# How do I calculate magnetic flux?

recently I've needed to buy a brushless motor, but because I couldn't find any motor with wanted characteristics, I've decided to make my own. I know that it's very precise job, but even if something goes wrong, I will enjoy just trying to construct motor. As perfectionist, first I must plan everything (if you aren't intrested in what I've already done, I suggest skipping to the end - there is my problem and question :P).

First I've tried to make a formula for calculating the number of turns on one coil ($n$). Maximal rotational speed in BLDC motor is the speed at which moving magnets induce voltage equal to negative voltage across the coil.

Faraday's law of induction: $\varepsilon = -\frac{\Delta \phi}{\Delta t}$

I have $n$ turns of wire, so: $$\varepsilon = -n \frac{\Delta \phi}{\Delta t}$$

In my case $\Delta t$ is equal to time, in which next magnet "appear" next to given coil: $$\Delta t = \frac{1}{K_{V} U m}$$ where:
$K_{V}$ - in my case it will be rotates per second per volt - not per minute
$U$ - voltage across one phase
$m$ - number of magnets in motor

$\Delta \phi$ is equal to change of magnetic flux during $\Delta t$. It means doubled magnetic flux of single magnet ($\phi$): $$\Delta \phi = 2 \phi$$

That means: $$\varepsilon = -\frac{2 \phi n}{\frac{1}{K_{V} U m}} = -2 \phi n K_{V} U m = - U_{c}$$ where:
$U_{c} = \frac{U}{N}$ - voltage across one coil
$N$ - number of coils per phase

Final effect: $$n = \frac{1}{2 \phi K_{V} N m}$$

And at this moment I need your help. When I'm trying to estimate how many turns coil should have, I need to know magnetic flux of single magnet (in my case neodymium one). In the Internet you can find tables containing properties of the materials the magnets are made of, but there isn't magnetic flux (what is understandable).

My question is: is it possible (if yes, how?) to calculate magnetic flux of magnet with given dimensions, knowing remanence, coercivity and "energy density" (the product of B and H) of material the magnet is made of?

Sorry for all my English mistakes and thanks for answers.

• Good luck with that.... Commented Mar 7, 2017 at 22:57
• yes, it's possible. Calculating motors isn't exactly a new field in electrical engineering (Siemens himself says hello). In practice, everyone building motors has (potentially pretty advanced) finite element simulators that make the analytic solution actually usable for anything that doesn't consist of "perfectly round, perfectly even conducting across their diameter, constant temperature, perfectly spaced" coils, magnetics and gaps. Commented Mar 7, 2017 at 23:29