A combined 1D-3D simulation approach for the energy
analysis of a high speed weaving machine
J.Croes1, A. Reveillere2, S. Iqbal1, D. Coemelck3, B. Pluymers1, W. Desmet1
1
KU Leuven, Department of Mechanical Engineering
Celestijnenlaan 300 B, B-3001, Heverlee, Belgium
e-mail: jan.croes@mech.kuleuven.be
2
LMS Imagine
Quai Charles de Gaulle 84, F-69006, Lyon, France
3
Picanol NV
K. Steverlyncklaan 15, B-8900, Ieper, Belgium
Abstract
Due to the ever increasing energy costs, energy efficiency has become a major factor in the total cost of
ownership of production machinery. In highly dynamic systems such as weaving machinery, the losses are
predominantly linked to friction in the bearings, gears and cam&followers and the electrical losses in the
motor. In order to virtually assess the energy consumption, a multiphysical model is required that not only
links the dynamic behavior of the mechanical system with the tribological aspects related to the relative
motion between the parts, but also models the influence of the electric motor. In this work, a methodology
is presented to model systems of multiphysical nature applied to a weaving machine with respect to energy
efficiency. The holistic model allows to pinpoint the most dominant sources of energy loss and to assess
how changes in components or topologies of the machinery may have an effect on the overall (dynamic
and energetic) behavior of the machine at system level. Due to the fact that different subsystems are
described into one integrated environment, design changes in the overall system lead to a more global
optimum instead of trying to improve the several subsystems independently.
1
Introduction
In recent years, there is a growing awareness regarding the importance of energy efficiency in production
machinery. The need for more efficient machinery is motivated by two main arguments:
1. Increasing energy prices start to dominate the total cost of ownership;
2. Legislation will enforce specific regulations regarding energy consumption in production
machinery.
The total cost of ownership (TCO) of a machine includes the purchase cost, maintenance cost and
operation cost of the machine. As various studies have shown [1] that the energy in production machinery
is mainly being consumed during the use phase, it becomes evident that the TCO will be one of the key
parameters when purchasing a machine. Moreover, a decrease in energy consumption has a direct
influence on the maintenance and lifetime of machinery as a decrease in frictional losses reduces the wear
in the system.
Also, as the earth’s supply of fossil fuels is depleting, the European Union[2] is currently setting up a
specific regulation to control, monitor and minimize the energy consumption of production machinery,
urging machine tool constructors to start looking for methodologies to quantify the energy consumption
and to develop strategies for its reduction.
2253
2254
P ROCEEDINGS OF ISMA2012-USD2012
Overall, the arguments above state that there is a clear need to identify and optimize the energy efficiency
in machinery. Over the years, production machinery has evolved from purely mechanical systems to
multiphysical mechatronic applications involving electrical actuators, cooling systems, hydraulic units etc.
As all these components are integrated into one design, the interaction between the different modules is no
longer negligible, especially when energy consumption is being investigated. Therefore a unified approach
is needed to model all types of physical systems, producing both linear and non-linear mathematical
models in one integrated environment. A bond graph [3] based approach is presented to couple systems of
various physical nature and different formalisms as it is based on energy formulations which are
independent of their physical origin. A second aspect related to the use of multiphysical simulation is the
scalability of the component models as coupling highly detailed component models will have a significant
effect on the computation time. This issue will also be addressed when explaining the methodology.
The novelty of this paper is that it proposes a methodology for energy efficiency on system level based on
physical formulations rather than looking at the problem from a purely experimental point of view. This
method also allows us to differentiate between the different loss sources at each point in time which is
nearly impossible based on purely experimental procedures.
Industry and the research community have already taken some first steps towards multiphysical modeling
based on different formalisms in an ad hoc fashion. In [4], an optimized thermal design of a vehicle
compartment is established using a combination of 1D/3D modeling. In [5], the strength of the integration
of 1D and 3D in the thermal/fluid mechanics domain is assessed. In [6], similar research activities have
been done for a turbocharged SI engine. These examples illustrate the need for combining different
modeling methodologies and show that a generic approach is necessary to combine components/modules
of different complexity and of multiphysical nature.
