Simcenter Amesim Generating vehicle data for vehicle dynamics models using the Simcenter Amesim McPherson demonstrator
2021-07-06T13:40:32.000-0400
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Summary
Using 3D mechanical model of a typical suspension architecture i.e. the McPherson to fill the front vehicle parameters of the functional 3D vehicle model for vehicle dynamics analyses.
Details
Executive summary and direct links to chapters
Filling a model with parameters is always cumbersome and needs to know where to find the experts who can provide the parameters. This is particularly true for vehicle dynamics and functional 3D vehicle models. After a general Introduction on the data process, a specific focus will be done on a McPherson front suspension.
From the 3D model of the Simcenter Amesim McPherson demonstrator and its App, a Python script is piloting the Simcenter Amesim model to automatically characterize the suspension kinematics and compliances. While this Python App secures the data to be imported within the functional 3D vehicle model, a validation between the resulting data and data recorded with a PEUGEOT vehicle is done. This guaranties that the McPherson model is consistent. Geometrical parameters like wheel centers location, center of gravity, kinematics and compliances… are becoming accessible for the functional 3D vehicle model at front. As the reader will see this process is straightforward. Even if it is completely based on Simcenter Amesim, other multibody software like Simcenter 3D, ADAMS or even CAD tools can be used. In order to validate a complete McPherson axle versus the functional 3D vehicle model for front, both models are put on the same sketch making as such easier the comparisons. Kinematics , compliances and also force feedbacks are compared for the 3D model and the functional 3D model. Anti jacking forces especially when braking and the rack force feedback are essential physical effects to guaranty their accuracy since vehicle dynamics performance analyses are the final targets.
Introduction and data process for Vehicle Dynamics
Getting parameters to fill appropriately the Simcenter Amesim functional 3D vehicle model is not always an easy task and users can be lost in doing so. Users are typically looking for the geometrical parameters of the vehicle especially its center of gravity, the wheel center locations, potentially the tire/ground contact points, the masses and inertia of all the bodies making the functional 3D vehicle model, the suspension kinematics tables, the compliances issued from the bushing stiffness in linear or in non linear … There is a lot of parameters the users have to gather and it is not always easy to get them all. To help users recovering all these data, processes are generally put in place especially at OEMs, not necessary at suppliers. Inside these processes, different tools and hardware (test rigs) are used. The data from the chassis itself can come from:
A standard norm allows to store all the parameters in a given format readable by normally any tools.
The figure below summarizes the different ways to get the vehicle parameters for the Simcenter Amesim functional 3D vehicle model.
This GUI is gathering the hardpoint locations forming the characteristics of a McPherson geometry as well as 3 extra points: the wheel center, the tire/ground contact point and a point along the wheel rotation axis located outside the vehicle. These 3 points are defining the wheel plan orientations. They are not really part of the McPherson hardpoints defining its geometry. These 3 points will give access to the so called toe and camber angles.
They are also giving access to the self rotation angle used by the Simcenter Amesim vehicle model. These 3 angles are forming a ZXY Euler decomposition characterizing as such uniquely the wheel plan orientation.
Going to the next step with the App, the user has to specify the sampling for Z the vertical wheel center displacement and the sampling for the rack displacement. This will allow tabulating the main suspension kinematics elements: the wheelbase variation, the half track variation, the toe, the camber and self rotation angles. These are the five quantities characterizing the wheel center and the wheel plan orientations. These five quantities are the main ones to consider for dynamics of wheel/strut and vehicle body when linked to the tire model. These are also quantities a K&C bench test will measure (as well as some others).
Running the App with the values shown for the sampling will allow to generate the kinematics tables.
The Simcenter Amesim McPherson demonstrator and its PYTHON App
The required look-up tables for the functional 3D vehicle model are now computed and stored. For front suspension, tables are function of Z (the current vertical stroke), Yrack (rack displacement) and Zop (opposite vertical stroke). This is generic to all architectures, dependent or independent. For the suspension known as independent the left to right dependency of the kinematics does not exist and thus dependency in Zop has normally no concern.
A previsualization of the tables is shown within the App. It allows giving a first view of the results.
The look-up tables being generated directly in the Simcenter Amesim format they are thus ready to be used by the functional 3D vehicle model. The Table Editor also allows a visualization of these tables.
First it is important to validate the 3D McPherson model versus or experiments or results from another MBS tool. It would bring more confidence on the model and allow saying that the model could be used as a template for other analyses.
Validation the Simcenter Amesim McPherson model as a possible architecture template
In this section the results from the App will be compared to previous results for the PEUGEOT 605 SRi. The results could be compared regarding the complete surface representing the tables as shown below.
However it is more visual to have just the contributions for steering rack equal to 0 i.e. only one curve and not a surface.
The variation of the wheel center in X and Y (the wheelbase and half track) are shown below compared to MBS results.
