How to Model Friction in SIMPACK
1. General
Modelling friction in multi-body systems is somewhat challenging.
The friction law itself is a simple function, see figure. However, if the relative velocity
between the two bodies that are connected by a friction element changes direction,
then the friction force will also change direction. The crucial point in modelling friction
is the handling of this sign change.
The SIMPACK friction models assume a damper force during the sign change, i.e. the
user defines a certain velocity ev at which the force transfers from a positive to a
negative value – shown by the dashed line in the figure above. This approach is realised
in the SIMPACK force elements 100 and 101.
2. Additional Features
This chapter also contains information about the Contact Force Element number 18 and
the solver option Root Functions.
3. Creating an Example Model
3.1 Concept
The model demonstrated is a basic friction model showing how to use friction elements
in SIMPACK: A brick slides over a plain surface with an initial velocity. It can move in all
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three translational directions, and it can rotate around the z-axis. An additional spring
defines the stiffness between the ground and the brick, which allows motion vertically.
Friction slows down the brick‘s movement and will bring the brick to rest. The spring
force between the ground and the brick is used as a normal force for the friction.
3.2 Modelling
1. Create a new model and enter the SIMPACK Pre Processor.
2. Redefine the reference frame primitive with the following parameters:
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3. Rename Body1 to Brick and change the primitive so it has the following
parameters:
All other parameters of the body remain unchanged.
4. Define the Joint of the Brick with the following parameters:
Please note that despite the fact that we are modelling a planar system, the brick is also
given the degree of freedom vertically direction. We will restrain this movement again
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by defining a spring between the plane and the brick. This is necessary as we need a
normal force as one of the inputs for the friction element.
5. Define a Force Element between the Brick and the Plane (i.e. the Inertia System)
with the following parameters:
We first allow the brick to move vertically by giving it the appropriate degree of
freedom in Step 4, but then define a spring/damper force to restrict this movement and
support the brick. In the final step this force will be used as a normal force in the
friction element. Please check whether your model behaves as expected by carrying out
a time integration.
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6. Define a Force Element for the friction
Create a new force element, name it Friction and select Force Element 100: Nonlinear
Friction Cmp.
In the first line of the parameter list select Friction Coefficient as the operating mode.
In the second line of the force element’s parameter list we are asked about the type of
output desired. Force and Torque are offered, i.e. Force Element 100 could be used as a
rotational as well as a translational element. In this case select Force.
The following two parameter lines are used to define the direction of the force. In line
number 3 the axis is selected from a list, in line number 4 you can define whether the
force should act in the direction of the axis defined, or alternatively in the plane vertical
to it. For our example select Z-Axis and Vertical to Axis. This means the friction force we
are defining will act in the X-Y-Plane.
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In the next three parameter lines the force element is defined, which delivers the
normal force used to calculate the friction. This normal force will be multiplied by a
factor (friction coefficient) or function later on to determine the friction force. SIMPACK
allows any other force element to be used as the normal force for the friction or
alternatively any constraint. Select Force Element and then the Force Element Ground.
As Ground is a component 3-dimensional spring, it offers forces in three different
directions. The force output values are listed in the documentation as Output work
quantities. In our example enter F_z given in M_i [N] to get the force in the vertical
direction.
In the next line the switch velocity ev (epsva) is defined. Small values support a higher
accuracy, but it might be somewhat time consuming to use too small values. As a rule of
thumb values between 0,01 and 0,001 m/s have turned out to be a reasonable
compromise between accuracy and performance.
3.2 Solver
Configure the Time Integration so the windows appear as follows
3.3 Results
The results of the simulation is that the velocity of the sliding brick decreases
exponentially to zero.
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4. Outlook
As the spring force between the brick and the ground was modelled as a one sided
contact spring element (Force Element 18), it also covers a simulation of a flying brick
hitting the ground. Modifying the initial vertical position of the brick to for instance to
0.14 m and re-starting the simulation will make the integrator output the following
message:
tact = 0.168944675447810
Root detected
* Active Root
1 of Force Element $F_Ground
This points at SIMPACK’s functionality to stop the integrator whenever strongly nonlinear behaviour in the relevant force element, called Root, occurs (in this case the brick
touching ground). Initialise it with the new force characteristics (spring force is now
active) and re-start the integrator. This allows SIMPACK to reliably and efficiently solve
all kinds of discontinuous system without encountering numerical problems.
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