Would each phase current in a BLDC be like 1/3 of the controller's max current?
No, because the controller can do voltage conversion to trade volts against amps unless it's limited by the supply of one or the other.
I think it depends on the condition (load, speed, etc.) and the controllers ability to provide phase amps. Note, this is opinion, based on reading different articles and posts and playing with the simulator to understand how my specific bike performs or can perform, but there are several folks on this forum that could explain it better than I can, and the technical aspects of these observations.
Using the Grin simulator, you can see the relationship between battery and motor amps. In this example, both systems are the same, with a 70A controller (battery amps). At full speed, the system is flowing 51.7A (battery), and the motor is pulling 57.7A (motor). If you drag the slider (dotted line) for system B to the left (bike accelerating under full throttle), both the battery and motor amps rise, but by the inflection point in the torque curve (40mph in the example), battery amps max out at 70A. Moving further to the left, battery amps remains pegged, but motor amps continues to rise all the way up to 176A at stall speed; battery amps still pegged at 70A.
Our ebike motor simulator allows you to easily simulate the different performance characteristics of different ebike setups - with a wide selection of hub motors modeled, and the ability to add custom batteries and controllers and set a wide variety of vehicle parameters you'll be able to see...
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In this example, the controller is able to provide the 176A of phase current, but not all controllers can do that. Seems like phase current typically falls somewhere between 2 and 3 times battery current for our controllers.