The old analyses done allow saying that the outputs given by Simcenter Amesim are matching the results obtained in the past. Wheelbase and half track variations are thus correct. Regarding the toe, camber and self rotation angles representing the wheel plan orientation using a ZXY decomposition we can also conclude that the Simcenter Amesim model is giving appropriate results.
This validates the 3D mechanical model regarding the hard point location set we have representing a PEUGEOT 605 SRi. This also validates that the look-up tables for the suspension kinematics are appropriate.
Additionally to the kinematics, the App allows generating compliance coefficients for the bushing stiffness. The McPherson model includes simple linear bushing stiffness. However due to modularity the stiffness can be non linear and even can be modeled with Maxwell cells with frequency dependency. When the kinematics tables are generated the user can go for compliance analysis.
When the bushing stiffness are filled the user specified the samplings for the longitudinal and lateral forces as well as the sampling for the torque around the vertical axis (similar to the tire self aligning torque).
Running the simulation using the App allows generating the bushing compliances. Only some contributions are computed, the ones that iCAR GUI is considering as the main contributors.
Even if the bushings are linear due to suspension geometry the compliance could be dependent on the suspension stroke for instance. This was explored for the PEUGEOT 605 SRi in the past.
The value given by the App should correspond to the value for 0 vertical displacement (and 0 rack displacement) i.e. almost 5.87e-7 rad/N while the App is giving 5.84e-7 rad/N for Toe4Fy and 4.05e-6 rad/Nm and the App 4.04e-6 rad/Nm for Toe4Tz. Again, the McPherson results are in agreements with the results from the PEUGEOT 605 SRi.
All these elements allow to say that the McPherson template model is accurate compared to previous analyses done for suspension kinematics and compliances applied to a PEUGEOT 605 SRi.
Right now, the 3D McPherson model does not care of the appropriate masses and inertia as well as the proper center of gravity for all the bodies. This model and its App are only used for generating quasi static data like the suspension kinematics tables and the compliances (coefficients in case of linear but also look-up tables for non linear contribution or even mathematical functions). We will see later in another communication how to manage the dynamics of the McPherson 3D model.
Additionally to the data required by the functional 3D vehicle model, the App is giving access to standard quantities suspension designers are looking at like the caster, the kingpin, the roll center…
Somehow these quantities also allow verifying that the model is giving appropriate quantities versus MBS tools.
The kinematics and compliance data have been generated like it could be done with a multibody software (MBS) like Simcenter 3D, MSC ADAMS or SIMPACK. Of course if one has access to the hardpoint locations of a McPherson suspension in such a MBS tool, he can reuse the demonstrator and its App to generate automatically the tables and coefficients. It would be just a matter of filling the hardpoint coordinates with the appropriate values.
Feeding the functional 3D vehicle model with geometrical parameters
Now let us go further with the functional 3D vehicle model and its geometry. The McPherson demonstrator gives access to the coordinates of the front wheel center and the tire/ground contact point in a given frame called the description frame. This given frame could be with X oriented to front or X oriented to rear. In most case with CAD and MBS tools, the coordinates are given with X oriented to rear. Looking to the data into the Simcenter Amesim McPherson demonstrator one can say that X coordinates are positive and the front point of the lower control arm (noted E1) is more positive than the rear one (noted E2). Consequently, X is oriented to front. Y coordinates being positive Y is oriented to left to form a (X,Y,Z) frame, Z being oriented upward. The coordinates correspond thus to a front left corner. This gives the users the orientation of the description frame of the vehicle. This is what Simcenter Amesim called Grid frame with X oriented to rear or behavior frame with X oriented to front (inversed grid frame).
To use the McPherson coordinates as they are, the Inv Car Grid frame option needs to be selected. Since the coordinates of the front suspension are known, their values are entered directly as they are in the MBS tool (here the Simcenter Amesim 3D McPherson model). This is done using the Global Parameters capability to gather all the parameters in one place to make life easier.
One can see that the front wheel center directly uses the coordinates of A defined into the App. The coordinates for the right wheel center are symmetrized left to right. The coordinates of the tire/ground contact point are used to compute the tire loaded radius. The steering rack center of gravity is supposed to be in the middle of the N point (the inside point for the tie rod). This is why it uses the X and Z coordinates of the N point.
The vehicle center of gravity could be coordinates difficult to get since it should be aligned with the load case considered and thus the tire loaded radius. In case of the McPherson demonstrator the vehicle center of gravity is also the origin of the description frame. This is why in the description frame, the vehicle center of gravity has (0,0,0) as coordinates.
The Zref (kinematics or suspension) are corresponding to the Z coordinates of the wheel center in the description frame. They are different from these values only in very specific cases that will not be explained here.
