How to model a McPherson Suspension

1. General
The basic component of all automotive models is its suspension. This guide shows how to set-up the most classical front suspension system of a passenger car. It gives a general overview about the topology of suspension models and can be used as a fundamental model for your further work. The model can be further extended or parameterised for use in various different applications. Please note that in the Automotive+ database a fully parameterised model of the McPherson suspension is available along with many other standard suspensions.

2. Additional Features
During the model set-up it will also be shown, how to perform equilibrium calculations and eigenvalue calculations as well as how to animate the mode shapes.

3. Creating an Example Model

3.1. Concept
The model is a simple model to allow you to understand the topology and the concepts in SIMPACK. Designing suspension systems is a complicated process due to the closed loops involved. Its very important to consider the topology of the system before starting to build-up the model in SIMPACK. You should build-up the model step-by-step. Define the bodies first and then connect them together in a chain. Finally close the loops. Force elements will be defined first with constant characteristics but later on you can define non-linear characteristics using input functions for your own models.

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3.2. Modelling
3.2.1 Try to separate a McPherson suspension into rigid bodies. Determine how the bodies are to be connected together including how many degrees of freedom they have and what forces act between them. We recommend when working with SIMPACK to first create the topology of the model to help you understand how your model is to go together. Look at the topology of the intended model with the explanation of the symbols used.

gz
damper_upper spring damper damper_lower

spring x, y, z
damper_upper

damper_lower

0 DOF damper chassis x, y, z steering_rod ?, ?

wheel_plate

wheel

arm
wheel z arm chassis tyre

Joints:

?,? Constraints:, ?
Force Elements:

tyre

3.2.2

Define a new model and start the model setup window, using the icons above.

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3.2.3 Define a new body, calling it Chassis as shown in the figure below.

Define Markers on the body

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The position of the markers is shown below: - Body: $B_chasiss 0.0000000D+00 1.2000000D-01 -1.6000000D-01 1.0000000D-01 0.0000000D+00 0.0000000D+00 4.1999999D-01 4.1999999D-01 3.7000000D-01 5.8999997D-01 0.0000000D+00 -1.2000000D-01 -1.2000000D-01 -7.0000000D-02 4.4000000D-01 $M_chasiss $M_chasiss_arm_front $M_chasiss_arm_rear $M_chasiss_steering_rod $M_chasiss_damper

3.2.4 To complete the body definition define the 3D Geometry. The 3D geometry window is found in the lower left hand corner of the body definition main window.

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3.2.5 After defining bodies in SIMPACK it is then necessary to define the joints, which gives motion to the bodies relative to other bodies or to the inertial system. Define a joint as follows between the marker $M_chasiss and $M_Isys. Set the joint type to 0DOF.

3.2.6 Define a new body, as in step 3 with the following data. Call the new body arm and defined the mass as 5kg. Leave the default Inertia Tensor properties. Define the following markers on the body: Body: $B_arm 0.0000000D+00 1.2000000D-01 -1.6000000D-01 0.0000000D+00 0.0000000D+00 0.0000000D+00 $M_arm 4.1999999D-01 -1.2000000D-01 $M_arm_chassis_arm_front 4.1999999D-01 -1.2000000D-01 $M_arm_chassis_arm_rear 7.2000003D-01 -1.2000000D-01 $M_arm_wheel_plate

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3.2.7 For the 3D geometry define 3 new primitives on the body, calling them arm1 to arm3. This time choose the type point to point primitive and the markers shown in the figure below.

Markers for arm2 primitive: $M_arm_chassis_arm_rear to $M_arm_wheel_plate Markers for arm3 primitive: $M_arm_chassis_arm_front to $M_arm_wheel_plate

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3.2.8 The joint of the body has, as shown on the topology map, a revolute Joint (type: 01) with the from marker $M_chasiss_arm_front and the to marker $M_arm_chassis_arm_front.

3.2.9 The next body is the wheel plate. Define 5kg as the mass and leave the Inertia Tensor values as the defaults. Define the following markers on the body: Body: $B_Wheel_plate
0.0000000D+00 0.0000000D+00 9.0000004D-02 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00 7.2000003D-01 -1.2000000D-01 7.3000002D-01 -7.9999998D-02 8.0000001D-01 0.0000000D+00 7.2000003D-01 0.0000000D+00 6.3000000D-01 0.0000000D+00 $M_Wheel_plate $M_Wheel_plate_arm $M_Wheel_plate_steering_rod $M_Wheel_plate_wheel $M_Wheel_plate_0 $M_Wheel_plate_damper

3.2.10 Define primitives to all connection points as shown in the picture above using the defined markers with point to point primitives.

3.2.11 Follow on the topology map the body chain and define the Joint from $M_arm_wheel_plate to $M_Wheel_plate_arm and use the Joint type 10.

