Motor Starting Time

The following is a quick extract from our site post  How to Calculate Motor Starting Time.

The image shows a typical motor torque curve (C_M) and a hypothetical load torque curve superimposed (C_L). The torque (C_a) available to accelerate the motor up to speed is given by the difference between motor torque and load torque (C_M - C_L).

As the speed increases both the motor and load torque vary.   The torque characteristic is also a function of the design and construction of the motor. 

Any torque used for acceleration needs to overcome both the inertia of the motor (J_M) and the load (J_L).  This is given by the equation for the time (t_a) to accelerate  from zero to the running speed (n₀):

Knowing the motor and load inertias and both the motor and load torque as a function of speed (C_M(n), C_L(n)) it is possible to calculated the starting time.  While it is possible to do this by solving the equation for an exact solution, in practice some numerical solution or piecewise approximation would generally be used..

With any complexity on the torque curves or starting arrangement, it is not a trivial matter to calculated the time.  For larger or particularly important motors the effort of dealing with this complexity would be justifiable.  If required, there are are software tools available to assist in the calculation.

The calculation uses simplifications to determine the starting time.

1. an average value of motor torque, C_M = 0.45 x (C_S + +C_max) is used, where C_S is the inrush torque and C_max the maximum torque   
2. an adjustment factor (K_L)  to take care of varying load torque (C_L) due to speed changes:
   Lift = 1, Fans = 0.33, Pistion Pumps = 0.5, Flywheel = 0

Using the simplifications, the approximate starting time is given by:

Where C_acc is the effective acceleration torque and is given by:

per unit voltage: this setting allows for reduced voltage starting scenarios.  For for direct online starting the motor would be operated at full voltage (per unit voltage =1).  For star-delta the voltage during starting would be 1/√3 of the normal running voltage  (per unit voltage = 0.577).  Similar situation for other starting methods.