How can these two motors produce the same torque if their volt/amp ratings are different and their watts/RPM are the same

My rudimentary understanding of a DC brushed motor is speed is proportional to voltage and torque is proportional current. Therefore a 36 volt 500 watt motor should have a higher RPM rating and a lower torque rating than a 24 volt 500 watt motor which should have more torque but less RPMs.

However, the datasheet suggests that even though the current ratings vary between the two voltages (as expected), the speed and the torque are the same, implying that torque is a function of watts rather than current.

Question 1. How can the voltage / current be different and the speed / torque be the same?

Question 2 Practically speaking, will the 36 volt motor be preferable to purchase since I would get the same torque as the 24V motor but less current (and the heat this produces) going through my circuit?

I know I have misunderstood something.

All help appreciated.

My rudimentary understanding of a DC brushed motor is speed is proportional to voltage and torque is proportional current...

correct as far as it goes for any particular motor

Therefore a 36 volt 500 watt motor should have a higher RPM rating and a lower torque rating than a 24 volt 500 watt motor which should have more torque but less RPMs.

Any given motor has a constant ratio of speed to voltage. A different motor may have a different ratio.

That ratio is dependent on how the motor is built. It depends on armature turns, armature pole area, and magnetic field. Typically motors of a given power will be offered in different voltages, where the difference between them is the number of turns on the armature, and the wire gauge, because some users will find one voltage more convenient than another.

You'll notice that the two motors you've highlighted are rated to produce exactly the same torque at the same speed, for the same electrical power input. I will wager that these motors are exactly the same mechanically, and the 36 V one has 50% more turns of thinner wire than the 24 V one.

The lower current for the 36 V motor does not mean less heat generated in it, as there are more turns on the armature. You will find you need smaller wires or get less heat externally though.

P=IV and that gives 640W for both.

If the designs are different ie number of windings etc then the voltage can be changed for a different current while delivering the same power at a given speed.

Now power = Force * distance * time

So, the torque is related to power.

For a long explanation, see:

http://www.epi-eng.com/piston_engine_technology/power_and_torque.htm

especially at the bottom of the page.

These two are actually the same physical motor - but the 36V one is wound with more turns of thinner wire. Therefore it requires more voltage to reach the same speed, and produces the same torque with less current, by generating the same flux (Ampere-turns) with more turns and fewer amps.

You can either think of the higher voltage motor as having a built-in step down transformer to match the lower voltage one, or having a different (electrical) gearing to the shaft.