Virtual Machine Tool
Y. Altintas1 (1), C. Brecher2, M. Weck2 (1), S. Witt2
Manufacturing Automation Laboratory-The University of British Columbia
Department of Mechanical Engineering, Vancouver, Canada
2
Laboratory for Machine Tools and Production Engineering, Chair for Machine Tools
Aachen University of Technology, Aachen, Germany
1
Abstract
This paper presents current state of Virtual Machine Tool Technology and related ongoing research challenges. The structural analysis of machine tools using Finite Element models and their experimental calibration 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 conditions 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 produce 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 economically 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 prototype 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 process and exercising design variations until the performance requirements are achieved, reduce the whole product development time and cost significantly. The advantages and the potentials of time savings by virtual prototypes are illustrated in Figure 1.
V2
V1
CONCEPT
DESIGN
PHYSICAL
PROTOTYPE
TESTING
CHANGE OF
DESIGN
CHANGE OF
PROTOTYPE
SETTING-UP
OPERATION
TRADITIONAL DEVELOPMENT TIME
DEVELOPMENT TIME WITH VIRTUAL PROTOTYPES
VIRTUAL
PROTOTYPING
VERIFICATION
CONCEPT
DESIGN
TIME SAVING
START OF PRODUCTION
PHYSICAL
PHYSICAL
PROTOTYPE
PROTOTYPE
TESTING
SETTING-UP
OPERATION
V2
V1
Figure 1: Comparison of the traditional design process and the design process with virtual prototypes.
Mechanics
Product
requirements
Process
Requirements on
Machine Tools
„
Fx
„
Control Loop
„
„
high static and
dynamic stiffness
high dynamic
properties of
the feed drives
high accuracy
low path
deflections
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 simulations 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 simulation of product properties has been enhanced significantly
Calculation of
Components
Finite-Element-Analysis
and Optimisation
Coupled flexible
Multi-Body-Simulation
Multi-Body-Simulation
z
y
∆
x
Control Loop
F(t)
FE-Beam-Model of the Spindle
Control Loop
F Drive (1)
∆
F Drive (2)
∆
Fx
Control Loop
M Drive (3)
1. Eigenfrequency f=331 Hz
t
Re
a
Matching of Simulation
and Measuring
2
1
1 Simulation
2 Measuring
Phase
y-axis [mm]
acceleration
Design
Compliance [um/N]
Con
c
ep
3D-CAD Design and
Kinematics Optimisation
n
atio
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 dynamics, computer numerical control system and the machining process as shown in Figure 2.
in recent years [114]. Advanced software and hardware
systems allow design engineers to evaluate and optimise
critical product characteristics with virtual prototypes before 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.
lis
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 machine 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 optimisation of the machine tool elements are explained. The
simulation model of the CNC system is presented in Section 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 stresstemperature 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 challenges 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”.
x-axis [mm]
Frequency [Hz]
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 traditional cartesian machine tools, and thus offer huge potential for optimisation. The 3D-CAD-Model of the machine
tool is exported to a kinematic analysis software environment. 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 FiniteElement-Method, are used effectively to find optimum
design variants under given restrictions, e.g. the minimisation of masses of moving machine components or the
maximisation of the static stiffness. The Finite-ElementAnalysis as well as the application of structural optimisation 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 illustrated in Section 2.6.
•
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 parameters 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 antagonistic to the design parameters, i.e. kinematic stiffness
vs. workspace.
•
There is a nonlinear relation between design parameters and performance.
•
Many performance values are of the type "best case worst case" over an up to six-dimensional workspace.
Since the performance characteristics vary within a workspace of complex shape a simple and unique performance 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 analysis- 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 estimates 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.
0,4
Crossover
1,4
0,4
0
Optimierte Konfiguration
Optimised
Configuration
START
Optimisation of the kinematic behaviour
0
Mutation
Selection
Storage of
pareto-optimal -0,4 0,8
Solutions
0.3
0,3
Clustering
0.2
no
OK ?
yes
Postprocessing
STOP
0
κmax = 2.75 -0,4
0,8
σmin = 0.51
σmax = 1.45
κmax = 1.8
0
σmin = 0.75
σmax = 1.37
0.3
0,3
0.2
0.1
0.1
y-axis [m]
Determination of the appropriate kinematic topology
1,4
Generation of
Startpopulation
Evaluation
•
•
Use of genetic
optimisation
Start Konfiguration
Start
Configuration
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 characteristics. 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].
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 individual 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].
y-axis
y-axis [m] [m]
Calibration of the Simulation Models
To realise a good correlation between the results of
measurements and Multi-Body-Simulation, the parameters of the simulation model, e. g. the damping and stiffness 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.
00
00
-0.1
-0.1
-0.2
-0.2
-0.3
-0,3
0.5 0.4 0.3
0,5
0.2
0.1
0 -0.1 -0.2 -0.3 -0.4 -0.5
-0,5
x-axis0
[m]
x-axis [m]
-0.3
-0,3
0.5 0.4 0.3
0,5
0.2
0.1
0
-0.1
x-axis0
[m]
x-axis [m]
-0.2
-0.3
-0.4
-0.5
-0,5
Figure 4: Optimisation of the kinematic performance.
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 consists 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 generated within the multi-body environment. Constraints define how the parts are attached and how they move relative 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 constraints 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 relationships.
•
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 simulation 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 assemble the mechanism in the modelled configuration.
This means that the underlying non-linear equation system 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. During 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 performance, 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.
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 behaviour has to be analysed and optimised [64], [113], [124].
The structural behaviour under static, dynamic and thermal loads is evaluated to derive an optimal machine design 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 applicable 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 hydraulic, electromagnetic and casting simulations.
Analysen
Finite-Elemente-Methode
Analysis
typesder
of the
Finite-Element-Analysis
Lineare
Statik
Linear
Static
Rigid Multi-Body
Multi-Body Model of a Machine Tool’s kinematics
Screw Joint
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 constraints are replaced by flexible connectors like 3dimensional spring-damper-elements. With the help of
this analysis the simulation of expected load histories of
machine components can be estimated for the dimensioning [20], [90], [76], [108].
During the analysis of inverse dynamics, the motion pattern 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 calculation where the MBS-system determines the state of equilibrium [64], [90].
The multi-body simulation provides an easy way to analyse the kinematic behaviour over the complete workspace of a machine tool as well as to determine load
histories of components or joints [64], [90], [123]. In addition, it helps to choose proper elements or detect weak
spots of a machine tool in the early design stages. However, the flexibility and strain of single machine parts
cannot be considered with the pure multi-body simulation
using rigid body models [113], [64].
Nichtlineare
Statik
Non-linear
Static
„ material
„ linear load-
Revolute Joint
deformationbehaviour
F
s [mm]
t [sec]
15
09
4
10
5
0.
17
63
4
0.05
0.1
0.15
0.2
stroke [m]
0.25
0.3
max. acceleration [m/s²]
max. acceleration [m/s²]
2.0
87
6
25
∆
necessary path jerk [m/s³]
25
mode analysis
state temperature
fields T(t) = const.
„ response-analysis
„ analysis in time
∆
„ analysis of transient
temperature fields
T(t) ≠ const.
t
„ radiation,
„ crash analysis
F
„ following load
Results of a Positioning Operation
Thermik
Thermal
„ analysis of steady
domain
∆
reachable path velocity [m/s]
1.
2
∆
Dynamik
Dynamic
„ linear normal
F(t)
„ snap F
through
„ buckling
20
„ contact F
∆
Translational Joint
Motion
F
r
v
convection
Q(t)
Q(t)
„ non-linear thermal
material behaviour
558
1.8
212
42
669.68
Figure 6: Analysis types of the Finite-Element-Analysis.
20
15
10
64.6128
5
0.05
0.1
0.15
0.2
stroke [m]
0.25
Figure 5: Multi-body Simulation of a rigid body model.
0.3
For structural problems the types of analysis can be divided 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 damping effects caused by time-varying loads. A static analysis
can, however, include steady inertia loads (such as gravity 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 relevant topic that can be examined using the thermal FiniteElement-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 simulation the three primary modes of heat transfer can be
considered: conduction, convection and radiation.
For machine tools the most important results in a FiniteElement-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 guidingsystems
•
Linear normal modes of vibration
•
Flexibility frequency response (with limitation)
•
Stress distribution, e.g. in highly loaded tool interfaces 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 (partitions). By this, a complex structure is fractionalised into
simple base geometry elements that allow easy meshing.
Defeaturing of the 3D-CAD-Model
and setup of the FEA-Model
Calculation & Optimisation of the
static behaviour
Calculation & Optimisation of the
dynamic behaviour
⎛k x ⎞
⎜ ⎟
k Spring = ⎜ k y ⎟
⎜k ⎟
⎝ z⎠
c
ati
St
Fx
CADÎFEM
Dy
na
mi
c
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 shellelements (2D-element types). The wall thickness of the
structure is contained as a physical property of each element. Compact parts are typically meshed with solid elements (3D-element types) [30].
