the next sections.

2.6.1 Coupled rigid multi-body simulation The rigid coupled multi-body simulation can be used to simulate the kinematic behaviour of the machine tool while considering the control loops of the drives [20], [76], [125]. The models of the structural components are stiff and cannot deform under load, and are connected by idealised joints. The simulation is valid for any possible position of the machine tool in the workspace. Therefore it is possible to simulate positioning operations in the work-space with this approach. Pritschow et al. [73], [74], [75] developed a simulation environment which is illustrated in Figure 12. The envi-ronment was developed for the coupled simulation of a rigid multi-body model and control loop models of a PKM machine tool.

CAD-Model MBS-Model PC-NC Model

Model of thecontrol loops

ForcesDisplacements

Velocities

Design in 3D-CAD-Systems -> Import into MBS-Software (MSC.ADAMS)adaptable level of detailcoupled model of the control loops (Matlab/Simulink) of the drivesdesired feed rates with PC-NC model

desired feed ratesVel

ocity

ForcesDisplacementsVelocities

TimeKv +- 1/Ks Kf 1/1000

PI

1/Tpc+-

+-

1/2 vber

2

1 1

Tigger

Xsoll

Xist

Fsoll

Figure 12: Coupled simulation of a rigid multi-body model

and control loop models of a PKM machine tool. The multi-body model of the machine tool is imported with the aid of an interface from the CAD-system into the MBS-environment. This approach enables the update of the model during the different design stages; if the layout is detailed during the design process these changes can easily be included [74]. The model is coupled with models of the control loop for each drive. The displacement and velocity of the measur-ing systems in the model as well as the forces of the drives are exchanged with the aid of interfaces between the MBS-environment and the Computer-Aided-Control-Engineering program. In addition the control loop models are coupled with a PC-based model of the numerical control, which generates the desired feed rate of each individual drive. Especially in the field of machine tools with parallel kine-matics the possibility to perform test runs of the numerical control before implementing new functionalities, like algo-rithms for path preparation, collision checks or coordinate transformations into the real machines is a significant improvement to avoid physical damage [75]. Rehsteiner et al. [83] used the multi body simulation to optimise the accuracy of machine tools under accelera-tion loads for the demands of high-speed-machining.

Neugebauer et al. [71] developed models to describe the interaction of machine and hydraulic drive system of form-ing machines. The methods use numerical simulations for the hydraulic systems.

2.6.2 Coupled Finite-Element simulation Another approach is the coupled Finite-Element simula-tion with reduced models of the control loops of the drives. Within this procedure the reduced stiffness, damp-ing and mass of the drive system are calculated with the help of a digital block-simulation and modelled with spe-cial elements in the FEA-model [20], [48], [76], [131]. Some FEA-programs provide special linear control ele-ments to represent the analogue model of the control loops. In this case only the settings of the controllers have to be specified as parameters of the elements in the FEA-model [17]. These kinds of elements are handled in the same way as conventional finite elements. The simulation of the dynamic behaviour of the x-slide of a turning centre with a linear direct drive is depicted in the following Figure 13 [20]. To simulate the error at the tool-centre-point during a positioning, a trajectory profile was generated as an input signal for the controller element. The signal of the measuring system was used as an addi-tional input signal. This signal was measured between two nodes at the two parts to which the measuring system is mounted on the real machine. At each simulation step of the dynamic analysis the controller element calculated the force of the linear direct drive which was applied as a pair of forces (action=reaction) on the primary and the secon-dary parts.

source: Gildemeister / Siemens Linear Motor Systems GmbH & Co. KG

error X in the measuringsystem [mm]

error X at TCP [mm]

counteracting force on the primary partsfeed force on the

secondary parts

measuringsystem

TCP

0 0.1 0.3 0.40

0.04

0.08

time [s]

0 0.1 0.3 0.4

-0.01

0

0.01

time [s]er

ror.

[mm

]

0 0.1 0.3 0.4

erro

r [m

m]

-0.01

0

0.01

time [s]0 0.1 0.3 0.4

-10

0

10

time [s]

required position [m]required acceleration [m/s²]

controller

Figure 13: Coupled FEA-simulation with control loops

This approach enabled the investigation of the influence of the position of the measuring system as well as differ-ent orientations of the linear direct drive. Thus the de-signer was able to optimise the drive of the x-slide in an early design stage and minimise the occurring errors during machining. Such changes of the principle design would be extremely expensive if they had to be realised at a physical proto-type, or impossible if the surrounding design space did not allow such changes. Berkemer [16], [17], [18] demonstrated the industrial use of the methodology for tuning of the SIEMENS controllers in a virtual environment, as well as recommending the modification of the machine tool dimensions to minimise inertial excitation of the machine during high speed con-touring where large accelerations occur. Van Brussel et al. [104], [105] proposed to treat the com-plete machine tool and control as an integrated mecha-tronics design system. The Finite-Element-Model of the machine tool and control algorithms are integrated in the simulation environment as shown in Figure 14.

The aim of the strategy is to optimise the machine tool’s mechanical components as well as the control laws during the design stage of the machine tool simultaneously.

Structural models (Finite element model):• Structural elements• Drive elements• Non-linear phenomena (friction,…)

Control models (Matlab® / Simulink):• Control laws• Digital implementation (DAC, ADC)• Measurement devices, filters

Structure-control integration:

Desired trajectories Resulting outputsMatlab®/Simulink

Finite-ElementModel

In1Out1

Figure 14: Integration of structural and controller models.

Zäh et al. [130], [131], [132] developed a Finite-Element-Model of the feed drive and simulated the performance of the axis control law under the influence of structural vibra-tions received by the position sensor.

2.6.3 Coupled flexible multi-body simulation The coupled flexible multi-body simulation is used to simulate the dynamic behaviour of the machine taking into account the behaviour of the control loops of the drives [48], [80], [115]. The models of the single compo-nents of the machine tool can represent the static as well as the dynamic behaviour and are coupled by flexible connectors. In reality, guiding systems and bearings ap-pear as joints between the components. These joints are approximated by spring-damper-elements in the flexible multi-body model. For example, for each guide shoe be-tween two structural components one spring-damper element with stiffness and damping values in the X, Y and Z-direction is defined. To consider the influence of the individual drives of the machine tool on the dynamic behaviour, the flexible multi-body model is coupled with a model of the control loops via an interface [14], [115], [126]. Different research activities in the field of coupled flexible multi-body simulation have been done by Reinhart et al. [14], [80], Weck et al. [108], [109], [110], [115], [116], [126], Großmann et al. [47], [49], Denkena et al. [33], [34] [100] and Turna . The model set-up as well as the different types of simula-tions are discussed in the next sections.

2.6.3.1 Model configuration Each structural component of the machine tool is mod-elled as a so-called flexible body [31], [115], [116]. The different elements which are used to connect the struc-tural components, such as guiding systems, mounting devices or ball-screw-drives, are modelled as a combina-tion of flexible connectors and joints depending on the specific configuration [14]. The individual flexible components of the multi-body model are connected by these flexible connectors de-pending on the direction of the internal force of the com-ponent (1D-element or 3D-element). The different model techniques of the different connectors in multi-body mod-els are pictured in Figure 15. Some typical modelling techniques of popular machine components are specified below. Mounting devices In most technical applications the machine tool is mounted with special mounting devices onto the founda-tion. The stiffness and the damping in three directions

have a strong influence on the dynamic behaviour of the machine tool. These components are modelled by three dimensional spring-damper-elements [126]. Guiding systems The guiding systems are used to determine a defined movement of different machine components relative to each other. Guiding systems are also modelled by 3D-spring-damper-elements. Parameters of these elements are the stiffness in two directions, perpendicular and transverse to the direction of movement. The stiffness in the direction of movement is nearly zero. The damping of such a guiding system is considered in three directions [126], [14].

