Hi Don
Yes I think I understand where you are coming from and will add my 2 cents worth
The only part I query is your statement of gained 'benefits' of torque doubling for a cost of only 1.4 increase in power.
Power = Constant * Torque * rpm (as you correctly say).
This is a linear equation and so a doubling in ONE factor on the right will double power. You have explained your concept by adjusting TWO factors on the right of the equation. You have doubled torque, and reduced speed. So here is your (balanced) equation now:
1.4Power = k * 2Torque * .7 rpm
Let's normalize the equation back to SAME rpm (divided both sides by 0.7). I hope you can now see by keeping all other factors constant you need to double power to double torque.
We come back to:
2Power = k * 2Torque * rpm
So your question
donob08 said:
The question is what's the tradeoff.
is now partly answered,
the trade off was speed in your example.
Hope this helps.
I would also like to present my laymen's interpretation of a motor in action to help explain the other trade off.
Using a DC permanent magnet motor for this explanation.
First lets remove the magnet so what we have is a simple coil, just like for an electromagnet.
A normal electromagnets coil resistance will be comparably higher than for a motor coil using the same voltage. This is because the electromagnet is designed to have
full current passing through the coil
continuously. So the electromagnet's coil current is limited solely by the coils resistance.
With a motor this is not always true, especially if we want the most "bang for bucks" from it. Motor windings generally have a lower resistance to allow a higher current flow for more power.
There are two ways a motor's current is controlled:
- 1. The controller - The controller limits current flow by quickly turn the voltage on and off. There are numerous methods used here, but for this explanation they are not important. So if the voltage is 50% on and 50% off the net result is 50% full current flow.
- 2. Back EMF - When a magnet is moved/rotated inside a coil, the coil will generate a voltage or EMF. So when a magnet is rotated inside a motor it generates a voltage. But this voltage is in opposition to the voltage being supplied to run the motor, so it has the effect of cancelling out the applied voltage.
Continuing on explaining the effect of Back EMF:
This back emf is at it's highest point when the motor has no load as that is when the magnet is spinning its fastest past the coils. The small amount of current used by the motor is to overcome real world loads of friction (bearing, wind, etc), motor losses (iron, copper) and small amount of heat generated in the coils.
Conversely, back EMF will be at its lowest when the motor is stalled, because there is no rotation, hence no EMF generated. This is also when the coil is conducting the highest amount of current. It is also when the coil is MOST VULNERABLE.
Why? (Glad you asked
)
A motor's windings are not always on during operation. They turn on and off during operation to create a rotating magnet field. This means that each coil has a duty cycle of approx 66% ( BLDC motor, 3 phase, on for 2 cycles). This means that a coil (of given size) can handle even more current than if it had to operate 100% of the time. So again, more 'bang for buck'.
A problem arises though when the motor stall or operates too slow. The coil will now exhibit properties of a heater.
Imagine a queue of people (electrons) filing into a stadium prior to the big game. Most of the time the queue is orderly and there is a wide enough aisle (conductor/wire) to accept the number of people. The trouble starts though when the game is about to start and the queue is too large for the aisle. People start to get more agitated and tempers flare (heating). If this state of affair continues then it is only a matter of time before there is a meltdown (meltdown )
So the final part of the answer to your question:
donob08 said:
Heat, resulting in lower efficiency and potential long term damage, creating either catastrophic failure or shortened life.
Your curves probably were also showing output power, and so efficiency would not affect these two graph lines. If you were to do same exercise considering
input power then you would see a worse power result (but then would be changing two factors again, power/eff or speed/eff).
Finally, back to gears and ratios (still in this post context). Your explanation of increasing torque by loading the motor (decreasing motor speed) is in essence correct. But remember this is a result of increased load, which can be increased by climbing a hill OR lifting up in gear. So I come full circle back to my comments that a bike has a wide range of gears (ave 24). Changing the driven gear ring is possible if that extra bit of fine tuning is desired, but I do not think it would be required for +99% of riders.
Cheers
Allan