Help Walk Me Thru Motor Sizing Calculations Please

[jeff davis]

TL;DR Summary

Hello; i am trying to work my way thru some motor sizing calculations on a semi-simple example so that i can more easily do it in the future. Could i get some guidance?

Summary: Hello; i am trying to work my way thru some motor sizing calculations on a semi-simple example so that i can more easily do it in the future. Could i get some guidance?

Hello:
I am trying to develop a good system for sizing motors (generally steppers). In the past i just guesstimated what was needed by either looking at other machines or just little research. I am now at a point where it bugs me a bit that i am not proficient at calculating the exact requirements and understanding how to best size a motor.
I am hoping to get some pointers as i work thru an example here. I will post my steps and if i am a moron somebody will surely correct me! :]

The setup will be a stepper motor driving a belt and two other pulleys. The two other pulleys are connected to shafts that spin rubber drive wheels that pass a tube over a pin. I will include a drawing or something hopefully. My largest struggle in understanding: how to combine the moments of inertia together with the force needed to push the tube, and also how to apply friction to the bearing that the shafts will be spinning into add to this.

In the picture "A" is the drive pulley attached to the motor, B and C are identical shafts which push the tube

Step 1) from what i have read i need to calculate the moment of inertia for each shaft:

Stepper motor and its pulley (A): i=.00107943 lbs/in^2
Shaft that has pulley and drive wheel attached(B and C): i = .008690876 lbs/in^2 --->(there are two of these)

So how do i add the belt and bearing friction and tube push force to this information in order to get my torque? And what other information do i need to gather in order to complete the motor sizing task?

 

[Dullard]

Addition.
The torque due to push force is just the linear force/wheel radius
The torque due to bearing friction is similar, but will depend on the form of the data that you have (from the manufacturer, presumably).

Both of these values will (presumably) be a function of speed. Pay attention to the way that stepper torque falls off with speed - missing steps really sucks in a blind indexing application.

 

[jeff davis]

Thanks for commenting:
I have had a few encounters with missing steps. Should i be considering a gear motor instead?

Since i have three different moments here, do i just add them all together? Since moment A is turning moments B and C, do i add anything special to "A" or is that done when adding them together (if you do add them)?

So let's say it takes 1lbforce to push the tube. Please excuse my use of lbs.

how would i incorporate this into my calculations?

The bottom pulley on the rod is .509" diameter and the rubber wheel at the top of the shaft is 1" diameter. This rubber wheel is what pushed the tube and saw the 1lb.

So the torque would be 1lbf in right? How do i combine this value to the moment of inertia i calculated for the shaft itself? And apply it to the whole system to get a required torque value for my motor?

Edit: it would be .5 in/lbs forgot to change to radius

thanks

jeff

 

[Dullard]

The shaft inertia will resolve to a torque when an acceleration is specified. The torques may then be summed for each pulley. Assuming that the drive pulley is a different diameter than the driven pulleys, convert the torques to local belt tensions. The sum of the tensions is zero. The motor torque requirement is the belt-induced torque on the drive pulley plus the drive shaft/pulley inertial torque (acceleration parameter required) plus the inertial torque of the motor itself (acceleration again). I hope I added more light than heat.

 

[jeff davis]

The shaft inertia will resolve to a torque when an acceleration is specified. The torques may then be summed for each pulley. Assuming that the drive pulley is a different diameter than the driven pulleys, convert the torques to local belt tensions. The sum of the tensions is zero. The motor torque requirement is the belt-induced torque on the drive pulley plus the drive shaft/pulley inertial torque (acceleration parameter required) plus the inertial torque of the motor itself (acceleration again). I hope I added more light than heat.

thanks, you are helping for sure.

Is "load inertia" the same as "Moment of inertia"? It is being used here and there sometimes in the same sentence.

My brain is about to crap its pants and die. I think that I am making this task harder than it should be. I just get hung up on little details a lot. The hardest part for me i think is that i don't have any "check" to see that my calculations are correct. I am still however plugging away.

 

[Tom.G]

Things to account for:

Remember the inertia of the tube, and add some friction force to account for the energy needed to deform the rubber drive wheels. The drive belts will add some friction too. With metal ball or roller bearings at light loads, the losses are almost entirely from the lubricant viscosity interacting with rotational speed. More difficult with dry self-lubricated bearings, e.g. Nylon sleeve.

Perhaps the easiest way to account for all the friction is to build a prototype with a hand crank instead of a motor, then use a spring scale on the crank to measure the torque.

