# Electric Motor Sweet Spot, Where?



## Yabert (Feb 7, 2010)

Nehmo said:


> Are there graphs describing this?


Yes. Two example below.


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## major (Apr 4, 2008)

Nehmo said:


> A gasoline-consuming internal combustion engine has a narrow range of RPMs in which it is efficient. That's the reason for the multi-ratio transmission. A diesel has an even narrower range of efficient RPMs, and its transmission accordingly has more ratios.
> Some e-vehicles get away with no transmission. The hub motors operate at one ratio and often without even gearing down. But this isn't the most efficient arrangement.
> What's the efficient range for an electric motor? Where is, and how wide is, the sweet spot? Are there graphs describing this?


Let's see if I can get this pasted in here  Sorry for the quality of this image but I had a hard time getting it at all. It shows a particular motor efficiency map over the range of torque and RPM. Probably 80% of the available operating area for the motor is above 90%. The regions where efficiency falls sharply are zones of low power where the losses aren't that great anyway or zones where you're unlikely to spend much operational time, so energy loss would be low. Electric motors have a big sweet spot compared to your ICE  










This graph was lifted from the EVO web site. I'll edit that in later.

http://www.evo-electric.com/inc/files/AFM-140-Spec-Sheet-V1.1.pdf


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## Ziggythewiz (May 16, 2010)

Because the EV motor has such a huge range of high efficiency, I don't think it's even worth considering much. You may get a 1-3% improvement by seeking the sweet spot, but your car's specific drivetrain efficiencies will probably matter much more.

My motor's supposed sweet spot indicates that I should do pretty much all my driving in 3rd, but I find that I use 10-15% less energy to go the same distance at the same speed in 2nd.


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## DavidDymaxion (Dec 1, 2008)

As you can see from the graphs, efficiency is surprisingly flat over the rpm range, except that it plunges as you near 0 rpm. Most cars are not near 0 rpm for very long, so not a big deal to lose a little briefly there. Cars with transmissions can keep the electric motor closer to its most efficient point, but on the flip side the extra gears add some weight and drag. If you live in San Francisco and regularly had to crawl up steep hills in heavy traffic, you'd want a transmission, but for most types of driving a single gear setup can work well, as the Nissan Leaf and EV-1 have shown.


Nehmo said:


> A gasoline-consuming internal combustion engine has a narrow range of RPMs in which it is efficient. That's the reason for the multi-ratio transmission. A diesel has an even narrower range of efficient RPMs, and its transmission accordingly has more ratios.
> Some e-vehicles get away with no transmission. The hub motors operate at one ratio and often without even gearing down. But this isn't the most efficient arrangement.
> What's the efficient range for an electric motor? Where is, and how wide is, the sweet spot? Are there graphs describing this?


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## Nehmo (Aug 11, 2011)

Allow me to start with the NetGain graph. 
If 
power (horsepower units in this case) = torque x RPM, 
and if RPM is a curve and torque is the _x_ axis,
then how can horsepower be linear? 

It seems it should be a curve because one of its factors is a curve.


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## Nehmo (Aug 11, 2011)

On the Motor Performance and Efficiency graph, why are there two lines for torque, Peak and Continuous. How can you have both simultaneously?


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## major (Apr 4, 2008)

Nehmo said:


> On the Motor Performance and Efficiency graph, why are there two lines for torque, Peak and Continuous. How can you have both simultaneously?


You can operate the motor at any point (torq, RPM) below the peak torque line and to the left of the peak RPM line. If your operational torque value is below the continuous torque line, you can operate there as long as you want. If your operational torque value is between the continuous and peak lines, the motor will reach a limiting temperature and must not be run there longer. The closer to the peak torque line, the shorter the duration which the motor can be run.

At any instant in time, the motor output will have a singular value for torque and a singular value for RPM. The motor efficiency plot depicts the entire area where those (torq, RPM) points can be. The continuous and peak lines are very much like ratings for a motor controller such as 200A continuous and 500A peak. Or like a battery showing 3C continuous and 8C peak.

Regards,

major


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## major (Apr 4, 2008)

Nehmo said:


> Allow me to start with the NetGain graph.
> If
> power (horsepower units in this case) = torque x RPM,
> and if RPM is a curve* and torque is the _x_ axis,
> ...


Hi Nehmo,

You are correct; it is not linear. We've commented a number of times on this forum about that graph being poorly drawn. I suggest you calculate the HP from the RPM trace at various torque value increments and plot it against the existing HP trace. You will see some deviation. But surprisingly small because the compression of scales, I guess 

Regards,

major

* edit: Even if the RPM trace is a straight line, the power trace will be curved.


