Hello. I am a noob to electronics/Arduino and engineering. Here goes...
I am working on an art project - an object that spins on a vertical shaft. Here are the requirements.
Shaft to spin at 60 rpm. Exact speed will be dialed by eye - it does not need to be exact.
Shaft accelerates to speed, then runs constantly. When switched off, it decelerates to stationary. Acceleration /deceleration speed is currently 10 seconds - this could change if necessary.
Mechanism / electronics to be as quiet as possible.
Relevant info:
Motor is currently a stepper. This can change if necessary.
The object is a complex form, mixed media - 3D printed plastic / metal with many hollow areas.
The vertical shaft is driven via a GT2 pulley (like an Ultimaker printer if you are familiar) I have a ratio of 1:2 motor:vertical_shaft to provide some mechanical advantage.
Questions:
How do I spec the motor torque? ( I’ve looked at several online tools, researched moment of inertia etc - I come unstuck with unknown parameters (density) and my lack of engineering knowledge - I’m looking for a way to ballpark this)
I assume torque requirements are the same for a stepper as for a DC motor?
You cannot really size the motor unless you know the load. Other then that everything else should be relatively easy to accomplish. You can empirically determine the motor size (this is by trial and error). Acceleration and deceleration should not have much influence as the rate is extremely slow. Your biggest problem will probably be the drag on the vertical shaft bearings.
Hi, thank you for your response. A couple of points that I don’t really understand.
[1]
“You cannot really size the motor unless you know the load”
Are you referring to axial load, or the load on the motor? If the latter, then it seems I cannot do that until I have a motor, which leads me to…
[2]
“You can empirically determine the motor size (this is by trial and error).”
This is my current approach, however, I understand I will get better performance, and likely less sound by specifying the motor correctly. Also changing motor size/type impacts the design of the mechanism (spacing etc)
To estimate the minimum torque required to spin up the disk, multiply the moment of inertia by the angular acceleration in radians/sec/sec or about 2PI(60 RPM/60 sec)/(time in seconds to spin it up). To take into account friction, double that value to arrive at the motor torque.
If the materials in the spinning disk are evenly distributed, then its moment of inertia is (1/2)MR2 or about 0.5* 2.5 kg * (0.19 m)^2 = 0.045 kg m2.
Presumably the weight of the spinning parts will be entirely supported by suitable bearings.
Thank you all for your replies! I’ve come across all the terms / formulas, this forum is helping me piece everything together...
Here’s my working out (using linked calculators above)
360 degrees in radians = 360/0.0174533 = 6.28 (final speed of 1 full rotation per second)
Initial angular velocity = 0 (its stationary)
Time = 10 (10 seconds of acceleration to from stationary to full speed)
Angular velocity = 0.628
I calculated the mass for the shaft and table and they are approximately the same as the weight given the density ranges. The artwork is a composite material and an irregular form with many hollows making mass calculation… complicated. Consequently I am substituting weight for mass.
Mass = 1 + 2.5 + 0.15 = 3.65 kg
Distance from axis of rotation = 15 inches / 2 = 7.5 = 0.1905m
Moment of inertia = 0.13245941249999998 kgm2
member:jremington (don’t know if/how to tag another member) states:
“multiply the moment of inertia by the angular acceleration”,
then,
“To take into account friction, double that value to arrive at the motor torque.”
No. The moment of inertia depends on the mass distribution.
The moment of inertia for a uniform disk is (1/2)MR2 or 0.53.65 kg(0.19m)2 = 0.066 kg m2
If you are swinging a point mass M at the end of an arm, length R, that would be MR2. The actual value is less than that and may be somewhere in between the two estimates. If the mass is not properly distributed (i.e. balanced), the disk will vibrate terribly at certain speeds and will probably wobble at others.
Assuming a uniform disk the minimum torque is 0.628 s-2*0.066 kg m2 = 0.04 N m
Double that for safety to get motor torque 0.08 N m or 0.8 kg cm
The weight is indeed uniform, thank you for the clarification.
Now that I have a torque specification, I am examining datasheets for motors. I notice that the torque terminology for stepper motors is different to DC gearmotors. Consequently I have more questions.
For a stepper motor I am looking at the holding torque?
For a DC geared motor I am looking at the rated torque?
Also…
If I am running pulleys with a ratio 1:2 does that mean I can ½ the required torque? My heart says yes, but my brain suggests it's probably not that simple!
On Earth, weight in kg = mass in kg
Ha! Disappointed that all my Googling did not reveal this simple answer.
I would not even consider a stepper for such an application. They are complicated to drive and inefficient.
For the gearmotor, of interest is the rated torque at the output shaft.
Pulleys and gears act as torque multipliers, so if you reduce the shaft speed by a factor of 2, you multiply the torque by 2, not counting frictional losses.
mrbrush:
Hello. I am a noob to electronics/Arduino and engineering. Here goes...
I am working on an art project - an object that spins on a vertical shaft. Here are the requirements.
Shaft to spin at 60 rpm. Exact speed will be dialed by eye - it does not need to be exact.
Shaft accelerates to speed, then runs constantly. When switched off, it decelerates to stationary. Acceleration /deceleration speed is currently 10 seconds - this could change if necessary.
Mechanism / electronics to be as quiet as possible.
