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## Main Question or Discussion Point

I'm a mechanical engineer and I am more specialized in structural calculations than dynamic calculations and now I'm faced with a basic dynamic problem and would need some help.

I have a solid cylinder (shaft) that I want to rotate around its axis. The cylinder is supported by two bearings at its ends. No other loads than the weight are applied to the cylinder. I already know how to calculate the torque required to start rotating the cylinder up to the desired speed within the required time. What I want to know is how to calculate the torque required to maintain the cylinder rotating at the desired speed once it reaches it. From what I understood, it is dependent on the friction at the bearings only.

The formula I have found is T=μ*m*g*R where :

T : the required torque

μ : the friction coefficient

m : the weight of the cylinder

g : earth gravity

R : radius at contact bearings/cylinder

1. I would like to know if the torque calculated using this formula is for only one bearing or is it independent of the number of bearings, in other words, the calculated torque is the final torque or should I multiply it by the number of bearings ?

2. In the case this formula is independent of the number of bearings, what happens if the bearings are different, shall I consider the bearing with the highest friction coefficient or is there another formula ?

3. Apart from the frictional torque, is there any other torque I should consider in my calculations of the required torque to maintain the cylinder at the required speed ?

4. If there are no other torques involved than the frictional torque, once the cylinder has reached its desired speed and if we assume there is no friction at all, does that mean that the cylinder will continue to rotate forever ?

Now back to the torque required to accelerate the system, the formula I know for accelerating the cylinder up to the desired speed is T=Jα where :

T : the required torque

J : moment of inertia of the cylinder

α : acceleration of the cylinder

5. During my studies I have only learned to use this formula since we always neglected the friction. Now that I'm faced with a real life case where the friction is very important to be neglected, I'm wondering if friction doesn't intervene in the calculation of the required torque to speed up the cylinder too ? Logically, as friction increases, the torque required to speed the cylinder up to the desired speed increases too, am I right ? If I am, how to calculate this torque ?

6. Once all torques calculated, what would be the final torque (power) I should consider for the choice of the motor ? Should it be the maximum of the torque required to speed up the cylinder up to the desired speed and the torque required to maintain it at that speed or should it be the sum of the two torques ?

7. An additional question that is not necessary for my case but would like to have an answer to if possible : what happens if there is a radial load applied on the cylinder in the following cases :

a. The load is fixed and doesn't rotate with the cylinder ?

b. The load is rotating with the cylinder ?

I would appreciate any answer or partial answer to my 7 questions. Also, any links for demonstrating these equations or explaining the phenomenons involved would be appreciated.

I have a solid cylinder (shaft) that I want to rotate around its axis. The cylinder is supported by two bearings at its ends. No other loads than the weight are applied to the cylinder. I already know how to calculate the torque required to start rotating the cylinder up to the desired speed within the required time. What I want to know is how to calculate the torque required to maintain the cylinder rotating at the desired speed once it reaches it. From what I understood, it is dependent on the friction at the bearings only.

The formula I have found is T=μ*m*g*R where :

T : the required torque

μ : the friction coefficient

m : the weight of the cylinder

g : earth gravity

R : radius at contact bearings/cylinder

1. I would like to know if the torque calculated using this formula is for only one bearing or is it independent of the number of bearings, in other words, the calculated torque is the final torque or should I multiply it by the number of bearings ?

2. In the case this formula is independent of the number of bearings, what happens if the bearings are different, shall I consider the bearing with the highest friction coefficient or is there another formula ?

3. Apart from the frictional torque, is there any other torque I should consider in my calculations of the required torque to maintain the cylinder at the required speed ?

4. If there are no other torques involved than the frictional torque, once the cylinder has reached its desired speed and if we assume there is no friction at all, does that mean that the cylinder will continue to rotate forever ?

Now back to the torque required to accelerate the system, the formula I know for accelerating the cylinder up to the desired speed is T=Jα where :

T : the required torque

J : moment of inertia of the cylinder

α : acceleration of the cylinder

5. During my studies I have only learned to use this formula since we always neglected the friction. Now that I'm faced with a real life case where the friction is very important to be neglected, I'm wondering if friction doesn't intervene in the calculation of the required torque to speed up the cylinder too ? Logically, as friction increases, the torque required to speed the cylinder up to the desired speed increases too, am I right ? If I am, how to calculate this torque ?

6. Once all torques calculated, what would be the final torque (power) I should consider for the choice of the motor ? Should it be the maximum of the torque required to speed up the cylinder up to the desired speed and the torque required to maintain it at that speed or should it be the sum of the two torques ?

7. An additional question that is not necessary for my case but would like to have an answer to if possible : what happens if there is a radial load applied on the cylinder in the following cases :

a. The load is fixed and doesn't rotate with the cylinder ?

b. The load is rotating with the cylinder ?

I would appreciate any answer or partial answer to my 7 questions. Also, any links for demonstrating these equations or explaining the phenomenons involved would be appreciated.