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# confusion about relationship between HP, torque, and RPM6

## confusion about relationship between HP, torque, and RPM

(OP)
Hi,

I have a 10 HP AC motor with nameplate 1750 RPM. This motor is being used for tension control in a winder application. The motor is controlled by a variable frequency drive that is configured for torque control mode. I can send the drive a 0-20 mA signal to vary the torque between 0-100%. I am having a hard time understanding what 0-100% relates to in actual torque. I believe the formula that relates torque, horsepower, and speed is torque = horsepower * 5252 / rpm. If I enter the nameplate information into this formula, I get:

torque = 10 * 5252 / 1750 = 30.01 lb-ft

I imagine (please correct me if I am wrong), that this would be the maximum torque that can be created by this motor at 1750 RPM. This makes me think that as I vary my control signal between 0-20 mA, the torque (at 1750 RPM) would vary accordingly between 0 – 30.01 lb-ft.
If my reasoning above is correct, I am not sure what the implications are of the fact that the motor will be running significantly slower than 1750 RPM during normal operation. Considering the equation Torque = HP * 5252 / rpm, it seems to me that if RPM decreases, either the torque or the horsepower must also change to preserve the accuracy of the equation. For a typical AC motor with a VFD in torque control mode, should I assume that the maximum torque (torque resulting from a 20 mA control signal) will be the same at all speeds (meaning HP decreases as speed decreases)? If this is not the case, the equation makes me think that if HP remains constant, then the maximum torque would have to increase as speed decreases.

If anyone here can clear this up for me, I would greatly appreciate it.

Paul

### RE: confusion about relationship between HP, torque, and RPM

The HP the motor is capable of producing continually varies linearly with speed, assuming you keep enough cooling air passing over the motor.

### RE: confusion about relationship between HP, torque, and RPM

(OP)
Thank you Lionel,

So if I am understanding your response correctly, if the HP the motor is capable of producing varies linearly with speed (assuming you keep enough cooling air passing over the motor), this would make be believe that as speed and horsepower decrease at the same rate, torque would remain constant. Am I correct?

Thanks again,
Paul

### RE: confusion about relationship between HP, torque, and RPM

Basic relationship

T = HP / (RPM / 5252)
However motor torque is proportional to motor amps. The simplifies limiting case is that regardless of speed do not exceed nameplate motor amps, and if you need to operate below 30% speed, expect short motor life unless you have taken measures to ensure heat removal.
I have never used a "torque control" mode, a quick survey of some quick start videos make me think your supposition is likely correct, that in torque mode, 04-20mA = 0% to 100% of the drive's opinion of the full load torque of the driven machine.

### RE: confusion about relationship between HP, torque, and RPM

My experience has been that using torque control on a motor, in order to control web tension, often does not work very well. This is particularly the case if there is a gear box on the motor. Friction and inertia in the drive train can be more than your tension load.

I worked on one machine where at low speed settings, like when starting, the winder would run slower than the rest of the machine, resulting in slack material.

### RE: confusion about relationship between HP, torque, and RPM

In Torque Control mode with a (good) VFD, what you are doing is PRIORITIZING the maintenance of a specific amount of torque rather than speed. So you are telling the VFD to override any speed command in favor of keeping torque constant.

Please note that in order to accomplish this with any reasonable accuracy, the VFD must be capable of what's called "Flux Vector Control" (FVC) or "Field Oriented Control" (FOC), which in many cases requires the use of an encoder feedback to the drive from the motor. Most inexpensive drives will be capable of "Sensorless Vector Control" (SVC) which, although able to IMPROVE torque capability compared to older drives without it, is not all that useful for actual torque control. There are a few high-end VFDs out there that can provide "Encoderless Flux Vector Control" now that can match the performance of FVC/FOC without needing an encoder, just don't confuse that with SVC, it's not the same.

FacEngPE, that formula on that website is incorrect. It's
T = (HP * 5250)/RPM

" We are all here on earth to help others; what on earth the others are here for I don't know." -- W. H. Auden

### RE: confusion about relationship between HP, torque, and RPM

The 10 HP motor will either be rated for a "constant" or "variable" torque load. If the nameplate does not specifically say "constant torque" (or CT range), then it isn't suited for it.

What that means is that it will (usually) cool itself for variable torque loads that approximate the affinity laws for centrifugal loads (i.e., per unit HP output is proportional to the square of the per unit speed). If you drop to half of rated speed, then the motor will (safely and continuously) operate at loads up to 0.5*0.5 = 0.25 per unit. For the specific rating in question, that means powering up to 2.5 HP when running at 875 rpm.

By contrast, a machine rated for constant torque would be able to sustain the same torque throughout the range: this means 5 hp at 875 rpm.

As jraef noted - to be able to operate under true torque control, you'd either need a really good (and very expensive) drive or some sort of speed sensing feedback loop to enable the drive to maintain the condition with any amount of accuracy.

Converting energy to motion for more than half a century

### RE: confusion about relationship between HP, torque, and RPM

Yes, that is how it works in theory, the motor produces a constant torque and the HP varies linearly with speed.

### RE: confusion about relationship between HP, torque, and RPM

(OP)
Hi Lionel, Jraef, CompositePro, and Gr8blu,

Thank you all for your responses. This winder (and associated drive system) are on a printing press that is at least 20 years old. While the printing press has been seen regular use over this period, this particular winder has not been used. As a new production requirement arose that would make it useful (or necessary), I was asked to see if I could get it to work. An ABB sales engineer very generously offered to take a look at it and was able to make it functional by correcting a few wiring and configuration issues. By the time he left, in a short trial, we were able to control tension within a range that "felt" good to the machine operators. I was not involved in the design of this machine, but I believe the designers were in fact relying on the theory (as Lionel mentioned) that the motor will produce a constant torque and the HP will vary linearly with speed. A potentiometer input is provided so that operators can control what this constant torque is. Being the machine has no instrumentation to measure spool diameter and adjust the applied torque as diameter increases, I expect that the operators might have to learn to do this manually. Experimentation will be required to see if we will be able to control tension with this control scheme throughout the required speed range and diameter range.

I have attached a picture I took of the motor nameplate. I don't see any mention of a constant torque (or CT) range. There is no gearbox between the motor and the rewind shaft - just a 1.83 : 1 belt/pulley reduction (slowing down the rewind shaft relative to the motor). The drive is an ABB ACS601. It is old, but I would say that it was a fairly sophisticated drive in its time. I'll have to read through the documentation to see if it supports any of the modes (FVC, FOC, or SVC) that JRaef mentioned. There is no encoder feedback.

At this stage, the drive seems to be able to control tension. We are planning to see if it can do this throughout the required speed and diameter range. Thanks to you guys, I now feel like I have a better grasp of the underlying theory of operation and a few things that might impose limitations on what we will be able to accomplish.

I really appreciate all your help!

Best regards,
Paul

### RE: confusion about relationship between HP, torque, and RPM

This seems to keep things straight for me -

A resource that I find useful is the Cowern Papers

### RE: confusion about relationship between HP, torque, and RPM

The ACS601 is a high-end drive that should be capable of FVC/FOC, but ABB often uses a slightly different approach called 'Direct Torque Control" (DTC) that is going to provide essentially the same net effect, just approached from a different perspective internally. In winder applications, torque = tension x roll radius, so torque control is what you want.

" We are all here on earth to help others; what on earth the others are here for I don't know." -- W. H. Auden

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