# DC Motor question

#### kevinthenerd

##### Platinum Member
What does the torque curve of a DC motor look like? I hear it's quite flat, but it drops off suddenly at high rpms. Why does this limiting factor exist? I think I may have an idea for yet another brushless design, but I want to see why the high rpm limit exists to begin with. Any personal ideas on high-revving DC motors would be appreciated too, such as your own ideas and opinions.

##### Diamond Member
The torque of a motor is generally proportional to the current, and the speed proportional to the voltage so as long as the current is constant, the torque of the motor will theoretically be constant. The high speed end drop-off could be attributed to several factors. I'm not sure myself, but friction within the motor may increase exponentially as the motor is pushed to its design specifications. Additionally, many motors have limiters to prevent overspeeding, so a drop-off in torque could also be attributed to that. The cooling fan of a motor can often serve as a limiter because the resistance of the fan increases exponentially as the rotational speed increases linearly.

#### Mark R

##### Diamond Member
For a typical permanent magnet DC motor (assuming nothing special about the control or the motor design) the torque curve is approximately a straight line. Maximum at stall decreasing linearly to 0 at maximum speed.

T = T0 * (1 - (V / Vmax))

T0 = stall torque
V = motor speed
Vmax = Maximum speed

This applies for both brushed and brushless motors - however, for reasons of heating (I is proportional to torque, and P = I^2.R) the continuous torque rating must often be considerably derated from the intermittant rating.

The effect of this derating is to simply limit the acceptable torque to a maximum. This gives a horizontal line, until the torque available begins to drop off linearly.

#### kevinthenerd

##### Platinum Member
An article in Racecar Engineer got me interested in the possibility of an electric racecar, so for my purposes here, longevity isn't as important as a few good laps of performance.

What you've described is nothing more than what a few minutes of Googling yielded me. Yes, a torque curve is typically a downward sloping straight line from max torque to max speed, but WHY? Physical meaning is what I'm asking for here. Why should the torque roll off when the speed goes up, and why is this rolling off linear instead of the quadratic rolling off predicted by air friction?

Has anyone ever bothered to optimize the interal components of an electric motor to minimize air resistance for high speed operation? Besides overheating, what limits somebody from overdriving the hell out of a motor to get more torque?

Has anyone ever thought about using superconductors in high-performance electric motors?

#### Mark R

##### Diamond Member
Originally posted by: kevinthenerd
An article in Racecar Engineer got me interested in the possibility of an electric racecar, so for my purposes here, longevity isn't as important as a few good laps of performance.

What you've described is nothing more than what a few minutes of Googling yielded me. Yes, a torque curve is typically a downward sloping straight line from max torque to max speed, but WHY? Physical meaning is what I'm asking for here. Why should the torque roll off when the speed goes up, and why is this rolling off linear instead of the quadratic rolling off predicted by air friction?

In most cases, frictional losses in electric motors are small - and tend to get smaller as the motors get bigger. For a 100 hp motor, frictional losses are in the region of 1% at full speed.

In the case of DC motors, the maximum power is determined by their nominal operating voltage. Torque is proportional to current, which is proportional to (supply voltage - back e.m.f). Back e.m.f is proportional to motor speed. Hence you get the simple linear relationship described above (assuming constant voltage).

Has anyone ever bothered to optimize the interal components of an electric motor to minimize air resistance for high speed operation?

Yes. Electric motors are enormous consumers of electricity - approx. 55% of all electricity in the US goes to power motors. In terms of cost, over its lifetime an industrial motor will cost about 100x as much to run, as to buy. Gaining an extra 1% efficiency is a very big deal, so manufacturers have put huge effort into optimising their motors - use of very high temperature insulation and smaller cooling fans is just one such optimisation.

Besides overheating, what limits somebody from overdriving the hell out of a motor to get more torque?

The effect of mechanical stresses on the coils or the core. Core saturation (where increasing the current doesn't increase magnetic field strength any further). Voltage rating on the motor insulation.

Has anyone ever thought about using superconductors in high-performance electric motors?

There's some interest in superconducting motors and generators, mainly for train and ship propulsion. Higher efficiency and lower weight/size are key benefits. The big problem is that the superconducting wire is very expensive and very fragile.

