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# Need advice from math gurus: ballscrew>sprocket>chain force

Posts: 3,681
I am experimenting with something and need to sort out the loads on the chains to adjust a sprocket ratio at the motor I am using to be able to provide enough torque. I never have tried any calculations like this. I want to first calculate how many lb's of static force would be on the chain assuming for simple math a 2" OD chain sprocket and a 3/4" ball screw with Lead = .25 ( 4 turns per inch travel). Basically under the load, how much lbs is required to hold the weight suspended if I were to reach out a grab the chain. If I can get that then I can sort out the rest ie type of chain to support load, motor torque in oz-in etc. I am trying to first understand what are the factors to consider to arrive at the load on the chain between the two ball screws supporting the load.

The image shows a simplified design. Two ball screws support the load. A chain is attached at the bottom on 2 sprockets that for now are 2" OD.
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• Posts: 11,079
One class I recall, used the concept of Virtual Work, which basically says that Fi*Di = Fo*Do
That means you take some arbitrary small movement of the load, then calculate how far the driver moves to cause that.
That distance ratio, is the inverse of the force ratio.
• Posts: 7,775
Without taking friction into consideration you have a sprocket with a 1 inch radius lifting 600lbs 0.25 inches per turn so the ratio 1/0.25 or 4 and the torque required would be 600/4 = 150 inch-lbs or 12.5 ft-lbs. Of course there will be friction so you will need more torque than that. I would shoot for about 2x, but the ball screw specs will provide a better idea of that.

The diagram looks a bit like a tensile tester. Is that what you are building?
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• Posts: 3,681
Thanks Jmg. so for 1@ travel of the weight there are 4 turns of the 2" sprocket. 4 * 2pi = 25.12". The ratio is 1/25.12 = .0398. So you're saying the load on the chain is 600 * .0398 = 23.76 lbs.
• Posts: 3,681
Thanks Kwinn. It is a piece of glass 10' wide 6' tall.
• Posts: 3,681
If I recall the gear motor has a peak 3750 oz in and running torque of 125 oz in. I intend to put some reduction to get the motor torque in range.
• Posts: 7,775
T Chap wrote: »
Thanks Kwinn. It is a piece of glass 10' wide 6' tall.

Glad to help. That's a big piece of glass. Must be fairly thick to be 600 lbs. About 0.75" or so?
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• Posts: 3,681
Something like that with a frame.
• Posts: 3,681
edited April 2017
They don't show my 12.5:1 gearbox. This one marked if the 75:1. I was dividing these numbers by 6 for my motor. Not sure what the oz in /A is on constant torque vs the oz in peak. But I am getting 750/6 = 125 oz in for my motor which is 7.81 lb in. 150 required lb in / 7.81 = 19.20 so I need to build in some reduction of greater than that.
• Posts: 1,063
In such an application, I would prefer to see a worm-reducer instead of the chain/sprockets.

JMO
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• Posts: 3,681
Is that because the weight cannot force the motor to spin? Excellent idea. I have a shaft mount s electro brake but the worm gear is much better idea!
• Posts: 3,681
One problem with worm gears in high ratio systems is it becomes difficult to detect over current on the motor and stop the the Motor before damage occurs especially if you need safety built in. A few years back I needed a way to retract the motor under stress when using a worm gear and got around that by adding a swing arm with idle sprockets and springs and switches. If the system gets under load in any direction the swing plate moves over and presses a switch and the motor reverses and shuts down.
• Posts: 1,063
T Chap wrote: »
One problem with worm gears in high ratio systems is it becomes difficult to detect over current on the motor and stop the the Motor before damage occurs especially if you need safety built in. A few years back I needed a way to retract the motor under stress when using a worm gear and got around that by adding a swing arm with idle sprockets and springs and switches. If the system gets under load in any direction the swing plate moves over and presses a switch and the motor reverses and shuts down.

Ah, yes, I do a lot of actual load-sensing/torque-limiting via monitoring/limiting of the PID output. However, I always spec my drive-train components beyond the power of the motor. You could always limit the motor torque or use a torque-limiting coupling between the motor-shaft and the reducer(?)

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• Posts: 7,775
Mickster wrote: »
In such an application, I would prefer to see a worm-reducer instead of the chain/sprockets.

JMO

Worm reducers are great for high ratio situations but they do have a down side. High friction, high heat generation, and high wear unless it is a ball screw worm gear. Not too much of a problem for intermittent operation but the heat generated by continuous operation will break down the grease and damage the gears.
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• Posts: 1,063
Yeah, I know, something like 40% static efficiency. Looks like the best solution for T Chap's application, though. Better than having shattered glass all over the place.
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• Posts: 3,681
I had forgotten about the worm gears on this project and I had originally given thought to just raising it with chain with a shaft connecting some sprockets on each side but with the worm gear driving the shaft I may revisit the idea of change raising it versus ball screws. An issue with the ball screws is they will be visible when the glass is raised and the ballscrews will need to be coated pretty good with grease as they are exposed. Rust is a concern long term on the carbon steel ball screws. With chain I can easily conceal the chain.
• Posts: 3,681
Here is the other concept that may be better and less headaches than dealing with the ball screws. If the ball screws rust it would be almost impossible to replace them. With an all chain system I think the life span would be improved.
• Posts: 1,063
No possibility of 100:1 directly on the main shaft?