This paper starts with a description of the architecture requirements and methodology in a general
framework, whereas the following chapter establishes the connection to the application.
2
2.1
Methodology
Architecture requirements
As no general framework exists for simulating multiphysical models, a set of architectural requirements
are defined below:
1. The architecture should allow individual component modeling without restriction on the choice of
the underlying formalism
2. The architecture should allow individual component models to interface with each other, since its
(energetic or dynamic) behavior not only depends on its own characteristics, but also on its
environment. As an example, we take a shaft supported by two bearings. In a supported shaft, the
resulting forces influence the losses in the bearings. For this reason, the bearing models have to be
coupled to the shaft. A local stiffness change in the shaft will alter the force distribution and affect the
losses in each bearing. In this case, the bearings are the components and the shaft is defined as the
environment.
3. The interfacing should take place in a consistent manner; meaning that the mathematical
description of the same physical component can be replaced without changing anything else in the
overall assembly model. For instance: a fast, but less accurate description of a bearing can be replaced
with a slower, but more accurate description, and this without changing anything to the model of the
gearbox in which the bearing component is used. The approach is used to adjust the computation time
and is most suitable to downscale high-fidelity models for real-time applications or vice versa.
4. The architecture should allow easy calculation and analysis of the energy flow between components
and maintain observability of the stored and dissipated energy in the components. This fourth
criterion is specifically applicable for energetic analysis.
M ULTI - BODY DYNAMICS AND CONTROL
2.2
2255
Bond graph theory as a basis for multiphysical modeling
As the bond graph theory forms the basis of the methodology, an overview of the basic building blocks is
given in table 1. The theory is based on physical modeling where different components are combined
based on power and flow exchange relationships. As the effort e and flow variables f are directly related
to the power P (1) and energy E (2), the power flow over the system can easily be obtained at each
point in the system. It is a 1D modeling approach since both effort and flow have no direction and the
geometry of each component is not explicitly modeled as in finite elements. The power parameters i.e.
effort and flow, have different interpretations in different physical domains. Yet, power can always be
used as a generalized co-ordinate to model coupled systems residing in several energy domains.
P = e⋅ f
(1)
t
E = ∫ e ⋅ f ⋅ dt
(2)
−∞
t
Inertial element
e = c1 ⋅ ∫ f ⋅ dt
−∞
t
capacitive element
f = c1 ⋅ ∫ e ⋅ dt
−∞
resistor
flow sources
effort sources
transformer
gyrator
0-junction
1-junction
f = g(e, c1 , c2 )
f = g(c1 , c2 )
e = g(c1 , c2 )
e1 = c1 ⋅ (e2 )

f = 1 ⋅(f )
 1 c1 2
e1 = g( f2 )

e2 = g( f1 )
e1 = e2 = ... = en

n

fi = 0
 ∑
i =1
 f1 = f2 = ... = fn

n

ei = 0
 ∑
i =1
Table 1: Different components of the bond graph theory
Bond Graph models use a causal approach. This means that for each block the effort is defined as an input
and the flow as an output or vice versa. This makes it easy to couple different components and prevents
the user to connect incompatible ports. As the Bond Graph Theory is predominantly applicable for 1D
systems, the authors propose to expand this causal way of exchanging energy variables to systems
described by different formalisms.
The key point is to translate each component submodel as an equivalent building block in a
consistent way as described in table 1. This implies that a causality assignment has to be imposed for each
particular submodel prior to the implementation in the full environment, which means that it should be
clearly specified which multiport variables are input and which one are output. A causal bond graph based
approach has the following benefits:
2256
P ROCEEDINGS OF ISMA2012-USD2012
•
The description of the equations can be tailored to have a beneficial effect on the computational
effort. It leads more easily to explicit equations and does not require the elaborated tools used in
acausal modeling;
It allows scalability of the submodels as each component can be seen as an I/O model with effort
and flow ports, and changing the complexity of the component keeps the consistency at system
level intact. In practice this means that a gearbox can be implemented as a simple ideal
transformer or as a very detailed flexible multibody contact without changing the consistency as
long as the input and output variables stay the same. The strength of such a technique is that the
model can serve as a high-fidelity model by using the most detailed description for each
component. It can also be downscaled by means of reduction techniques to be used for real-time
applications;
It leads to a generic procedure for assigning the interface points in co-simulation procedures
and provides guidelines for the implementation of control laws.
