
B-65262EN/03 SPECIFICATIONS FOR THE αiS/αi SERIES 3.SELECTING A MOTOR
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3.2.4 Calculating the Acceleration Torque
Calculate the acceleration torque required for the motor to accelerate
and then obtain the torque required for acceleration by calculating the
total torque including the constant load torque calculated before. Next,
confirm the result is included in the intermittent operation area for the
motor.
3.2.4.1 Calculating acceleration torque
Assuming that the motor shaft operates ideally in the acceleration/
deceleration mode determined by the NC, calculate the acceleration.
Multiply the acceleration by the entire inertia (motor inertia + load
inertia). The product is the acceleration torque.
In rapid traverse, there are linear acceleration/deceleration and feed-
forward during rapid traverse + bell-shaped acceleration/deceleration.
The equations for calculating the acceleration torque in each mode are
given below.
Acceleration torque in linear acceleration/deceleration
Time
Speed
Specified
speed
ctual motor speed
V
m
t
a
Torque
Speed
V
m
T
a
V
r
Point at which the maximum
torque is required
When the torque is T
a
and the speed is V
r
in the above figure, the
maximum torque is required. The equations for calculating T
a
and V
r
are given below:
)1()/(
1
60
2
as
LM
a
ma
tk
eJJ
t
VT
⋅−
−×+×××=
η
π
)}1(
1
1{
as
sa
mr
tk
e
kt
VV
⋅−
−
⋅
−×=
T
a
: Acceleration torque [N⋅m]
V
m
: Motor speed in rapid traverse [min
-1
]
t
a
: Acceleration time [sec]
J
M
: Motor inertia [kg⋅m
2
]
J
L
: Load inertia [kg⋅m
2
]
V
r
: Motor speed at which the acceleration torque starts to
decrease [min
-1
]
k
s
: Position loop gain [sec
-1
]
η : Machine tool efficiency
e : base of a natural logarithm (
2.71)