{ } [ ] { } [ ] { } { }vFuDukF +⋅+⋅= &

F

F

F

F

k

k

D

D

fixedbearing

ball screwspindle

spindle nut nut stiffness

Mh

2Fa ⋅⎟⎠⎞

⎜⎝⎛ ⋅

=π

F

Fh

F

F

k D + +

D , L

AEk ⋅=

+F

F

k DM

L(t)

MOUNTING DEVICESMOUNTING DEVICES

DRIVESDRIVES

GUIDING SYSTEMSGUIDING SYSTEMS

{ } [ ] { } [ ] { } { }vFuDukF +⋅+⋅= &

Figure 15: Model configuration for the flexible MBS. Ball-screw-drives These drives are used to realise translational movement of machine axes. Different components are used in such a drive system. The bearings and the ball screw-nut are modelled with 3D-spring-damper-elements with stiffness and damping parameters in all directions. The screw is modelled using flexible beam elements, which are able to rotate about the pitch attitude. The rotation of the screw, which is caused by the model of the servodrive in the control model, is transformed into a translational move-ment by the use of a nut. Thus it is possible to simulate the dynamic behaviour of such systems [113], [115], [116].

2.6.3.2 Generation of flexible multi-bodies To consider the flexibility of the machine components during the multi-body simulation, data from natural vibra-tion and deformation calculations of the individual compo-nents, the so-called Superelement Creation, are inte-grated in the multi-body model through an interface of the multi-body simulation program to popular Finite-Element-Programs [14], [76], [115] [116]. Superelement Creation uses a Finite-Element-Model to define a component of a complex structure, and a con-nection degree of freedom set (DOF) to specify the inter-face nodes, or attachment points, of the component to other components of the structural system and points where forces are applied. The software calculates fixed normal modes and static constraint modes to approximate the general behaviour of the component at those “inter-face node degrees of freedom”. The fixed normal modes contain the dynamic response of the superelement when all “connection degrees of free-dom” are fixed. The static constraint modes contain the static response assumed by the component when one degree of freedom of one interface point is given a unit deflection while fixing all other “interface degrees of free-

dom”. The solver performs Superelement Creation much like normal modes analysis using the Lanczos method, then uses the Craig-Bampton method to generate the superelement [31]. The different modes of a super-element creation are illustrated in Figure 16.

⎭⎬⎫

⎩⎨⎧⋅⎥

⎦

⎤⎢⎣

⎡=

⎭⎬⎫

⎩⎨⎧

=N

C

INICI

B

qq0E

uu

uΦΦ

Boundary-conditions(Craig-Bampton)

yzx

u physical DOFuB boundary DOFuI interior DOFE,0 Identity and zero matrices

ICΦ physical displacements of the interiot DOF

in the constraint modes

INΦ physical displacement of the interior DOF

in the normal modesqC modal coordinates of the constraint modesqN modal coordinates of the normal modes

Constraint modes

Unit translationof the hinge inx-direction

Unit translationof the guidewayin x-direction

f=1240 Hz

f=2275 Hz

Fixed-boundary normal modes

Figure 16: The Craig-Bampton theorem for the flexible

multi-body simulation. For the Craig-Bampton (CB) solution option, processing concludes at this point; the reduced mass and stiffness matrices as well as the fixed normal modes and static constraint modes are stored in an output file for the inter-face to the multi-body simulation program. Tönshoff et al. [100] developed an alternative approach to model the elasto-kinetic behaviour of machine tool struc-tures based on the theory of flexible multi-bodies.

2.6.3.3 Coupling of multi-body models with control loops To consider the dynamic behaviour of the control loop a coupling to commercial Computer-Aided-Control-Engi-neering (CACE) programs is possible with common multi-body simulation programs [34], [48], [110]. Especially for machines with linear direct drives, where no mechanical transfer elements occur, the consideration of the control loops is necessary for the approximation of the drive system stiffness [108], [110], [126]. The drive control loops generated in the CACE environment can communi-cate with the complete machine model in the multi-body system. Figure 17 depicts the general structure of this coupling for the coupled flexible multi-body simulation of machine tools.

flexible multi-body model

0 1,0

0

Time

Forc

e

force excitation TCP

displacement TCP

0 1,0

0

Time

Dis

plac

emen

t

zyx

zyx

control loop of the direct drive (x-y)

xist

control loop of the ball screw drive (z)zsoll

- -

isoll

current controller

velocity controller

position controllerzist

KLKp,TnpKi, Tni igesRA,LAKM

KE

--

uA

nist

control loop of the direct drive (x-y)ssoll 1

- -

isoll

Fa

position controller

KLKp TnpKi,Tni

s-

current controller

KF RA ,Tel

velocity controller

xist

x ist

A

,

-

uA

KE

iA

control loop of the direct drive (x-y)

xist

control loop of the ball screw drive (z)zsoll

- -

isoll

current controller

velocity controller

position controllerzist

KLKp,TnpKi, Tni igesRA,LAKM

KE

--

uA

nist

control loop of the direct drive (x-y)ssoll 1

- -

isoll

Fa

position controller

KLKp TnpKi,Tni

s-

current controller

KF RA ,Tel

velocity controller

xist

x ist

A

,

-

uA

KE

iA

Figure 17: Coupling of flexible multi-boidy models and

control loops.

The entire control system (incl. all non-linearities) delivers the resulting drive power of each axis to the multi-body system. The control loop itself is closed with the help of the velocities and displacements of the axes determined from the multi-body system.

2.6.3.4 Results of the coupled flexible multi-body simula-tion For the simulation of flexibility frequency response func-tions of the coupled flexible multi-body model, an excita-tion signal must additionally be defined. For this purpose, so-called INPUTS and OUTPUTS have to be generated. In the INPUT, a value is controlled from the outside for each time step during the calculation. Through the OUTPUT that can be applied as a force in the X-, Y- and Z-direction at any location of the multi-body model, the outer signal is directed into the structure [14], [47], [108], [110], [115], [126]. In case of machine tools an excitation at the machining interface (tool centre point) is useful, because it corre-sponds to the method for experimental investigations and best depicts the excitation through machining forces in the chip removal process [108], [114], [115]. Basically, sinus wobbles, noise or an impulse are considered as excitation signal types [114]. These frequency response functions are useful for the estimation of the interaction between the mechanical structure and the control during the design stage, as well as for the estimation of the influence of the controller parameters on the dynamic behaviour at the tool centre point [126], see Figure 18.

Simulation Resultssimulation of frequency response functions (FRF)

estimation of interactions between mechanical structure and control

influence of the controller settings on the dynamic behaviour at the tool centre point (TCP)

overshooting of the feed drives

0 100 200Frequency [Hz]

Com

plia

nce

[um

/N]

Lineardrive

Z-AxisKM =0,93 Nm/AKL =70 1/sKP =2,71 Nms/radTnp =10 ms

KF =103 N/AK L =70 1/sK P =3500 As/mTnp =8 ms

without control loopwith control loop

Figure 18: Simulated frequency response function

Especially for machine tools with small workspace dimen-sions, the potential of the installed drive power can only be used efficiently at high jerk settings. To optimise the dynamic behaviour of machine tools the coupled flexible multi-body simulation can be used to analyse the maxi-mum jerk settings of the feed drives. Therefore an input-signal for the control loops of the drives can be generated by a virtual controller. The simulation of such a positioning operation is illus-trated in Figure 19.