Then leave room for the next frame-size stepper, needed when you find that process variations (a burr on the tube end, diameter variations, temperature...) bite you!

 

[jeff davis]

Thanks Tom. G; I appreciate the help. I was definitely not thinking about the deformation of the rubber. Is there a standard number or percentage i should apply for these unforeseen frictions?

Also for the physical test; i agree that it would be easiest. I am trying to beat my brain around the calculations though. It is purely for curiosity sake. If i just do a search for this in google they have "tutorials" but most of them include using a software to figure it out. I really just want to know how it all comes together.

thanks,
jeff

 

[jeff davis]

I think that i have come upon an answer. 1.644 in-lbs. is the max torque the motor will see. now i have a few questions:
1. do i now need to apply a certain standard "oversize" percentage to this? 10% perhaps?
2. I neglected the belt but substantially increased the friction coefficient. Is this ok?
2. do you think it would be beneficial to anybody to write my complete calculations for this? Maybe in a guide? If so, does it need to be in a different thread?

 

[Tom.G]

I was definitely not thinking about the deformation of the rubber. Is there a standard number or percentage i should apply for these unforeseen frictions?

I could guess, but we'll see if @jrmichler can answer that one. That's more his field.

1. do i now need to apply a certain standard "oversize" percentage to this? 10% perhaps?

100% is the usual engineering safety factor, that is build it with twice the capability you think it needs. It's usually an awful lot cheaper than having to re-design & build 'Version 2."

If it is part of an in-house assembly line:
If it is a critical step on the assembly line (one that could shut down the whole line for hours or days) 200% is not unheard of, along with having a functioning spare to swap in.

If it is part of a low volume stand-alone product:
Often 100% is chosen and it is included on the customer 'Suggested Spares' list. Ultimately, that is a management decision.

If it is part of a high volume stand-alone product:
Then somebody gets to do an Estimated Lifetime calculation for the overall product and for each sub-assembly. (Ouch!)

2. I neglected the belt but substantially increased the friction coefficient. Is this ok?
2. do you think it would be beneficial to anybody to write my complete calculations for this? Maybe in a guide? If so, does it need to be in a different thread?

I'm not competent to respond to either of these.

If someone else doesn't address these in a few days, post here again and I'll try to recruit some others to chime in.

Cheers,
Tom

p.s. I'm curious, what is the product that is being assembled... that is if you can say without giving away any secrets!

 

[jrmichler]

I'll chime in with some general observations, several of which restate what has been posted earlier.

Make a sketch showing known sizes, ratios, diameters, and loads. Then calculate the torque at the motor for the worst case forces/loads at constant RPM. It's good practice to make a large sketch (pencil sketch is fine) that shows all forces and torques because that sketch is also your checklist to convince yourself that you did not miss something.

If acceleration torque is more than 5% to 10% of steady state torque, that needs to be calculated also.

All bearings have friction. Bearing friction information can be found from manufacturers web sites. Be careful, ball bearings have low friction, but sealed ball bearings have high seal friction.

A small system with rubber belts and rubber wheels will normally have a lot of friction relative to other loads. The friction will be a function of the rubber, the loads, the belt tension, pulley diameters, temperature, and other variables. It is not practical to calculate friction in this situation. Testing is needed. Try for the worst case. Rubber wheel friction increases with load, so test the worst case load.

Systems where the predominant torque is due to friction need large safety factors because friction can vary over a wide range. For example, the rolling friction of a rubber wheel is a function of both load and temperature. If the predominant load is friction, then time spent calculating is not real useful. Much better to build a prototype, wrap some fish line around a shaft, and pull with a fish scale to directly measure the torque.

Stepper motors need large safety factors to prevent missing steps. If anything in the system causes torque variations, they need larger safety factors. The fish scale torque test will show this also.

 

[jeff davis]

100% is the usual engineering safety factor, that is build it with twice the capability you think it needs. It's usually an awful lot cheaper than having to re-design & build 'Version 2."

I will go with 100% then. The motor i had originally designed around was 4 in-lbs so i think it should be sufficient. very good to know the other scenarios also. I have never done an estimated lifetime calculation before. I remember touching on this in some engineering economy course or other. It sounds like a brutal amount of paperwork! Do you do them?

p.s. I'm curious, what is the product that is being assembled... that is if you can say without giving away any secrets!

