2 Motion-Simulation (Multibody Dynamics)
2.3 Learning Tasks on Dynamics
2.3.1■Drop Test on Vehicle Wheel
This learning task explains how to deal with tasks that have to do with free movements. This could involve, for example, free-fall, inertial effects or similar problems. There are thus indeterminate degrees of freedom, and the movement arises due to forces. Experi- ence has shown that such problems are much more difficult to use in practice than is the case with the previously-considered kinematic systems. We therefore wish to clarify the principles on a very simple model.
The articulation function determines and displays exactly in which position the interference occurs .
Characteristic of dynam- ics is that there are indefinite degrees of freedom and that movement results from external forces .
Geometry of
environment
initial position
end position
motion track
Additionally to dynamics, also complex contacts play a role in this example which defi- nitely differ from the previously used purely kinematic joints. Hitting or lifting off parts of the contacts under consideration is possible. Thus, opportunities arise for the analysis of impact tests, friction effects, clearance or tolerances.
2.3.1.1■Task
In this learning object, a simulation shall be created, which shows how a wheel of RAK2 is released from a certain height and accelerates through gravity. It bumps against sev- eral stairs and finally remains lying on a plane. Finally, the movement has to be tracked and recorded, which describes the wheel during the fall.
2.3.1.2■Preparations
First some preparations must be made. These things are basically already known from the previous examples:
ÍLoad the file vr_rechts that contains the right front wheel of RAK2 and associated parts of the brake from the RAK2 directory.
ÍSwitch into the application Motion-Simulation and create a simulation file in the motion navigator. Accept the default option Dynamics.
ÍThen the Motion Joint Wizard appears – cancel this wizard.
ÍCheck to see in Environment whether the setting Dynamic is active, so that the analysis of indeterminate degrees of freedom is possible.
ÍAlso make sure that the direction of gravity points into positive y-direction: Change the default settings for motion (Preferences, Motion) at Gravitational Constant.
Next, the surrounding geometry must be imported. You can also create your own environ- ment geometry if you wish. If you want to create it yourself, turn into application model- ling and feel free creating your own geometry. If you prefer using the prepared geometry, which exists in part umgebung1.prt, proceed as follows:
Lifting off or hitting contacts often plays a role in dynamic tasks .
The steps to be performed for the learning task
ÍSwitch into the application Modelling . ÍSelect function FILE > IMPORT > PART . . .
ÍIn the next menu, confirm all settings with OK. Now, the dialog for file selection ap- pears.
ÍHere you select the file umgebung1.prt in the RAK2 directory and confirm with OK. ÍIn the next menu you confirm the position (0, 0, 0). Then cancel the menu.
ÍFill the screen.
ÍSwitch back to application Motion. Now the imported geometry can be viewed.
2.3.1.3■Assignment of Mass Properties
Prior to generating links in the next section, the assignment of mass properties for this dynamic analysis shall be performed. This is done by material properties, which are given to volumes or sheet bodies. Together with geometric characteristics which are already available from CAD geometry, the NX system is capable to calculate accurate mass prop- erties, i. e. mass, center of gravity and inertial properties.
In the following, these properties are applied to the bodies in the simulation file. Thus any other possibly existing material or density information of a body is overwritten. If a body does not have material or density, then by default the density of steel is active.
It is also possible and quite meaningful to assign the material information not only in the simulation file, but already in the CAD master part. This has the advantage that informa- tion is available in each assembly and each simulation file into which this master part is installed.
If material information includes not only the density, but also, for example, the Young’s modulus and Poisson’s ratio, this method even has the advantage that different applica- tions such as finite element analysis and multi-body simulation can be supported simulta- neously.
The functionality in NX allows the selection of stored materials from a library as well as the definition of new material properties.
To assign a user-defined material with the density properties of rubber to the tire in the simulation file, proceed as follows:
ÍSelect from main menu at Tools, Material Properties the function Assign Materials . ÍSelect from the graphics window the tire geometry.
ÍNow select (at the bottom of the window) the function Create Material .
ÍIn the next field Name, enter a material name, such as Rubber, and for Mass Density the value 1.3e-006 kg/mm3.
ÍConfirm with OK to create the material. On the next window, click APPLY to assign the material to the selected tire body.
A geometry will be imported .
The NX system calcu- lates mass properties for each moving body via assigned density .
The NX system has a library of standard materials . Own libraries can be created .
To assign the properties of steel (from the library) for the remaining parts, proceed as fol- lows:
ÍSelect the remaining geometry objects and after you have set the search criteria to metal, select the material Steel from the library list.
ÍConfirm with OK.
The second step of assigning steel is not necessary because of the general preference for steel.