Semi-automatic mesh generators are widely used in practise, helping the engineer to reduce the model generation
effort. In the semi-automatic meshing process, also called
mapped meshing, regular FEA meshes made of quadrilateral 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 compared 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 calculations 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 defined 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 postprocessing, the calculation results can be reviewed and
load cases of different operating conditions can be superimposed. While displaying the calculation results (e.g.
static, dynamic) in the post-processing program, the machine model can be examined with respect to displacements, 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 between 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 optimisation 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 machine 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 optimisation methods based on the Finite-Element-Method. These
methods will be explained and discussed in the next section.
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]. Depending on the necessary level of detail, different methods are used to find or improve the design of structural
components of machine tools.
The topology optimisation is used to define the best material 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 optimisation 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 minimised with regard to a desired static stiffness at the tool
centre point. The application of the parameter optimisation will be illustrated in Section 2.5.2.
The following Figure 8 illustrates the most common methods for structural optimisation.
Methods of structural optimisation
Topology
Optimisation
„ optimisation with
regard of the casting
core draw directions
Parameter
Optimisation
„ wall thickness
„ cross section
„ fiber orientation
Topography
Optimisation
„ optimisation of
creases and
reinforcements
Shape
Optimisation
„ parameter-oriented
optimisation
„ parameter-free
optimisation
design space
optimisation
result
source: Altair
source: Chiron / WZL
source: Altair
source: Altair
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 minimum design specifications, wherein the mass of the component 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 topology 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 component 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 NURBSsurfaces 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 approach for the topology optimisation of structural components which is called “coupled hybrid multi-body simulation with topology optimisation” (HMBS-TO). This software environment uses the multi-body simulation to calculate 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 reduction 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 CraigBampton modes [31], which are described in detail in
Section 2.6.3.2.
3. Setup of MBS Model and
Definition of Load Cases
Flexible
Body
Imposed
Motion
Interface
Node
Iteration
5. Determination of
Component Stress and
Topology Optimization
Design Cycle
4. MBS Result: Forces,
Deformations
100
Force [%]
6. Topology Optimization
Result
50
0
0.00
0.50
1.00
Time [s]
Figure 9: Workflow of the coupled hybrid multi-body simulation with topology optimisation.
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 optimisation 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-ElementAnalysis [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 HighPerformance-Cutting (HPC) machine tool are presented
in Figure 10.
tion the thickness of each wall of the structural components 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 accuracy of the finished workpieces
•
high dynamic properties of the feed drives to realise
highly dynamic positioning operations and movements to decrease the processing time of each workpiece
•
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 frequencies of the feed drives are coupled with lower natural
frequencies of the machine structure. To avoid instabilities 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 interactions 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
Finite Element Analysis (FEA)
140
5
6
percent [%]
120
Digital Block-Simulation (DBS)
-
optimisation column
1 vertical table - bottom
2 vertical table - top
4
3 pallet carrier
3
4 pallete
2
5 column
6 head Sprint Z3
7 fixation
PT2
mred kred
Start design
Optimised design
s
-
s
-
-
-
Cred
-
-
reduced model
of the mechanic
[M]; [K]; [C]
Design
Element
Frozen
Element
2. Computation of Craig
Bampton Modes
Rigid Body
Element
reduced model
of the drives
mred, kred, cred
1. Preparation of Flexible
Body
-
100
FEA
DBS
80
Coupled rigid Multi-Body Simulation (MBS)
60
MBS
Coupled flexible Multi-Body Simulation
MBS
180
160
„
„
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
percent [%]
„
1. eigenfrequency
optimisation table
z
Optimisation of a Milling Machine
„
over-all mass
140
120
100
80
60
40
20
0
Start design
Optimised design
interface
-
s
-
-
interface
interface
forces
0
y
x
position, velocity
7
1
interface
forces
20
position, velocity
40
-
-
DBS
s
-
-
-
DBS
Co-Simulation
Figure 11: Methods of coupled simulation of structural
dynamics and control loops.
over-all mass
1. eigenfrequency
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-
The different approaches can be classified as the simulation 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 simulation 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 workspace with this approach.
Pritschow et al. [73], [74], [75] developed a simulation
environment which is illustrated in Figure 12. The environment was developed for the coupled simulation of a
rigid multi-body model and control loop models of a PKM
machine tool.
MBS-Model
PC-NC Model
Velocity
CAD-Model
desired feed rates
Neugebauer et al. [71] developed models to describe the
interaction of machine and hydraulic drive system of forming machines. The methods use numerical simulations for
the hydraulic systems.
2.6.2 Coupled Finite-Element simulation
Another approach is the coupled Finite-Element simulation with reduced models of the control loops of the
drives. Within this procedure the reduced stiffness, damping and mass of the drive system are calculated with the
help of a digital block-simulation and modelled with special elements in the FEA-model [20], [48], [76], [131].
Some FEA-programs provide special linear control elements 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 FEAmodel [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 toolcentre-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 additional 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 secondary parts.
Tigger
1
Kv
+-
+-
Xsoll
1/Ks
Kf
1/1000
-+
1/Tpc
feed force on the
secondary parts
1
Fsoll
PI
1/2
counteracting force on the
primary parts
Xist
2
Displacements
Forces
Forces
Displacements
Velocities
Velocities
error X in the measuring
system [mm]
vber
error. [mm]
Time
Model of the
control loops
TCP
0.01
0
-0.01
„ Design in 3D-CAD-Systems -> Import into MBS-Software (MSC.ADAMS)
„ adaptable level of detail
„ coupled model of the control loops (Matlab/Simulink) of the drives
„ desired feed rates with PC-NC model
0
controller
measuring
system
10 required acceleration [m/s²]
0.04
-10
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 measuring 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-ControlEngineering 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 kinematics the possibility to perform test runs of the numerical
control before implementing new functionalities, like algorithms 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 acceleration loads for the demands of high-speed-machining.
0.01
error [mm]
0
0
0.1
time [s]
0.3
0.4
required position [m]
0.08
Figure 12: Coupled simulation of a rigid multi-body model
and control loop models of a PKM machine tool.
0.1 time [s] 0.3
error X at TCP [mm]
0.4
0 0
0.1
time [s]
0.3
0.4
0
-0.01
0
0.1 time [s] 0.3 0.4
source: Gildemeister / Siemens Linear Motor Systems GmbH & Co. KG
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 different orientations of the linear direct drive. Thus the designer 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 prototype, 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 contouring where large accelerations occur.
Van Brussel et al. [104], [105] proposed to treat the complete machine tool and control as an integrated mechatronics 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.
Control models (Matlab® / Simulink):
Structural models (Finite element model):
•
•
•
Structural elements
Drive elements
Non-linear phenomena (friction,…)
•
•
•
Control laws
Digital implementation (DAC, ADC)
Measurement devices, filters
In1
Out1
Structure-control integration:
Desired trajectories
Finite-Element
Model
®
Matlab /
Simulink
Resulting outputs
Figure 14: Integration of structural and controller models.
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 3Dspring-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].
DRIVES
fixed
bearing
F
k
Zäh et al. [130], [131], [132] developed a Finite-ElementModel of the feed drive and simulated the performance of
the axis control law under the influence of structural vibrations 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 components 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 appear 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 between 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 multibody 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 simulations are discussed in the next sections.
2.6.3.1 Model configuration
Each structural component of the machine tool is modelled as a so-called flexible body [31], [115], [116]. The
different elements which are used to connect the structural components, such as guiding systems, mounting
devices or ball-screw-drives, are modelled as a combination 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 depending on the direction of the internal force of the component (1D-element or 3D-element). The different model
techniques of the different connectors in multi-body models 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 foundation. The stiffness and the damping in three directions
D
ball screw
spindle
L(t)
+
spindle nut
+
F
k=
nut stiffness
F
E⋅A
,D
L
F
M
h
F
+k
D
F
⎛2⋅π⎞
Fa = ⎜
⎟ ⋅M
⎝ h ⎠
GUIDING SYSTEMS
F
k
D
{F} = [k ] ⋅ {u} + [D]⋅ {u& } + {Fv }
F
MOUNTING DEVICES
F
& } + {Fv }
D {F} = [k ] ⋅ {u} + [D] ⋅ {u
k
F
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 movement 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 vibration and deformation calculations of the individual components, the so-called Superelement Creation, are integrated in the multi-body model through an interface of the
multi-body simulation program to popular Finite-ElementPrograms [14], [76], [115] [116].