•
•
Each of these specific advantages will be elaborated in detail in the next paragraphs.
In practice, combining 3D systems in a causal Bond Graph approach is not straightforward since energy
cannot be represented as a spatial vector. For that reason, a 3D system or module should be kept as a
single entity and a multiport has to be added to establish a connection to the 1D environment. A rigid
multibody mechanism can be seen as a nonlinear inertial element where a torque or force (flow variable)
is applied to the submodel, while the rotational or linear velocity (effort variable) is the output of the
submodel as illustrated in figure 1a. The assignment of the causality in flexible multibody mechanisms is
less straightforward. In this case the component can be seen as a combination of inertial and capacitive
elements grouped in one model as shown in figure 1b.
Figure 1: (left) Schematic illustration of rigid multibody model ports, (right) Schematic illustration of
flexible multibody model ports
The causality rule is not a necessary condition for multiphysical modeling but the generality of the
proposed approach is lost and the scalability of the submodels is less obvious. However in some cases,
ignoring causality in a 1D environment can lead to unfeasible results. This can easily be illustrated based
on an example in figure 1 involving two masses and a force source. At each step of the integration, an
evaluation function is called which evaluates the output of all the components by calling them in the right
order. In the first step, the velocity of mass 1 will be calculated based on the value of the force source. In
the second step the velocity of the second mass is imposed since it is an input variable. This leads to a
break in the inertia link and causes unphysical results. Integral causality is generally preferred where the
cause is integrated to generate the effect. Differential causality requires information from the future and
hence may indicate serious violations in the principles of conservation of energy, as also was seen in the
previous example. The way to prevent this is to combine both masses into one equivalent mass or to place
a spring in between.
Figure 2: Example system with inconsistent causality
The integration of a 3D system which runs on a different solver in a 1D environment is practically not
straightforward since it requires continuous interaction between both components. Therefore, different cosimulation approaches are available to link different software packages. In the current state of the art, three
techniques are generally used. The most straightforward solution is to integrate the equations directly into
the 1D environment. This technique is called ‘model exchange’. In this case translation techniques are
M ULTI - BODY DYNAMICS AND CONTROL
2257
used to make the set of equations eligible for the specific package. The exchanged model can be seen as a
black box. The second option is to exchange system matrices. This technique is also known as strong cosimulation and is very popular in the vibro-acoustic analysis domain where the system equations are
solved as a whole. A third option is the usage of weak co-simulation. In this case, the models from
different software packages each run with their own solver and communicate at different points in time.
The Jacobi scheme and the Gauss-Seidel approach are most often used. These techniques have been
studied extensively and are available in several different forms. For a more detailed background, the
reader is referred to [7], [8], and [9].
Since a multiphysical system does not only consist of a physical component, the multiport has to be
expanded to deal with control laws which are not a physical part of the system. The inputs are
measureable physical quantities which will be processed into an output signal which controls the actuator.
For these components, effort and flow variables are not relevant. To allow exchangeability of signal based
models at system level, the definition of the inputs and outputs must also remain fixed.
Apart from the control laws, the interface variables between the different components cannot only be
established by means of the effort-flow formulations. For a bearing model, the description of the
dissipative behavior is dependent on the bearing loads resulting from the excitation forces (axial and radial
load) of the nearby components (figure 3). Implementing the radial and axial load in the bearing model
causes an implicit loop in the system since the frictional loss caused by the load also influences the
excitation forces in the system.
Figure 3: (left) Bearing model with its physical ports, (right) Schematic representation of the bearing
The addition of the implicit loops slows down the simulation and can result into failed convergence when
the evaluation of the excitation forces and the bearing loss model occur with different solvers. It changes
the ordinary differential equation ODE (which normally originates from a Bond Graph model) to a
differential algebraic equation DAE. A few general guidelines can be used to diminish the issue or break
the algebraic loop:
A.
B.
