
3.SELECTING A MOTOR SPECIFICATIONS FOR THE αiS/αi SERIES B-65262EN/03
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3.2.1 Calculating the Load Torque
When a part moves along an axis at a constant speed, the torque
obtained by multiplying the weight of the workpiece driving section
by the friction coefficient is always applied. On a vertical or slanted
axis, the motor keeps producing torque because it works against
gravity. In addition, the motor also produces torque when the machine
on the horizontal axis stops in proportion to the load friction. This
continuously applied load torque is the constant load torque.
In cutting feed, the load torque is applied by cutting thrust. This is the
cutting torque.
The above types of torque are generically called the load torque. The
load torque applied to the motor shaft is generally given by the
following equation:
f
T
lF
m
T +
×
=
πη
2
T
m
: Load torque applied to the motor shaft [N⋅m]
F : Force required to move a movable part (table or tool post)
along the axis [N]
l : Traveling distance of the machine tool per revolution of the
motor = P × (Z1/Z2) [m/rev]
η : Efficiency of the driving system (including a ball screw)
T
f
: Friction torque of the nut of the ball screw or bearing
applied to the motor shaft (input if necessary) [N⋅m]
The force (F) is mainly given by the following equations:
When cutting is not executed (vertical axis):
F=(w-w
c
)g=W-W
c
w
c
: Mass of the counterbalance [kg]
Wc : Weight of the counterbalance [kgf]
When cutting is not executed (horizontal axis):
F=µ(W+F
g
)
When cutting is in progress (horizontal axis) (constant load + cutting
thrust):
F=F
c
+µ(W+F
g
+F
cf
)
[Example of calculation for condition 1] Constant load torque
For a table with a horizontal axis as given as a model, the constant
load torque when cutting is not executed is calculated as follows:
Example F=0.05× (11760+490)=612.5[N]=62.5[kgf]
T
m
=(612.5×20×10
-3
×1)÷(2×π×0.9)+0.8
=3.0[N⋅m]=30.3[kgf⋅cm]