Motor Winding Calculations & Cooling Design


100 W
Oct 11, 2021
Hello guys,
I have been searching the internet for a log while, about formulas and books how to calculate the windings of a 3 phase motor, i.e. nr of turns, wire thickness etc.
I found some good theory books, some good sites explaining stuff, but haven't found an actual practical example with real numbers and dimensions.
So i asked a friend that worked at a winding shop how do they rewind a 3 phase motor if they have only the stator with no windings on it (like someone dismantled it before going to rewind shop with it )?
He puled a book from a shelf, it is from 1967 called in Romaian "Cartea Bobinatorului de Masini Electrice" ~ The Book of Electrical Machine Winder (it is available in pdf on the net).
That book has all the formulas and practical examples how to do the winding job, like "from scratch" a 36Kw 500V 3 phase motor
I made an excel document that calculates all that, down to how many Kg of cooper wire are needed, if you know the motor configuration (PP & Slots) and the applicable winding scheme (search "motor winding calculator" on net, that gives a nice site that does that winding scheme).
Now that being said, in those formulas they recommend to set the max flux density for stator to an conservative level of 0.78Wb/m^2 (0.78 T), and that gives a certain number of turns per phase at a certain frequency and stator dimension, but if higher max flux is given, say 1,2Wb/m^2 for the same freq and stat dim the number of turns is smaller. That makes perfect sense but, in my experience if i rewinded a motor with more turns at same voltage had slower max rpm.
The thing is, that i have a motor that is winded kinda "HOT" in the saturation zone of the core, and i want to rewind it such way that i does not reach saturation, but keep the same power Kv, rpm, voltage all that, and those formulas baffle me a bit compared to what i experienced so far.
I know about the core loses and eddie currents, thinner laminations and stuff, that is another subject.
So what do you think about this, any motor gurus chime in?
i attached the excel with my current motor setup(first) and some wanted flux density that does not saturate(second)...


  • Winding_Calculator.xls
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I'm not a expert but won't the core loss increase for higher flux, This will also depend on the saturation limit of the core material being used.
If you plan to run the motor in S1 duty cycle and have the flux at the saturation level then the motor will heat and would touch the thermal limits before equilibrium, So it is always best to keep the Flux and the Current density low for rated condition (Completely depends on what type of cooling is used in the motor)
I learned a lot just from this guys posts.
The motor flux is determined by the magnets predominantly for a permanent magnet setup. Your book is most likely dealing with induction motors which have no magnets and therefore the flux is determined by the winding.

So if you don't change the magnets but you wind with more turns then it will go slower. 2x the turns... Half the speed.
You cannot rewind your pmsm to be less "hot". Your motor core saturation is defined by the magnets at low loads and the magnets in quadrature with the coils at high loads.

To get a given torque, you need a given magnet strength and a given number of ampsxturns.

However you rewind it, the flux linkage x amps x turns will be the same for a given torque.

Don't try to apply induction motor equations to a pmsm. You'll go around in circles until you get lucky and then persuade yourself you did something clever. There are similarities so it might get you to the right ballpark but it will never be "right".