0

0

jerk

Time

[m/s

³]

00

velocity

[m/s

]

00

position

[m]

0

acceleration

[m/s

²]

Time

Time Time

Positioning operation of the Z-unit (5mm)

M (t)

F (t)

F (t)

Input

0

control loopz-axiscontrol loopz-axis

control looplinear drive 1control looplinear direct

drive 1∆=0

control looplinear drive 2control looplinear directdrive 2∆= 0

Figure 19: Simulation of a positioning operation. The influence of the jerk on the path deviation during a positioning operation was investigated in this case. The

desired path of the Z-unit was generated by a model of the controller and used as an input-signal for the control loop of the z-axis with different jerk settings. The z-unit started at standstill and was accelerated to the maximum speed of the z-drive. After a short movement with con-stant velocity the drive was decelerated to standstill. The results of this simulation are shown in Figure 20.

Time [sec]

Dis

plac

emen

t [m

m]

r=730 m/s³r=650 m/s³r=550 m/s³r=450 m/s³desired path

Excitation of the thirdeigenfrequency of themachine Frequency [Hz]

Com

plia

nce

[um

/N]

Gxx

Gyy

Gzz

displacement FRF

T3 = f3

Figure 20: Simulation results of a positioning operation. Such positioning operations always excite natural fre-quencies of the machine tool, which can lead to devia-tions of the desired tolerances of the workpiece or even to damaged tools dependent on the amplitude of the vibra-tion [14], [108], [110], [126]. The evaluation of the simulated vibration signals enables the allocation of the excited natural frequencies and the derivation of arrangements for improvements during the design process.

2.7 Validation and optimisation of the simulation models

Despite the rapid development of the available software tools in recent years, the correct estimation of the simula-tion parameters is still a problem, which limits the accu-racy of the results [107]. The prediction of stiffness and especially of the damping characteristics of machine components is extremely diffi-cult due to their dependence on many different influences, like lubrication, pre-loads or tolerances [53], [68]. Meas-urements of the dynamic behaviour of similar machine tools or components and the validation of existing simula-tion models can help to find better initial values for future simulations. The measurement of the dynamic properties of machine tools usually targets two characteristics [111]: • The Frequency Response Function (FRF) of the

compliance at the tool centre point (TCP) • The mode shapes of the machine with their associ-

ated resonance frequencies and dynamic amplitudes as well as the phase shift

Both characteristics can be measured with special ex-periments as depicted in Figure 21 for the FRF measure-ment. For the determination of the FRF, the TCP is ex-cited with a dynamic actuator and the reaction of the TCP is measured. Via Fast Fourier Transformation (FFT), a frequency spectrum or a locus curve can be generated. The results of both examinations can help the design engineer to validate the simulation models in order to find realistic values for the stiffness and damping behaviour of the machine components. Design modifications to im-prove weak points of the machine can be assessed ana-

lytically before they are implemented in the current design or in the next machine generation.

x F

Amplifier

A/D converter

FFT analyser

Force probe Excitor

• inductiveposition sensor

• accelerometer

Probe

real[µm/N]

0,1

0,1

-0,1-0,1

0.001

0 200 800frequency [Hz]

phas

e [°

]

180

-180

0

cohe

renc

eco

mpl

ianc

e[µ

m/N

]

1

0

Bode diagram

locus

imag

inar

y[µ

m/N

]

• strain gauge• piezo sensor

• impulse hammer• piezo actuator• hydraulic actuator

Amplifier

Figure 21: Measuring of a frequency response function. The calibration of simulation models, especially the pa-rameters of spring-damper-elements (stiffness- and damping-coefficients) is extremely difficult and very time-consuming. For the described example of the machine tool in Figure 15 the flexible multi-body model contains 48 different parameters to model the mounting devices, the guiding systems, different bearings and the mechanical components of the ball screw drive. It is obvious that a manual calibration of such complex simulation models of machine tools is nearly impossible. Witt and Brecher [24] developed an approach for an automated optimisation of simulation models with the help of measured frequency response functions. To match the results of the simulation and the measuring it is possible to model the stiffness and damping parameters as design variables and optimise them by using numerical optimisa-tion methods, e.g sequential quadratic programming (SQP). The design goal of this optimisation is the minimi-sation of the deviation of the measured and the simulated frequency response function. The principle approach of this optimisation is illustrated in the following Figure 22. Measuring of the Measuring of the Frequency Response Frequency Response Function Function

Coupled flexible Coupled flexible MultiMulti--Body Model of Body Model of the machine toolthe machine tool

Simulated Simulated FrequencyFrequency--ResponseResponse--FunctionFunction

ConvergenceConvergence

yes

no

Optimised parameters of the model: [K]actual, [D]actual

Optimised parameters of the model: [K]actual, [D]actual

Matching Measuring / SimulationMatching Measuring / SimulationMatching Measuring / Simulation

kax dax krot drot+kax dax krot drot+kax dax krot drot+

Frequency [Hz]

00

Com

plia

nce

[µm

/N]

Iteration1

10

Measured FRF

Measured Measured FrequencyFrequency--ResponseResponse--FunctionFunction

[K]start[D]start

Figure 22: Automated model update with measured fre-quency response functions.

This approach enables the calibration of the machine tool models for the simulation of the interaction between ma-chine tool and process. This kind of simulations requires models of the machine tools which represents the real static and dynamic behaviour in the best possible man-ner.

2.8 Virtual reality in the development process The virtual reality (VR) is mainly used in the automotive industry and as a marketing technique for the consumer goods industry at the present [88], [96], [133]. The auto-motive industry uses the virtual reality increasingly in the field of design and development as a tool for the investi-gation and error diagnostics of complex 3D-CAD designs [86]. Another application is the benchmarking with the help of virtual products [96]. Krause et al. [58] used the virtual reality for the simulation and evaluation of complex assembly and disassembly processes. Furthermore different approaches are known to use the virtual reality for the visualisation of simulation results, e.g. crash-tests or flow investigation in a virtual wind tunnel [19], [58], [86]. In the field of the machine tool industry Tönshoff et al. [99] used the virtual reality for the visualisation of NC-programming simulations in combination with a force feedback for a realistic impression for the user. Weck et al. [23], [108] developed an automated visualisa-tion environment for the evaluation of the machine kine-matics as well as for the results of Finite-Element-Analysis. Figure 23 illustrates the VR-environment for the investiga-tion of machine tools.

Triangulation of the FE-mesh

Import of the FE-Data Extraction of the components

Derivation of the kinematics

movement in x direction

guiding system (ky , kz,

ϕx , ϕy , ϕz)

ball screwdrive (kx)

3D-Visualisation in the “VR”

VR-CaveVR-Cave

Figure 23: VR environment for the investigation of ma-chine tools.

This environment enables the engineer to import Finite-Element-Models of machine tools. The software auto-matically extracts the single structural components and enables the engineer to get a realistic impression of the design.

