There is no rule of thumb. The run-up time will depend on the motor torque-speed characteristic and the driven equipment torque-speed characteristic under run-up conditions. It pays big to start up driven equipment unloaded or lightly loaded.
Most electrical analysis packages (EDSA, ETAAP etc) will do a motor starting study and work out the run-up time fairly quickly. If you do not have such a package, you can work out the run up time (t) pretty quickly manually via spreadsheet by using:
t = (M x N)/9.5Ta
Where:
Ta is the net accelerating torque, i.e. the motor torque minus the driven equipment torque in NM.
M is the moment of inertia of motor plus driven equipment in Kgm^2
N is the full load speed in RPM
You do a series of calculations on a spreadsheet, in 5% or 10% speed increments and total up the time taken to accelerate through each speed increment.
If using 10% increments for a 2-pole motor, N is 300. Ta becomes the average accelerating torque from speed n to speed n+300 and t is the time taken to go from speed n to speed n+300. Total up the t's and you have the run up time.
The motor vendor normally gives a full voltage torque-speed curve for the motor so to determine the torque at reduced voltage multiply the motor full voltage torque by the square in the reduction of voltage caused by the autotransformer. It pays to then multiply the torque by a factor between 0.8 and 1 to account for voltage reduction to the motor terminals due to other voltage drops (supply source impedance, cables, autotransformer losses etc). You can do a bit more work to accurately calculate the voltage at the motor terminals if you wish.
Its a rough but quick method but if you take into account that "standard" IEC autotransformer taps are 50%, 65% and 80%, the method is good enough to tell you which tap to use.
When you use the method, it is pretty important to draw the reduced voltage motor and the driven equipment torque speed curves. It is essential that the reduced voltage motor torque speed curve is above that of the driven equipment torque speed curve throughout the speed range, right up to full speed. If it is not, you will get a rotating stall.
Set the voltage so that the accelerating torque at any speed is never less than 10% of motor full load full voltage torque. Be sure to check that the run-up time is within the motor thermal withstand capacity.
Suggestion: Reference:
IEEE Std 399-1997 IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis, 9.6.5 The Speed-Torque and Motor-Accelerating Time Analysis on page 253