C.
D.
E.
Keep the implicit loop as small as possible
Estimate the value of the force by means of an extrapolation function
Use the value of the forces from the previous time step
Apply a filter to exclude the higher-order dynamics
Decouple the dynamic and energetic behavior by stating the Tloss equal to zero during the
simulation and calculate the power losses in a post-processing phase
Option A does not decrease the accuracy of the simulation whereas the other actions cause a
computational error. If the time step is small compared to the dynamics in the system, option B and C will
result in a significant decrease in computation time without compromising too much on the accuracy. The
consequences of a filter depend on the adopted cut-off frequency while the last option (E) can only be
used if the introduced losses in the system are a few orders of magnitude lower than the dynamic variables
(forces, torque).
2.3
Assessment of energy consumption in multiphysical models
As stated in the architecture requirements, the energy and power flow of each component has to be
observable at all times in order to evaluate the energy consumption at system level. The fact that effort and
flow are readily available at both the interface points makes it possible to assess the energy difference
between the interface points of the component. This does not give any information on whether the energy
2258
P ROCEEDINGS OF ISMA2012-USD2012
is stored as inertial, as capacitive energy or as if it has been dissipated. For this reason, each element
(component or module) has to compute all the inertial, capacitive and dissipative energy in order to
evaluate how much energy is dissipated in the system and which portion is temporarily stored in a
capacitive or inertial element. The computation of the power does not introduce any extra state variables
to the system since it is just a multiplication of certain effort and flow variables. The computation of
energy often does require a state variable if the power is numerically integrated over time as in (2). In
some cases, when an analytical solution is available for energy, the introduction of extra state variables
can be avoided. For example, this is the case for a spring and a mass as stated in (3) and (4):
E=
k ⋅ x²
2
(3)
E=
m ⋅v²
2
(4)
The energy variables can also be integrated later in a post processing phase by numerical integration by
the summation of the power at each point in the print interval multiplied by the print interval (5). This
results in a small error and can lead to the fact that input energy is no longer equal to the dissipation plus
the work.
E=
N
∑P
i
⋅ ∆ t pr int
(5)
i =1
3
3.1
Model of a high-dynamic weaving machine
System description
The proposed methodology has been applied to a weaving loom. In figure 4, a CAD drawing of the
mechanism under investigation is shown. It can be divided into 5 different modules:
• The control unit is a mean speed controller with a very low bandwidth to maintain a mean
velocity on the cam shaft over a few rotations. It is insensitive to oscillations within one period;
• The gearbox is the link between the motor and the cam shaft. It has the purpose to decrease input
torque while still maintaining a sufficient power supply to the complete drivetrain. The use of a
gearbox allows the motor to work in a more optimal working regime;
• The cam & follower module transfers a purely rotational motion into an oscillating motion at the
follower shaft; this motion is mechanically synchronized with the gripper motion. Two identical
mechanisms are placed in series to increase the robustness of the module;
• The 3D mechanism has a similar function as the cam & follower as it defines a kinematic
relationship between the rotational motion of the cam shaft to an oscillation motion of the rapier
wheel. The same mechanism is placed at both sides of the cam shaft. The difference with the cam
& follower module is that both its rotation vectors of input and output shaft do not have the same
orientation;
• The rapier wheel drives the linear motion of the gripper. Both grippers (left and right) meet each
other in the middle to pass a wire of the blanket. The gripper is not included in the model.
The working principle of the machine is as follows; the motor drives the main shaft on a more or less
constant velocity. The 3D mechanisms transfer the rotational motion to a linear motion of the gripper
(figure 5). One gripper takes a wire and transfers it to the other gripper between the partially woven
blanket. The cam & follower mechanisms push the wires together.
The specific modules are highly coupled because the removal of one particular module has a significant
effect on the global behavior, i.e. removing the rapier wheel causes a decrease in inertia and thus changes
the dynamic load and hence the motion of the system. Therefore the complete system has to be simulated
into one integrated environment.
