How to find the torque for a spiral and bowl for dough mixer

[Sampath cm]

Please help me...
Tell me how to find real torque for rotating spiral of dough mixer. We need to mix 25kg dough with adding water and Ingradients. Spiral made by ss rod of 25mm dia. Spiral dia is 250mm. Rotating speed is 250rpm(max). When start the machine rotate both spiral and bowl. Dough density appro 850kg/m^3.
Take time for mixing 10 min.
Bowl dia is 600mm, length 450mm, wall thick is 3mm.

Please guide me how to find torque and power for spiral and bowl?

Note. We running the machine by using 1.5 kw motor with 7.88 ratio gear box. Out put torque is 71Nm.(trial and error method).

For your reference I Attached one image for spiral with bowl (100kg dough mixer).

 

[Greg Bernhardt]

What have you tried so far?

 

[haruspex]

Not entirely sure what you are asking.

In the first part, it sounds like you are asking what torque and power you would need in order to mix the dough at a given rpm and with a given diameter blade. That will depend on the physical characteristics of the dough. What force is needed to drag the blade through the dough?

But then you specify the power and torque (max?) of the motor. Are you asking whether it will achieve the desired speed, or what actual torque it will develop?

 

[Sampath cm]

I need calculate the torque and power for mixing. Now I don't know the force exerted by blade because dough is gradually take more torque with respect to time(by friction) .
Here which formula we use for moment of inertia and acceleration.

In second paragraph I will give the power and torque for your reference this is used by thumb rule not exactly getting by calculation.
But this motor had run the machine successfully...
But I need what exact formula or design procedure for that.

 

[haruspex]

But this motor had run the machine successfully...

That gives you a datum, effectively measuring the resistance of the dough. Perhaps you now want a general formula, predicting the behaviour with a different motor and/or blade diameter?
Can you suggest how the speed will change if you alter the power or the blade? What equations do you know relating torque, force, velocity, power...?

 

[Sampath cm]

That motor and gear box choosing by another catalogs.. And
I already using formula of T=I. a
I=mr^2, a=(n2-n2) /60*5.
In this formula am getting very less torque.
This is not correct.
I will take mass 25kg dough+15kg blade weight+10kg(water and ingradients) =50kg.

 

[haruspex]

a=(n2-n2) /60*5.

What are these n2's? It looks like you are saying you measured a rotation rate after 5 minutes and used that to calculate an angular acceleration. That will not tell you the torque. After 5 minutes the speed will be constant, all the torque going into overcoming drag. You would need to use the acceleration in the first few seconds, which might be hard to find.

 

[haruspex]

mass 25kg dough+15kg blade weight+10kg(water and ingradients)

I doubt those have much relevance. Once the blades are moving at a steady speed, it costs nothing to keep their mass moving. For the dough, as I posted, the stickiness matters as much as the mass.

 

[Sampath cm]

Blade start rotates from 0 to 250 rpm in 5sec.
That formula I had simplified whether it is right or not I don't know.
But blade will rotate uniform rotations but in some cases we need 2 speed for blade that is first 1or 2 min it may rotate at 150rpm after that will be rotate at 250 rpm. This is achieved by electrical drives.
Bowl will rotate constantly at 25rpm by another mother.

 

[Sampath cm]

Yes you are right during mixing dough will create more friction that's why how to take that load or friction force?

 

[haruspex]

Blade start rotates from 0 to 250 rpm in 5sec.

Ok. Don't forget to multiply by 2π to convert to radians.

how to take that load or friction force?

As I posted, you would have to measure it, and the sample data you have is such a measure. What remains is to come up with the general form of the equation that allows you to extrapolate to other motors and blades.
If the motor were twice as powerful, what would happen to the top speed?
What if the blades were twice as wide? Twice as tall?

 

[Sampath cm]

We are using motor with gear box it will reduce the speed at 250rpm. Then torque will also increase. Max speed is 250rpm for mixing, it is enough. When increase the power then Increass torque also by using suitable gear box(it will convert 1440rpm to 250 rpm means 1:6 ratio) &
We using formula of power
P=2*PI*N*T/60.

 

[haruspex]

When increase the power then Increase torque also

It's not that simple. If you increase the power, the torque increases, but if the load is the same then the speed will increase, which then reduces the torque.

But I'm still not sure exactly what you are after.
As far as I understand it, you have an actual motor etc. that you will use, and you can measure:
- the acceleration at start-up, no load; from this you can deduce torque (though this might not be the torque that can be developed at normal operating speed)
- the operating speed for a given load (dough) and blade

You seem to want a theoretical basis that would predict these results. There is no way to obtain that without knowing complex details about the physical characteristics of the dough, and some fancy mathematical model for how this affects the operation.

But if you want to predict how the actual results you have would change if you were to change the motor, blades or quantity of dough then that might be achievable.

 

[Sampath cm]

But we already build 2 machine one 25kg mixer and 80kg mixer both are working now.
In 25kg. Mixer we use 1.5 kw power with 71nm torque
In 80kg mixer uses 7.5kw, with 280nm torque.. Both are same mixing speed but dough qty only varied.
For both machine we selected motor and torque by reference in other company machines.

So is it possible to find inertia and acceleration and friction by using above refference value and how?.

 

[haruspex]

Both are same mixing speed

If you just took two off-the-shelf motors and arbitrarily put 25kg dough in one and 80kg dough in the other then it would be an astonishing coincidence that they ran at the same speed. Is something else limiting the speed? Were they only approximately the same speed? Did you vary the dough quantities until you got the same speed?

 

[Nidum]

They could be driven by standard industrial induction motors . These generally run quite close to the speeds given on the label unless grossly overloaded .

So known running speeds of the motors may be a useful starting point for comparative evaluation of different motor/mixer configurations .

 

[Nidum]

It might be possible to model the actual dough mixing mechanics but that would be a major exercise . A simpler approach to this problem is needed .

If the different size mixers are geometrically similar in construction then maybe an exercise in dimensional analysis could provide a guide as to the relationship between sizes of machine - as measured by maximum dough capacity - and input power needed .

 

[haruspex]

They could be driven by standard industrial induction motors . These generally run quite close to the speeds given on the label unless grossly overloaded .

So known running speeds of the motors may be a useful starting point for comparative evaluation of different motor/mixer configurations .

But in that case it would not necessarily be consuming the rated power, so the known data offers no way to determine the torque being exerted. The necessary experiment would be to increase the dough mass until the rotation rate drops.