3 SIMULATION OF THE CNC SYSTEM The CNC system consists of a computer, power electron-ics components, such as motor amplifiers and electronic circuits, and servo actuators. The computer control unit receives ISO standard NC-programs which describe the tool path geometry, tool number, feed and spindle speed at each path segment [72], [76]. Simulation of the CNC system involves virtual modelling of the machine tool kinematics and feed drive dynamics, update of the workpiece geometry as the material is re-moved and motions of the drives and auxiliary units, such as tool and pallet changes. In short, the rigid body motion of the machine tool and the CNC functions must be pre-dicted as the workpiece is produced in order to realize a Virtual CNC system. Once the NC Program is generated in a CAD/CAM envi-ronment, the present Virtual CNC technology allows the

geometric update of the workpiece as the tool cuts the material at each NC block. In addition, the solid model of the machine tool, its multi-axis kinematics and the loca-tion of fixtures can be displayed in the CAD environment [127], [128].

3.1 NC-path simulation The present technology allows the prediction of tool colli-sion spots and correctness of the NC program by check-ing path errors and gauging on the workpiece surface graphically. Lauwers et al. [59], [60], [61], [62] take the CL file from the CAD system and simulate the machine mo-tion by modelling the kinematics of the machine tool for collision detection and avoidance. In some commercial controllers machining simulation systems are integrated. During machining the simulation system runs a number of blocks (e.g. 100) ahead, and if there is a danger of a collision, the controller stops the machine immediately, see Figure 24.

Work-piece

Tool

Machine Head

ClampingTable

CollisionArea

CLDATAfile

NC-program

N100 G01 X..Y..Z..A..B..

Postprocessor module

x,y,z,i,j,k

Kinematics engine

NC-formatting

Collisionavoidance

NC-simulation

N 50 G17N 55 F1000 S1000 G00 X-364.94 Y-61.67 Z150. M03N 60 G00 Z100.N 65 G01 Z0.N 70 X-359.94N 75 G03 X-324.94 Y-26.67 I0. J35.N 80 G01 Y84.N 85 G03 X-346. Y105.06 I-21.06 J0.N 90 G01 X-506.303N 95 G03 X-513.416 Y87.887 I0. J-10.06N 100 G01 X-480.648 Y55.118N 105 G02 X-477.729 Y48.678 I-7.099 J-7.099N 110 G03 X-460.589 Y-115.162 12134.642 J140.491N 115 G02 X-463.428 Y-123.689 I-9.938 J-1.428N 120 G01 X-487.625 Y-147.887N 125 G03 X-480.511 Y-165.06 I7.113 J-7.113N 130 G01 X-357N 135 G03 X-324.94 Y-133. I0. J32.06N 140 Go1 Y-22.33N 145 G03 X-359.94 Y12.67 I-35. J0.N 150 G01 G40 X-364.94N 155 G00 Z100.N 160 G00 X204.94 Y-34.755N 165 G01 Z0.N 170 G41 X199.94N 175 G03 X164.94 Y-69.755 I0. J-35.N 180 G01 Y-162.132N 185 G03 X167.887 Y-169.246 I10.06 J0.N 190 G01 X185.557 Y-186.916N 195 G03 X190.362 Y-186.519 I2.234 J2.234N 200 G01 X193.875 Y-181.606N 205 G02 X195.145 Y-180.149 I8.167 J-5.84N 210 G01 X206.296 Y-169.61N 215 G02 X231.316 Y-166.338 I14.767 J-15.625N 220 G02 X243.573 Y-174.115 I-50.726 J-93.491N 225 G03 X248.965 Y-175.801 I5.152 J7.011N 230 G03 X251.841 Y-174.534 I-0.115 J4.158

Section Index

Part Program Tape

Section beingmachined

Section beingSimulated

CNC

Section Index

Look

Ahe

ad D

ista

nce

Figure 24: Integration of NC-simulation and controller. However, a realistic simulation of machine tool motion and accurate prediction of final part geometry requires the inclusion of real time trajectory generation, dynamic be-haviour of actuators under axis control laws and cutting process disturbances. The architecture of the tool motion processing sequence in a typical CNC system is given by Altintas [4], [41], [42] [43], see Figure 25. The path segment is broken into discrete position commands as a function of jerk, accel-eration and feed speed by the trajectory generation algo-rithms of the CNC. Here, it is important not to violate jerk-acceleration and speed of individual drives which partici-pate in moving the tool along the specified path. If the axes limits are violated, the saturation of the actuators may cause deviations from the commanded path as well

as feed fluctuations which lead to poor surface finish marks on the workpiece. Smooth trajectory generation, especially in multi-axis contour machining of sculptured surfaces, are still subject to intensive research for high speed machining of dies, molds and aerospace parts to achieve good surface finish [41].

Position closed-loop

--

++

CAD/CAMSoftware Interpreter

CAD Model CL/APT FileN1 G00 X5 Y1N2 G01 X3 Y3N3 G03 X4 Y3 I1 J0...

x

y

s

x

ys

x

yTool path geometry

Feed motion planningDisplacement

Feedrate

Acceleration

JerkS...

S..

S.

St

t

t

t

Referenceposition

Controlsignal

Actual PositionAxis

Control LawFeed Drive

Servo

FeedbackMeasurements

Feedback

Act

ual P

ositi

onSimulate the contour errors generated from

Servo Control in „Virtual“enviroment

PredictedTrecking

Error

Optimization Process

-Reschedule Feedrate, Accel./Decel., Jerk Limit-Contour Error Reduction

Re-

proc

ess

r(t), r.(t),r..(t), r...(t)

Trajectory Generation

Figure 25: Virtual model of trajectory generation and control of axes positions.

There has been research activities to integrate machine motions and geometric removal of the material from the workpiece so that the part accuracy can be predicted ahead of actual production. Altintas et al. [127], [128] developed a reconfigurable, modular Virtual CNC simulation system by porting the experimentally proven real time algorithms from an actual open CNC. Ball screw or linear motor driven feed drives can be de-fined by specifying mechanical dimensions, servo motor and amplifier parameters, position-velocity-acceleration sensors and their resolution, friction field between the guide and drives and time varying cutting force distur-bances. The type of trajectory generation algorithm, such as “jerk continuous with actuator limits”, can be selected as well as the axis control law.

Experimental Result Simulation

Figure 26: Simulation of milling a spiral part on virtual CNC with marked tolerance violations caused by CNC.

The virtual CNC reads the CL file imported from the CAD/CAM system, and processes the NC program by simulating the physical behaviour of the machine in the prescribed CNC model. It predicts the tolerance violation

spots on the workpiece and the correct cycle time, by including acceleration and deceleration, as well as the time history of axes tracking errors and the acceleration-velocity-displacement of each drive. The Virtual CNC has built in auto-tuning of control laws, and they are currently extending the CNC to 5 axes systems and integrating structural dynamic models of the feed drives to the virtual CNC system [127]. An experimentally verified simulation of a tool path within the Virtual CNC is shown in Figure 26 for a spiral part. The green zones represent the tolerance violations caused by the contouring errors of the CNC [128]. Pritschow et al. [76], [77], [78] presented the simulation of an entire machine behaviour under real CNC system control. The actual CNC sends time stamped position commands to a model of the complete machine. Since the position commands contain velocity, acceleration and jerk, they excite the structural dynamics of the machine. The resulting vibrations are sent back to the CNC by mimicking an encoder measurement contaminated with machine tool vibrations.

