How Can I Determine The Functional Power Output Of A Motor

[electromateria]

Lets say I have 2 single phase industrial motors:

1) 120v / 8 amps / 1650 rpm

2) 120v / 16 amps / 1000 rpm

How can I determine which outputs the most force?

Is horsepower usually the best metric to go by? I noticed some motors are 1/3 HP but are around the same size as a 1 HP. What's up with that?

[bob91343]

This is not a simple subject.  The only accurate way of measuring motor output power is with a dynamometer.  This is a complex and expensive device.

Having said that, one can estimate the shaft power by using the power input when the motor is loaded and assuming a typical efficiency.  One horsepower is 746 Watts.  So if the motor is drawing 746 Watts you can assume its shaft output is 1 horsepower times an assumed efficiency.

Gears are inefficient so if it's got a transmission it will waste power therein.

[Berni]

If by "force" you mean torque then motor 2 will provide more since it draws more power and is designed for a lower rpm.

The physical size of the motor is not always the whole story. There are a bunch of different design parameters that the motor design has to strike a balance between. Having a large number of poles (low rpm) for example might make efficient use of copper inside more difficult so making it bigger, some motors might use better thicker insulation on the wire inside to make them more reliable but also bigger. Some designs focus more on efficiency and overspec the motor to make sure its running in an efficient area, others might underspec the motor making it smaller, causing it to be less efficient but compensate by sticking a bigger fan on the end of the motor to keep it from overheating.

When it comes to single phase motors there are also a few different designs in how to create the extra phase needed to start the motor, these also have implications on motor size and the amount of starting torque it can provide.

The full story of a motor is having the motors characterization charts that show exactly how the motor performs under various amounts of load. These are in the motors datasheet and measuring them requires a dyno test rig.

[Cerebus]

What's the best metric depends entirely what you want to do with the motor. Just like metrics vary if you're looking for an athlete, it's no good measuring weight if you're looking for basketball players, and height is a poor metric for wrestlers.

You've basically a choice of looking at torque or at power. Torque is a measure of "twisting force", power is what power always is, the ability to do work in terms of how fast something can deliver energy. The two are linked.

The instantaneous output power \$P\$ (SI unit Watts) of a motor is the product of the motor's torque and rotational speed \$P = \tau\omega \$ where \$\tau\$ is torque (SI unit Nm) and \$\omega\$ is angular speed in radians per second. If you're dealing with RPM the conversion from RPM => radians/sec is simply \$2\pi\frac{rpm}{60}\$. One imperial horsepower is about 745.7 Watts, one metric horsepower is about 735.5 Watts. One pound-foot of torque is 1.35582 newton metres, and one oz-in of torque is 0.00706155181 Nm (i.e. \$\frac{1}{16\times12}\$ pound-foot).

Ability to produce a given torque at a given speed varies between motor types. So as well as deciding what you need in terms of torque or of power, you also need to think about torque versus motor rotational speed. If you're looking at a motor to drive a lathe (which must operate at varying speeds), then something with a flat torque curve would be advantageous so you might pick a BLDC motor, if you're planning to only operate at one speed (say a motor to drive a conveyor belt) then you're only really interested in the torque/power that it can deliver at its rated constant speed (and might pick an AC induction motor or AC synchronous motor, probably the latter).

For a universal motor the torque versus speed curve looks like this:


For an AC induction motor it looks like this:


For an AC synchronous motor it looks like this:


For BLDC motor or Permanent Magnet Synchronous Machine it looks like this:

(the first part of the curve, where the torque line is flat is the normal operating zone for a BLDC motor)

Different types of motor have quite different characteristics, and the size of the motor if comparing different types can be misleading. Any permanent magnet motor will be physically smaller than a motor of similar power that has a winding instead of permanent magnets. Within motor types there's a pretty constant relationship between motor volume and motor power.

[pardo-bsso]

Besides what everyone else said, the convention (at least when I studied ) is that what the plaque says is the power at the shaft.
So at the rated speed you can just apply

$$ Power = \tau \cdot \omega $$

[David Hess]

Lets say I have 2 single phase industrial motors:

1) 120v / 8 amps / 1650 rpm

2) 120v / 16 amps / 1000 rpm

How can I determine which outputs the most force?

1 horsepower is about 750 watts so the first motor is 1 horsepower and the second motor is 2 horsepower.  Torque is proportional to power and inversely proportional to speed so the second motor has 3.3 times the torque of the first motor.

Is horsepower usually the best metric to go by? I noticed some motors are 1/3 HP but are around the same size as a 1 HP. What's up with that?

Are they really the same size in all dimensions?  Motors with different power ratings are often made in the same physical size for interoperability.

[Siwastaja]

Cerebus' set of curves comparing the motor types is really good, but I'd finetune the captions a bit, because the post classifies motor types as motors only, ignoring how the motor is driven, and silently assuming a certain (classical) way to drive it. So let me add some more insight:

For a universal motor the torque versus speed curve looks like this:

For a universal motor (which is just another name for series wound brushed DC motor), driven off a constant-voltage source, like would be the case with simple old-school power tools, the torque versus speed curve looks like this:


The curve looks like this because the rotation generates back-EMF voltage linearly relative to the RPM. Current (~ torque) flowing in the motor is the (Vsupply - Vback_EMF) / Z_motor, where Z_motor is approximately a constant. Hence, more torque can be had when Vback_EMF is small, to the point to "maxing out" or saturating the motor iron, necessitating a compromised motor design underdelivering at higher RPM. Think about: what if we lowered Z_motor (particularly resistance to increase efficiency) and then adjusted Vsupply dynamically to have just the torque we want??