Superelement Creation uses a Finite-Element-Model to
define a component of a complex structure, and a connection degree of freedom set (DOF) to specify the interface 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 “interface node degrees of freedom”.
The fixed normal modes contain the dynamic response of
the superelement when all “connection degrees of freedom” 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-
Constraint modes
Φ
Φ
physical DOF
boundary DOF
interior DOF
Identity and zero matrices
physical displacements of the interiot DOF
in the constraint modes
physical displacement of the interior DOF
in the normal modes
modal coordinates of the constraint modes
modal coordinates of the normal modes
IC
IN
qC
qN
f=1240 Hz
f=2275 Hz
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 interface to the multi-body simulation program.
Tönshoff et al. [100] developed an alternative approach to
model the elasto-kinetic behaviour of machine tool structures 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-Engineering (CACE) programs is possible with common multibody 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 communicate 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.
control loop of the direct drive (x-y)
control loop of the direct drive (x-y)
KF
force excitation TCP
iA
RA,Tel u Ki ,Tni
isoll
A
- xist
Fa
Force
KE
x ist
0
Time
1,0
KM
RA,LA
A
uA
0
z
nist
y
zist
Ki, Tni
isoll
-
i ges
Kp,Tnp
-
zsoll
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
Frequency [Hz]
200
Figure 18: Simulated frequency response function
Especially for machine tools with small workspace dimensions, 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 maximum jerk settings of the feed drives. Therefore an inputsignal for the control loops of the drives can be generated
by a virtual controller.
The simulation of such a positioning operation is illustrated in Figure 19.
jerk
KL
simulation of frequency
response functions (FRF)
with control loop
without control loop
Positioning operation of the
Z-unit (5mm)
acceleration
position controller
KE
1,0
ssoll 1
-
Simulation Results
Lineardrive
K F =103 N/A
K L =70 1/s
K P =3500 As/m
Tnp =8 ms
velocity controller
-
Time
KL
-
control loop of the ball screw drive (z)
displacement TCP
0
Kp,Tnp
-
x ist
0
Displacement
s
current controller
Z-Axis
K M =0,93 Nm/A
K L =70 1/s
K P =2,71 Nms/rad
Tnp =10 ms
0
M (t)
0
-
current controller
velocity controller
0
position controller
Time
0
Time
position
velocity
x
control loop
loop
Input control
z-axis
z-axis
[m]
Figure 17: Coupling of flexible multi-boidy models and
control loops.
[m/s]
flexible multi-body model
00
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.
Time
∆=0
00
Time
F (t)
u
uB
uI
E,0
Fixed-boundary normal modes
0 ⎤ ⎧qC ⎫
⋅⎨ ⎬
Φ IN ⎥⎦ ⎩qN ⎭
control loop
loop
control
linear drive
direct1
drive 1
control loop
loop
control
drive 2
linear direct
∆= 0 drive 2
F (t)
⎧u ⎫ ⎡ E
u = ⎨ B⎬ = ⎢
⎩ uI ⎭ ⎣Φ IC
Unit translation
of the guideway
in x-direction
Unit translation
of the hinge in
x-direction
x
[m/s²]
z y
[m/s³]
Boundary-conditions
(Craig-Bampton)
2.6.3.4 Results of the coupled flexible multi-body simulation
For the simulation of flexibility frequency response functions of the coupled flexible multi-body model, an excitation 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 corresponds 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.
Compliance [um/N]
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.
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 constant velocity the drive was decelerated to standstill. The
results of this simulation are shown in Figure 20.
lytically before they are implemented in the current design
or in the next machine generation.
Probe
• inductive
x
F
position sensor
Force probe
Excitor
• strain gauge
• piezo sensor
• impulse hammer
• piezo actuator
• hydraulic actuator
• accelerometer
Bode diagram
compliance
[µm/N]
Gxx
Gyy
Gzz
Amplifier
locus
Amplifier
0.001
180
0,1
A/D converter
-0,1
-0,1
FFT analyser
real 0,1
[µm/N]
coherencephase [°]
T3 = f 3
FRF
imaginary
[µm/N]
r=730 m/s³
r=650 m/s³
r=550 m/s³
r=450 m/s³
desired path
Compliance [um/N]
Displacement [mm]
displacement
0
-180
1
0
0
200 frequency [Hz] 800
Time [sec]
Figure 21: Measuring of a frequency response function.
eigenfrequency of the
machine
Frequency [Hz]
Figure 20: Simulation results of a positioning operation.
Such positioning operations always excite natural frequencies of the machine tool, which can lead to deviations of the desired tolerances of the workpiece or even to
damaged tools dependent on the amplitude of the vibration [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 simulation parameters is still a problem, which limits the accuracy of the results [107].
The prediction of stiffness and especially of the damping
characteristics of machine components is extremely difficult due to their dependence on many different influences,
like lubrication, pre-loads or tolerances [53], [68]. Measurements of the dynamic behaviour of similar machine
tools or components and the validation of existing simulation 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 associated resonance frequencies and dynamic amplitudes
as well as the phase shift
The calibration of simulation models, especially the parameters of spring-damper-elements (stiffness- and
damping-coefficients) is extremely difficult and very timeconsuming. 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 optimisation methods, e.g sequential quadratic programming
(SQP). The design goal of this optimisation is the minimisation 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.
Coupled flexible
MultiMulti-Body Model of
the machine tool
Measuring of the
Frequency Response
Function
kax
dax + krot
Measured
FrequencyFrequencyResponseResponseFunction
0
Simulated
FrequencyFrequencyResponseResponseFunction
Measured FRF
no
[K]start
[D]start
Convergence
Convergence
yes
0
Frequency [Hz]
Both characteristics can be measured with special experiments as depicted in Figure 21 for the FRF measurement. For the determination of the FRF, the TCP is excited 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 improve weak points of the machine can be assessed ana-
drot
Matching Measuring
Measuring // Simulation
Simulation
Matching
Compliance [µm/N]
„ Excitation of the third
1
10
Iteration
Optimised parameters
parameters of
of
Optimised
the model:
model: [K]
[K]actual
the
actual,,
[D]actual
[D]
actual
Figure 22: Automated model update with measured frequency response functions.
This approach enables the calibration of the machine tool
models for the simulation of the interaction between machine 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 manner.
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 automotive industry uses the virtual reality increasingly in the
field of design and development as a tool for the investigation 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 NCprogramming simulations in combination with a force
feedback for a realistic impression for the user.
Weck et al. [23], [108] developed an automated visualisation environment for the evaluation of the machine kinematics as well as for the results of Finite-ElementAnalysis.
Figure 23 illustrates the VR-environment for the investigation of machine tools.
 Import of the FE-Data
 Extraction of the components
‘ Triangulation of the FE-mesh
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 location of fixtures can be displayed in the CAD environment
[127], [128].
3.1 NC-path simulation
The present technology allows the prediction of tool collision spots and correctness of the NC program by checking 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 motion 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.
Postprocessor module
CLDATA
file
x,y,z,i,j,k
Kinematics
engine
NCformatting
NCsimulation
Collision
avoidance
NCprogram
N100 G01 X..Y..Z..A..B..
Workpiece
VR-Cave
Tool
Collision
Area
Clamping
Table
Machine
Head
Part Program Tape
’ Derivation of the kinematics
ball screw
drive (kx)
movement in
x direction
“ 3D-Visualisation in the “VR”
Figure 23: VR environment for the investigation of machine tools.
This environment enables the engineer to import FiniteElement-Models of machine tools. The software automatically extracts the single structural components and
enables the engineer to get a realistic impression of the
design.
Look Ahead Distance
guiding system
(ky , kz,
ϕx , ϕy , ϕz )
Section
Index
Section
Index
N 50 G17
N 55 F1000 S1000 G00 X-364.94 Y-61.67 Z150. M03
N 60 G00 Z100.
N 65 G01 Z0.
N 70 X-359.94
Section being
N 75 G03 X-324.94 Y-26.67 I0. J35.
machined
N 80 G01 Y84.
N 85 G03 X-346. Y105.06 I-21.06 J0.
N 90 G01 X-506.303
N 95 G03 X-513.416 Y87.887 I0. J-10.06
N 100 G01 X-480.648 Y55.118
N 105 G02 X-477.729 Y48.678 I-7.099 J-7.099
N 110 G03 X-460.589 Y-115.162 12134.642 J140.491
N 115 G02 X-463.428 Y-123.689 I-9.938 J-1.428
N 120 G01 X-487.625 Y-147.887
N 125 G03 X-480.511 Y-165.06 I7.113 J-7.113
N 130 G01 X-357
N 135 G03 X-324.94 Y-133. I0. J32.06
N 140 Go1 Y-22.33
N 145 G03 X-359.94 Y12.67 I-35. J0.
N 150 G01 G40 X-364.94
N 155 G00 Z100.