M ULTI - BODY DYNAMICS AND CONTROL
Figure 4: CAD drawing of the weaving loom
Figure 5: Illustration of the weaving principle
2259
2260
3.2
P ROCEEDINGS OF ISMA2012-USD2012
Modeling procedure
In figure 6, the model is shown as a set of building blocks. The 1D environment is setup within the
software package LMS Imagine.Lab AMESim[10] while the multibody model, in this case the 3D
mechanism, is described in LMS Virtual.Lab Motion[10]. The modules (control, gearbox etc.) are grouped
into the colored rectangle. This graphical approach of modeling is typical for modeling large systems since
it allows the user to maintain a clear overview of the system in question. The underlying equations can
vary from a simple relationship to a fairly complex representation of the physical phenomena. It is clear
that the underlying equations can be simplified without changing the consistency of the simulation at
system level. This makes it possible to gradually improve the level of detail in the system or downscale
the complexity of some components. In this paper, it is not the intention to give a full account of each
particular element in the system but rather give a helicopter view of the complete model with respect to
the methodology.
Figure 6: Multiphysical model of the weaving loom (the picture of the 3D mechanism is distorted on
request of Picanol)
The architecture requirements in 2.1 state the criteria for modeling a multiphysical system from a high
level point of view. If the model has to be tailored to evaluate the energy consumption in predominantly
mechanical systems, two extra criteria need to be added:
1. The loss models have to be valid within the working domain with a reasonable level of accuracy
2. The most dominant characteristic of the dynamic behavior has to be captured as it serves as an
input to the loss model
In most high level models, friction is often modeled with simple relations like Coulomb or viscous
friction. For such a representation it is difficult if not impossible to obtain the proper parameters. If there is
M ULTI - BODY DYNAMICS AND CONTROL
2261
little confidence in the choice of the parameters, the evaluation of the energy consumption has no value.
Therefore, three different options are available:
A. Do an experimental campaign to obtain the relationship between the parameters that influence the
dissipation and formalize it as a function or a multidimensional map
B. Acquire the dissipation characteristics/formulations of the specific component from the supplier
and implement them in a model
C. Model the component in detail from a phenomenological point of view to assess the dissipative
behavior
Even though options B and C do not necessarily require the use of measurements, it is advisable to
estimate the more uncertain parameters by means of experiments to gain confidence in the model. The
choice of the approach depends on the required accuracy of the simulation and the available information.
In this particular application, five different loss sources (figure 7) are modeled and each method is
addressed.
Figure 7: Different loss models from left to right: seal, bearing, electric motor, cam follower and gear
transmission.
3.2.1
Bearing and seal losses
The bearing model is implemented based on the information from the supplier, where the SKF models
[11] are used to estimate the friction as a loss torque as in (6). Mind that seal loss Tseal takes into account
the seal losses if they are integrated in the bearing itself. Equation 6 is implemented conform to the bond
graph theory in (7). tanh(ϖ 2 / e) defines the sign of the loss torque and removes the discontinuity from
the model. The value e determines the stretch of the tangent hyperbolic function. This formulation is only
valid when the velocity is varying over a wide range and does not turn into standstill. In custom made
bearings, the equations and parameters from the manufacturer are tailored to the specific bearing by means
of experiments or integrated as a multidimensional nonparametric loss map. More information about this
procedure can be found in [12]. The representation of the submodel as a building block is illustrated in
figure 3a.
Tfriction = Trolling + Tsliding + Tdrag + Tseal
(6)
T2 = T1 + T friction (ϖ 2 , FR , FA ) ⋅ tanh(ϖ 2 / e)

ϖ 1 =ϖ 2

(7)
The (external) seal losses are estimated as a viscous friction torque in a similar fashion and the slope is
acquired from the manufacturer.
3.2.2
Motor losses
The motor model is based purely on experimental results where the efficiency is determined by measuring
the input power coming from the electric grid, the torque and velocity at the output shaft. More
information regarding this procedure can be found in [13], [14], and [15]. The loss torque consists of a
2262
P ROCEEDINGS OF ISMA2012-USD2012
summation of the electrical losses (iron losses, cupper losses, convertor losses) and the mechanical losses
in the motor. In this case, the motor can be seen as a torque source.