3.2 Optimisation of NC-Programs for five-axis mill-ing

While it is satisfactory in three-axes machining to gener-ate NC-programs without considering the axial-specific dynamic parameters, practical experience has shown that it is insufficient for five-axis milling. The reasons for this are the highly variant dynamics of the involved rotation, panning, and translation axes [32], [119]. The analysis of NC-programs on different machines with respect to the required axis velocity and acceleration shows that, at positions with high feed rate drops, the dynamic limits of the rotation axes have to be considerably higher in order to follow the programmed path. This discrepancy arises because the CAM-system does not consider the dynamic capabilities of the machine while generating NC-tool paths. Weinert et al. [32], [119], [120], [129] developed an approach for the harmonisation of the rotation and swivel movements. As an intermediate step between CAM-programming and the milling process, the tool path is adjusted, so that at no time are the limits of the dynamic capabilities violated. The principle of this approach is illustrated in Figure 27.

Workpiece

Feed

Workpiece

Figure 27: Adjustment of tool movement to satisfy dy-

namic limits of the five axis machine tool. In addition to the general dynamic parameters especially the control-specific characteristics, which describe the behaviour of consecutive NC-steps, are considered. The manipulation of axes setting values may cause in princi-ple an originally collision-free NC-program to contain collisions between tool, tool holder, machine components, and workpiece. To prevent this, in addition to the optimi-sation algorithm, a process simulation is used, which calculates the intersection of the involved objects during a movement along the NC-path on the basis of a volume model [32], [120], [129].

4 SIMULATION OF METAL CUTTING The manufacturing process research should lead to im-proved design of tools, machine tool structures, spindle and feed drives and the optimal planning of individual machining operations based on physical constraints. The research activities and industrial applications of metal cutting process simulation are presented in the following sections.

The amplitude and frequency of cutting forces, torque and power are used in sizing machine tool structures, spindle and feed drive mechanisms, bearings, motors and drives as well as the shank size of the tools and the fixture rigid-ity. The stress and temperature field in the cutting tool edge, chip and finished work piece surface are used in designing the cutting edge shape as well as in optimising feed, speed and depth of cut to avoid residual stresses on the finished surface. Modelling the interaction between the cutting process and structural vibrations of machine tool, cutting tool and fixture leads to the identification of weak links in the machine structure and to the determina-tion of chatter vibration free spindle speeds and depths of cut [5].

The complete model of the machining process is there-fore used in both design of cutting tools and machine tools, as well as in planning of machining operations for maximum productivity and accuracy.

4.1 Analytical modelling of cutting processes The first step is to model the cutting process as a function of work material, tool geometry and material, chip load and cutting speed. The macro-mechanics of cutting lead to the identification of cutting coefficients, which are used in predicting the cutting forces, torque, power and chatter stability limits for a specified tool geometry and work ma-terial. The cutting coefficients can be modelled using either orthogonal cutting mechanics or mechanistic models [6]. The micro-mechanics of metal cutting on the other hand, are used to predict the stress, strain and temperature distribution in the chip and tool. This simulation results are primarily used for tool design, the analysis of material behaviour under high strain and temperature, and optimal selection of chip load and speed to avoid tool chipping, tool wear, and residual stresses left on the finished sur-face. The directions of cutting forces in turning and milling are given in Figure 28 [8].

Y

X

Chip loadFy(φ)

Fx(φ)

FrjFtj

nf

c

φstφ

φex

dFa

dFr

dFtZ

Y

X

Tool

Workpiecen

f

FaFr

Ft

Figure 28: Prediction of cutting forces for turning and milling operations.

The major cutting forces (Ff) act in the direction of cutting speed, followed by the thrust force (Fr) acting in the direc-tion of chip thickness and the axial force (Fa). The cutting forces are proportional to the instantaneous chip area which is expressed as a product of depth of cut (a) and uncut chip thickness (h). The cutting forces are typically expressed by shear (Ftc, Frc, Fac) and flank con-tact/ploughing (Fte, Ffe. Fae) edge components as

aKahKFFFaKahKFFFaKahKFFF

aeacaeaca

rercrercr

tetctetct

+=+=

+=+=

+=+=

where the chip shearing, cutting force coefficients ( Ktc, Krc, Kac) can be expressed as a function of tool’s rake angle, work material shear stress and average friction coefficient between the chip and tool rake face. The edge force coefficients (Kte, Kre, Kae) are found from cutting tests by extrapolating the measured forces at zero cut thickness (h = 0) intercept. The theory of this approach of analytical modelling of the cutting process can be found in [8]. It is also customary to use nonlinear cutting force coeffi-cients as proposed by Kienzle [55]:

ahKFahKFahKF

aa

rr

tt

=

=

=

where the cutting force coefficients (Kt, Kr, Ka) are usually expressed as a function of rake angle and chip thickness. It is most important to have a cutting coefficient data base which allows the user to select a work material for a vari-ety of tool geometries.

4.2 Numerical simulation of cutting processes For cutting processes involving geometrically defined cutting edges, high speed cutting (HSC) is widely used in aerospace, and the die and mold machining industry. High speed machining allows the operation of machine tool spindles in large stability pockets where deeper cuts are possible. While keeping small chip loads to avoid thermal overload of the tool edge and mechanical over-load of the spindle power limits, high material removal rates can be achieved with high spindle speeds and table feeds while maintaining a good surface finish on the part. However, the practical application of HSC methods de-pends on empirical cutting data which has to be obtained through cost- and time-consuming cutting experiments. The Finite-Element-Method (FEA) is a tool that is suited for optimisation of the cutting edge geometry and mate-rial. Hence the cutting edge can withstand high thermal and impact loads during machining [29]. Finite-Element-Analysis belongs to the class of micro-mechanics of metal cutting and is widely used by the cutting tool industry. However, the key bottle neck is to model the flow stress of the work material reflecting high strain, strain rate and temperature experienced in metal cutting processes. The thermo-plastic properties of the material is usually evalu-ated under high strain rate conditions using either Or-thogonal Cutting Tests or Hopkinson Bar tests [67]. Three main methods of mechanical formulation are com-monly used in Finite-Element-Modelling of metal cutting [12], [122]: • Eulerian formulation, where the grid is not attached to

the material, is computationally efficient but needs the updating of the free chip geometry [55].

• Lagrangian formulation, where the grid is attached to the material, requires updating of the mesh (remesh-ing algorithm) or the use of a chip separation criterion to form a chip from the workpiece [97].

• Arbitrary Lagrangian Eulerian (ALE) formulation, where the grid is not attached to the material and it can move to avoid distortion and update the free chip geometry [67].

A 3D FEA-Simulation of a Milling Process [85], [122] is presented in Figure 29.

3D CAD-Model FEA-Model

3D Simulation of a Milling Process

Figure 29: 3D FEA simulation of a Milling Process.

A successful simulation is dependent on the accurate knowledge of the boundary conditions and the material-behaviour which is different from simple metal models obtained from tensile tests due to the influence of large strain, strain rate, and temperature. In order to achieve an accurate prediction of chip flow, stress and temperature distribution within the chip and tool, an accurate model of flow stress of the material and friction between the rake face of the tool and chip is absolutely necessary. The validity of all numerical models is proven experimentally by comparing predicted forces, average shear angles and shear stresses in metal cutting tests. 5 INTEGRATED SIMULATION OF MACHINE AND

PROCESS Current NC tool path and machining simulation systems consider only the rigid body kinematics of the machine tool, and do not take the physics of the machining proc-ess into consideration. The magnitude of cutting forces, torque, power and thermal energy produced during ma-chining depends on the tool geometry, structural dynam-ics between the workpiece and the tool, work material properties, and cutting conditions such as feed, speed and depth of cut. Currently, the cutting conditions are selected from either tool manufacturers’ handbooks or experience, which may or may not lead to productive and accurate production of parts. The objective of next generation CAM systems is to in-clude the physics of manufacturing processes in order to produce the first part accurately and optimally. A sample architecture for Virtual Machining Process simulation was proposed by Altintas et al. [2] as shown in Figure 30.