As seen the main geometrical data of the functional 3D vehicle model are coming from the data inside the McPherson demonstrator and used exactly as they are. There is no difference between what we described inside Simcenter Amesim and what could be done in MBS or CAD tools.
Since we are just interested in validating the suspension kinematics and the compliances, knowledge of the masses and inertia is of no importance. The gravity was even set to 0 to avoid calculating the suspension spring preloads (suspension and tire).
Constructing a 3D McPherson axle to compare it with its functional representation within the Vehicle Dynamics library
In order to validate the functional 3D vehicle model compared to the McPherson, we have symmetrized the McPherson 3D model and adapted a bit the Simcenter Amesim K&C virtual demonstrator to our needs. The complete front axle using a McPherson architecture is shown below.
Inputs representing the K&C test rig are on the upper left side and the user pilots the left and right side at the same time for in phase or out of phase inputs i.e. pure bounce or pure roll and forces or torques leading to steering forces or no steering forces (inputs in same direction or opposite direction).
The McPherson architecture is now a super component to be reused from left to right. Its content is specific to the McPherson architecture and its hardpoints.
Piloting the steering system is a bit different from the initial demonstrator to allow piloting in opposite the left and the right side i.e. when the rack is moving it moves the two points N of the left and right sides.
The functional 3D model includes thus the suspension kinematics within the vehicle icon and the compliance coefficients within the compliance icons. Compliance coefficients from left are used for the right side taking care of the sign convention explained within the Help and recalled on the sketch to avoid mistakes.
Since the 3D McPherson model has bushings fixed on the ground i.e. no carbody, the clamping model of the standard Simcenter Amesim virtual K&C test rig has been reused. It allows blocking the vehicle center of gravity as well as its 3 rotations (yaw, pitch, roll). The two models are thus in the same configuration i.e. no vehicle motion, only motions of the struts and racks are possible.
Now comparisons between the 3D model and the functional model can be easily done for kinematics and compliances. Chery of the cake, this configuration also allows validating the main quasi static effects like anti jacking effect due to “tire” forces and torques and their force feedback on the rack.
Validating the functional 3D suspension kinematics for a McPherson architecture
First the suspension kinematics displacements are compared. The locations of the wheel centers are the same for variation of vertical displacement only and rack displacement only. The red curves correspond to the 3D model and the blue curves to the functional 3D vehicle model.
The strut angles issued from the 3D body model of the strut are also shown on the figures (in yellow) to be compared to the values of the wheel plan orientations. The strut has no initial angle and thus no offsets as the wheel plan. The strut being part of the McPherson has the variations corresponding to the McPherson architecture and its hard points. The wheel plan orientation calculation is based on 3 (non aligned) points connected to the wheel (not the strut). Again these 3 points are the wheel center, the tire/ground contact point and a point along the wheel rotation axis outside the vehicle. From these points a direct orthogonal frame can be evaluated and thus a Euler ZXY decomposition computed to extract the wheel plan orientation. As said before these points are generic to the wheel not generic to the suspension architecture.
These results allow saying that regarding the wheel center location and wheel plan orientations the 3D model and the functional 3D vehicle model are fully aligned “kinematically” speaking. Bushing effects have now to be validated.
Introducing the bushing compliances – rack force feedback and suspension anti jacking effects
The previous compliance evaluation tests within the App were a longitudinal force input, a lateral force input and a torque input around the vertical axis. The resulting stored coefficients were the longitudinal displacement (named X4Fx) and toe angle (Toe4Fx) for longitudinal forces, the lateral displacement (y4Fy), camber angle (Camber4Fy) and toe angle (Toe4Fy) for lateral forces and finally the toe angle for torque around Z (Toe4Tz). It will be these quantities that we have to look at to validate the contributions. If the iCAR assumptions are correct, the other contributions for force or torque inputs should be almost 0 (i.e. negligible).
The results for a longitudinal force input are the following for the displacements and orientations.
As expected, the longitudinal displacement and toe angle are quite similar for longitudinal force inputs. The lateral displacements and the camber angles are finally quite small in variation validating as such the iCAR “approximations”.
As said before the type of test can also give an idea of the anti diving effects when braking/accelerating due to suspension geometry as well as the rack force feedback due to the longitudinal force. The vertical forces piloting the wheel centers and the controller piloting the rack to stay at the center allow giving the forces we are looking at.
There is almost no rack force feedback from both the two models since the forces are symmetrical. They are finally canceling each other regarding the rack contribution. For vertical forces we are obtaining forces in the appropriate range. At high forces, the bushing deformations may become non linear and the kinematics is not really the one expected but results are good enough. This validated the “tire” force feedbacks due to the suspension geometry.
Now lateral forces are applied. In order to see an effect on the rack force feedback the right force at the wheel center is exactly the same as the left force and applied in the same direction. As such the rack should tend to move and the controller maintaining the rack at the middle should compensate for the force feedbacks. The wheel center displacements and wheel plan orientations are the following for both the 3D McPherson axle and the functional 3D vehicle models.