N 160 G00 X204.94 Y-34.755
N 165 G01 Z0.
N 170 G41 X199.94
Section being
N 175 G03 X164.94 Y-69.755 I0. J-35.
Simulated
N 180 G01 Y-162.132
N 185 G03 X167.887 Y-169.246 I10.06 J0.
N 190 G01 X185.557 Y-186.916
N 195 G03 X190.362 Y-186.519 I2.234 J2.234
N 200 G01 X193.875 Y-181.606
N 205 G02 X195.145 Y-180.149 I8.167 J-5.84
N 210 G01 X206.296 Y-169.61
N 215 G02 X231.316 Y-166.338 I14.767 J-15.625
N 220 G02 X243.573 Y-174.115 I-50.726 J-93.491
N 225 G03 X248.965 Y-175.801 I5.152 J7.011
N 230 G03 X251.841 Y-174.534 I-0.115 J4.158
CNC
Figure 24: Integration of NC-simulation and controller.
3 SIMULATION OF THE CNC SYSTEM
The CNC system consists of a computer, power electronics 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 removed 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 predicted as the workpiece is produced in order to realize a
Virtual CNC system.
Once the NC Program is generated in a CAD/CAM environment, the present Virtual CNC technology allows the
However, a realistic simulation of machine tool motion
and accurate prediction of final part geometry requires the
inclusion of real time trajectory generation, dynamic behaviour 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, acceleration and feed speed by the trajectory generation algorithms of the CNC. Here, it is important not to violate jerkacceleration and speed of individual drives which participate 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].
CAD Model
Tool path geometry
CL/APT File
CAD/CAM
Software
N1 G00 X5 Y1
N2 G01 X3 Y3
N3 G03 X4 Y3 I1 J0
...
y
Interpreter
y
y
s
s
x
x
x
Trajectory Generation
Position closed-loop
S Displacement
t
.
S
Feedrate
..
S
Re-process
...
S
Acceleration
Jerk
t
t
Reference
position
Axis
Control Law
.
r(t), r (t),
..
...
r (t), r (t)
Control
signal
t
Feedback
Optimization Process
-Reschedule Feedrate,
Accel./Decel., Jerk Limit
-Contour Error Reduction
Predicted
Trecking
Error
+
-
Feed Drive
Servo
Feedback
Measurements
Actual
Position
Actual Position
Feed motion planning
Simulate the contour
errors generated from
Servo Control in „Virtual“
enviroment
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 defined 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 disturbances. 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
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 accelerationvelocity-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 milling
While it is satisfactory in three-axes machining to generate 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 CAMprogramming 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.
Feed
Simulation
Workpiece
Workpiece
Figure 27: Adjustment of tool movement to satisfy dynamic limits of the five axis machine tool.
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
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 principle an originally collision-free NC-program to contain
collisions between tool, tool holder, machine components,
and workpiece. To prevent this, in addition to the optimisation 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 improved 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 major cutting forces (Ff) act in the direction of cutting
speed, followed by the thrust force (Fr) acting in the direction 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 contact/ploughing (Fte, Ffe. Fae) edge components as
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 rigidity. 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 determination of chatter vibration free spindle speeds and depths of
cut [5].
Ft = Ftc + Fte = K tc ah + K te a
The complete model of the machining process is therefore 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 material.
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 surface.
The directions of cutting forces in turning and milling are
given in Figure 28 [8].
dFa
Y
n
dFr
Z
Workpiece
Ft
dFt
Fr
Fa
X
Tool
f
Y
Fy(φ)
φst
n
φ
f
c
φex
Chip load
Frj
Ftj
X
Fx(φ)
Figure 28: Prediction of cutting forces for turning and
milling operations.
Fr = Frc + Fre = Krc ah + Krea
Fa = Fac + Fae = K ac ah + K ae a
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 coefficients as proposed by Kienzle [55]:
Ft = K t ah
Fr = Kr ah
Fa = K a ah
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 variety 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 overload 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 depends 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 material. Hence the cutting edge can withstand high thermal
and impact loads during machining [29]. Finite-ElementAnalysis 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 evaluated under high strain rate conditions using either Orthogonal Cutting Tests or Hopkinson Bar tests [67].
Three main methods of mechanical formulation are commonly 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 (remeshing 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
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 evaluated at feed rate increments using solid modelling techniques. The intersection geometry is required to solve
machining process simulation algorithms [93]. The machining process simulation engine is based on the laws of
metal cutting mechanics and dynamics, it pulls the required 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 MODEL
Tool, Material,
Machine-Tool
Data Base
NC Tool Path
Cutter Geometry
3D Simulation of a Milling Process
Cutter-part
intersection
calculations
FINAL PROCESS
PLAN
Optimized Speed,
Feed, Depth,
Width, Error
Compensation
Virtual
VirtualMachining
Machining
process
simulation
MONITORING
MONITORINGAND
AND
CONTROL
CONTROLDATA
DATA
PATH PLANNER
CL File
Path Strategy
Analysis
Peak force,
torque, power,
tracking error,
modal frequencies
M
A
C
H
I
N
E
T
O
O
L
Figure 30: Virtual machining process simulation and optimisation architecture.
Figure 29: 3D FEA simulation of a Milling Process.
A successful simulation is dependent on the accurate
knowledge of the boundary conditions and the materialbehaviour 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 process into consideration. The magnitude of cutting forces,
torque, power and thermal energy produced during machining depends on the tool geometry, structural dynamics 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 include 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.
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 process 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 computational time is rather unaffordable and long at the present
time, and considerable research efforts are directed towards developing efficient computational models and
parallel processing of algorithms at multiple central processing units (CPUs).
Although some commercial NC Simulation systems provide feed optimisation, their algorithms are not based on
the laws of cutting mechanics, hence they do not represent 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 simulation 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] presented 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 number of researchers presented mechanics of cutting models 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].
...
N9 X-8.0056
N10 X- 7.9655 Y49.3901
N11 X-6.3125
N12 G3 X28.2708 Y49.1355 I17.3496
J7.7454
N13 G1 X42.8735
N14 G3 X102. Y- 7.5278 I67.1265 J10.8645
N15 G1 Y-8.
N16 X23.083
N17 Y-3.2
N18 Y1.6
...
Spindle nose
Cutting
Tool
Toolpath
Workpiece
Tool Toolholder Housing
4
FRF-Magnitude[m/N]
NC Code:
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.
x 10
Pulley
-8
Experiment
Simulation
2
1
500
Figure 31: Simulation of virtual machining of a part with
features.
1000
1500
2000
Frequency [Hz]
2500
3000
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 manufacturing 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.
Depth of cut [mm]
8
6
Initial design 1
Initial design 2
Initial design 3
Optimized design
Desired
Cutting
Potint
4
2
0
200
Contact force [N]
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 column, 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 dynamic 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 borrowed 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 dynamic 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
Bearing
3
0
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.
Hydraulic
fluid
Shaft
150
2000
4000
6000
8000
Spindle speed [rpm]
10000
12000
Bearing 1
Bearing 2
Bearing 3
Bearing 4
Bearing 5
100
50
0
0
Preload period
0.01
After cutting force is applied
0.02
0.03
Time [s]
0.04
0.05
Figure 33: Virtual design and testing of spindles.
Dynamic Flexibility
Stability Simulation
G [µm/N]
Modular FE-Model of the Spindle-Bearing-System
Fx(t)
GFxx
Workpiece with Chatter Marks
Stability Lobe
x(t)
GFyx
GFzx
GFxy
y(t)
GFyy
bcr [mm]
Fy (t)
Fz(t)
GFzy
GFxz
GFyz
z(t)
GFzz
dzFx(t)
unstable
j [°]
dzF y(t)
Tt
dzFz(t)
kcb
dyFx(t)
b
kcb
dyFy(t)
b
kcb
dyFz(t)
b
f [Hz]
stable
Tt
dxF x(t)
dxF y(t)
dxF z(t)
Tt
n [min-1]
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 characterised 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.
Bad Correlation between
Measurement and Simulation
15
Stable Process
Chattering
Experimental Results
Simulation
10
unstable
5
stable
0
18000
19000
20000
21000
22000
spindle speed [min-1]
unstable
5
0
23000 18000
stable
19000
20000
21000
22000
23000
spindle speed [min-1]
16
feed rate fz=0,18 mm
166
Stable Process
Chattering
Experimental Results
Simulation
feed rate fz=0,18 mm
20
10
Good Correlation between
Measurement and Simulation
axial depth of cut, ap [mm]
15
axial depth of cut, ap [mm]
Another example is shown in Figure 34 where the spindle
and tooling are specifically designed to machine aluminium 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-bearingsystems 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 behaviour of the spindle bearings.
