i've had some thoughts on this for a long time now, and a while ago i bought 6 inch by 2 inch by 1" thick ferrite magnets, but never got around to building a stator core for an induction motor, i had a different design in mind at the time.
but i've come up with what i think is a better method and can use any combination of ferrite magnets you have on hand, provided you can epoxy them together into a square of approximately 1 third or less, the depth of your motor core.
Take a cylinder of steel, about twice as long as the stator core depth of your motor, could be a heavy wall pipe, or solid, doesn't matter.
for a 4 pole motor, you need a pipe that is at least 25% as thick as the diameter. for a 4" outside diameter rotor, the pipe needs to be half inch wall thickness, or 3 inch inside diameter. such pipe is available but hard to find, can be ordered online. however, it makes fabrication of the rotor easier because you can use a cut off wheel on an angle grinder instead of a bandsaw to make the cuts, then after the angle grinder, follow up with machining the surface flat.
for a 4 pole motor, bandsaw cut the cylinder to make it a square. The middle square is waste. so now you've got 4 slices of a cylinder that will fit inside your motor leaving a big square space internally. for a thick wall pipe, make the 4 cuts with a bandsaw or 8 cuts with an angle grinder.
slightly smaller round stock can be used, it just makes the air gap bigger.
you can also fabricate these steel pieces, for a 4" inside diameter and 4" deep stator core, you need 4 strips of 1/4" steel 2.5 inches wide and 8" long, then weld in the middle of each one, a 1.5" wide strip. you then have to turn it on a lathe or grind it down to make the radius match the inner diameter of your motor, so that all 4 will fit inside your motor, leaving a 2.8" square space internally.
so now you've got 4 strips of steel with the inside diameter of your induction motor stator, twice as long as the induction motor, that you slip inside the motor.
then you cut your ferrite magnets up in the most efficient manner to make a square. but in slices. you need 8 square magnets the same size, about 1 inch thick if your induction motor is 4 inches deep.
insert 1 magnet inside the core of the motor. use wood wedges to hold the steel and magnet in place.
juice the motor with a significant dc current, this will magnetize the ferrite magnet. you might need to use a variac, step down transformer and rectifier, to avoid the stored energy in the inductance of the motor from demagnetizing the magnet when you turn the power off.
do this for all 8 magnets one at a time.
then pull the steel pole pieces out of the motor, hold them in a jig, orient all the magnets the right way, epoxy the entire mass together.
once its all glued together you can turn the whole thing on a lathe to clean up the outside radius, and remove some of the steel and the magnet at both ends of the rotor assembly and shrink fit a stainless steel or other non magnetic metal cup over the ends of the rotor magnet assembly, both to hold it together as the epoxy fails over time, and attach your motor shaft.
geometrically, there is diminishing returns to making the magnet more than twice as longer than the stator.
the cross sectional area of the difference between the square magnet and the cross sectional area of the steel "(|" pieces is about 30%.
But the steel can sustain 1.7T or so compared to the ferrite magnet of about .4T peak. So you can extend the magnet significantly out beyond the stator core, because the half round pole piece will conduct a lot of flux into the motor from the magnets that extend outside the stator core.
in my example of a rotor core that is twice as long as the stator core, it effectively takes your .4T ferrite magnets and doubles them to .8T, which is then concentrated further in the stator core (back iron). The actual air gap flux density will probably max out at .7T. i don't think there is any improvement beyond this for off the shelf induction motor stator cores. for short stator cores you can extend the magnets out further than twice the length. but as the pole count gets higher, the pole pieces are less cross sectional area and the improvements decrease. you would have to make the magnets smaller inside the core so that the pole pieces would have greater cross section in order to conduct the magnetic flux into the motor from outside it.
for a 2 pole motor, you could probably make ferrite magnets 4 times as long as the stator and still get a net benefit.
By making the rotor magnet assembly twice as long as the rotor, you can double that airgap flux density assuming no leakage flux around the magnets.
regarding specific numbers:
A stator core 4" diameter and 4" long, there is a 2.8" square space in the center of the motor. each magnet pole inside the motor is 2.8" by 4" for 11.2 square inches. At 0.4T that is 4.48 square inch teslas. divide this by 12.5, the square inches of area of the air gap flux (per pole) and you get 0.35T air gap flux.
But the sliver of metal which turns that flat magnet into a cylinder.. can conduct flux into the motor from both sides, and in the case of a 4" diameter rotor, it has a cross sectional area of 1.17 square inches, multiply this by 1.7T and its worth 1.98 square inch teslas. to make this much flux enter the rotor from a .4T ceramic magnet, you need 2 square inch teslas divided by .4 teslas and you get 5 square inches of magnet needed. divide this by 2.8, the width of the magnet, which means the magnet must extend 1.8" beyond the core. (on both sides.)
now there is leakage of course, (which is why you make the magnets stick out from the stator core a little more than just twice the stator depth, and there is the issue of the flux doesn't flow in straight lines through the magnets... which is why you magnetize the rotor magnets, one at a time, inside the core as if they are the only ones present. each magnet will then have a saturated field in the direction it would go if the iron were saturated. this can be done with ferrite magnets because you don't need more than 1.9T to magnetize them fully.