For this test we should mainly look at the lateral displacements (Y4Fy), the camber (Camber4Fy)and toe (Toe4Fy) angles. The other quantities should remain with small variations. The results show that the lateral displacement as well as the camber and toe angles are in good agreements between the two models. Longitudinal displacement and self rotation angle are remaining quite small validating as such the assumptions done in the App regarding the compliance contributions.
Regarding the force feedbacks i.e. anti jacking force and rack force feedback we have the following results:
The rack force feedbacks are again very similar between models as well as the anti jacking forces. The lateral “tire” forces are thus generating the same amount of anti jacking effects and rack force feedback due to suspension geometry for the two models.
Same as for the lateral forces, the torques around the vertical axis at left and right are in the same direction to allow rack force feedback. The wheel center displacements and wheel plan orientation are the following.
As expected, the toe angles for “tire” self aligning torque (Toe4Tz) are the same for both models. Variations of the other quantities are pretty small and again the assumption taken in iCAR as main contributors looks again validated.
Regarding the force feedbacks we are obtaining the following results.
Again the rack force and the anti jacking vertical forces generated from the “tire” self aligning torque and the suspension geometry are aligned between the pure 3D McPherson model and the functional 3D vehicle model.
Conclusions and main take away
First, the model of a McPherson architecture included into the Simcenter Amesim demonstrator has been validated versus former results taken from a PEUGEOT 605 SRi. This model is validated as McPherson architecture template. When entering the appropriate parameters, this template should give the appropriate expected results (in quasi static). It can thus be reused as such for other applications.
Note that it is already the case within the Simcenter Amesim demonstrator related to clutch judder into the Drivetrain demonstrator section. We will see in a next communication that this model can be modified to include the masses and inertia as well as the centers of gravity of all bodies in order to have a model that can be used dynamically i.e. having appropriate internal eigen modes.
According to the results previously shown, we can say that the suspension included into the functional 3D vehicle model represents statically all the effects a 3D McPherson axle experienced. There is almost no difference regarding the kinematics and its related effects between the two models for wheel center positions, wheel plan orientations, rack force feedbacks and anti jacking effects. For compliances and thus bushing stiffness, the location of the wheel centers and the wheel plan orientations are also in accordance between the functional model and the complete 3D McPherson model. Only slight differences are foreseen that should not prevent the vehicle model to be accurate regarding ride and handling performances. As well the functional 3D vehicle model includes a rack dynamics and matches perfectly the rack force feedback allowing to explore all the performances related to the steering system.
We also have seen that the front geometry of the vehicle is now included within the functional 3D vehicle model using data from a MBS tool i.e. the locations of the wheel centers, the tire/ground contact points and the vehicle center of gravity. The coordinates of these points are directly used as they are in both models. The kinematics tables and compliance coefficients allow “correcting” the wheel center locations and wheel plan orientations due to suspension kinematics (elevation and rack changes) as well as external tire forces and torques applied on the system (the suspension corner).
In a next step, a double wishbone suspension architecture will be explored in the same way as the McPherson one. It will use the double wishbone Simcenter Amesim demonstrator. The same validation will be done but only for rear this time. This will allow building the complete functional 3D vehicle model based on a McPherson geometry at front and a double wishbone at rear.
Author:
Marc Alirand
Business Developper
Simcenter system simulation
Filling a model with parameters is always cumbersome and needs to know where to find the experts who can provide the parameters. This is particularly true for vehicle dynamics and functional 3D vehicle models. After a general Introduction on the data process, a specific focus will be done on a McPherson front suspension.
From the 3D model of the Simcenter Amesim McPherson demonstrator and its App, a Python script is piloting the Simcenter Amesim model to automatically characterize the suspension kinematics and compliances. While this Python App secures the data to be imported within the functional 3D vehicle model, a validation between the resulting data and data recorded with a PEUGEOT vehicle is done. This guaranties that the McPherson model is consistent. Geometrical parameters like wheel centers location, center of gravity, kinematics and compliances… are becoming accessible for the functional 3D vehicle model at front. As the reader will see this process is straightforward. Even if it is completely based on Simcenter Amesim, other multibody software like Simcenter 3D, ADAMS or even CAD tools can be used. In order to validate a complete McPherson axle versus the functional 3D vehicle model for front, both models are put on the same sketch making as such easier the comparisons. Kinematics , compliances and also force feedbacks are compared for the 3D model and the functional 3D model. Anti jacking forces especially when braking and the rack force feedback are essential physical effects to guaranty their accuracy since vehicle dynamics performance analyses are the final targets.