However, the process stability can be significantly improved by a selective setting of the machining parameters. In particular, the variation of the spindle speed according 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 frequency 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 springdamper-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 timeconsuming measurements [117].
With a supplementary program for the simulation of the
stability behaviour of milling processes a complete simulation chain for the calculation of stability lobes is available, as illustrated in Figure 34.
179
Figure 35: Simulated and measured stability lobes for the
HPC machining of aluminium.
As illustrated in Figure 35 the results of the stability simulation of high performance processes often have variations in the accuracy. An essential part of the cutting
process and stability simulation are the time varying direction factors diFj, which project the forces at each cutting
edge into the machine coordinates. Furthermore, the
cutting forces are determined by the cutting force coefficient kcb and the cutting depth b. The theoretical background of these effects are still unexplored for HPCmachining processes and requires intensive investigations [117].
5.2 Frequency and Time domain simulation of machine 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 operations. As discussed earlier, the cutter – part intersection
along the tool path must be identified at feed rate increments 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 structure. If the process becomes unstable with chatter vibrations, 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 provide a direct relationship between the dynamic stiffness of
the machine and the process, the time domain simulation
allows prediction of dynamic cutting forces and dimensional 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].
Stability Lobes for Bull Noes Cutter and Al7075
6
Analytical
Time domain
Axial depth of cut [mm]
5
(9500 rpm)
(A=7mm)
(1400 rpm)
(A=7mm)
4
3
2
1
0
4000
2000
0
[N]
1500
8000
6000
10000
Spindle speed [rev/min]
[N]
1500
Exeperimental Resultant Force
1000
16000
Exeperimental Resultant Force
500
0
0
1000
2000
Rmax=12 um
3000
5000
4000
Rotation Angel [deg]
6000
0
7000
5
-5
3
2
Z [mm]
1
(axial direction)
0
0
0,5
1
2,5
2
1,5
Z [mm]
(feed direction)
3
FFT for Resultant Force
60
40
2000
6000
7000
5
-5
3
2
Z [mm]
1
(axial direction)
0
0
0,5
1
3
2,5
2
1,5
Z [mm]
(feed direction)
FFT for Resultant Force
Tooth Passing
Frequency
(467 Hz)
80
60
40
20
3000
5000
4000
Rotation Angel [deg]
Surface Roughness
15
[Amp.]
100
Chatter
Frequency
(1448 Hz)
80
1000
Rmax=2 um
15
[Amp.]
100
0
Surface Roughness
Y [um]
Y [um]
14000
1000
500
0
12000
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 relative displacement between tool and workpiece which
changes the instantaneous chip area which affects the
cutting process again. This approach enables the investigation 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 simulation environments, see Figure 38.
The approach for a coupled simulation of the manufacturing 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 manufacturing process [36].
20
0
200
400
600
800
1400 1600 1800 2000
Frequency [Hz]
0
0
200
400
600
800
1400 1600 1800 2000
Frequency [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 simulations 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 resulting quality of the workpiece was predictable prior to the
start of production. The principle procedure of an integrated Simulation of machine tool, workpiece and process
in time domain is shown in Figure 37.
CNC
G01 x100 y50 z10
G01 x101 y50 z10
S
Drives
-
&
S
Machine Tool
FDrive
Disp.
FPro.
Process
∆
F
Vel.
Integrated Simulation of
Machine Tool, Workpiece
and Process
0
FPro.
Workpiece
∆
t
f
F(t)
xd
Results
Quality and Tolerances
result
Process Stability
Depth of Cut [mm]
reference
stable
unstable
limit of stability
Figure 37: Integrated simulation of machine tool, workpiece 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
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 calculation techniques the possibility of studies concerning
model complexity and extent is given. Due to the nonlinear 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.
Rough Part
Finished Part
planned process chain
Forces
Forces
Simulation Module
Cutting Process
Motions
Positions/Velocities
Nominal values
Virtual
NC-Kernel
Simulation Module
Control/Drives
To realise the industrial application of the integrated simulation 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.
NC-Code
Simulation Module
Machine Tool Structure
Integrated
IntegratedSimulation
simulationand
andOptimisation
optimisationofofthe
theProcess
processChain
chain
Forging
RoughMachining
Hardening
HardMachining
Grinding
Measuring
Workpiece Properties
Figure 40: Scenario of a simulated process chain.
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 scenario.
6
RESEARCH CHALLENGES: “THE VIRTUAL
WORKPIECE PRODUCTION”
As mentioned above the interaction between machine tool
and manufacturing process causes variations of the characteristics of the workpieces.
It would be of great economic interest for the design of
machine tools as well as for the design of single processes or complete process chains if the resulting quality
of the workpiece was predictable prior to the start of production. The aim is to determine the ideal process parameters 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 production of extremely complex, or very expensive components, the simulation and optimisation of single processing 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 coupled simulation of manufacturing process and machine
tool, but without any industrial application.
Until now the integrated simulation of the interaction between machine tool, manufacturing process, workpiece,
fixture, and the history of the single manufacturing processes is not realised.
Thus it is not possible to simulate the workpiece quality in
consideration of the individual steps of an industrial process chain. A possible scenario of a simulated process
chain for the manufacturing of a gearshaft is shown in
Figure 40.
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, workpieces, 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 dynamically.
The Finite Element model is reduced to a multi-body
model of the machine which consists of rigid links connected via flexible springs. The rigid and flexible machine
tool models are analysed under various jerk, acceleration,
velocity and control profiles at high speeds. The interaction 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 process, 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 simulation 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 Brussel, Denkena, Fleischer, Groche, Klocke, Lauwers,
Pritschow, Weinert and all colleagues and industrial companies who sent valuable contributions for the preparation
of the article.
9
REFERENCES
[18]
Berkemer, J., 2003, Gekoppelte Simulation von
Maschinendynamik und Antriebsregelung unter
Verwendung lienarer Finite Elemente Methode,
Dissertation, TU Stuttgart.
[19]
Bernard, A., Fischer, A., 2002, New Trend in
Rapid Product Development, Annals of the CIRP,
51/2: 635-652
[20]
Brecher, C., Denkena, B., Giesler, M., Gölzer, P.,
Hamann, J., Kelichhaus, T., Prier, M., Prust, D.,
Reinhart, G., Quein, M., Weck, M., 2002, Effiziente
Entwicklung von Werkzeugmaschinen – Mit virtuellen Prototypen direkt zum marktfähigen Produkt,
Tagungsband Aachener Werkzeugmaschinen Kolloquium, 157-190, Aachen.
[1]
Albertz, F., 1995, Dynamikgerechter Entwurf von
Werkzeugmaschinen, Dissertation, TU München
[2]
Altintas, Y., Spence, A., 1991, End Milling Force
Algorithms for CAD Systems, Annals of the CIRP,
40/1:31-34.
[3]
Altintas, Y., Budak, E., 1995, Analytical Prediction
of Stability Lobes in Milling, Annals of the CIRP,
44/1:357-362.
[4]
Altintas, Y., Erol, N.A., 1998, Open Architecture
Modular Tool Kit for Motion and Machining Process Control, Annals of the CIRP, V47/1:295-300.
[5]
Altintas, Y., 2000, Manufacturing Automation:
Metal Cutting Mechanics, Machine Tool Vibrations,
and CNC Design, Cambridge University Press.
[21]
Brecher, C., 2002, Vergleichende Analyse von
Vorschubantrieben für Werkzeugmaschinen, Dissertation, TH Aachen.
[6]
Altintas, Y., 2000, Modeling Approaches and Software for Predicting the Performance of
Milling Operations at MAL-UBC, International
Journal of Machining Science and Technology,
4/3:445-478.
[22]
Brecher, C., Witt, S., 2004, Static, Dynamic and
Thermal Behaviour of Machine Tools with Regard
to HPC, Proceedings of International CIRP Conference of High Performance Cutting (HPC),
Aachen, 227-240.
[7]
Altintas, Y., Engin, S., 2001, “Generalized Modeling of Mechanics and Dynamics of Milling Cutters”,
Annals of the CIRP, 50/1:25-30.
[23]
[8]
Altintas, Y., 2003, Cutting Process Simulation and
Optimisation, Tagungsband Fertigungstechnisches
Kolloquium, pp. 219-246, Stuttgart.
Brecher, C., Weck, M., Müller-Held, B., 2005, FEErgebnisdarstellung mit Hilfe der Virtual Reality
und Maschinenbeurteilung im Arbeitsraum, Proceedings of WZL Seminar – Messtechnik und
Strukturanalyse von Werkzeugmaschinen, Aachen.
[9]
Altintas, Y., Weck, M., 2004, Chatter Stability in
Metal Cutting and Grinding, Annals of the CIRP,
Key Note Paper of STC-M, 53/2:619-642.
