Motor Across-the-Line Acceleration Time
How long a motor takes to bring its load up to speed started direct across the line: t = WK^2 x dN / (308 x T_net), the rotational form of F = m x a, where WK^2 is the total inertia (lb-ft^2) reflected to the motor shaft, dN is the speed change (rpm), and T_net is the average net accelerating torque (motor torque minus load torque, lb-ft). A 100 lb-ft^2 inertia reaching 1,750 rpm on 50 lb-ft of net torque takes 100 x 1750 / (308 x 50) = 11.4 s; double the inertia or halve the net torque and the time doubles. A long start heats the rotor -- check it against the motor's thermal-limit (stall-time) curve, or the overload trips. A screen; the motor's speed-torque and thermal-damage curves, the reflected load inertia, and the drive govern.
Formula and source
accel_time_s = WK^2 x dN / (308 x T_net), where WK^2 is the reflected inertia (lb-ft^2), dN the speed change (rpm), and T_net the average net accelerating torque (lb-ft = motor torque - load torque). The 308 folds 2*pi/60 and g.
Motor across-the-line acceleration-time formula (the rotational form of F = m x a; standard motor-engineering references), by name; the motor's speed-torque and thermal-limit curves govern.
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