The geometric model of the part, blank and NC tool path in the form of a standard CL file are imported from current CAD/CAM systems using IGES or STEP NC standards. The cutter – part intersection along the tool path is evalu-ated at feed rate increments using solid modelling tech-niques. The intersection geometry is required to solve machining process simulation algorithms [93]. The ma-chining process simulation engine is based on the laws of metal cutting mechanics and dynamics, it pulls the re-quired machine tool and work material parameters from the data base and predicts the cutting forces, torque, power, static and dynamic deformations of the machine tool-part-fixture along the tool path. For a given set of constraints, such as maximum power-torque-dynamic stiffness of the machine and chip thickness limit of the cutting edge, the speed and feed can be optimised to maximise the material removal rate.

CAD MODELNC Tool Path

Cutter Geometry

FINAL PROCESS PLAN

Optimized Speed, Feed, Depth,Width, Error

Compensation

PATH PLANNERCL File

Path Strategy Analysis

MONITORING ANDCONTROL DATA

Peak force, torque, power, tracking error,

modal frequencies

Cutter-partintersectioncalculations

Virtual Machining process

simulation

Tool, Material, Machine-Tool

Data Base

CAD MODELNC Tool Path

Cutter Geometry

CAD MODELNC Tool Path

Cutter Geometry

FINAL PROCESS PLAN

Optimized Speed, Feed, Depth,Width, Error

Compensation

FINAL PROCESS PLAN

Optimized Speed, Feed, Depth,Width, Error

Compensation

PATH PLANNERCL File

PATH PLANNERCL File

Path Strategy Analysis

MACHINE

TOOL

MACHINE

TOOL

MONITORING ANDCONTROL DATA

Peak force, torque, power, tracking error,

modal frequencies

Cutter-partintersectioncalculations

Virtual Machining process

simulation

Cutter-partintersectioncalculations

Virtual Machining process

simulation

Tool, Material, Machine-Tool

Data Base

Figure 30: Virtual machining process simulation and opti-misation architecture.

Although intensive research efforts are under way at present, there are several key requirements, that have to be met before a virtual simulation of the machining proc-ess can be realised. The cutter-part intersection along the feed increments requires intensive computational time since the part geometry must be updated as the material is removed at feed increments [45]. Researchers used Constructive Solid Geometry – CSG [93], Boundary Representation – Brep [51], and z- buffer techniques to model material removal [15]. The computa-tional time is rather unaffordable and long at the present time, and considerable research efforts are directed to-wards developing efficient computational models and parallel processing of algorithms at multiple central proc-essing units (CPUs). Although some commercial NC Simulation systems pro-vide feed optimisation, their algorithms are not based on the laws of cutting mechanics, hence they do not repre-sent the true process. However, considerable effort has been undertaken to integrate the true process physics into NC program optimisation. Altintas and Spence presented a 2 ½ axis end milling process simulation system [94]. Altan et al. [15], Spence et al.[95], Weinart et al. [118], [121] and Lazoglu et al. [26] presented a process simula-tion and optimisation strategy for dies and molds. They illustrated that the machining cycle time can be decreased significantly by scheduling feed rates along the tool path while respecting tool deflection, tool breakage, torque and power limits of the machine tool. Altintas et al. [7] pre-sented algorithms which can handle arbitrary cutter shapes in predicting the forces, torque, power and chatter vibrations during milling.

Kapoor and Devor [40], Armarego et al. [11] and a num-ber of researchers presented mechanics of cutting mod-els to predict the cutting forces for milling, turning, drilling, boring and tapping operations. The aim of the present research is to integrate the mechanics of machining into a CAD/CAM system so that the process of machining a complete part can be simulated as shown in Figure 31 [51].

Cutting Tool

ToolpathToolpath

WorkpieceWorkpiece

NC Code:...N9 X-8.0056N10 X- 7.9655 Y49.3901N11 X-6.3125N12 G3 X28.2708 Y49.1355 I17.3496

J7.7454N13 G1 X42.8735N14 G3 X102. Y- 7.5278 I67.1265 J10.8645N15 G1 Y-8.N16 X23.083N17 Y-3.2N18 Y1.6...

NC Code:...N9 X-8.0056N10 X- 7.9655 Y49.3901N11 X-6.3125N12 G3 X28.2708 Y49.1355 I17.3496

J7.7454N13 G1 X42.8735N14 G3 X102. Y- 7.5278 I67.1265 J10.8645N15 G1 Y-8.N16 X23.083N17 Y-3.2N18 Y1.6...

Figure 31: Simulation of virtual machining of a part with features.

Similar to machining, the process forces during forming and grinding have also been studied, however mainly for process and machine design purposes. The goal of virtual production is to integrate all steps of the manufacturing cycle into the simulation environment in order to achieve a true digital factory.

5.1 Simulation of chatter vibrations in cutting The dynamics of the machine tool have a major influence on the productivity of machine tools. The designers must consider the interaction between the process and the structure in the virtual environment so that the optimal dynamic stiffness is achieved during the design stage of the machine and spindle system [9]. While the major parts of the machine tool, such as col-umn, headstock and table dynamics influence the stability of low speed machining with large cutters, the stability of high speed machining is usually determined by the dy-namic behaviour of the spindle-bearing-system and the tool. The dynamic stiffness of the spindle-bearing-tool assembly can be improved by optimising the locations of the bearing and direct drive motor along the shaft [63]. Typically, a Finite Element model of the prototype spindle is modelled by including kinematics of the angular contact bearings, speed effects and preload. The validity of the Finite Element model is tested experimentally, and the mathematical model is improved until realistic results are obtained. Only the damping ratios of the spindle are bor-rowed from the measurements collected from past spindle designs, since it is not possible to predict the damping analytically. The FE model as well as the predicted and measured Frequency Response Function of a sample spindle are given in Figure 32 [27]. The locations of the bearings are automatically optimised either to achieve maximum dy-namic stiffness in all major natural modes, or a stable stability pocket is created at the desired speed for a given spindle and cutting tool pair, see Figure 32 [63]. While maximising the dynamic stiffness is preferred for machines which need to use multiple tools, maximum

material removal rate at the desired speed is preferred for dedicated machine tools for mass production of parts like in the automotive industry. Once the spindle is designed, its performance can be tested in the virtual environment by applying cutting forces at the tool tip. The results are illustrated in Figure 32.

ShaftHousing BearingHydraulic fluid

ToolholderTool

Spindle nose

Pulley

500 1000 1500 2000 2500 30000

1

2

3

4x 10-8

Frequency [Hz]FR

F-M

agni

tude

[m/N

] ExperimentSimulation

Figure 32: FRF-Simulation of a spindle. The stiffness changes and contact forces at the bearings and static and dynamic displacements along the spindle shaft assembly can be simulated instead of manufactur-ing and testing the spindle on a real machine which is a lengthy and costly process. Figure 33 shows the optimisation of the bearing locations to achieve maximum depth of cut at 9000 rev/min spindle speed for a four fluted end mill machining aluminium alloy, and a simulation of bearing contact loads during milling with the same tool [10]. The spindle was unstable at the desired spindle speed of 9000 rev/min before the optimisation of bearing locations.

