The problem with measuring the force in a planar joint

Hello! I want to ask you for help. I am a post-graduate student of the machine-building academy from Ukraine. I use Matlab to build a model for the transportation mechanism of slabs. I built the model but there were difficulties. I use a planar connection for 4 wheels. All is well. But I need to analyze the forces at the points of contact of the wheels with the rails. If the planar connection is replaced by a welded joint, then the reactions of the supports are calculated correctly. If I use planar connections, then the reactions of the supports are not calculated correctly. Please tell me what I'm wrong. Thank you in advance.

My MODEL

Model with planar joint - MODEL_PLANAR.zip

Model with weld joint - MODEL_WELD.zip

Frame step model - SBORKA.zip

Wheel step model - KOLESO.zip

FOR WELD JOINT

FOR PLANAR JOINT

[Nicolas Schmit]

Please upload your Simscape model.

[Vitaly Aksonov]

OK. I uploaded my Simscape model and step files.

Answer 1

[Nicolas Schmit]

Simscape is having a hard time calculating the forces because the model is over constrained. The moving tray (RAMA) has 6 degrees of freedom in a 3D space (3 translations, 3 rotations). If you connect it to the ground with 4 planar joints, each imposing 3 constraints, you impose a total of 4*3=12 constraints. As a result, the system as 12-6 = 6 geometric constraints to satisfy. In the real system, these constraints are satisfied by small elastic deformations of the parts.

To have correct calculation of the forces in Simscape, you want to remove the redundant constraints and allow for small elastic deformations at the contact points between the wheels and the rails.

I attached a corrected file to this post. I added some stiffness and damping to the prismatic and 6DOF joints. The system bounces for about 0.5 s before stabilizing. You might want to increase the stiffness to reduce the displacement along the z axis.

You might need the latest version of MATLAB (R2017b) to open this file.

[Vitaly Aksonov]

Can you convert this model to 2016b version? Please!

[Vitaly Aksonov]

I have one more question. My job is to investigate the contact of the wheel and rail. To simulate this process, I need to limit the rotation of the wheel with some stiffness. Can I do this if I use the 6DOF joint. I understand how to do this in the planar joint , but what about the 6DOF joint? It has a spherical rotation that can not be controlled. Or am I wrong?

[Vitaly Aksonov]

I change my model as you recommended. Normal forces for 4 wheels are correct. I measured it at total force along z axes. I decided to activate the movement along the x-axis and these normal forces began to change. But Fn = mg. Why do they change when frame driving? Excuse me for so many questions I just want to understand when I'm wrong.

[Nicolas Schmit]

This is a screenshot of the modified model. I don't have R2016b installed so I cannot convert it back.

The translational stiffness and damping for the prismatic and 6DOF joints are 2e6N/m and 1e5N/(m/s) respectively.

I am not sure about what you mean by "activate the movement". If you mean applying a force along the x axis, then except if this force is applied at the height of the center of mass it will create a moment around the y axis. This moment will cause the value of the normal forces to change.

I you want to model more accurately the contact between the wheels and the rails, I suggest you have a look at the Simscape Multibody Contact Forces Library. You will find examples of how to model rolling contacts.