# Quadratic relationship between amps and torque?



## Batterypoweredtoad (Feb 5, 2008)

I have one of the big 13" GE motors talked about recently on this site. Here is the tag:










My first questions are about the relationship between amps and torque:

1) I have heard it referred to as a "Quadratic relationship". My interpretation of this is that if I take the labeled 467 amps and double them I get 4 times the labeled torque of 140 ft/lbs (560 ft/lbs). Is that correct?

2)If my reasoning is correct in question 1, then what happens when you triple the label amps? Do you get 9 times the label torque (1260 ft/lbs)? 


My next question is about saturation. I have read that the relationship for amps/torque goes linear after motor saturation. 

a) What would be a good estimate for how many amps a motor of this size can handle before saturation?

My third, and final batch of questions are about the volt requirements to make a motor run at that many amps. 

-Is that relationship linear? For example-if I double the volts do I get twice the amps (and 4 times the torque) at the same rpm? 

-What happens if I triple the voltage? 

-If I double the voltage do I now get the label torque at 4 times the label rpm?

Thanks, I hope at least some of my reasoning is valid.


----------



## major (Apr 4, 2008)

Batterypoweredtoad said:


> I have one of the big 13" GE motors talked about recently on this site. Here is the tag:
> 
> 
> 
> ...


No. This is only true at light loads before saturation comes into play. You're better off using a linear relationship. Double the current, it doubles the torque. All this assuming it is a series wound motor.



> 2)If my reasoning is correct in question 1, then what happens when you triple the label amps? Do you get 9 times the label torque (1260 ft/lbs)?


No. Reasoning was incorrect. 3 times the current, triple the torque.



> My next question is about saturation. I have read that the relationship for amps/torque goes linear after motor saturation.
> 
> a) What would be a good estimate for how many amps a motor of this size can handle before saturation?


Hard for me to tell from here with just a nameplate, but I'd guess about 300 to 400 amps.



> My third, and final batch of questions are about the volt requirements to make a motor run at that many amps.
> 
> -Is that relationship linear? For example-if I double the volts do I get twice the amps (and 4 times the torque) at the same rpm?


No. You either have to go back to the motor curves or the equations which I have posted recently. It is the inter relationship of 2 separate functions. The torque-current (Tem = Kt * Ia * Flux) and the speed-voltage (Eg = Kt * RPM * Flux). Once saturated, Flux stays pretty constant. Machine constant, Kt is constant. So what you get is speed is proportional to voltage and torque is proportional to current.

At a given load (torque), if you increase voltage, you increase the RPM. Period. That is linear. Now if at a given speed, you increase the voltage, yeah, the current and torque go up, but that is not linear. To figure that, you need the curves, or a more complete model of the motor, including the resistance.



> -What happens if I triple the voltage?


At a given load (torque) it goes approximately 3 times faster, at the same current as before.



> -If I double the voltage do I now get the label torque at 4 times the label rpm?


No.



> Thanks, I hope at least some of my reasoning is valid.


You're welcome and I hope you follow what I said. Look back at some of my previous posts about motors and you can find further explanations and examples.

Regards,

major


----------



## Batterypoweredtoad (Feb 5, 2008)

Major,
Thanks, makes sense. The numbers I was getting seemed too spectacular.

With saturation-what are the contributing factors? The motor in question is a 13" GE that weighs around 350lbs. Steel everything (end housings not aluminum).

I am curious about another thing as well, how is it that white zombie gets such high amps with only about 110v applied to each motor before the series parallel shift?


----------



## samborambo (Aug 27, 2008)

Batterypoweredtoad said:


> 1) I have heard it referred to as a "Quadratic relationship". My interpretation of this is that if I take the labeled 467 amps and double them I get 4 times the labeled torque of 140 ft/lbs (560 ft/lbs). Is that correct?


Basically, yes. I assume you're talking about series-DC motors.

In a series-DC motor, the current passes through the field and armature windings. Therefore doubling the total current through the circuit will result in four times the force between the two poles. If this was a permanent magnet field, the relationship between torque and current would be linear because the field is a fixed strength.

Be aware that as the field strength increases, the back EMF voltage at a fixed speed increases linearly. BEMF is also linear to speed.



> 2)If my reasoning is correct in question 1, then what happens when you triple the label amps? Do you get 9 times the label torque (1260 ft/lbs)?


Theoretically, until you hit core saturation.



