Trailing Arm + Brace
- Matt Suski
- Devon Copeland
Summary
Background Information
Requirements
The trailing arm and brace are integral parts of the rear suspension, and require a safety factor of 3
Loading and Boundary Conditions
The trailing arm and brace were simulated in a loading condition where the vehicle is accelerating and cornering. Both the inside wheel and the outside wheel loading conditions were tested. The forces of the road acting on the tire are outlined in the following table.
Table 1: Summary of Suspension Loading Conditions
| Case | Frx (kN) | Fry (kN) | Frz (kN) |
|---|---|---|---|
| Accelerating & Cornering (Inside Rear Wheel) | 1.53 | 0.94 | 0.73 |
| Accelerating & Cornering (Outside Rear Wheel) | -1.53 | 1.94 | 0.73 |
The equivalent loading on the trailing arm from the tire was then used to find the reaction forces on the mounting components. The forces were translated and the accompanying moments were calculated and added to the trailing arm. It was assumed that the forces and moments act on the center of the bore for the motor.
Table 2: Reaction Moments Action on the Trailing Arm from the Road Forces
| Case | MDx (kNm) | MDy (kNm) | MDz (kNm) |
|---|---|---|---|
| Accelerating & Cornering (Inside Rear Wheel) | 0.1945 | 0.0588 | 0.4835 |
| Accelerating & Cornering (Outside Rear Wheel) | 0.1945 | 0.0588 | -0.2514 |
With these forces and moments acting on the trailing arm, a forces analysis can be used to determine the reaction loads on A, B, and C.
In addition the following assumptions were made in order to simplify the problem
-unless otherwise stated, there are reaction forces at A,B, and C in the X, Y, and Z directions that are unknown
-There is no X force on the coilover because there is no contact between the coilover and the trailing arm
-The coilover is a ridgid rod in the worst case loading scenario, making it a two force member
-Only one of the rod ends has an X component, making it a worst case scenario (both a only, and b only were tested to find the true worst case loading scenario)
With this the unknowns are Ay, Az, Bx, By, Bz, Cy, and Cz. The six net force and moment equations were written, and one equation that relates the Cy and Cz forces.
Edit: Equation 4 should be (Dx)(Dad(z)) not (Dx)(Dad(y))
The following distances were taken from the CAD model
Table 3: Distances of the Rear Suspension
| Term | Distance (mm) |
|---|---|
| d(AB(x)) | 164.002 |
| d(AD(y)) | 89.5521 |
| d(AC(z)) | 155.0708 |
| d(AC(y)) | 1.7462 |
| d(AD(z)) | 286.6926 |
| Theta | 69.6 degrees |
The equations were then placed in a matrix solver in order to solve for the reaction loads. Those loads are outlined in the follownig table:
Table 4: Final Reaction Loads
Similar to the front suspension, the trailiing arm was simulated using a dummy body as the wheel. A force was applied to the contact patch and supports were added to the rod end, plain bearing and coilover clevis on the trailing arm.
Results
| von Mises Stress |
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|---|---|
| Displacement |
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| Mesh Independence |
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