[24]
[10]
Altintas, Y., Cao, Y., 2005, Virtual Design and
Optimization of Machine Tool Spindles, Annals of
the CIRP, 54/1:.
Brecher, C., Witt, S., 2005, Abgleich von Berechnungs- und Simulationsergebnissen bei SpindelLager-Systemen und Werkzeugmaschine”, Proceeding of WZL Seminar – Messtechnik und
Strukturanalyse von Werkzeugmaschinen, Aachen.
[25]
[11]
Armarego, E. J. A., Whitfield, R. C., 1985, Computer Based Modelling of Popular Machining Operations for Force and Power Predictions, Annals
of the CIRP, 34/1: 65-69.
[12]
Arrazola, P.J., Meslin, F., Marya, 2003, Numerical
cutting sensitivity study of tool-chip contact, Material Science Forum, 426-432: 4519-4524.
Asbeck, J., 1997, Automatischer Entwurf optimaler
Bauteile durch Integration von CAD und Strukturoptimierung, Dissertation, TH Aachen.
Brecher, C., Broichhausen, K.-D., Flegel, H., Fleischer, J., Friedrich, D., Herrscher, A., Klocke, F.,
Lung, D., Marczinski, G., Queins, M., Raedt, H.W., Steffens, K., Wagner, P., Willms, H., Witt, S.,
2005, Integrierte Simulation von Prozess, Werkstück und Maschine, Tagungsband 25. Aachener
Werkzeugmaschinen Kolloquium, 307-350.
[26]
Budak, E., Lazoglu, I., Guzel, B.U., 2004, Improving Cycle Time in Sculptured Surface Machining
Through Force Modeling, Annals of the CIRP,
53/1: 103-106.
[27]
Cao, Y.Z., Altintas, Y., 2004, A General Method for
the Modeling of Spindle-Bearing Systems, Trans.
ASME, Machine Design, 126: 1089-1104.
[28]
Campomanes, M. L., Altintas, Y., 2003, An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions, Trans. ASME,
Manufacturing and Engineering and Science,
125(3): 416-422.
[29]
Ceretti, J.E., Fallbehmer, P., Wu, W.T., Altan, T.J.,
1996, Application of 2D FEM on Chip Formation in
Orthogonal Cutting, Mater. Preocv. Tech., 59: 169181.
Cook, R., Malkus, D., Plesha, M., 1988, Concepts
and Applications of Finite Element Analysis, 3.
Edition, John Wiley, Madison.
[13]
[14]
Baudisch, T., 2003, Simulationsumgebung zur
Auslegung der Bewegungsdynamik des mechatronischen Systems Werkzeugmaschine, Dissertation, TU München.
[15]
Bergs, T., Rodriquez, C.A., Altan, T., Altintas, Y.,
1996, Tool Path Optimization for Finish Milling of
Die and Mold Surfaces - Software Development,
Transactions of the NAMRI/SME, XXIV: 81-86.
[16]
Berkemer, J., 1998, Simulation der Antriebsregelung in Werkzeugmaschinen, Proceedings of
PERMAS User Meeting, Stuttgart, Intes GmbH
1998.
[17]
Berkemer, J., Knorr, M., 2002, Gekoppelte Simulation von Maschinendynamik und Antriebsregelung
bei lineargetriebenen Werkzeugmaschinen, WT
Werkstattstechnik online 92 H.5, Springer-VDIVerlag, Düsseldorf, 226-235.
[30]
[31]
Craig, R.R., Bampton, M. C.C., 1968, Coupling of
substructures for dynamics analyses. AIAA Journal, 6(7): 1313-1319.
[32]
Damm, P.; Friedhoff, J.; Stautner, M., 2004, Maschinenoptimiertes
5-Achsen-Simultanfräsen
nimmt Einzug in die Welt des Werkzeugbaus,
Schmiede-Journal, 3 (2004): 22-26.
[46]
Groche, P., Schneider, R., 2004, Method for the
Optimization of Forming Presses for the Manufacturing of Micro Parts, Annals of the CIRP, 53/1:
281-284.
[33]
Denkena, B., Tracht, K., Rehling, S., 2002, Simulationsmodul für Maschinendynamik im Rahmen
eines Fertigungssimulationssystems, WT Werkstattstechnik online 92, Springer-VDI-Verlag, Düsseldorf, 223-225.
[47]
Großmann, K., Muehl, A., 2002, Auf dem Weg
zum virtuellen Zerspanungsprozess, Proceedings
th
of 4 Dresdener WZM-Fachseminar, Dresden
[48]
Großmann, K., 2003, “Die digitale Simulation für
den Entwurf der Werkzeugmaschine”, Autonome
Produktion, Springer-Verlag, Berlin Heidelberg,
459-472
[49]
Großmann, K., Muehl, A., 2003, Gekoppelte Simulation von Systemdynamik von Werkzeugmaschinen und Zerspanungsprozess, Proceedings
of Mechatronik Seminar, Herbert Utz Verlag, München, 3.1-3.23.
[50]
Hessel, C., 2003, Integration der Topologieoptimierung in den CAD-gestützten Entwicklungsprozess, Dissertation, TH Aachen.
[34]
[35]
Denkena, B. Rehling, S., Tracht, K, 2002, Application of ADAMS/SDK as part of a comprehensive
st
machine tool simulation system, Proceedings 1
MSC.ADAMS European User Conference, London.
Denkena, B., Tönshoff, H.K., Tracht, K., Klobasa,
I., 2002, Simulation of Cutting Processes, Proceedings of XIII Workshop on Supervising and Diagnostics of Machining Systems. Open and Global
Manufacturing Design. Karpacz. Machine Engineering 2 / 1-2: 111-116.
[36]
Denkena, B., Clausen, M., Jivishov, V., 2003,
Deviation analysis of FEM based cutting simulation, Proceedings of the 6th International
ESAFORM Conference on Material Forming,
Salerno, Italien.
[51]
Huang, X., Yip-Hoi, D., 2004, Cutter Engagement
Feature Extraction from Solid Models for End Milling, Proceedings of the ASME International Mechanical Engineering Congress and Exposition,
Anaheim, California, Nov 14-20.
[37]
Denkena, B., Tracht, K., Clausen, M., 2003,
Hybride Methode der Zerspanungsmodellierung
und –simulation, wt Werkstattstechnik online 93 H.
11/12, 768-790.
[52]
Inasaki, I., Karpuschewski, B, Lee, H.S., 2001,
Grinding Chatter - Origin and Suppression, Annals
of the CIRP, 50/2: 515-534.
[53]
Ispaylar, M., 1996, “Betriebseigenschaften von
Profilschienen-Wälzführungen, Dissertation, TH
Aachen.
[54]
Jedrzejewski, J., Kwasny, W., 2001, XII Workshop
on Supervising and Diagnostic of Machining Systems, Wroclaw University of Technology.
[55]
Kienzle, O., Victor, H. 1957, Spezifische Schnittkräfte bei der Metallbearbeitung, Werkstofftechnik
und Maschinenbau, 47/5: 224-225.
[56]
Kim, K.W., Sin, H.C., 1996, Development of
Thermo-Viscoplastic Cutting Model using Finite
Element Method, Int. J. Mach. Tools and Manuf,
36: 379-397.
Kirchner, J., 2001, Mehrkriterielle Optimierung von
Parallelkinematiken, Dissertation TU Chemnitz.
[38]
[39]
Denkena, B., Tracht, K., Rehling, S., 2005, Modelling and calibration process of mechatronical machine tool models, Annals of the German Academic Society for Production Engineering, XII / 1.
Denkena, B., Tracht, K., Clausen, M., 2005, Material Parameter Determination for Turning Process
Simulation, Annals of the German Academic Society for Production Engineering, XII / 1.
[40]
Ehmann, F.K, Kapoor, S.G., Devor, R.E., Lazoglu,
I., 1997, Machining Process Modeling: A Review,
th
(invited paper), the 75 Anniversary Issue of the
ASME Journal of Manufacturing Science and Engineering, 119: 655-663.
[41]
Erkorkmaz, K., Altintas, Y., 2001, High Speed
CNC System Design: Part I - Jerk Limited Trajectory Generation and Quintic Spline Interpolation,
41: 1323-1345.
[42]
Erkorkmaz, K., Altintas, Y., 2001, High Speed
CNC System Design: Part II - Modeling and Identification of Feed Drives, Int. J. Machine Tool
Manuf., 41: 1487-1509.
[43]
Erkorkmaz, K., Altintas, Y., 2001, High Speed
CNC System Design: Part III - High Speed Tracking and Contouring Control of Feed Drives, Int. J.
Machine Tool Manuf., 41: 1637-1658.