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## Nehmo (Aug 11, 2011)

major said:


> You can operate the motor at any point (torq, RPM) below the peak torque line and to the left of the peak RPM line.


There is no peak RPM line. Do you simply mean the right edge of the graph?



major said:


> ...
> At any instant in time, the motor output will have a singular value for torque and a singular value for RPM. The motor efficiency plot depicts the entire area where those (torq, RPM) points can be.


Continuous Torque = The amount of torque that can be provided by the motor under normal running conditions.

So at 4000 RMP and 150 N-m torque, we get 93% efficiency.
At the same RMP and 200 N-m torque, we get 94% efficiency.
Same RPM and 350 N-m torque, we get 93% efficiency again.

So the motor operates at different torques at the same speed, and there's a most efficient range of torques at any particular speed.

Am I correct so far?


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## lithiumlogic (Aug 24, 2011)

The first picture has a caption "with 600V inverter" which makes me think it's an AC motor, perhaps of the large industrial variety. AC motors efficient over a wider rpm range than dc motors yes?


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## major (Apr 4, 2008)

Nehmo said:


> There is no peak RPM line. Do you simply mean the right edge of the graph?


Yes. Without any other information on that particular motor I assumed 5000 as the max or peak RPM.



> Continuous Torque = The amount of torque that can be provided by the motor under normal running conditions.
> 
> So at 4000 RMP and 150 N-m torque, we get 93% efficiency.
> At the same RMP and 200 N-m torque, we get 94% efficiency.
> ...


The motor can operate at different torque at a particular speed depending on the load and on how it is controlled. 

Your RPM, torque, eff numbers appear to be correct per that graph. One should not try to use such a graph to pick apart efficiency down to a percent or two. Efficiency calculations or measurements are a reduction from many factors. All of which have tolerance. An efficiency map or graph like that is useful for trends. But I wouldn't alter an application (like gear ratio) to get an extra 1% from that graph which might not really be there. So I would say that efficiency at 4000 RPM between 150 and 350 Nm is 93-94%.

Regards,

major


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## major (Apr 4, 2008)

lithiumlogic said:


> The first picture has a caption "with 600V inverter" which makes me think it's an AC motor, perhaps of the large industrial variety. AC motors efficient over a wider rpm range than dc motors yes?


I added the link to post #3. http://www.evo-electric.com/inc/files/AFM-140-Spec-Sheet-V1.1.pdf


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## Nehmo (Aug 11, 2011)

major said:


> One should not try to use such a graph to pick apart efficiency down to a percent or two. Efficiency calculations or measurements are a reduction from many factors. All of which have tolerance. An efficiency map or graph like that is useful for trends. But I wouldn't alter an application (like gear ratio) to get an extra 1% from that graph which might not really be there...


No, I wan't trying to calculate to the accuracy of a percent; I was only using the numbers in principle.
But my real concern is if gears are necessary in an e-vehicle, and in particular, an e-bike. Lot's of people make an effort to place the e-motor driving the traditional chain to use the rear derailleur transmission. But an electric motor, once geared down, has a wide efficiency range. I'm trying to figure out exactly what is gained by "going through the gears" and is it worth the weight and complexity.
Yes, I realize there are opinions. But the issue isn't one of opinion. There should be a definite answer on what is gained in terms of efficiency or in terms of performance.


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## major (Apr 4, 2008)

Nehmo said:


> I'm trying to figure out exactly what is gained by "going through the gears" and is it worth the weight and complexity.
> Yes, I realize there are opinions. But the issue isn't one of opinion. There should be a definite answer on what is gained in terms of efficiency or in terms of performance.


Hi Neh,

O.K. I see where you're coming from. Gears (or more specifically reduction ratios) are used to gain mechanical advantage. Just like you'd use a lever to increase force, a small person can lift a large weight.

When it comes to electric motor application, you select the motor based on the power requirement and then gear it to meet the application torque requirement. Typically the size of the motor is determined by the torque of the motor. Larger motors will produce more torque, smaller motors produce less torque. Power is the product of torque and RPM, so for a given power requirement, a higher speed motor means a smaller motor......generally speaking. There are exceptions. 

The wheel size and speed on the EV determine the wheel RPM requirements. The road load (rolling friction and aero drag) and the acceleration requirements (primarily dependent on mass) determine the wheel torque requirements. From this data, one can figure the motor power requirement and profile. The designer now has an infinite selection of ratios to choose from when determining the motor RPM for the required power. Too low motor RPM----massive motor. Too high motor RPM----maybe issues with durability, efficiency, cost, availability, etc. You have to work within the real world of design constraints, not the least of which is cost, and make your best choice.

Regards,

major


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