Your best bet is a quality brushed motor like a Maxon or a brushless (sensored) motor. Stepper is
no-go as they are the noisiest motors at low speed by a big margin. Avoid gears, esp. metal, belt drive is
probably the quietest approach. This means your motor will have to spin very slowly (typical motors
are rated 2400 rpm upwards, you'll probably need about 600) - so it will be running at well below
nominal voltage.
Electronics won't make noise.
Relevant info:
Motor is currently a stepper. This can change if necessary.
See above - entirely inappropriate for this too, you aren't doing precision position control!
The object is a complex form, mixed media - 3D printed plastic / metal with many hollow areas.
Find something which is a worst case for MoI (largest/heaviest), and rig up a string round a drum
to turn it - you can measure torque by measuring force on the string times radius of drum.
The vertical shaft is driven via a GT2 pulley (like an Ultimaker printer if you are familiar) I have a ratio of 1:2 motor:vertical_shaft to provide some mechanical advantage.
You need much more ratio so the motor can run suitably fast to be stable - trying to control a motor
at a few percent of its max speed is in the friction-dominated zone and unstable. 10:1 or 20:1 would be
good. Large timing belt sprockets can be laser-cut or 3D printed, or you can rely on friction in fact (even
use the edge of the MDF table, though that might crumble if not protected)
Questions:
How do I spec the motor torque? ( I’ve looked at several online tools, researched moment of inertia etc - I come unstuck with unknown parameters (density) and my lack of engineering knowledge - I’m looking for a way to ballpark this)
The motor torque needs to overcome its own friction, the belt friction, bearing friction, and provide enough
left over for the angular acceleration. The last part is torque = MoI x acceleration (in kgm^2 and rad/s/s),
but measuring/estimating it with string and drum is probably simpler. Since MoI can vary massively its
important to get a meaningful estimate of it, guessing is unlikely to work.
I assume torque requirements are the same for a stepper as for a DC motor?
Steppers are very very different, and torque depends massively on speed, but as I said
above, not suitable.
Hi,
Once again, thank you for all the responses. I am going to try and condense everything here.
A quick summary:
A disk of 4.675 kg distributed evenly on a table of radius 0.2159m accelerates over 10 seconds to a speed of 60 rpm, then runs continuously.
Torque = 6.85 kg cm
Torque*2 = 13.7 kg cm 190 oz in (account for friction)
The pololu website states on its page for DC gearmotors: “Stalling or overloading gearmotors can greatly decrease their lifetimes and even result in immediate damage. For these gearboxes, the recommended upper limit for instantaneous torque is 15 kg-cm (200 oz-in); we strongly advise keeping applied loads well under this limit. Stalls can also result in rapid (potentially on the order of a second) thermal damage to the motor windings and brushes, especially for the versions that use high-power (HP) motors; a general recommendation for brushed DC motor operation is 25% or less of the stall current.”
Torque24 = 54.8 kg cm or 761 oz in
I understand it's more efficient to run the motor at the specified speed. I have selected the following motors.
Torque*2 running at approx 60 rpm with no pulleys ratio required:
Torque24 running at 120 rpm with 1:2 pulley ratio as I can only select a motor that way:
Other info:
The space in which the mechanism and electronics need to fit are relatively small. A cylinder of diameter15” and height 5”
MarkT: I cannot go around the edge of the table due to design constraints. I think I would struggle to get a pulley ratio much larger than 2:1 on the table shaft due to physical constraints (getting everything else in there) and ensuring I have enough teeth engaging.
Questions:
Do the motor selections [at least] match my specifications (I think they do)
Am I miss understanding the the statement on the Pololu website quoted above? Do I need a motor with torque * 2 (and then *4 ) ?
I don't mind spending some money to ensure I have good quality components - I don’t want to hear that this thing has conked out once installed. The difference between Pololu and Maxon is considerable. Is the quality equally different?
MarkT:
The motor torque needs to overcome its own friction, the belt friction, bearing friction, and provide enough left over for the angular acceleration. The last part is torque = MoI x acceleration (in kgm^2 and rad/s/s), but measuring/estimating it with string and drum is probably simpler. Since MoI can vary massively its important to get a meaningful estimate of it, guessing is unlikely to work.
If I understand correctly, I will gain more accurate data if I:
rig up a string round a drum to turn it - you can measure torque by measuring force on the string times radius of drum
My Google skills are failing me, “measuring the torque on the string” - could you point me somewhere please?
More of a rant than a question … why do these sites mix units of measurement ? It’s so annoying !
Re-read the Pololu link in reply #8 to refresh your memory. Use a baggage scale or similar to measure force.
Aha! Now I understand. But are we saying my prior calculations are not reliable and I should buy a luggage scale? Or, I will get more accurate data this way?
mrbrush:
Hi,
Once again, thank you for all the responses. I am going to try and condense everything here.
A quick summary:
A disk of 4.675 kg distributed evenly on a table of radius 0.2159m accelerates over 10 seconds to a speed of 60 rpm, then runs continuously.
torque required = acceleration x M.o.I. = 0.63 * 0.11 = 0.07 Nm (approx). Plus some for
friction losses (depends on bearing/suspension system).
[BTW using SI throughout really reduces the chance of error - convert all values to SI,
work in SI, if necessary convert back at the end (hopefully don't have to if motor torques
are specified in Nm ]
