30 – Pvd3675_Gb_Ey_Septembre_2017
3.2.6. Time constants of the motor
3.2.6.1. Electric time constant :
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].
Example:
Motor series EY630EAK
L
ph_ph
= 7.26 mH or 7.26.10
-3
H
R
ph_ph
at 25°C = 0.674 Ohm
σ
elec
= 7.26.10
-3
/0.674 =
10.8 ms
An overall summary of motor time constants is given a little further.
3.2.6.2. 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 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
]
1
-
tr.min
1000
/
[
_
]
/
/
[
_
π
rms
rms
V
ph
ph
s
rad
V
ph
ph
Ke
Ke
=
Example :
Motor series EY630EAK
R
ph_ph
at 25°C = 0.674 Ohm
J = 147.10
-5
kgm²
Ke
ph_ph
[V
rms
/
1000
𝑡𝑡𝑡𝑡
.
𝑚𝑚𝑚𝑚𝑚𝑚
−1
] = 73 [V
rms
/
1000
𝑡𝑡𝑡𝑡
.
𝑚𝑚𝑚𝑚𝑚𝑚
−1
]
Ke
ph_ph
[V
rms/rad/s
] = 73/(2*
π
*1000/60) = 0.697 [V
rms/rad/s
]
σ
mech
=0.5*0.674*147.10
-5
/(0.697²) =
1.02 ms
Summary of Contents for EY Series
Page 1: ...1 Pvd3675_Gb_Ey_Septembre_2017 Servomotors EY Series Technical Manual PVD 3675 EY Series...
Page 37: ...37 Pvd3675_Gb_Ey_Septembre_2017 3 3 Outline drawings 3 3 1 EY310E...
Page 38: ...38 Pvd3675_Gb_Ey_Septembre_2017 3 3 2 EY420E EY430E...
Page 39: ...39 Pvd3675_Gb_Ey_Septembre_2017 3 3 3 EY620E EY630E...
Page 40: ...40 Pvd3675_Gb_Ey_Septembre_2017 3 3 4 EY820E EY840E EY860E...
Page 44: ...44 Pvd3675_Gb_Ey_Septembre_2017 3 5 2 2 EY420 3 5 2 3 EY430...
Page 45: ...45 Pvd3675_Gb_Ey_Septembre_2017 3 5 2 4 EY620 3 5 2 5 EY630...
Page 46: ...46 Pvd3675_Gb_Ey_Septembre_2017 3 5 2 6 EY820 3 5 2 7 EY840...
Page 47: ...47 Pvd3675_Gb_Ey_Septembre_2017 3 5 2 8 EY860...