Also remember that neodymium magnets were not used in motors in 1967.
After a week of reading and studying(+500pages), i got some answers.
I found a really good book(by pure luck) that discuses PMSM to, not just Induction motors, it's name is Design of Rotating Electrical Machines, and from multiple sources of information, i got some knowledge to do the calculations.
Yes indeed, you can not calculate a PMSM Machine like Induction Machine, but there are similarities in the equations and parameters, and most important is the explanation of how and witch to use, practical examples.
So i revised my calculator xls (also updated the attachment), it still needs some work but has enough to give a good picture about how and what is needed in the motor.
The Electrical, Magnetic, Thermal and Mechanical design, they all MUST be done, and one of the most overlooked is the Thermal design, it is easy to assume, "ah... i'l be fine, the wind will cool it....", obviously not enough.
As i mentioned before my motor was a scaled up version of a smaller one, so only a small part of the needed design i knew how to do back then (8 years ago).
Now i calculated almost every parameter, it came out pretty decent, but one thing that was not calculated from the beginning was its thermal design, it was just assumed "the wind will cool it", and now i'm in the situation of overheating simply because it can not dissipate heat at the rate it generates it at full load, and not even at 2/3 load.
Basically at 20Kw the copper loses(winding) are 1Kw (I^2*R).
The core(Iron) losses are about 350W, the reason it heats up even with no load.
So at full load i have 1,4kw of "heat" to dissipate thru forced convection(or else) in 30degC ambient so that the motor does not go over 80degC, and having only the surface of the windings and the inner surface of the backiron(stator yoke), not much contact area for dissipation.
In the past i calculated the thermal performance of power electronics, and even an audio power amplifier class B 2x500Wrms/8ohm needs a hefty heatsink, if you need full load all "night long".
Now, the "fixes" that i found, i have some options:
1. machine 6 pie shaped Al heatsinks and attach them on the inner surface of the stator, in between the bearing hub spokes.
2. machine a new bearing hub that has a circular exterior with fins toward interior, this is the most elegant
3. machine a new bearing hub with water cooling passages, this one is the best in terms of heatsinking but ads complexity and weight.
I studied some manufacturer motors the same type/shape/application/size/power and air cooled, they all have continuous operating load less than half of full load, 8kw continuous 20kw max short period. Only water cooled counterparts can do better.
The main restriction is the mass and volume of these motors, 20kw in 8kg and D210xL50mm volume, witch limits the heatsinking performance, in air cooled type. An industrial 500v 20kw Motor has about 220Kg and that can do full load all day long, it has enough volume, mass, and surface to be air cooled, even in 40degC ambient, plus it can go to 130-150degC max but that is another story.
I have done some studying regarding cooling options for electric motors, especially liquid cooling, and i stumbled on Direct Winding Heat eXchanger "DWHX" (it may be trade mark....).
Basically there is a T or I shaped heat exchanger (liquid cooled) between the windings of the stator teeth, and that has a better heat transfer than a liquid jacket around the stator or than passages in the stator, i.e. lower thermal resistance because of being directly in contact with the windings. In this article they talk about its benefits: Electric Motor Thermal Management for Green Transportation | Electronics Cooling
Now its implementation is tricky, those T/I heat exchangers ("DWHX") must not be "magnetizable", yet be heat resistant enough not to deform or melt, some high powered motors use ceramic ones.
Another option for big motors (hundreds to thousands of Kw) is the copper conductor of the windings to be tube shaped , liquid goes thru the conductor, i.e. the entire winding itself is the heat exchanger. This however is not easy/practical to implement in our "smaller" motors.
Colling of high power density motors is a serious task.
Hey there, I read through your thermal problem you described... actually, in industry, there are sometimes similar issues. For instance, when an existing machine needs to work with worse conditions, hotter environment etc. than originally planned. One way that is sometimes helpful is "trickle impregnation" of the windings. A thin epoxy based liquid is dripped onto the windings and gets seeped up between then, making the windings a contiguous block, also thermally. Before, the wires did touch only in many points, with the impregnation, they are much more thermally connected. Additionally, the mass of the motor goes up, so it takes longer for the power losses to heat up all this mass. Yes, epoxy is not the best heat transfer material, but many times better than resting air in between the windings. As this is a process that is not reversable (you can only "unwind" the motor with a hacksaw and a hammer), you may want to experiment in terms of processing and amount of thermal improvement on a (smaller) spare motor. And for sure it is not environmentally friendly, the materials are often hazardous to human health.

Just a thought,
Here i found a good explanation for some winding "type" decisions. These guys know they're business well. Also a very good explanation of skin effect in conductors. Enjoy.
Damn, that was a good video, thanks!