Introduction and data process for Vehicle Dynamics
Getting parameters to fill appropriately the Simcenter Amesim functional 3D vehicle model is not always an easy task and users can be lost in doing so. Users are typically looking for the geometrical parameters of the vehicle especially its center of gravity, the wheel center locations, potentially the tire/ground contact points, the masses and inertia of all the bodies making the functional 3D vehicle model, the suspension kinematics tables, the compliances issued from the bushing stiffness in linear or in non linear … There is a lot of parameters the users have to gather and it is not always easy to get them all. To help users recovering all these data, processes are generally put in place especially at OEMs, not necessary at suppliers. Inside these processes, different tools and hardware (test rigs) are used. The data from the chassis itself can come from:
- K&C test rigs. Here MTS, Morse Measurements and AB Dynamics are the main providers.
Courtesy of MTS: https://test.mts.com/en/products/automotive/full-vehicle-test-system
These hardware are giving access to the suspension kinematics and compliances data mainly. Suspension stiffness (bounce and roll) are also measured. These test rigs are used by OEMs to validate their multibody models of their own vehicles or to “spy” the competition vehicles.
- Multibody Dynamics tools like MSC ADAMS, Simcenter 3D or even CAD. These tools are providing templates of typical architectures i.e. McPherson, double wishbone, multilink, twist beam… from which a user can start with. The coordinates of the hardpoints of the suspension architecture of concern are known by the users. Generally speaking Chassis design department is the main concern. In this case all the characteristic points are known as well as all the masses and inertia of the bodies making the suspension architecture. All these tools are providing virtual K&C test rig to give access to the kinematics tables and compliances values.
- on road test measurements. In that case, the vehicle is equipped with a lot of sensors. From guestimates of some main parameters, parameter identification can be done. It is often a way for suppliers to get parameters of an existing vehicle they are using as reference for chassis subsystems studies.
- The tire is also an essential piece of the puzzle regarding ride and handling. It is important to have the correct tire parameters for the tire in used. For this, tire manufacturers and OEMs are using a flat track test machine to get access to the so called Pacejka coefficients. For this Simcenter Tire and the expertise linked could help having a data base of the most current tires.
A standard norm allows to store all the parameters in a given format readable by normally any tools.
The figure below summarizes the different ways to get the vehicle parameters for the Simcenter Amesim functional 3D vehicle model.
Here a focus on the process linked to 100 % Simcenter Amesim. From an existing 3D MBS model one can get most of the parameters he needs. One can proceed similarly within Simcenter 3D, MSC ADAMS, SIMPACK or another MBS tools, even with CAD tools. The process will be demonstrated using the Simcenter Amesim McPherson demonstrator.
Using the McPherson demonstrator like if it was a model from MBS tool
The McPherson demonstrator is the following:
The McPherson demonstrator is the following:
It is a kind of virtual bench test applying for a suspension corner. An App is piloting the hard point locations characterizing a McPherson geometry. The coordinates of the points are corresponding to a PEUGEOT 605 Sri a quite old vehicle and thus known by everyone.
This suspension architecture is mostly used because of its cost and even at OEMs known for their luxury vehicles like BMW.
The parameters below are thus the ones of a PEUGEOT 605SRi McPherson front suspension. In a next blog the rear suspension of the PEUGEOT 605 SRi will also be used to demonstrate almost the same stuff but with a double wishbone suspension architecture.
The parameters below are thus the ones of a PEUGEOT 605SRi McPherson front suspension. In a next blog the rear suspension of the PEUGEOT 605 SRi will also be used to demonstrate almost the same stuff but with a double wishbone suspension architecture.
This GUI is gathering the hardpoint locations forming the characteristics of a McPherson geometry as well as 3 extra points: the wheel center, the tire/ground contact point and a point along the wheel rotation axis located outside the vehicle. These 3 points are defining the wheel plan orientations. They are not really part of the McPherson hardpoints defining its geometry. These 3 points will give access to the so called toe and camber angles.
They are also giving access to the self rotation angle used by the Simcenter Amesim vehicle model. These 3 angles are forming a ZXY Euler decomposition characterizing as such uniquely the wheel plan orientation.
Going to the next step with the App, the user has to specify the sampling for Z the vertical wheel center displacement and the sampling for the rack displacement. This will allow tabulating the main suspension kinematics elements: the wheelbase variation, the half track variation, the toe, the camber and self rotation angles. These are the five quantities characterizing the wheel center and the wheel plan orientations. These five quantities are the main ones to consider for dynamics of wheel/strut and vehicle body when linked to the tire model. These are also quantities a K&C bench test will measure (as well as some others).
Running the App with the values shown for the sampling will allow to generate the kinematics tables.
The Simcenter Amesim McPherson demonstrator and its PYTHON App
The required look-up tables for the functional 3D vehicle model are now computed and stored. For front suspension, tables are function of Z (the current vertical stroke), Yrack (rack displacement) and Zop (opposite vertical stroke). This is generic to all architectures, dependent or independent. For the suspension known as independent the left to right dependency of the kinematics does not exist and thus dependency in Zop has normally no concern.