T2 = T1 + Tloss (ϖ 2 , T2 ) ⋅ tanh(ϖ 2 / e)
(8)
In this case, the no-loss torque T1 and the rotational velocity are ϖ 2 are the inputs, while T2 is the motor
output torque. In figure 8b, an example is given how the implicit equation is solved within the model. As
the user defines the causality himself, he/she determines the solver algorithm and accuracy for the specific
component. The advantage is that the user can choose a compromise between accuracy and computation
speed for each component. It is important to notice how extra robustness is implemented by limiting the
number of iterations for extreme cases like very small variables again tailored to each component. This is
in contrast with acausal modeling where only a relationship between the input and output is defined. In
that case, automated procedures are implemented to solve the equations as a whole. This procedure is not
as robust and fast as compared to the causal approach.
Figure 8: (left) Schematic representation of the ports in the motor model, (right) Solver procedure to
calculate motor output torque
3.2.3
Cam & follower losses
The cam & follower losses are modeled from a phenomenological point of view, where all the different
loss sources are described by mathematical relationship. The bearing in the roller is modeled by a SKF
model where the rolling loss and the sliding loss equations can be found in almost any tribology reference
work [16],[17]. For those sources the rolling vrolling and sliding velocity v sliding are important as well as the
normal force FN , fluid film thickness hfilm and friction coefficient µ film . The different contributions to the
loss torque are summed and translated to a torque loss at the cam shaft. To avoid numerical problems
around zero velocity, the addition of the Gauss curve gaus (ϖ / e) is added.
Ploss = Pbearing (ϖ bearing , Fr ) + Prolling (v rolling , FN , h film ) + Psliding (v sliding , FN , µ film )
Tloss =
Ploss
ϖ + gaus(ϖ / e)
(9)
(10)
M ULTI - BODY DYNAMICS AND CONTROL
3.2.4
2263
Gear losses
The gear losses are in this case modeled with a constant efficiency of 99% since the gears are straight and
literature has shown that the variation around this value is fairly small. The sign of the loss torque for the
cam & follower as well as the gears are modeled in the same way as for the bearings.
3.2.5
Multibody model
Special attention has to be drawn to the implementation of the multibody model of the 3D mechanism in
the 1D environment. The integration of a multibody model deemed necessary as the rotation vectors
changed in magnitude and orientation which was unfeasible to model in a 1D environment. The bodies are
modeled as rigid parts since they are designed to be very stiff. As the joints in the mechanism suffer from
high dynamic loads, the losses in these bearings in the mechanisms are not negligible. Therefore a very
dense coupling was established where the solvers continuously interact with each other.
The 3D mechanism consists out of 6 joints as shown in figure 6. Joint 1 and 6 are connected to
(capacitive) spring elements in the 1D environment and their input torque and output velocity form the
ports of the equivalent inertia. These ports are indicated on the left side of the ‘3D mechanism block’ in
figure 9. On the right side of the block, the velocity and force variables for each joint are added as outputs.
The variables are fed into the bearing models (which are described in the 1D environment) which calculate
the friction torque for each joint. This friction torque is applied as a torque in each respective joint in
opposite direction of the rotational velocity. As the multibody model consists out of rigid parts, the
degrees of freedom in the joints have to be divided in order the reach on isostatic configuration. This
implies that axial forces in the joints attached to one particular shaft have to be divided arbitrarily in the
bearing model. This is for example the case for joints 3 and 4. This arbitrarily assignment of the axial
forces in the bearings can be avoided by implementing a flexible model of the respective bodies. If the
degrees of freedom of the flexible body are decreased by projecting them on a reduced base like illustrated
in [18], this extra obtained accuracy does not significantly influence the computation time
Figure 9: Schematic representation of the ports of the 3D mechanism
Special care has to be taken when implementing such a model as stated below:
•
•
•
•
Mind the local axis definition in order to get the load and velocity in each joint in their local axis
system;
Mind the sign conventions in 1D and 3D which differ from each other, the same goes for the
model units;
Make a well considered choice regarding the (macroscopic) communication interval and the
solution tolerances and step size of each solver.
Add low-pass filter to the output variables of the multibody signals if they are of discrete nature as
the solver used is bond graph methods are designed to handle continuous signals. The filter is also
necessary to remove possible glitches in some of the variables in the MB model.
