Electric motor scaling laws and inertia in robot actuators

4 days ago

Electric motor scaling laws and inertia in robot actuators are discussed, focusing on fundamentals without prescribing specific solutions.
Three actuator designs with different motor sizes and gear reductions are compared for reflected inertia, defined as rotor inertia times gear ratio squared.
First-order motor scaling laws are explored, showing how torque, mass, power dissipation, and rotor inertia scale with motor length and radius.
A size-invariant figure of merit (FoM) is introduced, normalized by mass and motor radius, to compare motor efficiency across different sizes.
The FoM relates to reflected inertia and gear ratio, revealing that reflected inertia is primarily a function of power dissipation at a given torque, not gear ratio or motor size.
Real-world motor data from TQ's frameless motors supports the FoM's invariance across a wide range of motor sizes, with some exceptions for shorter stack lengths.
Motor topology generally does not significantly affect FoM, with exceptions like transverse flux motors that bypass Lorentz-force limits.
The analysis highlights limitations, such as ignoring peak torque, saturation, heat transfer, and the non-ideal nature of real gears (mass, inertia, efficiency).
Key takeaway: Reflected inertia in actuators is determined by power dissipation for a given torque, not by gear ratio or motor size, supported by theoretical and empirical evidence.

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