Determine Centrifuge Torque w/o Acceleration

[dozer811]

I am trying to determine the torque exerted by a motor running a centrifuge at constant speed. How do you determine torque when there is no acceleration? I know it's there somewhere...

 

[Daiquiri]

It is there, but you need to know the geometry of the centrifuge to (try to) calculate it. The torque is due to the friction acting at the shaft bearings, and to the aerodynamic drag acting on the rotating parts.
Not a simple task.

 

[dozer811]

Thats what I thought. The reason I am asking is because we can rotate the centrifuge at 600RPM with no load, but only about 250 RPM before the motor starts to overheat (it's big). Is the extra torque produced with an added load due only to the increase in friction?

 

[Daiquiri]

600 RPM sounds like an industrial centrifuge, and it is not a big speed. So I guess the friction due to load (or due to non-centered load) is predominant here.

The overheating problem can be also be due to bad gear ratio for that specific motor/load coupling.

 

[dozer811]

If friction is the cause of the torque at constant speed, then why can a disk rotate much faster than two objects of the same total mass rotating at a greater distance?

 

[Daiquiri]

I have to admit that I'm having difficulty in visualizing the situation you're describing...

 

[dozer811]

We took a centrifuge that rotated a large metal disk (~15" radius) that could rotate up to 600RPM. The disk was removed and replaced with a beam (~30" radius) which holds a mold at each end. The total mass of the beam and two molds is about the same as the disk. However, the beam/mold configuration can only achieve about 250RPM before the motor overloads. I am trying to figure out where the difference is coming from.

 

[Daiquiri]

Ok, I'm almost sure it's about wrong gear ratio, and it could be due to aerodynamic drag.

You have doubled the radius of the load application point, and the motor has responded by falling from 600 rpm to 250.
But, if you calculate the tip speeds in two cases, you obtain:
with rpm=600 and r=15" : V=79 ft/s
with rpm=250 and r=30" : V=66 ft/s

Not very dissimilar values.

If the geometric form of the molds are similar, you basically have almost the same aerodynamic drag force but you have doubled the torque, because the application point of the force has passed form 15" to 30".
But I think that the torque now is even bigger than that, because a beam + 2 molds at the ends doesn't sound nice from the aerodynamic point of view. :D
And if you didn't balance that stuff dynamically, it will even generate en extra torque due to higher friction at the bearings.

So, you have more than a double torque in the motor's low RPM zone, and that's overheating.

Now, this is a simplification because I'm writing it without having seen the centrifuge, so take it as a guess. If you have a pic of it, this is the time to show it. ;)

 

[jlorda]

Think of a figure skater. When her arms are out she rotates at one speed. As she brings her arms in she speeds up. But the same mass.

 

[dozer811]

I understand that a larger torque must be applied to speed up the rotation, but once the system is running at a steady speed (ie no angular acceleration), then the only torque applied is to overcome friction. The two setups should have the same friction because the mass differences are neglible. The force is being applied by a motor via belt to the centrifuge. The application force is not changing between the two.

 

[dozer811]

This is a rough sketch of the situation. Note that I am concerned with steady state and that the masses are roughly equal.

 

[Daiquiri]

I understand that a larger torque must be applied to speed up the rotation, but once the system is running at a steady speed (ie no angular acceleration), then the only torque applied is to overcome friction. The two setups should have the same friction because the mass differences are neglible. The force is being applied by a motor via belt to the centrifuge. The application force is not changing between the two.

I hope you have read what I wrote about the aerodynamic drag before writing this.
I can't see the jpg you have attached (it says: "Attachments Pending Approval"), I'll try again tomorrow.

 

[dozer811]

I didn't think the air drag would make that much of a difference, but it does get pretty windy in there when its running. Also I meant to say that the application point of the force is not changing.

 

[Daiquiri]

Anyways, if you need to resolve the problem with the motor overheating at 250 RPM, then you need to change the pulleys and the belt, in order to (at least) double the gear ratio. Even better if you manage to multiply it by factor of about 2.5 with respect to the present situation.

On the other side, if you need to arrive to 600 rpm with this configuration, you would have to change the motor and install one with about 8 times the actual HP. Baut that would be a very risky job because you don't know if the centrifuge's structure has been designed for that power.

Actually, I have to warn you that the latter solution can lead to a catastrophic failure of the centrifuge, which can endanger the persons around.