A previsualization of the tables is shown within the App. It allows giving a first view of the results.
The look-up tables being generated directly in the Simcenter Amesim format they are thus ready to be used by the functional 3D vehicle model. The Table Editor also allows a visualization of these tables.
First it is important to validate the 3D McPherson model versus or experiments or results from another MBS tool. It would bring more confidence on the model and allow saying that the model could be used as a template for other analyses.
Validation the Simcenter Amesim McPherson model as a possible architecture template
In this section the results from the App will be compared to previous results for the PEUGEOT 605 SRi. The results could be compared regarding the complete surface representing the tables as shown below.
However it is more visual to have just the contributions for steering rack equal to 0 i.e. only one curve and not a surface.
The variation of the wheel center in X and Y (the wheelbase and half track) are shown below compared to MBS results.
The old analyses done allow saying that the outputs given by Simcenter Amesim are matching the results obtained in the past. Wheelbase and half track variations are thus correct. Regarding the toe, camber and self rotation angles representing the wheel plan orientation using a ZXY decomposition we can also conclude that the Simcenter Amesim model is giving appropriate results.
This validates the 3D mechanical model regarding the hard point location set we have representing a PEUGEOT 605 SRi. This also validates that the look-up tables for the suspension kinematics are appropriate.
Additionally to the kinematics, the App allows generating compliance coefficients for the bushing stiffness. The McPherson model includes simple linear bushing stiffness. However due to modularity the stiffness can be non linear and even can be modeled with Maxwell cells with frequency dependency. When the kinematics tables are generated the user can go for compliance analysis.
When the bushing stiffness are filled the user specified the samplings for the longitudinal and lateral forces as well as the sampling for the torque around the vertical axis (similar to the tire self aligning torque).
Running the simulation using the App allows generating the bushing compliances. Only some contributions are computed, the ones that iCAR GUI is considering as the main contributors.
Even if the bushings are linear due to suspension geometry the compliance could be dependent on the suspension stroke for instance. This was explored for the PEUGEOT 605 SRi in the past.
Reference data issued from PEUGEOT 605 SRi - 1994
The value given by the App should correspond to the value for 0 vertical displacement (and 0 rack displacement) i.e. almost 5.87e-7 rad/N while the App is giving 5.84e-7 rad/N for Toe4Fy and 4.05e-6 rad/Nm and the App 4.04e-6 rad/Nm for Toe4Tz. Again, the McPherson results are in agreements with the results from the PEUGEOT 605 SRi.
All these elements allow to say that the McPherson template model is accurate compared to previous analyses done for suspension kinematics and compliances applied to a PEUGEOT 605 SRi.
Right now, the 3D McPherson model does not care of the appropriate masses and inertia as well as the proper center of gravity for all the bodies. This model and its App are only used for generating quasi static data like the suspension kinematics tables and the compliances (coefficients in case of linear but also look-up tables for non linear contribution or even mathematical functions). We will see later in another communication how to manage the dynamics of the McPherson 3D model.
Additionally to the data required by the functional 3D vehicle model, the App is giving access to standard quantities suspension designers are looking at like the caster, the kingpin, the roll center…
Somehow these quantities also allow verifying that the model is giving appropriate quantities versus MBS tools.
The kinematics and compliance data have been generated like it could be done with a multibody software (MBS) like Simcenter 3D, MSC ADAMS or SIMPACK. Of course if one has access to the hardpoint locations of a McPherson suspension in such a MBS tool, he can reuse the demonstrator and its App to generate automatically the tables and coefficients. It would be just a matter of filling the hardpoint coordinates with the appropriate values.
Feeding the functional 3D vehicle model with geometrical parameters
Now let us go further with the functional 3D vehicle model and its geometry. The McPherson demonstrator gives access to the coordinates of the front wheel center and the tire/ground contact point in a given frame called the description frame. This given frame could be with X oriented to front or X oriented to rear. In most case with CAD and MBS tools, the coordinates are given with X oriented to rear. Looking to the data into the Simcenter Amesim McPherson demonstrator one can say that X coordinates are positive and the front point of the lower control arm (noted E1) is more positive than the rear one (noted E2). Consequently, X is oriented to front. Y coordinates being positive Y is oriented to left to form a (X,Y,Z) frame, Z being oriented upward. The coordinates correspond thus to a front left corner. This gives the users the orientation of the description frame of the vehicle. This is what Simcenter Amesim called Grid frame with X oriented to rear or behavior frame with X oriented to front (inversed grid frame).
