I'm trying to solve a design problem involving the dimensioning of a gearmotor that drives a rack & pinion system to move a cart.

The cart weighs 600 kg and is supported by 4 V-shaped steel wheels such as those in the picture which are in contact with an L-shaped steel profile.

enter image description here

Now, the design speed for the cart is 0.5 m/s and the acceleration has a ramp of 0.5 m/s2.

I want to find the maximum tangential force on the pinion in order to choose the appropriate motor, and I know that it has two components:

  • acceleration * mass
  • mass * friction coefficient (600 * 9.81 * u)

Which is the appropriate value for the friction coefficient? I believe it should be the rolling friction between steel and steel (i.e. 0.005), but do I also need to take into account the radius of the wheel or something?

Thank you for any advice.


Unless your wheels are skidding, they're in rolling contact. Use the rolling coefficient.

| improve this answer | |
  • $\begingroup$ Ok, so if the rolling coefficient is 0.005 the final formula is 600 * 9.81 * 0.005 or do I have to consider the radius of the wheel somehow? $\endgroup$ – Nico Sep 14 at 17:59
  • $\begingroup$ No. Friction is unchanged. If your track is at an angle (inclined or declined) you would need to compensate for the change in your normal force though. $\endgroup$ – jko Sep 14 at 18:24

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