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3.2.12 The next body should be the wheel with mass 10kg, also with the default Inertia properties like the other bodies already defined. You dont need any extra markers on this body. For the 3D representation, define a primitive from type cylinder with 0.6 m diameter, 0.2 m width and 32 planes.

3.2.13 The Joint of the wheel should $M_Wheel_plate_wheel to $M_wheel be a revolute joint, type 02 from

3.2.14 The kinematic loop needs to be closed; define next the Body Steering_rod. Leave the mass and inertia properties as the defaults. Define the following markers on the body: Body: $B_Steering_rod
0.0000000D+00 1.0000000D-01 9.0000004D-02 0.0000000D+00 3.7000000D-01 7.3000002D-01 0.0000000D+00 $M_Steering_rod -7.0000000D-02 $M_Steering_rod_chassis -7.9999998D-02 $M_Steering_rod_wheel_plat

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3.2.15 Define a point to point primitive between $M_Wheel_plate_steering_rod and $M_Steering_rod_chassis the markers

3.2.16 The joint is to be a user defined joint (type 25), where you have to allow the rotation about x and z. The Joint is defined between $M_Wheel_plate_steering_rod and $M_Steering_rod_wheel_plat.

3.2.17 To close the kinematic loop, you also have to connect this body using a constraint to the Chassis.

Pick on the icon above and define a new constraint calling steering. For the markers and parameters look at the figure below.

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3.2.18 To complete the other kinematic loop, we have to define two more bodies. Define next the body Damper_lower with default mass and inertia properties. Markers on the body: Body: $B_Damper_lower
0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00 6.3000000D-01 5.8999997D-01 6.0500002D-01 0.0000000D+00 $M_Damper_lower 0.0000000D+00 $M_Damper_lower_wheel_plate 4.4000000D-01 $M_Damper_lower_upper 3.0000001D-01 $M_Damper_lower_spring

3.2.19 Use a point to point primitive between the markers $M_Damper_lower_wheel_plate and $M_Damper_Upper_upper.

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3.2.20 The Joint of the body goes from $M_Damper_lower_wheel_plate with 0DOF. $M_Wheel_plate_damper to

3.2.21 The last body is the Damper_upper, which has also default mass and inertia properties. You have to define the following markers on it: Body: $B_Damper_Upper 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00 6.0500002D-01 5.8999997D-01 0.0000000D+00 $M_Damper_Upper 3.0000001D-01 $M_Damper_Upper_lower 4.4000000D-01 $M_Damper_Upper_upper

3.2.22 Use a point to point primitive between the markers $M_Damper_Upper_lower and $M_Damper_Upper_upper.

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3.2.23 The Joint of the body goes from $M_Damper_lower_spring $M_Damper_Upper_lower with a prismatic Joint ( type 06). to

3.2.24 This body is the last element of the kinematic loop, so please define a constraint as in step 18) with the name damper between the markers $M_Damper_Upper_upper and $M_chasiss_damper. Use the user defined joint again and lock all the translational freedoms.

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3.2.25 To carry out the kinematic loop calculations select the icon below and follow the instructions for the joint states.

3.2.26 As a last step in the model setup, we will define the spring-damper unit. Click on the icon below, define a new force element and type the parameters in the window as shown in the figure.

Pick on the icon and define 0.15m for the diameter and 10 windings for the representation of the force element

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3.2.27 Save the Model! 3.2.28 Close the Model Setup window and define the solver settings in the Main window! In the Menu Calculation/Time Integration/Configure set end time of the simulation to 5 seconds, save the settings and exit the window. Click on the icon below to perform the time integration + measurements!

3.2.29 Nominal Force Calculation With the icon above or in the calculation menu in the main window you can open the nominal force calculation block, see below. Click on selection of force parameters and pick in the new window; Init with all possible forces. Then close the window and select perform. After the calculation save the results and reload your model. First select the force parameters with all possible forces, then perform the calculations and save the results

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3.2.30

Using the nominal force calculations you set your system to the equilibrium state. It is now possible to carry out eigenvalue calculations. You can start the eigenvalue calculations either from the menu calculation or directly from the icon above. Just select perform, save the results and reload the model. In the model setup window; menu Animation/Model Shapes opens the Animation control panel. Select eigenvalues, set the scaling and start the animation.

4. Outlook
As a general multi-body simulation system SIMPACK offers many ways to set up a McPherson suspension. The modelling style which was shown in this tutorial was chosen to guarantee an easy understanding of the essentials of SIMPACK, however, there are more sophisticated and more effective ways of creating such a model which better fit the needs of professional users. For instance the suspension library of SIMPACK Automotive+ includes fully parameterised, easily extendable suspension models which are compatible with the according steering, chassis and subframe models. Please contact INTEC for additional information.

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