The materials database of NX can be customized and provided with additional materials. Also very useful is the opportunity to create your own private libraries. Functions of this can be found in NX at TOOLS > MATERIAL LIBRARY MANAGER. The format used for material data in NX is a standardized XML format that is compatible with many other software programs.
2.3.1.4■Definition of Links
The definition of links is easy if they are solid bodies to which material properties have already been assigned.
In principle, only one link for the wheel would be required in this example. The environ- ment geometry does not move, so there is no need for creating a link for this. However, each MBD mechanism needs at least one link that is connected to the fixed ground via a joint to be calculated. Because the wheel will float freely in space and therefore will get no joint, there would be no joint-fixing to the ground at all. For this reason the environ- ment geometry will be defined as a link and connected by a fixed joint to the fixed ground. Alternatively, at any other location a joint could be added to the ground.
Proceed as follows for the definition of the moving body in the wheel: ÍSwitch into the application Motion.
ÍSelect the function for generating motion bodies (Link) .
ÍSet a selection filter to Component and select, easiest in the assembly navigator, the component vr_rechts.
ÍMake sure that the option for mass properties is set to Automatic. ÍConfirm with OK. The link is now generated.
Consider that the creation of this link may take some time to complete, because the geo- metry is complex and therefore the mass properties analysis is correspondingly complex. If no material is
assigned NX assumes steel density .
A link may already be made associated with ground at the creation process .
ÍNow create the Link for the ambient geometry.
ÍSet the selection filter this time on Solid Body and select the environment geometry. ÍTo immediately fix this link to ground, activate Fix the Link in the menu.
Alternatively, you can also create a joint of the type Fixed afterwards that connects the
environment geometry with the ground. ÍConfirm with OK. The link is now generated.
Now both moving bodies are generated and there exists a joint to the fixed ground. You can now perform a dynamic test run if desired, in which the wheel would fall through the environment geometry, because still no contact element has been defined. This contact element will be discussed and constructed in the following two sections.
2.3.1.5■Operation of 3D Contacts
Using the feature 3D Contact , the collision behavior of two solid bodies is modeled. This contact can take place either between two moving bodies or between one moving and one stationary environment body.
The settings on the contact differ depending on whether the RecurDyn or Adams solver is used. However, the basic operation is the same for both. Our explanations are used in a way that the findings can be used for both solvers.
Furthermore, we restrict our explanations to the default contact type Solid, which is the
recommended one. The other two types Facetted and Fitted are useful only for compatibil-
ity purposes with older NX models.
If 3D contacts are included in the motion model, the system has to divide the movement into many small steps. There will be performed even subdivisions pwhich go beyond the user specified number of steps. Therefore, there will be considerably higher computation times in the presence of 3D contacts.
During each step all involved surface pairs must be examined with respect to their con- tact behavior. If a contact surface pair penetrates, the system immediately calculates con- tact restoring forces and additional forces that are responsible for friction and damping behavior. In the next computation step these forces ensure that the involved bodies are prevented from further penetration and that realistic frictional effects arise.
The movement is divided into small steps .
In contact analysis, there will be small penetrations, because moving bodies are assumed to be not flexible .
The basic equation for analysis of contact restoring forces F is:
F = K · xe
In this equation K is stiffness, x penetration and e is the force exponent for nonlinear contact stiffness. The stiffness and force exponent values can be changed by the user, but there are default settings for these parameters, which can be used in many cases. To give more realistic results, these parameters must be adjusted, for example, by measurements during experiments.
Additionally to contact restoring forces, in order to describe contact behavior even more realistic, friction and damping forces can occur, which will be described in the following section.
2.3.1.6■Operation of Friction on 3D Contact
Friction is calculated according to the Coulomb model. Frictional forces are determined from pressing forces between two components, and a user-definable coefficient of friction μ. This coefficient of friction results from a coefficient of static friction and one for sliding friction.
In addition to friction coefficients, two speeds must be specified: Stiction Velocity and Friction Velocity, which are applied by the system as follows (see figure below).
The smaller velocity must be Stiction Velocity. This indicates up to what speed the coeffi-
cient of static friction should apply. The greater velocity must be the Friction Velocity. This
indicates the speed at which the coefficient of sliding friction is applied. Between these two speeds there remains a speed range in which the coefficient of friction is linearly transferred from static friction to sliding friction.
The two velocities should not be chosen too close to each other, since otherwise, due to very abruptly applied forces, the convergence behavior of the internal analysis may be disturbed.
For all these friction parameters there are presets, which can be used in many cases.
2.3.1.7■Operation of Damping on 3D Contact
Damping properties reduce velocities at movements. When using the Adams Solver, damping can be defined by the user by specifying a Force Model. In the RecurDyn solver
only the model Impact is possible. We will explain this below.
The contact restoring forces are calculated with a non-linear rela- tionship .
Friction is calculated according to Coulomb’s law .
