Motor torque over base hertz? 1

[dangnm]

Many years ago I read that motor torque over the base frequency was calculated by the formula (base hz/run hz)^2. For example a standard 1 hp, 3 ph, 4 pole, 60hz motor running at 120hz could only produce 25% of full load torque. (60/120)^2=.25
If I remember this was due to the increasing inefficiency of the motor due to the volts/hertz ratio being skewed. For example a 240 VAC 60 HZ motor with a nominal 4:1 ratio would only have a nominal 2:1 ratio at 120 hz. The losses due to the volts/hertz ratio were not linear and really started falling "off the cliff" after 80 hz. I have heard of the trick of running a 240V motor with a 480V VFD and setting the base frequency at 120 HZ but have never tried it.
When testing motor and vfd combos in the past it seemed that the above formula worked if you used 70 hz as your base frequency. I always assumed this was due to the service factor of the motor. Somewhere around 90 hz there seemed to be be sharply increasing current/heat and slip. While the testing I did was not very accurate or high tech it did seem to be as calculated.
What is the correct formula for torque over base frequency? Is it really linear, constant horsepower? Is there any limit due to the changing volts/hertz ratio or is the limit all mechanical.
I have tried searching the web and keep finding charts showing constant horsepower out to 120hz but I am not sure I believe them. Someone please set me straight.

Any links to actual test results/charts would be greatly appreciated.

Barry1961

 

[jraef]

Hmmm... You said a lot and buried somewhere in there are some pertinent questions.

No the relationship is non-linear. So at 70Hz your torque loss is minimal compared to your torque loss at 120Hz.

No it is not an issue of efficiency per se. A 460V 60Hz motor is designed to operate at 7.67V/Hz to attain the stated torque output. Once you get to 460V, your voltage can no longer increase as the frequency does, so you begin to operate in a constant HP mode. In addition you start to saturate the motor windings. That saturated condition can be thought of as a decrease in efficiency, but that is a consequence rather than a cause.

Yes the 230V motor strapping trick works just fine, I do it all the time. When strapped for 230V, the drive can go to 460V output at 120Hz and still maintain the 3.83V/Hz ratio.

Mechanical limits are very real. Most manufacturers of small HP motors don't bother to have multiple bearing systems for each base speed, so they are typically built to 2 pole design limits, i.e. 3600rpm. Therefore it is relatively common to be able to run an 1800rpm motor at 120Hz, but rarely can you go over that without buying a motor specifically designed for that purpose. Many manufacturers now offer "spindle motor" designes with that in mind, some capable of being driven at 400Hz, i.e. cutting tools. There are however a lot of caviats to running over frequency. Cooling fans may no longer function correctly for instance. Mounting and coupling issues can be problematic as well.

If you want to do it, check with the motor manufacturer. Most of the major players now recognize this application as somewhat common and have maximum speed ratings available for the asking.

As to you not believing the charts that you see, I can't help you there. You may be able to find some test results from some university program that uses them to teach the subject to students, but it has been such a widely acknowledged phenomenon for so long, I doubt anyone has test reports available on the web.

"Venditori de oleum-vipera non vigere excordis populi"

 

[dangnm]

I think I am missing some basic understanding of torque available over base frequency. It seems to me one of the following two statements is wrong.

1. If you are operating at a constant horsepower over base speed your torque loss is linear.

2. If torque loss over base speed is non-linear your are not operating at a constant horsepower.

If I run a motor designed for a 3.83V/Hz ratio at 1.9V/Hz how much does that effect the efficiency of the motor? Is there a nominal formula to calculate this?

If I seem a little "slow" here it is because I am.

Barry1961

 

[dangnm]

Thanks jraef.

I took your advice and did some research on the motors. I see now that a standard motor can only be run at constant horsepower up to 1.5 times base speed. Above 90 Hz at constant horsepower I am guessing a standard motor will overheat.

I am still trying to find a general formula for the effect of running a motor over base speed on efficiency or current draw.

Barry1961

 

[DickDV]

Barry, for a moderate distance over base speed, you are operating at constant horsepower as jreaf said. However, if you would plot the torque derating it by the inverse of the overspeed as you mentioned (don't square it!) you will find that the curve is not linear but curved. Just plot 2/3 torque at 3/2 speed and 1/2 torque at 2/1 speed and you will see that they are not a straight line from 1/1 torque at 1/1 base speed. An inverse curve is always curved.

Changes in efficiency are not a big issue here altho, in overspeed, the losses due to the faster cooling fan speed are higher. At slower speeds, as long as the V/Hz ratio stays constant, the motor will develop torque at a constant level as well. Also, motor amps will hold pretty much the same at lower voltages and speeds for the same torque loading.

 

[mc5w]

The loss of torque with increase frequency is partly due to loss of magnetizing current with increased frequency leading to your formula. Once you get past a certain frequency the steel laminations lose ability to operate at such a high frequency which causes torque to fall off even faster.

If you want to go above 133 Hertz the motor's iron structure has to be built especially for the operating frequency. One woodworking machine that I saw on the job used a motor generator to step up to 200 Hertz and then used 200 Hertz motors to operate high speed drills. This avoided using a bank of itty bity gearboxes and very long small diameter 60 Hertz motors.

Mike Cole, mc5w@earthlink.net