Belt Driven Spindle: Calculating Power & Choosing Speed/Diameter

[Tekneek]

The system is similar to above. Say I have calculated the required power at the spindle and various speeds (rpm) the spindle needs to run at. I am not sure on how to choose the constant speed of the counter shaft. For the motor HP i am thinking it is just Pmotor = Pspindle/Efficiency.
Also not sure how I should go on about choosing the spindle shaft diameter.

 

[CWatters]

Say I have calculated the required power at the spindle and various speeds (rpm) the spindle needs to run at. I am not sure on how to choose the constant speed of the counter shaft.

I'm not sure I understand your question. The speed (rpm) of the spindle and counter shaft are related by the ratio of the pulley diameters...

Spindle RPM / Countershaft RPM = Countershaft Pulley Diameter / Spindle Pulley Diameter

The example in the picture is..

563/800 = 4.75" / 6.75" = 0.704

There is no "right" answer for the countershaft rpm. Pulleys are only available in certain standard sizes so the problem is one of finding a motor (with suitable rated RPM) and combination of pulleys that give the right answer for the spindle rpm(s). Perhaps start with a pulley catalogue and set up a spreadsheet?

For the motor HP i am thinking it is just Pmotor = Pspindle/Efficiency.

Correct.

 

[Tekneek]

I'm not sure I understand your question. The speed (rpm) of the spindle and counter shaft are related by the ratio of the pulley diameters...

Spindle RPM / Countershaft RPM = Countershaft Pulley Diameter / Spindle Pulley Diameter

The example in the picture is..

563/800 = 4.75" / 6.75" = 0.704

There is no "right" answer for the countershaft rpm. Pulleys are only available in certain standard sizes so the problem is one of finding a motor (with suitable rated RPM) and combination of pulleys that give the right answer for the spindle rpm(s). Perhaps start with a pulley catalogue and set up a spreadsheet?
Correct.

But how would I choose the spindle diameter? I understand that I can change the pulley diameters to get the desired rpm for the spindle. But wouldn't the inner diameter of the pulley depend on how big or small the spindle shaft diameter is?

 

[CWatters]

But how would I choose the spindle diameter? I understand that I can change the pulley diameters to get the desired rpm for the spindle. But wouldn't the inner diameter of the pulley depend on how big or small the spindle shaft diameter is?

The diameter of the spindle and/or countershaft don't effect the RPM. They only have to be strong enough to handle the torque. It's normal to oversize so that the shaft can handle the twice the maximum torque of the motor. If you know the max power then...

Power (Watts) = Torque (Newton Meters) * Angular Velocity (Rads/S)

Angular Velocity can be calculated from the RPM.

or if you prefer

Power (HP) = Torque (pound-feet) * RPM/5252

Once you have the max torque (with a safety factor) there are tables for typical shaft diameters...

http://joycedayton.com/products/system-accessories/shafting/shafting-diameter-chart

or you can work out the diameter based on the material and the max allowed stress but that's beyond my experience.