2000 4000 6000 8000 10000 120000

2

4

6

8

Spindle speed [rpm]

Dep

th o

f cut

[mm

]

Initial design 1Initial design 2Initial design 3Optimized design Desired

Cutting Potint

0 0.01 0.02 0.03 0.04 0.050

50

100

150

200

Con

tact

forc

e [N

]

Time [s]

Bearing 1Bearing 2Bearing 3Bearing 4Bearing 5

Preload period After cutting force is applied

Figure 33: Virtual design and testing of spindles.

Another example is shown in Figure 34 where the spindle and tooling are specifically designed to machine alumin-ium aerospace parts [22], [117]. The stability of HPC-processes with high spindle speeds is mainly determined by the dynamic behaviour of the spindle-bearing-system and the tool. In this case the dynamic behaviour of the structural components of the machine tool is of secondary importance. But especially the static and dynamic flexibility of spindle-bearing-systems for high rotational speeds up to 30,000 min-1 can hardly be optimised, because an increase of the spindle diameter is limited by the kinematic and thermal behav-iour of the spindle bearings. However, the process stability can be significantly im-proved by a selective setting of the machining parame-ters. In particular, the variation of the spindle speed ac-cording to so-called stability charts is an effective method to enhance the performance of machining processes. Stability charts can either be determined experimentally or they can be calculated on the basis of the dynamic flexibility behaviour given in the form of a flexibility fre-quency response function. Due to the fact that the experimental measurement of the dynamic behaviour of a spindle-bearing-system for each tool is very time-consuming, a simulation software was developed to calculate the flexibility frequency response function of spindle bearing systems on the basis of a beam FEA model. The bearings are modelled as spring-damper-elements in the FEA model. It is useful to match the stiffness and the damping parameters of the bearings with the results of a measurement for one spindle tool configuration. Using this matched model the dynamic flexibility behaviour even for a large number of different tools can be determined efficiently without time-consuming measurements [117]. With a supplementary program for the simulation of the stability behaviour of milling processes a complete simu-lation chain for the calculation of stability lobes is avail-able, as illustrated in Figure 34.

Workpiece with Chatter MarksModular FE-Model of the Spindle-Bearing-System

b cr [

mm

]

n [min-1]f [Hz]

G [µ

m/N

]j [

°]

GF x

GF x

GF x

GF y

GF y

GF y

GF z

GF z

GF z

x(t)

y(t)

z(t)

Fx(t)

Fy(t)

Fz(t)

x

x

x

y

y

z

y

z

z

dzF (t)

dzF (t)

dzF (t)

kcb

kcb

kcb

b

b

b

Tt

Tt

Tt

dyF (t)

dyF (t)

dyF (t)

dxF (t)

dxF (t)

dxF (t)

z

y

y

y

z

z

x

x

x

stable

unstable

Stability LobeDynamic Flexibility Stability Simulation

Figure 34: Simulation of stability chart for the milling of aluminium aerospace parts.

For HPC processes of aluminium parts typically tools with two or three cutting edges are used which are character-ised by a time varying behaviour. In this case the time varying behaviour is caused by the change of the cutting force direction. For this reason time domain simulation techniques are used for the simulation of the stability of the cutting process. For this simulation the simulated dynamic behaviour of the spindle-bearing-system is used as an input. With the help of this simulation chain the theory of the stability behaviour of cutting processes which is known for a long time becomes applicable for end-users in the area

of HPC, i.e. the manufacturing of aluminium parts for the aircraft industry with high material removal rates. Different results of a simulation of stability lobes for the HPC machining of aluminium are shown in Figure 35.

0

5

10

15

18000 19000 20000 21000 22000 23000

axia

l dep

th o

f cut

, a p

[mm

]

stable

0

5

10

15

18000 19000 20000 21000 22000 23000

spindle speed [min-1]

axia

l dep

th o

f cut

, a p

[mm

]

Experimental ResultsSimulation

Stable ProcessChattering

stable

unstable

Good Correlation between Measurement and Simulation

Bad Correlation between Measurement and Simulation

spindle speed [min-1]

20

179

feed rate fz=0,18 mm feed rate fz=0,18 mm

16

166

unstable

Experimental ResultsSimulation

Stable ProcessChattering

Figure 35: Simulated and measured stability lobes for the HPC machining of aluminium.

As illustrated in Figure 35 the results of the stability simu-lation of high performance processes often have varia-tions in the accuracy. An essential part of the cutting process and stability simulation are the time varying direc-tion factors diFj, which project the forces at each cutting edge into the machine coordinates. Furthermore, the cutting forces are determined by the cutting force coeffi-cient kcb and the cutting depth b. The theoretical back-ground of these effects are still unexplored for HPC-machining processes and requires intensive investiga-tions [117].

5.2 Frequency and Time domain simulation of ma-chine tool and process

The simulation of machining process is done in two modes: rigid or flexible models of the machine tool. The rigid simulation does not consider the interaction between the machine structure and the cutting process, hence the predicted cutting forces, torque and power only can be used for basic process planning of the machining opera-tions. As discussed earlier, the cutter – part intersection along the tool path must be identified at feed rate incre-ments for the process simulation [2], [3], [28]. However, in realistic process planning as well as machine tool/spindle/tool design, the relative elastic displacements between the cutting tool and part must be considered. The vibrations lead to changes in the chip thickness, which in turn vary the cutting forces that excite the struc-ture. If the process becomes unstable with chatter vibra-tions, the cutting load on the machine may grow a few times more than the rigid case and leads to poor surface finish, short tool life and damage on the spindle/machine structure [6]. While Frequency Domain chatter stability solutions pro-vide a direct relationship between the dynamic stiffness of the machine and the process, the time domain simulation allows prediction of dynamic cutting forces and dimen-sional surface errors for complex tools and processes while machining a specific part under defined cutting conditions. A sample prediction of stability lobes in both frequency and time domain for an indexed cutter milling aluminium alloy is shown in Figure 36. The simulation also shows predicted and experimentally measured dimensional form errors at one specific cutting condition [7].

1000 2000 3000 4000 5000 6000 7000

Surface Roughness

0

1000

0

500

Rmax=12 um

FFT for Resultant Force

(9500 rpm)(A=7mm)

(1400 rpm)(A=7mm)

AnalyticalTime domain

Rotation Angel [deg]

Y [u

m]

5-5

15

3

Z [mm](axial direction)

21

0 0 0,5 Z [mm](feed direction)

1 1,5 2 2,5 3

200 400 600 800 1400 1600 1800 2000Frequency [Hz]

ChatterFrequency(1448 Hz)

00

20

40

60

80

100[Amp.]

Exeperimental Resultant Force1500

[N]

1000 2000 3000 4000 5000 6000 7000

Surface Roughness

0

1000

0

500

Rmax=2 um

FFT for Resultant Force

Rotation Angel [deg]

Y [u

m]

5-5

15

3

Z [mm](axial direction)

21

0 0 0,5 Z [mm](feed direction)

1 1,5 2 2,5 3

200 400 600 800 1400 1600 1800 2000Frequency [Hz]00

20

40

60

80

100[Amp.]