It actually is a bit secretive. I had to remove a lot of the detail from my drawing before i posted. Hopefully my boss won't skin me alive. Sometimes i just have to ask questions to a bunch of great and smart people like you lot!
The mechanics I am sure are nothing special. its just the concept of what we are doing may be unique to the product. It is for a medical catheter introducer... and i want to tell so bad... but alas; its not my product so i will have to plead the fifth.

If acceleration torque is more than 5% to 10% of steady state torque, that needs to be calculated also.

hello jrmichler,
Thanks for your input. I really appreciate you guys lending me your knowledge for a bit. I actually did calculate for the acceleration torque. It was quite a bit more. I think 20% if i remember correctly. I had to then take the root mean square of the various torques, I am not sure why this was a step because it gave me a value around 1/2 of what the max torque needed would be. I just went with the max torque i saw during calculations as my value. This seems to make more sense to me. Have you heard of this?
I am also going to do the fish scale test once everything is built. Id like to see how far off i was.

 

[jrmichler]

I'm much more familiar with servo motors than with stepper motors, so take this as a reason to study the manufacturer's data sheet for your stepper motor. Servo motors have two different torque ratings, RMS torque and peak torque. RMS, which is an acronym for Root Mean Square, is the maximum torque at which a motor can run continuously without overheating. Since servomotors rarely run at constant speed and/or torque, it is calculated as the root mean square of the worst case motion profile.

Peak torque is the maximum torque the motor will deliver. Typical peak torque is 2 to 4 times the RMS torque. A servomotor can run at peak torque only until it reaches a maximum temperature, after which it needs to run at reduced torque until it cools off.

If you overload a servomotor, the drive will either just shut it off or limit the torque, while an overloaded stepper motor will miss steps.

 

[jeff davis]

I'm much more familiar with servo motors than with stepper motors, so take this as a reason to study the manufacturer's data sheet for your stepper motor. Servo motors have two different torque ratings, RMS torque and peak torque. RMS, which is an acronym for Root Mean Square, is the maximum torque at which a motor can run continuously without overheating. Since servomotors rarely run at constant speed and/or torque, it is calculated as the root mean square of the worst case motion profile.

Peak torque is the maximum torque the motor will deliver. Typical peak torque is 2 to 4 times the RMS torque. A servomotor can run at peak torque only until it reaches a maximum temperature, after which it needs to run at reduced torque until it cools off.

If you overload a servomotor, the drive will either just shut it off or limit the torque, while an overloaded stepper motor will miss steps.

I have only ever used steppers with an encoder for position feedback. Except for the tiny robotics servos on RC stuff.
I would be interested in some tips for servo application if you have any more than you have already shared. Is it easy to find continuous rotation servos? Do you have a preferred company?
I usually get my motor controller from "geckoDrives". it seems that they have a servo board as well. I was reading the documentation and it is driven very similarly to a stepper. It has a direction input and pulse input. If i remember correctly the RC ones are done by a voltage range? EX: 3v makes it sit at 30 degrees or something.

 

[jrmichler]

My experience is with industrial servomotors, such as those made by Allen-Bradley. Their smallest MPL series motor has 6.8 in-lbs peak torque: https://literature.rockwellautomation.com/idc/groups/literature/documents/pp/mp-pp001_-en-p.pdf, and their big HPK series motors go up to 17,000 in-lbs (1927 Nm) torque: https://ab.rockwellautomation.com/Motion-Control/HPK-Series-High-Power-Servo-Motors.

For a general overview of what is available from on manufacturer, both rotary and linear, see the Allen-Bradley Motion Control Selection Guide: https://literature.rockwellautomation.com/idc/groups/literature/documents/sg/knx-sg001_-en-p.pdf. Allen-Bradley is popular in North America, while Siemens is popular in Europe. Siemens has a similar product line to Allen-Bradley.

These are industrial duty products. They are designed last for years while running 24/7 at full rated torque and RPM. But they are not appropriate for somebody building something in their garage. It takes an electrical engineer working with a mechanical engineer to properly apply them.

I'm not familiar with the tiny servos used for RC stuff.

 

[jeff davis]

These are industrial duty products. They are designed last for years while running 24/7 at full rated torque and RPM. But they are not appropriate for somebody building something in their garage. It takes an electrical engineer working with a mechanical engineer to properly apply them.

Ouch, Harsh assumption. LOL

I actually stay away from allen-bradley because i am not a fan of PLC's. I used to build injection molding machines that used an allen-bradley plc and it was like a hostage situation. I prefer PC applications.

Allen-bradley does however have a nice selection of motors from what your links are showing. They are a prosperous company for a reason.