> My next question is about saturation. I have read that the relationship for amps/torque goes linear after motor saturation.
> 
> a) What would be a good estimate for how many amps a motor of this size can handle before saturation?


There's no "rule of thumb" for estimating motor saturation. You can calculate it if you know the core dimensions and windings, etc. Much easier to but it on the dyno and get a real world measurement.



> My third, and final batch of questions are about the volt requirements to make a motor run at that many amps.
> 
> -Is that relationship linear? For example-if I double the volts do I get twice the amps (and 4 times the torque) at the same rpm?


No. Voltage is made up of two parts - back EMF and volt drop. Volt drop is simply V=IR of the windings. Back EMF is the product of speed and field strength.



> -What happens if I triple the voltage?
> 
> -If I double the voltage do I now get the label torque at 4 times the label rpm?


No. If you fix the current, double the voltage you will develop the same torque at twice the speed.



> Thanks, I hope at least some of my reasoning is valid.


When you're trying to work out motor parameters, double check your findings by using a balanced equation. Work out the electrical power (Ohms Law) and the mechanical power seperately and see if they correspond. You will see an efficiency loss in the calculation due to volt drop on the windings. Efficiency is slightly worse than that, however, due to eddy currents in the armature. Eddy currents aren't that easy to calculate.

Mechanical power is simply P = wt. P is power (W), t is torque (Nm) and w is angular velocity in radians/second. 

Sam.


----------



## Batterypoweredtoad (Feb 5, 2008)

Very cool-2 smart motor guys in one thread! Score!


----------



## frodus (Apr 12, 2008)

just adding one more tidbit..... when people say Quadratic, it doesn't mean its x4 or ^4

it means that the curve can be written as a quadratic equation....


----------



## samborambo (Aug 27, 2008)

Ah, see the difference in answers between Major and myself..... Major's got far more practical experience with series-DC.


----------



## major (Apr 4, 2008)

Batterypoweredtoad said:


> With saturation-what are the contributing factors?


The size and shape of the magnetic circuit and the number of turns and the current thru them on the field coils. Oh yeah, and the material characteristics, the B vs H curve of the steel.



> I am curious about another thing as well, how is it that white zombie gets such high amps with only about 110v applied to each motor before the series parallel shift?


Low motor resistance and low RPM (low RPM means a low back EMF or Eg as I call it). If the motor resistance is on the order of 0.01 ohm and RPM is low enough to generate only 30 volts, then (110v-30v) / 0.01 ohm = 8000 amps. Obviously he'd be still current limited. Even if his motor resistance was double and his RPM (and Eg) was higher, you get the picture.

Regards,

major


----------



## major (Apr 4, 2008)

frodus said:


> just adding one more tidbit..... when people say Quadratic, it doesn't mean its x4 or ^4
> 
> it means that the curve can be written as a quadratic equation....


Maybe technically correct, frodus. I took it to mean that the value changes with the square of the variable, which is a common usage, I think


----------



## major (Apr 4, 2008)

samborambo said:


> Ah, see the difference in answers between Major and myself..... Major's got far more practical experience with series-DC.


Yeah samb,

About 35 years. Your answers are not incorrect, depending where saturation occurs. My guess was 400 amps or so. Maybe it is 5 - 600 amps. But when the guy is talking about doubling the rated current which is 467A, real good bet it is going into saturation soon. My experience is that the motors are petty near if not into saturation at the one hour rating. This is a monster torque machine which I never saw in my days with lift trucks. So I am just guessing here. He doubles current and starts spitting driveline parts out the side, don't blame me 

Regards,

major


----------



## Batterypoweredtoad (Feb 5, 2008)

major said:


> He doubles current and starts spitting driveline parts out the side, don't blame me
> 
> Regards,
> 
> major


I can only hope!


----------



## bipole (Sep 8, 2009)

Batterypoweredtoad,

I got one of the same motors from the same guy on ebay. Mine turned out to have a separately excited field. I had exchanged at least half a dozen emails with the guy about various motors before bidding and I was explicit I wanted a series motor. He never directly answered that is wasn't series, so my bad for not knowing.

Mine turned out to have six fan blades broken off, a fractured brush and some comm trauma from what appears to be a stalled rotor event. All fixable, but not the "good used!" he advertised.

