Omron M1 Series User Manual page 800

Appendix
 Calculation of motor-shaft conversion torque and effective torque
Calculate the acceleration torque from the motor-shaft conversion load inertia, the motor-rotor iner-
tia and the acceleration. Then, calculate the load torque from the external force (gravity and ten-
sion) and friction force applied to the load. Finally, combine these calculation results to calculate
the torque required for the motor.
• Calculation of acceleration torque (T
• Calculation of motor-shaft conversion load torque (T
F
• Calculation of combined torque and effective torque
A-12
)
A
Speed (rotation speed)
N
η
J Motor
L
t
A
J
M
D
TW
Z
T
Motor
Z
T
2π・N
＝
·
T [N m]
A
60・t
：Acceleration torque [N
T
A
：Motor-shaft conversion load inertia [kg
J
L
：Motor-rotor inertia [kg
J
M
：Efficiency of transfer part (η≦1)
η
：Acceleration time [s]
Time
t
A
N：Motor rotation speed [r/min]
)
L
D
TW [N·m]=F· ×10 -3
2
TW: Load torque (Load-shaft conversion) [N·m]
F: External force [N]
D: Diameter of cylinder [mm]
(Generally, the friction force can be calculated as below:)
F= μ Mg [N]
μ: Coefficient of friction
M: Mass of motion part [kg]
g: Acceleration of gravity (g≈9.8 [m/s
G
T [N·m] = T ·
η
T : Motor-shaft conversion load torque [N·m]
T : Load torque (Load-shaft conversion) [N·m]
Z : Number of motor-side gear teeth
Z : Number of load-side gear teeth
G : Gear ratio (Speed reduction ratio) = Z / Z
M1 Series Standard Type User's Manual (I669)
J
L
＋
J
M
η
A
·
m]
2
·
m ]
2
·
m ]
2 ])