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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.

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

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  • $\begingroup$ 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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