Torque required for a sand mixer

[caprock]

Hi everyone,I am designing a mixer that will combine silica sand with a small amount of sulfuric acid and need to properly size a motor/speed reducer assembly for this application.

The mixer will be run at an operating speed of 60 rpm.

The blade configuration in the mixer will be similar to the attached image.

I am having difficulty in determining the torque requirements.

Assuming that I can accurately determine the torque required to rotate the mixer assembly itself… How can I evaluate the additional torque requirements due to the resistance on the mixer blades from the sand?

(I am using the equation Tmotor = (Tload+Tacceleration)*Safety Factor)

Thanks!

 

[jack action]

I don't see how you can find out simpler than actually measuring the torque required by turning the blade into the desired mix and container. Even if you had viscosity, density, etc. of the fluid, the estimation of the resistance would not be simple (FEA may be the only way?).

 

[Mech_Engineer]

Your worst-case torque might be approximated to occur if the mixture is stuck in one side of the drum, and you want to accelerate it to 60 rpm within whatever acceleration time frame you have in mind (10 seconds maybe? 5?). Alternatively, you could perhaps approximate it as a uniform layer inside the drum, but all of it on one side would be worse from a static moment standpoint). If you calculate the moment of inertia for the drum with the (estimated as solid) mixture inside, this could give you a start. That plus a safety factor, and you're off and running.

 

[Baluncore]

Is the drum fixed with a vertical axis or does the drum rotate on a diagonal axis like a concrete mixer?

If the blades rotate in a fixed drum the torque will be determined by the force on the blades. That force will be proportional to the density of the material being mixed multiplied by the submerged cross section of the blades and the linear velocity squared.

 

[Nidum]

like a concrete mixer?

Literally - just have a look at one that is about the right size . No calculations needed . You could even buy one and adapt the components .

If only a very small machine is needed then look at kitchen mixer/blenders instead .

 

[caprock]

Hey guys!

Thanks for all of your input.

If only a very small machine is needed then look at kitchen mixer/blenders instead .

Actually using a kitchenaid mixmaster right now! I'm trying to automate the process and to mix larger batches.

Is the drum fixed with a vertical axis or does the drum rotate on a diagonal axis like a concrete mixer?

I should have mentioned, the drum will be stationary and inclined at an angle of 60 degrees from horizontal. The blades will rotate within the mixer.

If you calculate the moment of inertia for the drum with the (estimated as solid) mixture inside, this could give you a start. That plus a safety factor, and you're off and running.

Good idea, I have now calculated the torque needed to accelerate the load, (i.e. the drivetrain and the volume of sand as a solid from their moments of inertia (about 0.5 N*m). I am planning on calculating the torque load under operating conditions (torque needed to overcome frictional resistance once it is up to speed). I will use
F = 0.5 C ρ A V^2 (as suggested) for the drag on the blades, but how should I account for the frictional losses in the gearbox, bearing, seal etc.? Is this the step where those should be accounted for or should I try to estimate an overall power transmission efficiency and apply it afterwards? I am also going to factor in torque from gravity working against the mixer (sand weight on the blades as the mixer will be on an incline) simply as a force acting a certain distance away from an axis.

Thanks!

 

[Mech_Engineer]

I have now calculated the torque needed to accelerate the load, (i.e. the drivetrain and the volume of sand as a solid from their moments of inertia (about 0.5 N*m)

This sounds low for a torque required to turn a mixing drum full of sand, are you sure you calculated correctly?

 

[caprock]

This sounds low for a torque required to turn a mixing drum full of sand, are you sure you calculated correctly?

Yes, it is pretty low, but that figure does not include drag from the sand or any frictional forces. Only the torque that it would take to accelerate the load up to speed in 5 seconds based on an overall moment of inertia. Also, it will be quite a small drum as it will only handle about 7.2kg of sand per batch. I calculated the overall moment of inertia to be 0.12206 kg.m^2.

 

[Mech_Engineer]

Can you provide more detail from your calculations? What are the dimensions and weight of your drum?

 

[Nidum]

This is much easier to do experimentally . Just measure the torque needed .

 

[Baluncore]

… how should I account for the frictional losses in the gearbox, bearing, seal etc.?
…

Apply a 5% estimate at the end if necessary. The mechanical parts will not get very hot and will not require special cooling. The total mechanical losses will be small compared with the errors in the estimation of the power needed for mixing.

Measure the power drawn by the "kitchenaid mixmaster", estimate the mass of material mixed per second.
Scale that to the power of a bigger machine in proportion to mass mixed per second.

 

[caprock]

Thanks everyone.

Apply a 5% estimate at the end if necessary. The mechanical parts will not get very hot and will not require special cooling. The total mechanical losses will be small compared with the errors in the estimation of the power needed for mixing.

Thanks, I'll account for the minor frictional losses that way.

Can you provide more detail from your calculations? What are the dimensions and weight of your drum?

I attached pictures of my calculations, I did make a mistake before, but I corrected it and ended up with a smaller torque requirement. It is not the vessel that is rotating, but the blades inside of the vessel. The vessel will be 11.2 inches in height and 8 inches in diameter. The vessel will be approximately half-filled with sand during mixing.

The total acceleration torque needed I calculated to be 0.168 N.m, I then calculated the load torque from the drag on the blades at full speed and determined a torque of 50 N.m! This seems enormous! I know the formula used is for fluids, but is there a better way to estimate the drag for a granular material? Is that a reasonable torque for such a small vessel?

 

[jack action]

I then calculated the load torque from the drag on the blades at full speed and determined a torque of 50 N.m! This seems enormous!

I did not look at your calculations, but 50 N.m @ 60 rpm represents 300 W of power. It doesn't seem that big to me. The power for this KitchenAid mixer is 325 W for a 5-quart bowl filled with dough and with blades that offer probably less resistance than yours. Your bowl is roughly 9 quarts, half-filled with sand ...