With the model Impact a value for Material Damping and a Penetration Depth are speci-
fied. The damping value is not immediately fully applied at penetration, but is gently ris- ing, so that it grows to its full value only at the predetermined depth. This method pre- vents any suddenly applied loads from disturbing convergence behavior of the internal analysis. Furthermore, the contact stiffness is defined in this menu.
2.3.1.8■Solver Settings for Contacts and Accuracy
Among the default settings for kinematics (PREFERENCES > MOTION), there are some parameters that can affect the analysis of 3D or 2D contacts. These settings have strong effects on performance in calculating contacts, but they are also of interest for all other motion analyses. The following settings and recommendations apply to the RecurDyn solver, however, they are very similar to those of Adams.
Maximum Step Size: This value controls the step increment in the numerical solution of
differential equations performed by the solver. The default value of 0.01 forces the solver not to allow major steps. If error messages like “Solver Lock-Up” occur when cal- culating the model, this may be the result of suddenly occurring forces which can occur in contacts, for example. In this case it is recommended to reduce the Maximum Step Size parameter (e. g. by one power), so that smaller increments are done, but of course
this leads to higher computation times.
Error Tolerance: This tolerance value, which controls the accuracy of the computed dis-
placements, can be scaled down in order to get more accurate solutions, again an in- crease in computation time must be taken into account.
For the consideration of damping, there exist two different models .
These preferences control the numerical solution of the RecurDyn solver .
2.3.1.9■Creating 3D Contact
3D contact is defined between two solid bodies. In case you want to calculate a contact at several solid bodies, correspondingly several 3D contact elements must be inserted in the model. Remember that each additional 3D contact increases the analysis time signifi- cantly. It should also be noted that contact elements between complex geometry objects also lead to considerable computational delays because the number of contact checks is much larger then.
By the way, an efficient method to use contacts is to use only bodies with spherical or planar surfaces as contact bodies, because the contact tests are simpler. If necessary, bod- ies with complex geometry can be divided into several simpler bodies which are respec- tively connected to each other by fixed joints.
In our example two points of contact shall be considered: on the one hand between tire and environment geometry and on the other hand between the brake body and the envi- ronment geometry. For sake of simplicity, all default settings of the system shall be accepted here. This will also demonstrate that default settings are useful in many cases. Follow these steps for the generation of first 3D-contacts:
ÍCall the function 3D Contact . ÍSelect the solid body of the tire.
ÍSelect the solid geometry of the environment.
ÍConfirm with OK. The contact element is then produced.
You will find the contact element in the motion navigator below group Connectors. Here
you can manipulate the element if necessary.
ÍIn a corresponding way, you create a contact between the brake body (vr_radtraeger_
rechts) and the ambient geometry.
2.3.1.10■Solving and Animation of Results
ÍNow create a Solution , if you have not already done so. Select Normal Run and a realistic simulation time, such as five seconds, and a step number of 300, for example. ÍSelect a y-direction for the direction of gravity.
ÍConfirm with OK. ÍSolve the solution.
Consider that the computation may consume a few minutes, depending on the configura- tion of hardware.
ÍNow you can perform the Animation .
2.3.1.11■Generating a Trace of Movement
In order to produce a trace of the wheel during the movement, it is useful to record a point in the wheel center, for example. However, in a similar manner it would be also pos- sible to record an entire solid or any other geometry. In the following we want to create a point in the center of the wheel, which is associated with the motion link of the wheel, so Each contact increases
the processing time noticeably .
The 3D contact is defined between two solids .
The solving of the simulation can take considerably longer with contacts .
A trace is useful for representation of the path without animation .
that it moves with the wheel. Then, the point is defined as a trace object and is recorded in the animation. To proceed with this method, follow these steps:
ÍCreate an ordinary point approximately in the center of the wheel using the function of the main menu INSERT > DATUM/POINT > POINT . . . .
Now add the new point to the motion link of the wheel:
ÍRMB select the Link in the motion navigator and select EDIT from the context menu. ÍIn the appearing dialog box select the point. Possibly it is helpful to set the selection
filter to Point.
Sometimes it helps to hide the geometry of the wheel. ÍConfirm with OK. The point now is added.
ÍSelect the function Trace under the function group Analysis. ÍNow select the newly created point and confirm the menu with OK.
A trace object is inserted into the motion navigator. A new analysis is not required. ÍCall the animation function to perform a movement.
ÍIn the options of the animation menu you find the switch in the Packaging Options to activate the trace object. Switch it on.
ÍNow use the function Play to start the motion.
At each motion step the point is logged once, and therefore yields the desired track. Upon request you can yet perform modifications, for example, to the coefficients of friction of the contact, and check the changed wheel movement (see figure below).
One point for the record is created, activated in the animation and dis- played in the navigator .
Thus, we conclude this dynamic learning task.