Not a fan of chains, myself, because of stretch issues. Have you looked at belt-drive?
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• Posts: 3,681
The smallest sprocket I find in ansi 40 is 9 tooth. The largest 96. With the worm gear off the gear motor it will be minimal load on the motor. I use belts mostly with steel cord but in this case chain is more robust over 1000lb working load each so 2 chains on the glass gives almost 4x rating. Belt can slip under certain conditions chain won't slip even if pretty loose.
• Posts: 1,897
Have you thought of a small home made "hydraulic" cylinder made of 4" ABS sewer pipe and driven by water pressure from a tap? If your lift stroke is long, you could add a chain length multiplier resulting in a shorter cylinder, albeit with greater force/diameter. Would give great control by regulating the flow from a tap.

Seems very doable to me.

Cheers,
Peter (pjv)
• Posts: 1,063
T Chap wrote: »
The smallest sprocket I find in ansi 40 is 9 tooth. The largest 96. With the worm gear off the gear motor it will be minimal load on the motor. I use belts mostly with steel cord but in this case chain is more robust over 1000lb working load each so 2 chains on the glass gives almost 4x rating. Belt can slip under certain conditions chain won't slip even if pretty loose.

Yikes, I was referring to toothed-belts/pulleys. The same as used on car-engines where overhead cam timing is critical.

There are belts for all kinds of loads, no noise, no lube required and no stretch.

PropBASIC ROCKS!
• Posts: 3,681
Yes I understood tooth type belt. I will look at some tomorrow from my supplier to see if there is something compatible to chain
• Posts: 7,775
If you are considering chains you should look at chain hoists. They may be able to do what you want without using a worm gear.

I do like pjv's suggestion, although that would require at least 25psi of pressure. Not sure if 4inch ABS pipe would handle that. Might be worth buying a piece to test it though.
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• Posts: 114
I think I'd also add an 'Otis Brake' (Safety brake designed for elevators)
• Posts: 7,775
MrBi11 wrote: »
I think I'd also add an 'Otis Brake' (Safety brake designed for elevators)

Oh yes. Definitely want something to keep it from coming crashing down if something breaks.
In science there is no authority. There is only experiment.
Life is unpredictable. Eat dessert first.
• Posts: 7,775
@T Chap

MrBi11's suggestion got me thinking about elevators and their counterweights. Have you considered steel cables and counterweights? That would require a much smaller motor and allow for somewhat faster movement.
In science there is no authority. There is only experiment.
Life is unpredictable. Eat dessert first.
• Posts: 3,681
Yes I thought about that but there is no space for weights. The speed is not a concern. The worm gear gives a nice built in fail safe against movement without the motor causing it. With over 4x overrating on chain working load I feel pretty good.

I am trying to understand a mystery regarding torque. In one case if you have a pulley that is 10 teeth driving a 100 tooth then the ratio of torque should be 10:1. However the radius difference in the 10 tooth and 100 tooth sprockets is not 10x. If you connect a chain to a lever at 1" radius (as in a 1" radius pulley) then 10x torque would be the same as tying the chain to a 10" lever or equivalent 10" radius pulley for the same effect of torque = length * force. I am trying to find the discrepancy of radius versus teeth count. Torque = force * length. But it can also be represented as a ratio of teeth count, but teeth count is not linear with radius. The radius is smaller than 2x on a 20 tooth sprocket versus 10 tooth. It doesn't add up.
• Posts: 11,079
T Chap wrote: »
... But it can also be represented as a ratio of teeth count, but teeth count is not linear with radius. The radius is smaller than 2x on a 20 tooth sprocket versus 10 tooth. It doesn't add up.

Circum is 2 * Pi * r, so that certainly is linear with radius.
The radius that matters on a gear, is the ~centre of the teeth, where they mesh, & that should ratio with teeth count, if they expect to mesh correctly.

• Posts: 1,063
edited April 2017
kwinn wrote: »
@T Chap

MrBi11's suggestion got me thinking about elevators and their counterweights. Have you considered steel cables and counterweights? That would require a much smaller motor and allow for somewhat faster movement.

The way I imagine this is that; the 600LB load might be present and then it might not so a fixed counterbalance might present a problem. I have used a pneumatic cylinder for this purpose, where I can apply, remove or regulate the air pressure. Blocking the ports also makes for a very effective brake.

Edit: I once used a rotary pneumatic counterbalance (with cable) but a quick look on the web didn't find one.
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• Posts: 18,955
edited April 2017
I've learned to DOUBLE whatever forces & torques I calculate from static gear mechanism analysis. When you factor in friction and efficiency losses, that's about where you end up for SLOW motion. If things are moving fast then dynamic forces come into play and you have to allow for that too.

Edit: I see you have two ballscrews there, which are pure rubbing friction and very inefficient (much like worm gears), even if they are slathered in grease. Triple the calculated forces required for reliable long-term operation.
"When you make a thing, a thing that is new, it is so complicated making it that it is bound to be ugly. But those that make it after you, they don’t have to worry about making it. And they can make it pretty, and so everybody can like it when others make it after you."

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• Posts: 7,775
erco wrote: »
........

Edit: I see you have two ballscrews there, which are pure rubbing friction and very inefficient (much like worm gears), even if they are slathered in grease. Triple the calculated forces required for reliable long-term operation.

Actually, ballscrews have much lower friction than worm gears or acme screws, although higher friction than an equivalent geared transmission. Ball screws were used on gamma cameras to lift heads that could weigh over 3,000 pounds, and in tensile testers up to about 2000 pounds.
In science there is no authority. There is only experiment.
Life is unpredictable. Eat dessert first.