Spur Gear, Friction and Energy Loss

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For an analysis of a robot component: a Spur gear drive/train.

How can I account for friction losses?
I can calculate the torque, with neglecting friction.


And what about the change in energy?
I know power = torque*angular velocity
 
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first you need a way to estimate the frictional force F on part.

this frictional force, acting on a shaft of radius R will exert a torque FxR.

You can tell your engine to exert that much more torque and it will cancel out the frictional losses.

If you want to calculate the energy lost:
Power lost = F x velocity
Power lost = F x (R * angular velocity)
Power lost = ( F x R ) * angular velocity

to find the energy lost, you would have to integrate this function. If the angular velocity is constant and the motor is run for a time t, the equation simplifies to:

Energy lost = ( F x R ) * angular velocity * t