Motor Torque, Speed and Inertia: A Preliminary Sizing Path

Sizing a motor from a single running-speed torque figure is the most common way a drive project loses its cycle time later. The motion profile has phases, and each phase asks a different question of the drive. Steady running torque covers friction and load once everything is moving. Acceleration adds a second demand that depends on inertia, not on load, and it is easy to miss when a spreadsheet only checks the cruise segment.

Consider a mechanism that reaches its target speed without complaint, then still comes in late on takt time. Nothing about the running phase looked marginal. The overlooked term was acceleration torque, which scales with how fast the load and rotor must change speed together, not with how hard the load resists motion once it is already turning at speed.

Reflected inertia is the quantity that connects the gearbox ratio to this problem. Every stage of gearing divides reflected load inertia by the square of its ratio, which is why a modest ratio change can move acceleration torque by a large margin. Efficiency losses stack the same way, in the opposite direction, reducing usable output torque at every stage.

A duty cycle turns an instantaneous torque number into a thermal question. A motor that clears peak torque for one second of a ten-second cycle may still overheat if the root-mean-square torque across the full cycle exceeds its continuous rating. Stopping energy deserves the same scrutiny, because a controller or brake absorbing repeated high-speed stops has its own duty limit independent of the motor.

Direct drive removes the gearbox and its backlash and maintenance, but it usually asks for more torque and a larger frame to hit the same acceleration. A geared solution reaches the acceleration target with less motor torque, at the cost of reflected inertia mismatch, lash, and an added failure path. Neither choice is correct in general. It is correct or incorrect for the specific speed range, packaging limit, and duty in front of you. A belt or coupling between motor and load adds its own compliance and lash on top of any gearbox lash, which matters most for a position-control application where backlash shows up directly as positioning error at the load.

The linked engines split this into separable questions: running torque, acceleration torque with reflected inertia, gearing selection, and duty-cycle thermal loading. Work them in that order, because an error in an early step changes every later one. Record the motion profile you assumed, the reflected inertia you calculated, and the duty cycle you used, since those three numbers are what a supplier or a later reviewer will ask for first.

Regenerative and overhauling loads deserve a separate look, because a load that can drive the motor rather than be driven by it, such as a descending vertical axis, changes the drive electronics question from delivering torque to absorbing it. A controller sized only for motoring torque may lack a path to dissipate or return that energy, which shows up as a fault trip or an uncontrolled speed increase rather than a smooth deceleration.

A preliminary sizing pass earns its keep by turning a vague motor choice into a specific torque-speed-duty target that a manufacturer curve can be checked against. It does not replace that check. Confirm the actual torque-speed curve, controller current limits, gearbox torque and radial load rating, thermal class, and any braking energy limit against current manufacturer documentation before committing to a frame size or ratio.