2264
P ROCEEDINGS OF ISMA2012-USD2012
Although these actions seem straightforward, mistakes are easily made since the variables coming from
the multibody model are simply coming from several sensors and are not conform to the sign and
modeling units of the 1D environment. The best practice is to do a thorough check of the submodel before
implementing it in the integrated environment. The macroscopic communication interval and solution
tolerance have to be determined by means of trial and error. A very coarse communication interval can
lead to a long convergence time for each step and can sometimes cause the simulation to be unstable or
completely break down. A smaller communication interval will speed up the convergence between time
steps but when it is chosen too small, it becomes very inefficient. The effect of the solution tolerance is
also very hard to predict because in some cases it is even possible that a smaller tolerance leads to a faster
computation time.
In this model, the Gauss-Seidel weak co-simulation procedure with equidistant macro time steps is used
where the 1D model is the master, but experience and literature [7],[8],[9] has shown that this is by no
means the best option. A more efficient approach is to use a variable macro time step approach where the
step size is controlled by the solver which integrates the system with the lowest frequency content (in this
case the multibody model). This reduces the number of (unnecessary) evaluations of the slower system.
3.2.6
Implicit loop handling
As stated in 2.2, several models like the bearings are not only linked by their effort and flow variables
with other components but have other inputs from nearby components. In this paper, the generated
implicit loops related to the bearings are broken by means of a first-order low-pass filter (figure 10).
Figure 10: Illustration of implicit loop handling
The main reason for this approach is the fact that the bearing loss models are designed for static behavior
and are not validated for dynamic behavior. The assumption is made that the high frequency oscillations
on the radial and axial forces have no significant influence on the general loss behavior. This results in a
decrease in computation time as the profile of the output variables is much smoother and easier to
integrate by the solver. The implicit loops generated by the interaction with the multibody model are
handled in the same way since the loss torque which is fed into the MB model is filter by a low-pas filter
as show in figure 9.
M ULTI - BODY DYNAMICS AND CONTROL
4
2265
Results
In this paper, only a brief description of the results is given whereas of more detailed analysis will be
published in the near future. Figure 11 lists the contribution of the losses per component type. This
particular application consists of over 30 bearings, which naturally consume most of the energy. A more
detailed look (not discussed here) of the share of each individual bearing with respect to the total loss
allows us to pinpoint exactly which sources are most critical to address. A second slightly surprising effect
is the significant contribution of motor losses since it is only one component in the system and an electric
motor is generally very efficient. Therefore it is important when one wants to assess whether it is worth
improving the energetic behavior to check the energy consumption instead of the energy efficiency. Since
the motor is the first part of the power stream in the mechanical system, a slight decrease in energy
efficiency can lead to a significant change in overall power consumption.
Figure 11: Relative energy consumption of the different components in the system
5
Discussion
In this paper, the different architecture requirements are highlighted to model a multiphysical system with
respect to energy efficiency. The requirements have led to an expanded version of the Bond Graph theory
for integrating systems of different formalisms into a single environment and were solved simultaneously
to evaluate the energetic behavior at system level. The key points involve the translation of each element
as an equivalent bond graph block by stating that the interface points between the models have to consist
of energy and flow variables. A second point of attention is the use of a causal approach where the input
and output are clearly defined and not just as a relationship between two interface points of the submodel.
As a third item, the definition of the interface points have to be fixed in order to maintain consistency
when the underlying formalism of the submodel changes. This approach has been applied on a weaving
machine and an overview is given on how the different loss models are translated into a bond graph
approach. The value of such a model is that it gives a clear overview of the loss distribution in the system.
This gives the machine manufacturer the opportunity to make changes in the design to assess how the
distribution of the power consumption is changing and which actions lead to a more efficient design.
Acknowledgements
The authors are grateful to the European Commission seventh framework programme (FP7/2007-2013)
under the project name ESTOMAD (no. 247982) for the financial assistance. Also the IWT Flanders and
the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science
Policy Office, are gratefully acknowledged for its support.