[44]
Fleischer, J., Stengele, G., Neithardt, W., Albers,
A., Broos, A., 2004, Optimization of Machine Tools
with Hybrid Kinematics Structure Using Coupled
Multi-Body Simulation and Finite Element Analyth
sis, 4 Chemnitzer PKM-Seminar, 545-555.
[45]
Fussell, B.K., R.B. Jerard and J.G. Hemmett,
2001, Robust Feedrate Selection for 3-axis Machining Using Discrete Models, ASME Journal of
Manufacturing Science and Engineering, 123, 2:
214-224.
[57]
[58]
Krause, F.-L., Neumann, J., Rothenburg, U., 2000,
VR-unterstütztes
Montageund
Demontageplanungssystem, WT Werkstattstechnik online
92 H.7/8, Springer-VDI-Verlag, Düsseldorf, 287291.
[59]
Kruth, J.P., Lauwers, B., Klewais, P., Dejonghe,
P., 1999, “NC-postprocessing and NC-simulation
for five-axis milling operations with automatic collision avoidance”, International Journal for Manufacturing Science and Technology, 1(1), 1999, 12-18.
[60]
Lauwers, B., Kruth, J.P., Dejonghe, P., Vreys, R.,
2000, Efficient NC-programming of multi-axes milling machines through the integration of tool path
generation and NC-simulation, Annals of the
CIRP, 49/1/2000: 367-370.
[61]
Lauwers, B., Van der Poorten, E., De Baerdemaeker, H., 2003, CAD/CAM based generation of
collision free robot programs through the integration of a virtual machining environment, European
Journal of Mechanical and Environmental Engineering, 47/4: 215-220.
[62]
Lauwers, B., Dejonghe, P., Kruth, J.P., 2003,
Optimal and collision free tool posture in five-axis
machining through the tight integration of tool path
generation and machine simulation, ComputerAided Design, 35 (5): 421-432.
[77]
Pritschow, G., Röck, S., Korajda, B., 2003, Verification of machine tool functionality by using Hardware in the Loop and manufacturing simulation,
th
Proceedings of the 4 Wrolaw CIRP symposium
AP.
[63]
Maeda, O., Cao, Y.Z., Altintas, Y., Expert Design
and Optimization of Spindles, Int. J. Machine Tool
Manuf. Eng. (in press).
[78]
Pritschow, G., Röck, S., 2004, Hardware in the
Loop Simulation of Machine Tools, Annals of the
CIRP, 53/1: 295-298.
[64]
Melchinger, A., Schmitz E.-U., Fleischer J.,
Neithardt, W., 2004, Simulation im Werkzeugmaschinenbau, Simulation 1/04, FEM-Portal, 8086.
[79]
Reinhart, G., Meindlschmidt, J., 2000, Optimierung
von Werkzeugmaschinen am virtuellen Maschinenprototyp, ZWF 95, 550-553.
[80]
[65]
Merlet, J.-P., 1997, A Design Methology for the
Conception of Robots with Parallel Architecture,
Robotica, 15, 367-373.
[66]
Merlet, J.-P., 1998, The Importance of Optimal
Design for Parallel Structures, Proceedings First
European-American Forum on Parallel Kinematic
Machines, 31.8.-1.9.1998, Milano, Italy.
Reinhart, G., Baudisch, Th. Patron, Ch., 2000,
Perspektiven und Lösungsansätze für die integrierte
virtuelle
Produktentstehung,
WT
Werkstattstechnik online 90, Springer-VDI-Verlag,
Düsseldorf, 278-281.
[81]
Reinhart, G., Baudisch, T., 2001, Mechatronic
Simulation Environment of Machine Tools, Proth
ceedings of 8 IEEE Conference of Mechatronics
and Machine Vision in Practice, Hong Kong.
[82]
Reinhart, G., Oertli, Th., Zeller, W., 2001, Auslegung von NC-Antrieben unter Berücksichtigung
strukturdynamischer und prozessbedingter Wechselwirkungen, VDI-Bericht 1630, 187-206.
[83]
Rehsteiner, F., Weikert, S., Rak, Z., 1998, Accuracy Optimization of Machine Tools under Acceleration Loads fort he Demands of High-SpeedMachining, Proceedings of the ASPE 1998 Annual
Meeting.
[84]
Sauter, J., Lauber, B., Meske, R., 2001, Integrierte
Topologie- und Gestaltoptimierung in der virtuellen
Produktentwicklung, Konstruktion 3/2001, 56-60.
[85]
Schmidt, J., Söhner, J., 2002, Use of FEM simulation in manufacturing technology, ABAQUS Users’
Conference, May 29-31 2002, Newport, RI, USA.
[86]
Scharf, 1999, Auf dem Weg zur virtuellen Autoproduktion, CAD World – Management heute, Vol.
2.
[87]
Schneider, C., 2000, Strukturmechanische Berechnung in der Werkzeugmaschinenkonstruktion,
Dissertation, TU München.
[88]
Schulz, M., Reuding, Th., Ertl, Th., 1998, Analysing Engineering in a Virtual Environment, IEEE
Computer Graphics & Applications, 18(6).
[89]
Schumacher, A., 2004, Optimierung mechanischer
Strukturen – Grundlage und industrielle Anwendung, Springer-Verlag, Hamburg.
[90]
Schwertassek, R., Wallrap, O., 1999, Dynamik
flexibler
Mehrkörpersysteme,
vieweg-Verlag,
Braunschweig.
[91]
Spath, D., Neithardt, W., Bangert, C., 2001, Integration of Topology- and Shape-optimization in the
Design Process, Int. CIRP Design Seminar Stockholm, 267-270.
[92]
Spath, D., Neithardt, W., 2002, Optimized design
with topology and shape optimisation, Journal of
Engineering Manufacture, 219 Part B: 1187-1191.
[93]
Spence, A., Altintas, Y., Kirkpatrick, D., 1990,
Direct Calculation of Machining Parameters from a
Solid Model, Journal of Computers in Industry, 14
(4): 271-280.
[67]
Movahhedy, M.R., Altintas, Y., Gadala, M., 2002,
Numerical Analysis of Cutting with Chamfered
Tools, Trans. ASME, J. Manufacturing Science
and Engineering, 124 (2), 178-188.
[68]
Nebeling, P.H., 1999, Abgleich der dynamischen
Eigenschaften numerischer Modelle mit realen
mechanischen Strukturen, Dissertation, TH Aachen.
[69]
Neithardt, W, 2002, Dynamische Optimierung von
Bauteilen und Maschinen, iViP Abschlussbericht,
244-245.
[70]
Neithardt, W., 2004, Methodik zur Simulation und
Optimierung von Werkzeugmaschinen in der Konzept- und Entwurfsphase auf Basis der Mehrkörpersimulation, Dissertation, TH Karlsruhe.
[71]
Neugebauer, R. Noack, S., Klug, D., 2003, Simulation of Energy Flow in Hydraulic Drives of Forming
st
Machines, 1 International Conference on computational Methods in Fluid Power Technology, Melbourne, 333-348.
[72]
Pritschow, G., Altintas, Y., Javone, F., Koren, Y.,
Mitsuishi, M., Takata, S., Van Brussel, H., Weck,
M., K. Yamazaki, 2001,Open Controller Architecture-past, present and future, Annals of the CIRP,
50/2: 446-463.
[73]
Pritschow, G., Cronn, N., 2002, Wege zur virtuellen Werkzeugmaschine, WT Werkstattstechnik online 92 H.5, Springer-VDI-Verlag, Düsseldorf, 19419.
[74]
Pritschow, G., 2002, Echtzeitfähige Maschinenmodelle – Abbildung von Antriebsstötkräften bei
Parallelkinematiken, WT Werkstattstechnik online
92 H.5, Springer-VDI-Verlag, Düsseldorf, 187-193.
[75]
Pritschow, G., Cronn, N., 2002, Simulation Environment for Machine Tools, Production Engineering 9 / 2: 63-66.
[76]
Pritschow, G., Berkemer, J., Bürger, T., Croon, N.,
Korajda, B., Röck, S., 2003, Die simulierte Werkzeugmaschine, Tagungsband Fertigungstechnisches Kolloquium Stuttgart, 219-246.
[94]
Spence, A., Altintas, Y., 1994, Solid Modeller
Based Milling Process Simulation and Planning
System, Transactions of ASME Journal of Engineering for Industry, 116: 61-69.
[95]
Spence, A.D., Abrari, F., Elbestawi, M.A., 2000,
Integrated Solid Modeller Based Solutions for Machining, Computer Aided Design, Special Issue on
Solid Modeling ‘99, 32 (8-9): 553-568.
[96]
[97]
[98]
[99]
Spur, G., Krause, F-L., 1997, Das virtuelle Produkt
– 5 Virtualisierung der Produktentwicklung, Hanser
Verlag, München Wien, 398-469.
