3D Static Analysis of a Automotive Suspension

[Leon666]

Hello, my name is Leon and I attend to a Mechanical Engineering College.
(I'm sorry for any grammar mistakes, English is not my first language)

I'm trying to calculate the reactions of a Formula SAE car's suspension to the chassis, but I'm getting some strange answers. I hope someone here can help me.

Homework Statement

Here's the layout of the suspension, and free body diagram:
(Every connection is spherical, i.e, no torque is transmitted. Except the connection of point 0 to member 6-7)

And the coordinates of each point:

Homework Equations

Next thing I did was to try and set up the equations of a static analysis.
The first 3 equations are setting up the know forces of braking (Fx0), lateral grip (Fy0) and weight (Fz0).
The rest of the equations are simple forces and torques sum.

But here's the odd thing, If I take the last sum of torques equation (which is Mxx around 5) and replace it by the equation of sum of torques Myy around 5 I get diferent answers... Am I overlooking some basic principle? I've checked and rechecked for math errors about 10 times now, without luck.

The Attempt at a Solution

Here's the solution I'm getting from this system of equations (I've used excel to solve it):

I have attached the excel sheet in case anyone wants to take a look.

 

[KataKoniK]

Hi Leon,

Thank you for sharing your question and calculations with us. I understand that you are trying to calculate the reactions of a Formula SAE car's suspension to the chassis, and you are getting some strange answers. I will try my best to help you with this problem.

Firstly, I want to commend you for setting up the equations for a static analysis. It seems like you have a good understanding of the forces and torques involved in this system. However, I noticed that you have not taken into account the reaction forces at the connection points between the suspension and the chassis. These reaction forces are essential in determining the reactions of the suspension to the chassis.

To solve this problem, you will need to set up additional equations for the reaction forces at the connection points. These equations can be obtained by taking the sum of forces in the x, y, and z directions at each connection point.

For example, at point 1, we can write the following equation:

∑Fx1 = Fx1 + Rx1 = 0

Where Fx1 is the force acting on point 1 in the x direction, and Rx1 is the reaction force at point 1 in the x direction. Similarly, we can write equations for the y and z directions at point 1.

You will need to set up similar equations for all the other connection points (2, 3, 4, 5, 6, and 7). This will give you a total of 21 equations (3 equations for each connection point).

Once you have these additional equations, you can solve them simultaneously with your current equations to obtain the reactions of the suspension to the chassis.

I hope this helps you to solve your problem. If you have any further questions, please do not hesitate to ask.