Stepper torque calculation to drive a solid cylinder

[MOTASH]

Hi All,

I'm working on some design and apparently my physics expertise are getting rusty,i'd appreciate some help with the following:-
I need to calculate the required torque for a stepper motor to rotate a solid cylinder with the following properties:-
radius : 20cm
height: 12cm
density : the cylinder shall be made of ABS, but having cavities(symmetrically spaced) filled with liquid(water), for simplicity i am assuming a homogeneous density of 1.1g/cm3
The cylinder is suspended vertically on bearing and i am ignoring static friction , the rotation is around the vertical axis

The stepper is expected to have 1.8deg/step, and speed of 30rpm

I've done some math trying to calculate the torque required to rotate one step from rest :
Torque = Moment of inertia * Angular Acceleration

Cylinder mass : 16.587kg
Moment of inertia : 0.33175 kg.m2

Step time (@30rpm) : 10ms
Ang. velcoity : 3.14159 rad/s
the acceleration figure will be ridiculous, leading to a very large torque(compared to the holding torque i get in datasheets)
what's wrong with the approach/units or should the result be compared to the stalling torque(never mentioned in datasheets of common steppers)
Any help is much appreciated

 

[jrmichler]

You need to work a problem like this from a different direction. You choose a motion profile, then specify a motor to make the load follow that motion profile. The motion profile consists of two curves, one for acceleration vs time and the other for velocity vs time.

Get the speed torque curve for your stepper motor. Search terms stepper motor speed torque curve will bring up good information on interpreting these curves. A general rule is that your motion profile should use a maximum of 1/3 to 1/2 of the available stepper torque.

It is good practice to include the bearing friction in your calculations even if it is small. As a practical matter, bearing friction can be ignored if it is less than about 5% of the acceleration torque. But, since you need to calculate the bearing friction to know that, you might as well include it in your calculations.

If your maximum speed is 30 RPM, you may have trouble finding a stepper motor that will drive the load directly. A solution is to add a gear reducer.

 

[MOTASH]

You need to work a problem like this from a different direction. You choose a motion profile, then specify a motor to make the load follow that motion profile. The motion profile consists of two curves, one for acceleration vs time and the other for velocity vs time.

Get the speed torque curve for your stepper motor. Search terms stepper motor speed torque curve will bring up good information on interpreting these curves. A general rule is that your motion profile should use a maximum of 1/3 to 1/2 of the available stepper torque.

It is good practice to include the bearing friction in your calculations even if it is small. As a practical matter, bearing friction can be ignored if it is less than about 5% of the acceleration torque. But, since you need to calculate the bearing friction to know that, you might as well include it in your calculations.

If your maximum speed is 30 RPM, you may have trouble finding a stepper motor that will drive the load directly. A solution is to add a gear reducer.

I'm having a problem characterizing the load, to select a proper motor
I'm not sure if i understand your point : by looking into motor curves how can i select which one fits?

regarding the speed of 30rpm,i hope i could make it 300rpm :),but into the eqn this would mean a higher angular velocity and hence a higher torque requirement

 

[jrmichler]

Do the search I suggested, then spend a few hours studying what you find. There are no shortcuts if you want to build something that works. You need to have a good general understanding of stepper motor speed and torque curves in order to understand what was said in Post #2. Getting that understanding will be a few hours well spent. In addition, some of those sites are better written than anything I can do.

You can drive your load at whatever speed you want, and accelerate to that speed in whatever time you want. The calculations are the same for low speed and acceleration as for high speed and acceleration. The difference is in the cost of the motor and drive.

The process is iterative. You start with the speed and acceleration you would like. If the motor size (and cost) is too high, then reduce speed and/or acceleration, and try again.

 

[MOTASH]

Do the search I suggested, then spend a few hours studying what you find. There are no shortcuts if you want to build something that works. You need to have a good general understanding of stepper motor speed and torque curves in order to understand what was said in Post #2. Getting that understanding will be a few hours well spent. In addition, some of those sites are better written than anything I can do.

You can drive your load at whatever speed you want, and accelerate to that speed in whatever time you want. The calculations are the same for low speed and acceleration as for high speed and acceleration. The difference is in the cost of the motor and drive.

The process is iterative. You start with the speed and acceleration you would like. If the motor size (and cost) is too high, then reduce speed and/or acceleration, and try again.

if you forget about the motor:
what is the torque needed to rotate the above cylinder by 1.8deg from rest in 10ms