To use the McPherson coordinates as they are, the Inv Car Grid frame option needs to be selected. Since the coordinates of the front suspension are known, their values are entered directly as they are in the MBS tool (here the Simcenter Amesim 3D McPherson model). This is done using the Global Parameters capability to gather all the parameters in one place to make life easier.
One can see that the front wheel center directly uses the coordinates of A defined into the App. The coordinates for the right wheel center are symmetrized left to right. The coordinates of the tire/ground contact point are used to compute the tire loaded radius. The steering rack center of gravity is supposed to be in the middle of the N point (the inside point for the tie rod). This is why it uses the X and Z coordinates of the N point.
The vehicle center of gravity could be coordinates difficult to get since it should be aligned with the load case considered and thus the tire loaded radius. In case of the McPherson demonstrator the vehicle center of gravity is also the origin of the description frame. This is why in the description frame, the vehicle center of gravity has (0,0,0) as coordinates.
The Zref (kinematics or suspension) are corresponding to the Z coordinates of the wheel center in the description frame. They are different from these values only in very specific cases that will not be explained here.
As seen the main geometrical data of the functional 3D vehicle model are coming from the data inside the McPherson demonstrator and used exactly as they are. There is no difference between what we described inside Simcenter Amesim and what could be done in MBS or CAD tools.
Since we are just interested in validating the suspension kinematics and the compliances, knowledge of the masses and inertia is of no importance. The gravity was even set to 0 to avoid calculating the suspension spring preloads (suspension and tire).
Constructing a 3D McPherson axle to compare it with its functional representation within the Vehicle Dynamics library
In order to validate the functional 3D vehicle model compared to the McPherson, we have symmetrized the McPherson 3D model and adapted a bit the Simcenter Amesim K&C virtual demonstrator to our needs. The complete front axle using a McPherson architecture is shown below.
Inputs representing the K&C test rig are on the upper left side and the user pilots the left and right side at the same time for in phase or out of phase inputs i.e. pure bounce or pure roll and forces or torques leading to steering forces or no steering forces (inputs in same direction or opposite direction).
The McPherson architecture is now a super component to be reused from left to right. Its content is specific to the McPherson architecture and its hardpoints.
Piloting the steering system is a bit different from the initial demonstrator to allow piloting in opposite the left and the right side i.e. when the rack is moving it moves the two points N of the left and right sides.
Doing as such allows to compare the front axle in pure 3D with the front axle of the functional 3D vehicle model. Both models are in the same sketch to make easier the comparisons. The functional 3D model is the following. It uses the same techniques and thus inputs than the 3D mechanical model.
The functional 3D model includes thus the suspension kinematics within the vehicle icon and the compliance coefficients within the compliance icons. Compliance coefficients from left are used for the right side taking care of the sign convention explained within the Help and recalled on the sketch to avoid mistakes.
Since the 3D McPherson model has bushings fixed on the ground i.e. no carbody, the clamping model of the standard Simcenter Amesim virtual K&C test rig has been reused. It allows blocking the vehicle center of gravity as well as its 3 rotations (yaw, pitch, roll). The two models are thus in the same configuration i.e. no vehicle motion, only motions of the struts and racks are possible.
Now comparisons between the 3D model and the functional model can be easily done for kinematics and compliances. Chery of the cake, this configuration also allows validating the main quasi static effects like anti jacking effect due to “tire” forces and torques and their force feedback on the rack.
Validating the functional 3D suspension kinematics for a McPherson architecture
First the suspension kinematics displacements are compared. The locations of the wheel centers are the same for variation of vertical displacement only and rack displacement only. The red curves correspond to the 3D model and the blue curves to the functional 3D vehicle model.
Regarding the wheel plan orientations, the results are also the same. Only variations for a steering rack input are shown.
The strut angles issued from the 3D body model of the strut are also shown on the figures (in yellow) to be compared to the values of the wheel plan orientations. The strut has no initial angle and thus no offsets as the wheel plan. The strut being part of the McPherson has the variations corresponding to the McPherson architecture and its hard points. The wheel plan orientation calculation is based on 3 (non aligned) points connected to the wheel (not the strut). Again these 3 points are the wheel center, the tire/ground contact point and a point along the wheel rotation axis outside the vehicle. From these points a direct orthogonal frame can be evaluated and thus a Euler ZXY decomposition computed to extract the wheel plan orientation. As said before these points are generic to the wheel not generic to the suspension architecture.
These results allow saying that regarding the wheel center location and wheel plan orientations the 3D model and the functional 3D vehicle model are fully aligned “kinematically” speaking. Bushing effects have now to be validated.