#### MrDudeMan

##### Lifer
Originally posted by: kevinthenerd

Has anyone ever thought about using superconductors in high-performance electric motors?

the problem is making it into wires. it is being done now but superconductors still dont exist at a high enough temperature to make them practical for this type of application.

#### dkozloski

##### Diamond Member
As the speed of a DC motor increases, the rotating armature cuts magnetic lines of force and generates a back EMF that counters the supply current. When Back EMF equals the supply the motor stops accelerating. You guys need to go back to the most basic of DC motor theory. It also makes a hell of a difference whether you're talking about a permanent magnet, a series motor or a shunt wound motor.

#### kevinthenerd

##### Platinum Member
Originally posted by: dkozloski
As the speed of a DC motor increases, the rotating armature cuts magnetic lines of force and generates a back EMF that counters the supply current. When Back EMF equals the supply the motor stops accelerating. You guys need to go back to the most basic of DC motor theory. It also makes a hell of a difference whether you're talking about a permanent magnet, a series motor or a shunt wound motor.

Will a permanent magnet, series motor, or shunt wound motor make a difference in the operating characteristics at high speeds? My whole goal here is to generate a large amount of mechanical power in the lightest package possible, so I figured getting the rpms up is the key to this end (as it is in the design of IC engines). For a given torque, a higher rpm will generate more work in a shorter period of time.

#### JohnCU

##### Banned
Originally posted by: kevinthenerd
Originally posted by: dkozloski
As the speed of a DC motor increases, the rotating armature cuts magnetic lines of force and generates a back EMF that counters the supply current. When Back EMF equals the supply the motor stops accelerating. You guys need to go back to the most basic of DC motor theory. It also makes a hell of a difference whether you're talking about a permanent magnet, a series motor or a shunt wound motor.

Will a permanent magnet, series motor, or shunt wound motor make a difference in the operating characteristics at high speeds? My whole goal here is to generate a large amount of mechanical power in the lightest package possible, so I figured getting the rpms up is the key to this end (as it is in the design of IC engines). For a given torque, a higher rpm will generate more work in a shorter period of time.

check out a differentially compounded DC motor. as your load increases, your speed increases and burns the motor out...pretty nasty.

#### dkozloski

##### Diamond Member
You want to be using a permanent magnet motor with rare earth magnets.

#### kevinthenerd

##### Platinum Member
Originally posted by: sdifox
check out the Eliica http://www.eliica.com/

I can't read whatever the hell language that's in, but 0-400m is a roughly a quarter mile, and the one on the right column can do it in 11.3 seconds, which isn't too shabby for a purely electrical car. It's not quite as fast as the hill-climber electric car I saw the other day in the magazine Racecar Engineering, however. I wonder what the acceleration figure directly above it is... whether it's lateral acceleration or something else

Edit: Using (1/2)a*t^2, it looks like it could be some kind of straight-line acceleration figure

Google is good for this stuff.

#### mtnd3vil

##### Member
Originally posted by: dkozloski
As the speed of a DC motor increases, the rotating armature cuts magnetic lines of force and generates a back EMF that counters the supply current. When Back EMF equals the supply the motor stops accelerating. You guys need to go back to the most basic of DC motor theory. It also makes a hell of a difference whether you're talking about a permanent magnet, a series motor or a shunt wound motor.

This is 100% correct.

I used to not understand what factor was at play here either. But then I, surprisingly, learned something I cared about in my college physics class a few semesters ago, I was amazed.

Another thing to note, that might help your understanding is that a DC motor pulls the most current at 0 RPM and the least at it's maximum speed.

Interesting result of these principles is that electric motors are awsome for powering things that continuously run at max motor speed and have varrying loads. A lawn-mower for example. An electric lawn-mower will always spin the blade at maximum motor speed--it's most power effiencent. But when you get to a thick patch of grass, and the motor RPM starts to drop, the 'throttle' on the electric motor is opened(so to speak), and the motor is able to make more torque to return to maximum speed.

I would never buy an electric lawn-mower, but I respect them

#### kevinthenerd

##### Platinum Member
Originally posted by: mtnd3vil
I would never buy an electric lawn-mower, but I respect them

Once they start using the high-powered electric motor technologies being developed for cars, they might be worth the trouble some day, but for the time being, they don't make nearly enough power.