John in CR said:
When I see different core types being more sensitive to frequency, would that frequency include our controllers' PWM frequency (pulses of DC) or just our motors' electrical operating frequency (the AC frequency) that increases with rpm? If it's the later, then ideally wouldn't we want a non-linear inductor for more torque from retarded timing and better controller protection at low frequency, and then the inductance rapidly rolls off with e-rpm for better high speed timing and controller protection coming from the motor's BEMF?
The frequency effects of the core material apply to losses, not to the inductance. Losses are mostly hysteresis losses, which are a property of the material itself, and eddy current losses, which are a function of how the core is assembled (lamination thickness, etc.). The inductance value will not vary with frequency.
John in CR said:
Core saturation- To me this is the biggie as well as the biggest unknown. On the motors I have, I want to get to where I can safely run phase currents of 300-500A. With relatively low value inductors in the range of 20-40uH, is it reasonable to avoid saturation at these kinds of currents without coils so big that 3 become ridiculously large and heavy. What material core would be best and still keep turn counts within reason for say 3ft of large gauge wire?
Saturation will be a major issue at those high currents. It will cause the inductance to decrease at high currents, which is exactly when you need the inductance the most. Saturation depends on the material. Most steels have saturation flux density in the range of 1.6-2 T (T = Tesla), depending on the alloy. I did a quick Google search and it looks like most ferrite materials saturate around 0.3-0.4 T, again depending on the exact material. It's important to point out that, due to the B-H curve shapes of these materials, the inductance value will begin to decrease well below saturation flux. You'd probably want to keep a steel core below 1 T, and a ferrite below around 0.2-0.25 T to keep some useful inductance.
Fortunately for designers, the inductance of a coil is directly linked to the flux density. L = N * Psi / I, where N is the number of turns and Psi is the flux [Wb = Weber = T*m^2] (total flux,
not flux density), and Psi = B * A, where B is the flux density [T] and A is the core cross-sectional area [m^2]. Using this formula, given a max current and a target max flux density, you can figure out how much core area is required for a given number of turns. For example, let's say N=10 for your 20 uH inductor that you want to carry 500 A. That gives Psi = L * I / N = 0.001 Wb . Allowing 0.2 T for a ferrite core, that will require a cross-sectional area of A = Psi / B = 0.005 m^2 = 50 cm^2, roughly 7 x 7 cm. That's a pretty big toroid. Using steel at 1.0 T, it would be 0.001 m^2 = 10 cm^2, which is still not exactly small.
An iterative design process is probably needed, where you assume a geometry, figure out how many turns are required to get the inductance you want, then check for saturation, modify the geometry, repeat. When specifying how much inductance you want, you should calculate the turns for a higher value because any online calculator will assume no saturation. 50%-100% higher would not be excessive. Obviously there's a trade-off between fewer turns for less resistance, but a larger core.