Exeperimental Resultant Force1500

[N]

Stability Lobes for Bull Noes Cutter and Al7075

00 2000 4000 6000 8000 10000 12000 14000Spindle speed [rev/min]

16000

1

2

3

4

5

6

Axi

al d

epth

of c

ut [m

m]

Tooth PassingFrequency(467 Hz)

Figure 36: Chatter stability, force, vibration and surface error prediction in milling.

The details of the chatter vibrations for metal cutting and grinding are given by Tlusty [98], Altintas et al. [9], and Inasaki et al. [52] in previous CIRP key note papers. Nowadays the simulation of single processes or machine characteristics is state of the art. Generally, these simula-tions are carried out separately for the process as well as for the ma-chine tool. Interactions between machine tool, workpiece and process cause variations of the tolerances and characteristics of the workpiece, which are not taken into account by common simulation approaches [25]. It would be of great economic interest for the design of machine tools as well as for process planning if the result-ing quality of the workpiece was predictable prior to the start of production. The principle procedure of an inte-grated Simulation of machine tool, workpiece and process in time domain is shown in Figure 37.

Drives Machine Tool

Workpiece FPro.

Process

∆

Disp.

FDrive

Vel.

-

F(t)f

xd

t

F

0

Integrated Simulation ofMachine Tool, Workpieceand Process

ResultsQuality and Tolerances Process Stability

FPro.

∆S&

SG01 x100 y50 z10G01 x101 y50 z10

CNC

stableunstablelimit of stability

reference

result

Dep

th o

f Cut

[mm

]

Figure 37: Integrated simulation of machine tool, work-piece and process.

An analysis and optimisation of the production process is only possible if all interactions between machine tool, workpiece and process can be simulated accurately. Due to its time-dependent behaviour the simulation of the

machine tool and process has to be carried out in time domain. The aim of the research project SindBap is to develop an approach for the integrated simulation and optimisation of industrial processes [25]. This co-operative project is founded by the German Federal Ministry of Education and Research. For the integrated analysis and optimisation of industrial production processes time domain simulation models of the process and the machine tool as well as the workpiece are coupled. The cutting forces cause a rela-tive displacement between tool and workpiece which changes the instantaneous chip area which affects the cutting process again. This approach enables the investi-gation of effects of the machine tool, the workpiece and the process. Denkena et al. [33], [35], [37], [101] developed the cutting simulation system CutS which combines different simula-tion environments, see Figure 38. The approach for a coupled simulation of the manufactur-ing process is to combine separate simulation models via interfaces and also to include the supporting software tools, e.g. FEA-systems for the simulation of the manu-facturing process [36].

Data exchange

Figure 38: Environment for the coupled simulation of machine tool and process.

The advantage of such an architecture is a relatively simple exchangeability of single simulation sub models. Through variation of model parts, modelling and calcula-tion techniques the possibility of studies concerning model complexity and extent is given. Due to the non-linear system behaviour, the simulation has to be solved in the time domain [37], [101]. The data flow of such a coupled simulation is shown in Figure 39. Input data for such a system in general is the NC-code derived from a CAM-system which is converted in the virtual NC-kernel. In this part simulation, nominal values for the drives of the machine tool are generated. The simulation module of the Control/Drives generates the force of each drive which act on the model of the machine tool [37], [101]. The process forces are applied on the machine structure which results in a displacement at the tool centre point. This displacement changes the instantaneous chip area which leads to changed cutting forces. To simulate these interactions between machine tool and process, forces and displacements are exchanged via interfaces at each simulation step between the modules [37], [101].

For the simulation of the manufacturing process either an analytical, an empirical or a semi-empirical approach can be integrated.

ForcesMotions

Forces

Positions/Velocities

Simulation ModuleControl/Drives

Simulation ModuleCutting Process

Simulation ModuleMachine Tool Structure

VirtualNC-Kernel

Nom

inal valuesN

C-C

ode

Figure 39: Principle approach for the coupled simulation of cutting process and machine tool.

Machine process interaction is facing the challenge to increase the speed of both the single simulation models and the data exchange. Apart from the uncertainties within the separate simulation modules concerning e.g. damping in machine tools [38] or the material parameters for cutting [39], the main problem is the high amount of calculation operations in the material removal scenario due to the high resolution of the material removal sce-nario. 6 RESEARCH CHALLENGES: “THE VIRTUAL

WORKPIECE PRODUCTION” As mentioned above the interaction between machine tool and manufacturing process causes variations of the char-acteristics of the workpieces. It would be of great economic interest for the design of machine tools as well as for the design of single proc-esses or complete process chains if the resulting quality of the workpiece was predictable prior to the start of pro-duction. The aim is to determine the ideal process pa-rameters for each step of the process chain to fulfill the required tolerances and characteristics of the workpiece. Especially for the large-volume production and the pro-duction of extremely complex, or very expensive compo-nents, the simulation and optimisation of single process-ing steps as well as the complete process chain is of particular importance. Nowadays different simulations of single processes and machines are state of the art in many industrial fields. The quality of the simulation result depends on the respective standard of knowledge. Many research activities today concentrate on the cou-pled simulation of manufacturing process and machine tool, but without any industrial application. Until now the integrated simulation of the interaction be-tween machine tool, manufacturing process, workpiece, fixture, and the history of the single manufacturing proc-esses is not realised. Thus it is not possible to simulate the workpiece quality in consideration of the individual steps of an industrial proc-ess chain. A possible scenario of a simulated process chain for the manufacturing of a gearshaft is shown in Figure 40.

To realise the industrial application of the integrated simu-lation of workpiece properties both the simulation of the machine process interaction and the simulation of the workpiece properties have to be improved in the future.

Rough Part

planned process chain

Integrated simulation and optimisation of the process chainIntegrated Simulation and Optimisation of the Process Chain

ForgingRough-

Machining HardeningHard-

Machining Grinding Measuring

Workpiece Properties

Finished Part

Figure 40: Scenario of a simulated process chain. For an integrated modelling of the machine tool and manufacturing system, first research studies exist. The necessary further developments are integrated methods, improved models for machine tools, processes, work-pieces, clamping systems, controls and tools as well as models for the entire process chain. 7 CONCLUSIONS The aim of virtual machine tool engineering is to design, test, optimise, control and machine parts in a computer simulation environment. The machine is designed in a CAD environment. The CAD model is exported to Finite Element system for the structural analysis of the machine tool statically and dy-namically. The Finite Element model is reduced to a multi-body model of the machine which consists of rigid links con-nected via flexible springs. The rigid and flexible machine tool models are analysed under various jerk, acceleration, velocity and control profiles at high speeds. The interac-tion between the specific CNC control model and machine tool structure can be simulated, and either the machine tool or control system, or both, can be modified based on the simulation. The digital model of the machine tool is integrated to the numerical simulation of the cutting proc-ess, hence the machine tool can be tested to machine particular parts under desired cutting conditions. The present technology allows Finite Element, multi-body, kinematics and control engineering concepts. However, the virtual machine tool technology still requires fundamental research in the area of process simulation, integration of all analysis modules in a user friendly simu-lation program for the users. This goal is being rapidly realised by the research community at the present. 8 ACKNOWLEDGMENTS The authors wish to thank Professors Arrazola, van Brus-sel, Denkena, Fleischer, Groche, Klocke, Lauwers, Pritschow, Weinert and all colleagues and industrial com-panies who sent valuable contributions for the preparation of the article.

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