For an AC induction motor it looks like this:

For an AC induction motor driven off the constant-frequency grid (which is getting more and more obsolete every day, although will remain in use for those use cases where it is good enough like simple fan motors) it looks like this:


It looks like this because when the RPM is dropping, the slip frequency (difference between f_supply and f_rotation) goes outside the optimal range, efficiency drops, power factor drops, and less torque is generated. Think about: what would happen if we adjusted f_supply dynamically??

For an AC synchronous motor it looks like this:

For a certain type of AC synchronous motor driven off the constant-frequency grid, I'm not actually sure how usual such curve is.



And finally,

For BLDC motor or Permanent Magnet Synchronous Machine it looks like this:

For a BLDC (aka trapezoidal PMAC), or PMSM aka PMAC aka sinusoidal PMAC motor, which are almost the same thing (for basic analysis, the difference doesn't matter), driven with an appropriate inverter drive aka VFD, because unlike the previous motor types, these types basically refuse to work at all unless driven with the proper controller, it looks like this:



Now comes the catch, and this is important: basically all the motor types shown perform roughly to this curve set when driven properly*! So actually the motor characteristics shown by Cerebus are characteristics not of the motors themselves, but of the combination of the motors, and how the power is supplied to said motor types. There always is the option to deliver the power to the motor the better way, for example buy a so-called VFD or Variable Frequency Drive, which is now a low-cost off-the-shelf item for an AC induction motor. If you do this, then the AC induction motor starts behaving according to the last graph.

*) not saying directly-connected-to-grid usage isn't proper if the designer knows the compromised result is good enough for the job, or if the better way is not available, as was the case in the past

(the first part of the curve, where the torque line is flat is the normal operating zone for a BLDC motor)

Though, there is nothing abnormal running them in field weakening, when more RPM is needed at the expense of torque. Depends on what is needed. Your comment has the right idea though because looking at that particular curve, the constant-power region occupies, what, 2/3 of the curve, where in reality, not many systems operate on the right-hand end of the curve.

The idea of having constant torque, or said even better: whatever torque is asked for (below some maximum, obviously), is the key to understanding the idea of using proper motor drives. The advances in semiconductors and control electronics have made such motor drives more appealing during last three decades, making the curve sets as seen here (except the last one!) more and more obsolete as days go by.

And yes, I have designed and built such drives for many motor types: for "universal motors", brushed DC, steppers (which is actually a special case of a 2-phase reluctance motor), 3-phase induction, obviously BLDC, but also 1-phase induction (actually a special case of 2-phase induction). And when you drive them properly, they perform completely differently to how they are "supposed" to perform when driven "traditionally" i.e. suboptimally.

[james_s]

1 horsepower is about 750 watts so the first motor is 1 horsepower and the second motor is 2 horsepower.  Torque is proportional to power and inversely proportional to speed so the second motor has 3.3 times the torque of the first motor.

We don't know how many watts these motors draw though, without knowing the power factor that can't be calculated and we don't know the efficiency, 746W is about 1HP of input energy but you get less than that out in mechanical energy. It's much more reliable to go by the horsepower rating on the nameplate.

[Cerebus]

Cerebus' set of curves ...
... suboptimally.

Yup to all of that, I was just trying to drop some hints in the OP's direction, not offer an in depth motor analysis. As far as using VFDs to drive everything, I'd concur, it's much more satisfactory in almost any non trivial application to use active motor drive from some variant of inverter. The OP seemed, by implication, to be looking at off-line motors, and there's such a thing as chucking too much information all in one go, I was just trying to cover all the points he'd touched without being too shallow.

As far as BLDCs/PMSM operating region, I'd grabbed graphs from disparate places just by searching for 'X motor torque curve' and the BLDC one had such a different scale from the rest I wanted to draw attention to the left hand constant torque region. For the record, something that hasn't been mentioned, the knee on the BLDC/PMSM torque curve is the 'rated speed' that will appear on the rating plate on a motor; ideally for clarity in the graphs shown it ought to coincide with the peak torques to the right of the other synchronous motors' graphs. With adequate drive it's possible to pull two or three times the continuous rated torque out of a BLDC/PMSM for a limited period, and that too doesn't show up on that torque curve.

[David Hess]

1 horsepower is about 750 watts so the first motor is 1 horsepower and the second motor is 2 horsepower.  Torque is proportional to power and inversely proportional to speed so the second motor has 3.3 times the torque of the first motor.

We don't know how many watts these motors draw though, without knowing the power factor that can't be calculated and we don't know the efficiency, 746W is about 1HP of input energy but you get less than that out in mechanical energy. It's much more reliable to go by the horsepower rating on the nameplate.

Most motors are very efficient and the ones that are not, like shaded pole motors, are not as large as described.

The numbers given are actually consistent with the power factor of common 1 and 2 horsepower induction motors when including power factor.