Strenkowski, J.S., Moon, K.J., 1990, Finite Element Prediction of Chip Geometry and ToolWorkpiece Temperature Distribution in Orthogonal
Metal Cutting, Trans. ASME, J. Eng. Ind., 112:
313-318.
Tlusty, J., 1978, Analysis of the State of Research
in Cutting Dynamics, Annals of the CIRP, 2: 583589
Tönshoff, H. K., Rackow, N., Böß, V., 2000, Virtual
Reality
in
der
NC-Programmierung,
WT
Werkstattstechnik online 92 H.7/8, Springer-VDIVerlag, Düsseldorf, 297-301.
[100] Tönshoff, H.K., Rehling, S., Tracht, K., 2002, An
Alternative Approach to Elasto-Kinetic Modelling of
th
Machine Tool Structures”, Proceedings of 6 International Conference on Advanced Manufacturing Systems and Technology (AMST’02), Udine,
215-223.
[101] Tönshoff, H.K., Clausen, M., Selle, J., 2003,
Hybrid cutting force prediction, Proceedings of the
36th CIRP-International Seminar on Manufacturing
Systems, Saarbrücken, Germany.
[102] Turan, A. 2005, Linear drive and linear encoder –
how to optimize interaction, Proceedings of the
Laser metrology and Machine Performance VII,
Lamdamap: 563-573.
[103] Van Brussel, H., Morelle, P., 2004, SAMCEF for
Machine Tools resulting from the EU MECOMAT
project, Proceeding of the NAFEMS Seminar
“Mechatronics in Structural Analysis”, Wiesbaden,
2004.
[104] Van Brussel, H., Sas, P., Németh, I., De Fonseca,
P., Van den Braembussche, P., 2001, Towards a
Mechatronic Compiler, Proceedings of IEEE/
ASME Transaction on Mechatronics, 90-105.
[105] Van Brussel, H., Symens, W., 2003, An Integrated
Virtual Engineering Environment for Machine
Tools, Autonome Produktion, Springer-Verlag,
Berlin Heidelberg, 474-487.
[106] Weck, M., Giesler, M., Pritschow, G., Wurst, K.H.,
1996, Den hohen Anforderungen gerecht – Neue
Maschinenkinematiken für die HSC-Bearbeitung,
Schweitzer Maschinenmarkt, 45, 28-35.
[107] Weck, M., Queins, M., 2000, Abgleich experimenteller und virtueller Modalanalyse von Werkzeugmaschinen, Proceedings VDI-Schwingungstagung
2000, VDI-Bericht 1550, Düsseldorf.
[108] Weck, M., Müller-Held, B., 2000, Virtuelle Produktund Prozessentwicklung, Konstruktionsarbeitsplatz
für die Werkzeugmaschinenentwicklung, WT
Werkstattstechnik online 92 H.7/8, Springer-VDIVerlag, Düsseldorf, 302-306.
[109] Weck, M., Queins, M., 2000, “Virtuelle Modalanalyse mit Hilfe der Mehrkörpersimulation”, Proceedings of Dresdner Tagung für Simulation im
Maschinenbau, Dresdner Freundeskreis der
Werkzeugmaschinen- und Steureungstechnik,
Dresden
[110] Weck, M., Queins, M., 2001, Kopplung von Antriebs- und Strukturdynamiksimulation in Werkzeugmaschinen, VDI Bericht 1630: 167-186.
[111] Weck, M., 2001, Werkzeugmaschinen – Messtechnische Untersuchungen, Kompendium der
Werkzeugmaschine Band 5, Springer-verlag, Berlin Heidelberg
[112] Weck, M., Giesler, M., 2002, Anwendungsorientierte Mehrkriterienoptimierung für Werkzeugmaschinen, WT Werkstattstechnik online 92
H. 7/8, Springer-VDI-Verlag, Düsseldorf, 361-368.
[113] Weck, M., Hessel, C., 2002, Flächenrückführung
topologieoptimierter FE-Modelle, WT Werkstattstechnik online 92 H. 7/8, Springer-VDI-Verlag,
Düsseldorf, 377-381.
[114] Weck, M., Queins, M., Witt, S., 2003, Effektive
Entwicklung von Werkzeugmaschinen, VDI-Z Nr.
145 (2003), Springer-VDI-Verlag, Düsseldorf, 3236.
[115] Weck, M., Queins, M., Witt, S., 2003, Coupled
Simulation of Structural Dynamics and Control
Loops for the Development of Machine Tools, Proceedings of the euspen International Topical Conference, Aachen, 117-120.
[116] Weck, M., Queins, Q., Brecher, C., 2003, Coupled
Simulation of Control Loop and Structural Dynamics, Annals of the German Academic Society for
Production Engineering, X/2: 105-110.
[117] Weck, M., Brecher, C., Schulz, A. ,Keiser, R.,
2003, Stabilitätsanalyse bei der HSC-Bearbeitung,
WT Werkstattstechnik online 93 H. 1, SpringerVDI-Verlag, Düsseldorf, 63-68.
[118] Weinert, K.; Surmann, T., 2001, Approaches for
Modelling Engagement Conditions in Milling Simulations, Fourth CIRP International Workshop Modelling of machining operations, Delft, August
17-18 2001: 67-69.
[119] Weinert, K., Damm, P., 2003, Maschinengerechte
Optimierung des 5-achsigen Fräsens von Freiformflächen, Proceedings of a Conference at Universität Dortmund, 71-82.
[120] Weinert, K.; Mehnen, J.; Peters. C.; Stautner, M.,
2004, Combining Finite Element Analysis and
Simulation of Cutting Engagement Conditions,
Production Engineering – Research and Development, Annals of the German Academic Society for
Production Engineering, Vol. XI/2: 105-108.
[121] Weinert, K., Surmann, T., Damm, P., 2004,
Real Time Solid Modelling of the Milling Process
Production Engineering – Research and Development, Annals of the German Academic Society for
Production Engineering, XI.2: 135-138.
[122] Weule, H., Schmidt, J., Söhner, J., 2000, Simulation of the High Speed Milling Process, Production
Engineering, VII/2: 23-26.
[123] Weule, H., Albers, A.., Haberkern, A., Neithardt,
W., Emmrich, D., 2002, Computer Aided Optimisation of the Static and Dynamic Properties of Parallel Kinematics, Proceedings of the 3rd Chemnitz
Parallel Kinematic Seminar, 527-546.
[124] Weule, H., Fleischer, J., Neithardt, W., Emmrich,
D., Just, D., 2003, Structural Optimization of Machine Tools including the static and dynamic
Workspace Behavior, Proceedings of the 36th
CIRP International Seminar on Manufacturing Systems, Saarbrücken, 269-272.
[125] Winkler, H.-H., Prust, D., 2003, Konzeptionen für
hochdynamische Maschinen, Tagungsband Fertigungstechnisches Kolloquium Stuttgart, 89-137.
[126] Witt, S., Queins, M., Brecher, C., 2004, Coupled
Simulation of Structural Dynamics and Control
Loop with MSC.ADAMS for the Development of
High-dynamic Machine Tools, Proceedings of Virtual Product Development Conference EMEA
München.
[127] Yeung, C.Ho, Altintas, Y., Erkorkmaz, K., 2004,
Virtual CNC System, Part I: Architecture and Auto
tuning of CNC Systems, Trans. ASME, J. Machine
Tool Manuf. Eng.Manufacturing Science and Engineering.
[128] Yeung, C.Ho, Erkorkmaz, K., Altintas, Y., 2004,
Virtual CNC System, Part II: Virtual Part Machining
and auto correction of contouring errors, Trans.
ASME, J. Manufacturing Science and Engineering.
[129] Zabel, A., Stautner, M., 2005, Einsatzfelder der
mehrachsigen Frässimulation, WT Werkstattstechnik online 95 H.1, Springer-VDI-Verlag, Düsseldorf, 56-61.
[130] Zaeh, M., Englberger, G., Oertli, Th., 2002,
Mechatronic System Simulation of NC Drives in
Machine Tool Design, Drive World (Asia/ Australia), 18-21.
[131] Zaeh, M., Engelberger, G., Oertli, Th., Siedl, D.,
2004, Strukturdynamik und Mechatronik in der
Werkzeugmaschinenentwicklung, Proceedings of
Mechatronik Seminar, München, 2.1-2.26.
[132] Zaeh, M., Oertli, Th., 2004, Finite Element Modellingf of Ball Screw Feed Drive Systems, Annals of
the CIRP, 53/1: 289-292.
[133] Zachmann, G., 1998, “ VR-Techniques for Industrial applications“, Springer Verlag, Berlin.
[134] Zatarain, M., 1998, “Modular Synthesis of Machine
Tools”, Annals of the CIRP, 47/1: 333-336.