I was going to look for series coils for it but I weighed it today on a pair of bathroom scales, it turns out the motor weighs 498 pounds! Yes, I rechecked the scales. I was planning on a big single or twin 9's so I was ready to accept 300 to 350 pounds, but not 498 pounds. I'm now negotiating the return, but the return shipping is as much as I paid for the motor. We''ll see if the guy takes care of me or not. I'd be really upset, but I'm only out a few hundred bucks at most. If a lift motor ends up working for me, I'll still be way ahead on cost.

I guess I'm more experienced now, I'll do better next time.

Oh, beware, his idea of good-used is that it is at least repairable and you should expect it to need the comm turned and new brushes. Not my idea of good-used, but I'm not a salesman.

I think this one will end up in the corner of the shop. If I can get some series coils for it, maybe it'll be worth putting a few bucks into it. Maybe it will end up in my gross polluter 8000lb gasser forkift.


----------



## frodus (Apr 12, 2008)

major said:


> Maybe technically correct, frodus. I took it to mean that the value changes with the square of the variable, which is a common usage, I think


I didn't mean to single anyone out, just wanted to clarify quadratic for some that might search and find this thread. Its been discussed a little lately.


----------



## Batterypoweredtoad (Feb 5, 2008)

bipole said:


> Batterypoweredtoad,
> 
> I got one of the same motors from the same guy on ebay. Mine turned out to have a separately excited field. I had exchanged at least half a dozen emails with the guy about various motors before bidding and I was explicit I wanted a series motor. He never directly answered that is wasn't series, so my bad for not knowing.
> 
> ...


Wow! 498 lbs is huge! I think mine is what was pictured in the ad, but now I will look harder. All of the parts look intact and it does spin with 12v, but that is all I know so far. The guy I emailed was slightly confused, but I didn't guess dishonest.


----------



## Georgia Tech (Dec 5, 2008)

Boy this has beenone of the BEST threads on this forum!!


----------



## Georgia Tech (Dec 5, 2008)

bipole said:


> Batterypoweredtoad,
> 
> I got one of the same motors from the same guy on ebay. Mine turned out to have a separately excited field. I had exchanged at least half a dozen emails with the guy about various motors before bidding and I was explicit I wanted a series motor. He never directly answered that is wasn't series, so my bad for not knowing.
> 
> ...


I am glad you said this about this dude..I was about to jump out the window and buy one of his motors....gues I got to pay 400.00 for one here local that I can see..


----------



## samborambo (Aug 27, 2008)

bipole said:


> I was going to look for series coils for it but I weighed it today on a pair of bathroom scales, it turns out the motor weighs 498 pounds! Yes, I rechecked the scales. I was planning on a big single or twin 9's so I was ready to accept 300 to 350 pounds, but not 498 pounds. I'm now negotiating the return, but the return shipping is as much as I paid for the motor. We''ll see if the guy takes care of me or not. I'd be really upset, but I'm only out a few hundred bucks at most. If a lift motor ends up working for me, I'll still be way ahead on cost.


What's most concerning is that bathroom scales in America go up to 500lbs! 

Sam.


----------



## Batterypoweredtoad (Feb 5, 2008)

samborambo said:


> What's most concerning is that bathroom scales in America go up to 500lbs!
> 
> Sam.


I think he used two of our standard 300lb models. 

It wouldn't surprise me to see them increase that range, 300+ isn't all that uncommon here.


----------



## bipole (Sep 8, 2009)

Batterypoweredtoad said:


> Wow! 498 lbs is huge! I think mine is what was pictured in the ad, but now I will look harder. All of the parts look intact and it does spin with 12v, but that is all I know so far. The guy I emailed was slightly confused, but I didn't guess dishonest.


I just got off the phone with him and he is totally taking care of me. He wants the 13" back, he's paying shipping, and we made a deal on a 9" series GE. Without me even asking he said he's going to send the 9 out for a full rebuild before shipping it out to me on his dime. Wow.

He's got a good thing going on Ebay, doesn't want to mess it up I guess.


----------



## Batterypoweredtoad (Feb 5, 2008)

bipole said:


> I just got off the phone with him and he is totally taking care of me. He wants the 13" back, he's paying shipping, and we made a deal on a 9" series GE. Without me even asking he said he's going to send the 9 out for a full rebuild before shipping it out to me on his dime. Wow.
> 
> He's got a good thing going on Ebay, doesn't want to mess it up I guess.


Very nice! Great news, let us know how it turns out.


----------

