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Member

Join Date: Oct 2016
Posts: 5

# Sprocket Size and Motor Torque

06/02/2017 9:49 AM

I am trying to build a motorized cable drum which retracts the cable lying on the ground. I am using a 165rpm 1.3Nm (continuous torque) spur geared DC motor. I have a small sprocket (05-B1 standard, 22 teeth) connected to the motor shaft and have a bigger sprocket (05-B1 standard, 50 teeth) connected to the drum. A chain (05-B1 standard)is used to connect these two sprockets vertically and hence engage the motor with the drum. The diameter of the small sprocket is 50mm and the big sprocket is 125mm. The weight of the small sprocket and big sprockets are 200 and 500 grams respectively. The length of the chain is 900mm (8mm wide). The diameter of the drum is 200mm. The total weight of the cable that the drum must reel in is 5 kgs. Now, since the sprocket reduction reduction ratio is 2.27(50/22), the total torque available at the drum to pull the cable inside should be 1.3Nm x 2.27 which is 2.951Nm (29.51 kgcm). Is this calculation right ? Do I have to take any other factors into consideration here ?

Also, I believe this torque should be enough to pull the cable inside. If not I should either use a motor with higher torque or increase the number of teeth on the bigger sprocket so that the gear reduction ratio increases. Which among these two methods is recommended ?

Pathfinder Tags: gears motors torque
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Guru

Join Date: Apr 2010
Posts: 5762
#1

### Re: Sprocket size and motor torque

06/02/2017 10:43 AM

Is this calculation right? Do I have to take any other factors into consideration here?

Yes, TMI. All you need is the teeth number ratio.

The torque required (at the drum) would be the radius of the drum times the weight of the chain to be lifted, i.e., the weight of the chain from ground level to the top of the drum.

You would have to calculate the cost (in both time and material) to either replace the motor or sprocket if you do not have enough torque.

Member

Join Date: Oct 2016
Posts: 5
#2

### Re: Sprocket size and motor torque

06/02/2017 10:47 AM

I believe I have to also consider the weight of the cable (5 kgs) to be reeled inside onto the drum from the ground , right ? The diameter of my drum is 200mm.

So, for a weight of 5 kgs (49N)and drum diameter of 200mm (0.2m), the torque required at the drum would be 9.8Nm and at the motor , the torque required would be 4.31Nm. Please correct me if I am wrong.

PFA pictures of my system below.

Guru

Join Date: Apr 2010
Posts: 5762
#6

### Re: Sprocket size and motor torque

06/02/2017 1:00 PM

The amount of force from the cable weight would only be the weight of the length of cable from ground level to where it rolls on the drum. The cable laying on the ground is supported by the ground, the cable on the drum is supported by the drum shaft.

Guru

Join Date: May 2007
Location: Annapolis, Maryland
Posts: 4179
#7

### Re: Sprocket size and motor torque

06/02/2017 1:13 PM

Very true, if we knew the height of the drum's axle relative to the ground, and the weight of the cable per unit length, then maybe the 5 kg is actually much less which would reduce the 9.8 Nm requirement. (And add some friction for dragging the cable across the ground).

Guru

Join Date: May 2007
Location: Annapolis, Maryland
Posts: 4179
#3

### Re: Sprocket Size and Motor Torque

06/02/2017 12:00 PM

Do you have a time limit in which to recover this cable?

Is there a maximum torque or pulling force on this cable that you have to stay under to prevent rendering of the cable?

How much cable are you recovering?

Do you need to employ a level-wind system?

Have you considered the increase in diameter as the cable is wound onto the drum?

I'd just buy the stuff and try it out. One test is worth a thousand expert opinions.

Member

Join Date: Oct 2016
Posts: 5
#4

### Re: Sprocket Size and Motor Torque

06/02/2017 12:25 PM

I need to recover the cable completely inside the drum in 25 seconds. The length of the cable is 25 feet. I am using a stepper motor and a leadscrew to guide the cable uniformly onto the drum.

Guru

Join Date: May 2007
Location: Annapolis, Maryland
Posts: 4179
#5

### Re: Sprocket Size and Motor Torque

06/02/2017 12:59 PM

Sounds similar to an RV power cord reel.

Given that the reel in speed needs to be 1 foot per second that means that a 200 mm diameter drum which has about 25 inches of circumference will need to rotate at about 30 RPM. (12.133757 revolutions in 25 seconds = 29.12 RPM) This of course ignores the diameter increase if you are winding multiple layers on the drum.

Also, since you have a geared motor that runs at 165 RPM, if you have a 22 tooth sprocket and a 50 tooth sprocket that gives you a drum rotation of 72.6 RPM. Is that too fast? (neglecting the torque for the moment, no pun intended)

For the torque issue, the 9.8 Nm force to lift the cable would require a gear reduction of at LEAST 9.8 Nm / 1.3 Nm = 7.54 to use the existing motor.

Looking at the retrieval speed again, 165 RPM / 7.54 = 21.88 RPM at the drum which is less than the 30 RPM needed to meet the time requirement.

This is what we call a conundrum.

A more powerful motor would be required to meet the time requirement or if the time requirement can be relaxed, then going to a 15 tooth sprocket (about as low as you can practically go) would require a 114 tooth sprocket on the drum to get the torque you need to use the existing motor.

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#10

### Re: Sprocket Size and Motor Torque

06/08/2017 11:31 AM

Thanks for replying back. Regarding your calculation of rpm, I am indeed winding multiple layers of cable on the drum (3 layers). The diameter of the cable is 18mm. How would RPM calculation change now ?

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#8

### Re: Sprocket Size and Motor Torque

06/02/2017 1:25 PM

165rpm is, er....tap....tap...press equals....17.3 radians per second.

Multiply by 1.3Nm is, er....tap...tap...22W at the motor shaft.

So, say the efficiency of this whirly-mangle is 75%.....multiply by 22W is, er.....tap....tap...17W, or 17 Newton-metres per second at the hook. There's 5kg of weight laying on the ground, with, say a coefficient of friction of 0.2 between it and the ground, meaning the pull needed is 1kg multiplied by g which is 9.81 Newtons. 17 Newton-metres per second divided by 9.81 Newtons gives a maximum retract rate of 1.7 metres per second.

The diameter of the drum is 0.2m and it is doing 17.3 radians per second multiplied by 22/50 gear ratio which means its actual retract rate is 0.2*17.3*22/50, which is, er....tap....tap....tap...equals 1.5 metres per second, so on the face of it this whirly-mangle will do the job with 11% in hand. Happy days.

Looking forward to seeing an overload protection device on that motor, though....

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Guru

Join Date: May 2016
Posts: 884
#9

### Re: Sprocket Size and Motor Torque

06/05/2017 1:55 PM

You need to include one other thing and it could be a biggie. You need to estimate friction on the bearings, chain and guides for the cable. For something like the power cord reel, flexure of the cable will also be a factor. Lubrication also factors in since in some cases dry operation coefficients of friction will stall a system while in others the viscosity of the lubricant (say, heavy grease) can generate enough drag to stall a system.

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