Evo,

I cut and pasted the info below from the Emoteq Megaflux catalog (emoteq.com). It supports Guests' definition from above, and also includes a mechanical definition of a motors time constant.

Electrical Time Constant (TE)

is the ratio of inductance

LM in Henries, to the resistance RM in Ohms. This is the

inductance and resistance as measured across any two

phases in a delta or wye configuration.

TE = LM/RM

Note: This definition is from a brushless motor catalog, You would measure through the armature leads with a brush motor.

Mechanical Time Constant (TM)

is the time required to

reach 63.2% of the motors maximum speed after the

application of constant DC voltage through the commutation

electronics, ignoring friction, windage, and core

losses.

TM = JM * RM/ KT*KB

I hope this helps.