
B-65302EN/01 SPECIFICATIONS FOR THE βiS SERIES 3.SELECTING A MOTOR
- 79 -
Torque constant : K
t
[N⋅
⋅⋅
⋅m/Arms] [kgf⋅
⋅⋅
⋅cm/Arms]
This is known as torque sensitivity and represents the torque
developed per ampere of phase current. This value is a motor-specific
constant, and is calculated by the flux distribution and location of
coils in the armature, and the dimensions of the motor.
The torque constant decreases by 0.11% for the βis series according
to the temperature coefficient of the magnet every time the
temperature of the magnet increases by 1°C after it exceeds 20°C.
Back EMF (electromotive force) constant: Kv [Vrms⋅
⋅⋅
⋅sec] [Vrms⋅
⋅⋅
⋅sec/rad]
This indicates the strength of a permanent magnet and is a motor-
specific constant. This is the voltage generated when the rotor is
externally and mechanically rotated.
Back EMF is a motor-specific constant, and is also calculated by the
flux distribution and location of coils in the armature, and the
dimensions of the motor. Expressed in [min
-1
] units, back EMF has
the dimensions of [Vrms/min
-1
]. The relationship can be given as:
[Vrms⋅sec/rad] = [ 9.55×Vrms/min
-1
] (9.55=60/2/π)
The back EMF constant is indicated as the RMS voltage per phase, so
multiple by
3 to obtain the actual terminal voltage.
The relationship between the torque constant (K
t
) and back EMF
constant (K
v
) can also be given as:
SI unit
]sec/[3]/[ radVrms
v
KArmsmN
t
K ⋅=⋅
Gravitational system of units
]sec/[6.30]/[ radVrms
v
KArmscmkgf
t
K ⋅=⋅
For this reason, when back EMF constant (K
v
) drops lower than the
demagnetization of the magnet, the torque constant (K
t
) also drops by
the same ratio.
Winding resistance : R [Ω
ΩΩ
Ω]
Resistance per phase of the motor
Mechanical time constant : t
m
[sec]
This is a function of the initial rate of rise in velocity when a step
voltage is applied. It is calculated from the following relationship.
vt
am
m
KK
RJ
t
⋅
⋅
=
J
m
: Rotor inertia [kg⋅m
2
]
R
a
: Resistance of the armature [Ω]
Thermal time constant : t
t
[min]
This is a function of the initial rate of rise of winding temperature at
rated current. It is defined as the time required to attain 63.2 percent
of the final temperature rise.
Axis friction torque : T
f
[N⋅
⋅⋅
⋅m] [kgf⋅
⋅⋅
⋅cm]
This is the no-load torque required just to rotate the rotor.