2266
P ROCEEDINGS OF ISMA2012-USD2012
References
[1] W. Dewulf, A pro-active approach to ecodesign: framework and tools, Katholieke Universiteit
Leuven, Departement Werktuigkunde, Leuven (2003).
[2] Commision of European communities, Consultation on the future EU 2020 strategy, Commission
working document, http://ec.europa.eu/eu2020/pdf/eu2020_en.pdf (2009)
[3] C. Karnopp, D. L. Margolis, R. C. Rosenberg, System Dynamics Modeling and Simulation of
Mechatronic Systems, John Wiley & Sons, inc., Hoboken, New Jersey (2006)
[4] P. Baker, M. Jenkins,St. Wagner & M. Ellinger, An Optimised Thermal Design and
Development Process for Passenger Compartments of Vehicles, www.flowmaster.com
(2009).
[5] U. Renberg, 1D engine simulation of a turbocharged SI engine with CFD computation on
components, Department of Machine Design, Royal Institute of Technology, Stockholm
(2009).
[6] Vdovin, Cooling performance simulations in GT-Suite, Department of Applied Mechanics,
Division of Vehicle Engineering & Autonomous Systems, Chalmers institute of technology,
Göteborg (2010).
[7] M. Busch, B. Schweiser, Stability of co-simulation methods using hermite and lagrange
approximation techniques, J.C. Samin, P. Fisette, Multibody dynamics 2011, ECCOMAS
Thematic Conference, Brussel, Belgium, 2011 July 4-7, Brussels (2011).
[8] R. Schmoll, B. Schweizer, Co-simulation of multibody and hydraulic systems: comparison of
different coupling approaches, J.C. Samin, P. Fisette, Multibody dynamics 2011, ECCOMAS
Thematic Conference, Brussel, Belgium, 2011 July 4-7, Brussels (2011).
[9] M. Friedrich, M. Schneider, H. Ulbrich, A parallel Co-simulation for Mechatronic Systems, The first
joint Conference on Multibody System Dynamics, Lappeenranta, Finland, 2010 May 25-27,
Lappeenranta (2010).
[10] LMS, http://lmsintl.com
[11] T. Cousseau, B. Grac, A. Campos, J. Seabra, Friction torque in grease lubricated thrust ball
bearings; Tribology international, Vol 44, No 4 Academic Press (2010), pp. 609-625.
[12] S. Iqbal, F. Al-Bender, J. Croes, B. Pluymers, W. Desmet, Frictional power loss in solid-grease
lubricated needle roller bearing; Lubrication Science, 10.1002/ls.1195., John Wiley & Sons Ltd.
(2012).
[13] W. Deprez, D. Vanhooydonck, W. Symens, S. Dereyne, J. Driesen, Iso Efficienct contours as a
Concept to Characterise Variable Speed Drive Efficiency, International Conference on Electrical
Machines, Rome, Italy, 2010 September 6-8, Rome (2010).
[14] K. Stockman, S. Dereyne, D. Vanhooydonck, W. Symens, J. Lemmens and W. Deprez, Iso
Efficiency Contour Measurement Results for Variable Speed Drives, International Conference on
Electrical Machines, Rome, Italy, 2010 September 6-8, Rome (2010).
[15] Vanhooydonck, W. Symens, W. Deprez, J. Lemmens, K. Stockman and S. Dereyne, Calculating
Energy Consumption of Motor Systems with Varying Load using Iso Efficiency Contours,
International Conference on Electrical Machines, Rome, Italy, 2010 September 6-8, Rome (2010).
[16] R. D. Arnell, P. B. Davies, J. Hailing, T.L. Whomes, Tribology Principles and Design Applications,
Macmillan education LTD, London (1991).
[17] R. Gohar, H. Rahmejat, Fundamentals of tribology, The MIT Press,Cambridge, Massachusetts
(2008).
M ULTI - BODY DYNAMICS AND CONTROL
2267
[18] W. Heylen, S. Lammens, P. Sas, Modal Analysis Theory and Testing, Katholieke Universiteit
Leuven, Departement Werktuigkunde, Leuven (1997).
2268
P ROCEEDINGS OF ISMA2012-USD2012