Mixer Shaft Loads

[leisure17]

I want to design a simple flat 4 bladed paddle mixer. I know the torque & speed, paddle sizes etc but I need to know the side load on the shaft to size the shaft & bearings.
I suppose in ideal conditions all the loads would cancel out but I know you boys put some factor in to calculate a "side force".
Can anyone point me in the right direction re calculating this load
Cheers

 

[MikeHalloran]

I'd start by assuming a jam sufficient to stall the motor, applied to just one paddle.



Mike Halloran
Pembroke Pines, FL, USA

 

[leisure17]

That's a bit drastic isn't it Mike?

 

[MikeHalloran]

Well, if a bag of the stuff you're trying to mix is hardened up like concrete from old age, and it falls in without being broken up first, do you want to just remove the jam and reset the circuit breaker, or do you want to replace the shaft, blades, bearings, etc?

Either way is a legitimate design decision, but it impacts the business, too, so you might want to kick the question to a higher pay grade unless it's already answered by a specification. And if there isn't a specification, maybe there should be.





Mike Halloran
Pembroke Pines, FL, USA

 

[leisure17]

I ourght to add the mixture has a constituancy something like tomato soup. I will take your comments on board Mike but I'm sure I've seen formulaes for shafts based on T/R multiplied by some sort of factor for the blade type, SG etc.

 

[flash3780]

I agree with Mike. You don't know what's going to happen in service, and it'd be best to design for the worst-case. In the event of some sort of jam, you'd want your electric motor to stall rather than break something.

As for the side-loading during standard operation, perhaps you could determine the maximum eccentricity and determine the forcing function to be f(t) = m*e*omega^2*sin(omega*t)?

 

[geesamand]

If there is the possibility of a jam, use that criteria, but only check that against a limit like yield stress. Don't forget in this case to solve for the stresses caused by a single embedded blade. Likewise, if there is solid material that collects on the blades.

However, in reality the hydraulic force applied resulting from the instability is highly variable. It moves around and changes in magnitude at all times. As well, other effects outside of the mixer design itself can *significantly* affect the loads. I cannot discuss details about this force estimation as I know them because I work for a leading mixer manufacturer and it would be inappropriate for me to discuss it here. I suspect there is literature out there which describes a basic force estimation.

After making some basic assumptions on impeller force, you will gain an understanding of how critical it is to your mixer design. For a 5hp mixer it may be quite affordable to oversize the shaft and move onto other things.

If shaft failure or sizing is especially critical (large scale, high reliability, high alloy material, etc), I encourage you to pursue the help of industry professionals. Mixer shaft stress is a rich study and entirely based upon empirical studies.

David

 

[geesamand]

I hadn't made this clear, but the jammed impeller assumption typically applies a much higher torque than normal but no effect on side loads.

Only a side load calculation will cover that aspect of the design.

 

[geesamand]

If you google "mixer hydraulic force" you should find a very good link at the top of the list.

Note that this formula only applies to a simple agitator in a baffled tank free of outside flow influences.

 

[flash3780]

I hadn't made this clear, but the jammed impeller assumption typically applies a much higher torque than normal but no effect on side loads.

Wouldn't a single paddle being jammed result in a significant side load? (great link suggestion, btw).

It's a bit of a moot point if you check geesamand's link, but per my previous comment you'd also want to consider the dynamic pressure on the paddle as well as the eccentric load. Going at this cold, I would start with max/min loads and work out the cycles to failure. I'd also try to make the mixer stiff enough to push natural frequencies out of the operating range of the mixer.

 

[geesamand]

Applied to just one impeller blade (paddle), there is indeed significant bending load. Applied to all blades equally, there is none. Both cases would assume full motor startup torque. Sorry I had glossed over that difference. The single embedded blade applies only for solids that settle hard and such that the settled surface coincides with an impeller. If there are not enough settled solids to immerse the impeller, these will be very conservative sizing methods.

First critical speed is quite important. Stay below 75%; others are more conservative.

Out of caution I did not post that link directly, but today I confirmed that the equation for hydraulic force has been in the literature for quite some time. It applies nicely to centered 4-bladed impellers mixing waterlike fluids in a baffled tank. However, that is the best case as far as loads go. There are many popular variations on mixer design and layout that increase this load significantly, and the characterization of those variations is what remains proprietary and not documented in the literature. If your initial design method indicates that cost is a driving factor or the process performance (output or efficiency) of the mixer is of great value, consult a professional with the right R&D background to support the design.

David

 

[leisure17]

Thanks to all. As usual the forum has been very helpful.