Help needed to solve a static analysis for the design of the Shaft for a Grinding Machine

[fabianv19]

Hello everyone, this is my first post on the forum. I am analyzing the following system: a shaft that contains a transmission pulley, a support, and a grinding wheel used for polishing tanks. I want to design the shaft and calculate the required torque to select the motor.

I have encountered some problems with the static analysis of the shaft because, according to my calculations, I have more unknowns than equations. In the attached image, I show the four equations I have formulated:

1. Sum of moments in the X direction.
2. Sum of forces in the Y and Z axes.
3. An additional equation that relates the tensions in the pulleys.

This gives me a total of four equations, but I have five unknowns:

• N (the normal force or the reaction from the workpiece).
• T1 and T2 (the tensions in the pulley).
• The reactions at the support. (BY and BZ)

It seems that I cannot obtain more static equations without introducing additional unknowns. To solve this, I assumed that the normal force N is equal to the force F1, which is the force applied by the operator during polishing, plus the weight of the wheel. However, I am not sure if this assumption is valid.
Could anyone help me determine if this is correct or if there is another way to solve the system? Any suggestions would be greatly appreciated.

Thanks in advance!

 

[Baluncore]

Welcome to PF.

I believe the problem arises because the spindle position is not fixed, as it has only one spindle support bearing.

You need a bearing at each end of a practical grinder spindle.
One bearing will predominantly counter the drive belt tension, while the other will predominantly counter the contact force of the wheel against the work.

 

[erobz]

The operator is responsible the normal force I believe so it is a parameter, not an unknown?

 

[erobz]

Also, do a FBD of the shaft if you intend to analyze stress and deflection of the shaft. Just show the shaft and effective loadings on it.

 

[tech99]

These are just my suggestions as an amateur scientist.
The analysis is of the forces applied to the shaft only.
Eqn (3) you do not need a term for the reaction of the table to the bearing as we are considering only the shaft.
Eqn (4), friction. You do not need to consider friction provided there is no slip. I suggest you check for slip as a separate exercise and increase pre-tension if required.
I think you need a term for pre-tension, as T1-T2 = pre-tension.
Eqn (2) I think you need to include the horizontal component of force applied by the workpiece, presumably N x mu.
I think you need to numerically specify the force N applied by the workpiece.
I also notice that you do not analyse the bending moments on the shaft, Post #2 is applicable here.