Mechanical time constant of a PM brushless motor

[Clyde38]

Below is the formula for calculating the mechanical time constant (Parker Hannifin).

Tau(m) = (R*J)/(Ke*Kt)

R: winding resistance
J: rotor inertia
Ke : back EMF constant
Kt : torque constant

For a three phase PM brushless motor is the resistance line to line or phase? What are the units for inertia (kg per square meter)? Is the back EMF constant and torque constant RMS or peak? Any additional information would be helpful.

Clyde Hancock
Design & analysis of electric motors and generators

http://www.motorconsultants.com

 

[FacEngrPE]

The attached document

ELECTRIC SERVO MOTOR EQUATIONS AND TIME CONSTANTS
George W. Younkin, P.E.
Life FELLOW – IEEE
Industrial Controls Consulting, Div.
Bulls Eye Marketing, Inc
Fond du Lac, Wisconsin​

found at

https://support.controltechnologycorp.com/

provides a detailed explanation of the OP's question.

 

[Clyde38]

Thanks FacEngPE,
I have read this paper. The one thing that it doesn't address is whether the Ke and Kt is peak or RMS. For comparisons it doesn't really matter so much as long as I use the same for all motors being compared however, if I want to report the mechanical time constant for a specific motor it will make a difference.

Clyde Hancock
Design & analysis of electric motors and generators

http://www.motorconsultants.com

 

[waross]

Back to basics:
Another name for RMS current is effective current.
That may be a clue.
As a check, find the specs on a motor that does list the time constants and do the calculations.
And as far as peak current is concerned, when the power is first applied, the first quarter cycle peak may range from 1.414 to 2.828 of the RMS. That does not affect the time constant.
By the way, if your check calculations show a small error, double check the temperature used for the factory calcs.
Calculations at different temperatures will show small errors.
RMS vs Peak will show a discrepancy in the range of 1.414:1.
--------------------
Ohm's
law
Not just a good idea;
It's the LAW!