Introducing the bushing compliances – rack force feedback and suspension anti jacking effects
The previous compliance evaluation tests within the App were a longitudinal force input, a lateral force input and a torque input around the vertical axis. The resulting stored coefficients were the longitudinal displacement (named X4Fx) and toe angle (Toe4Fx) for longitudinal forces, the lateral displacement (y4Fy), camber angle (Camber4Fy) and toe angle (Toe4Fy) for lateral forces and finally the toe angle for torque around Z (Toe4Tz). It will be these quantities that we have to look at to validate the contributions. If the iCAR assumptions are correct, the other contributions for force or torque inputs should be almost 0 (i.e. negligible).
The results for a longitudinal force input are the following for the displacements and orientations.
As expected, the longitudinal displacement and toe angle are quite similar for longitudinal force inputs. The lateral displacements and the camber angles are finally quite small in variation validating as such the iCAR “approximations”.
As said before the type of test can also give an idea of the anti diving effects when braking/accelerating due to suspension geometry as well as the rack force feedback due to the longitudinal force. The vertical forces piloting the wheel centers and the controller piloting the rack to stay at the center allow giving the forces we are looking at.
There is almost no rack force feedback from both the two models since the forces are symmetrical. They are finally canceling each other regarding the rack contribution. For vertical forces we are obtaining forces in the appropriate range. At high forces, the bushing deformations may become non linear and the kinematics is not really the one expected but results are good enough. This validated the “tire” force feedbacks due to the suspension geometry.
Now lateral forces are applied. In order to see an effect on the rack force feedback the right force at the wheel center is exactly the same as the left force and applied in the same direction. As such the rack should tend to move and the controller maintaining the rack at the middle should compensate for the force feedbacks. The wheel center displacements and wheel plan orientations are the following for both the 3D McPherson axle and the functional 3D vehicle models.
For this test we should mainly look at the lateral displacements (Y4Fy), the camber (Camber4Fy)and toe (Toe4Fy) angles. The other quantities should remain with small variations. The results show that the lateral displacement as well as the camber and toe angles are in good agreements between the two models. Longitudinal displacement and self rotation angle are remaining quite small validating as such the assumptions done in the App regarding the compliance contributions.
Regarding the force feedbacks i.e. anti jacking force and rack force feedback we have the following results:
The rack force feedbacks are again very similar between models as well as the anti jacking forces. The lateral “tire” forces are thus generating the same amount of anti jacking effects and rack force feedback due to suspension geometry for the two models.
Same as for the lateral forces, the torques around the vertical axis at left and right are in the same direction to allow rack force feedback. The wheel center displacements and wheel plan orientation are the following.
As expected, the toe angles for “tire” self aligning torque (Toe4Tz) are the same for both models. Variations of the other quantities are pretty small and again the assumption taken in iCAR as main contributors looks again validated.
Regarding the force feedbacks we are obtaining the following results.
Again the rack force and the anti jacking vertical forces generated from the “tire” self aligning torque and the suspension geometry are aligned between the pure 3D McPherson model and the functional 3D vehicle model.
Conclusions and main take away
First, the model of a McPherson architecture included into the Simcenter Amesim demonstrator has been validated versus former results taken from a PEUGEOT 605 SRi. This model is validated as McPherson architecture template. When entering the appropriate parameters, this template should give the appropriate expected results (in quasi static). It can thus be reused as such for other applications.
Note that it is already the case within the Simcenter Amesim demonstrator related to clutch judder into the Drivetrain demonstrator section. We will see in a next communication that this model can be modified to include the masses and inertia as well as the centers of gravity of all bodies in order to have a model that can be used dynamically i.e. having appropriate internal eigen modes.
According to the results previously shown, we can say that the suspension included into the functional 3D vehicle model represents statically all the effects a 3D McPherson axle experienced. There is almost no difference regarding the kinematics and its related effects between the two models for wheel center positions, wheel plan orientations, rack force feedbacks and anti jacking effects. For compliances and thus bushing stiffness, the location of the wheel centers and the wheel plan orientations are also in accordance between the functional model and the complete 3D McPherson model. Only slight differences are foreseen that should not prevent the vehicle model to be accurate regarding ride and handling performances. As well the functional 3D vehicle model includes a rack dynamics and matches perfectly the rack force feedback allowing to explore all the performances related to the steering system.
We also have seen that the front geometry of the vehicle is now included within the functional 3D vehicle model using data from a MBS tool i.e. the locations of the wheel centers, the tire/ground contact points and the vehicle center of gravity. The coordinates of these points are directly used as they are in both models. The kinematics tables and compliance coefficients allow “correcting” the wheel center locations and wheel plan orientations due to suspension kinematics (elevation and rack changes) as well as external tire forces and torques applied on the system (the suspension corner).
In a next step, a double wishbone suspension architecture will be explored in the same way as the McPherson one. It will use the double wishbone Simcenter Amesim demonstrator. The same validation will be done but only for rear this time. This will allow building the complete functional 3D vehicle model based on a McPherson geometry at front and a double wishbone at rear.
Author:
Marc Alirand
Business Developper
Simcenter system simulation