30 - PVD3627-August 2011
3.1.9.
3.1.9.1. Electric time constant:
Time constants of the motor
ph
ph
ph
ph
elec
R
L
_
_
=
τ
With following values given in the motor data sheet
L
ph_ph
inductance of the motor phase to phase [H],
R
ph_ph
resistance of the motor phase to phase at 25°C [Ohm].
Motor series MGV840CAP
Example:
L
ph_ph
= 15.4 mH or 15.4E-3 H
R
ph_ph
at 25°C = 0.823 Ohm
τ
elec
= 15.4E-3/0.823 =
18.7 ms
An overall summary of motor time constants is given a little further.
3.1.9.2. Mechanical time constant:
3
*
)
3
*
3
(
*
*
5
.
0
*
*
_
_
_
_
_
ph
ph
ph
ph
ph
ph
n
ph
n
ph
mech
Ke
Ke
J
R
Ke
Kt
J
R
=
=
τ
2
_
_
)
(
*
*
5
.
0
ph
ph
ph
ph
mech
Ke
J
R
=
τ
With following values obtained from the motor data sheet:
R
ph_ph
resistance of the motor phase to phase at 25°C [Ohm],
J
inertia of the rotor [kgm²],
Ke
ph_ph
back emf phase coefficient phase to phase [V
rms
/
rad/s
].
The coefficient
Ke
ph_ph
in the formula above is given in [V
rms
/rad/s]
To calculate this coefficient from the datasheet, use the following relation:
60
1000
*
*
2
]
1000
/
[
_
]
/
/
[
_
π
rpm
V
ph
ph
s
rad
V
ph
ph
rms
rms
Ke
Ke
=
Motor series MGV840CAP
Example:
R
ph_ph
at 25°C = 0.823 Ohm
J = 0.0186 kgm²
Ke
ph_ph
[V
rms
/
1000rpm
] = 113 [V
rms
/
1000rpm
]
Ke
ph_ph
[V
rms/rad/s
] = 113/(2*
π
*1000/60) = 1.079 [V
rms/rad/s
]
τ
mech
=0.5*0.823*0.0186/(1.079²) =
6.5 ms
