Omron RX Series User Manual page 678

Appendices
Calculation of motor-shaft conversion torque and effective torque
Calculate the acceleration torque from the motor-shaft conver-
sion load inertia, the motor-rotor inertia, and the acceleration.
Then, calculate the load torque from the external force (gravity
and tension) and friction force applied to the load. Finally,
combine these calculation results to calculate the torque
required for the motor.
• Calculation of acceleration torque (TA)
J
L
T
J
J
η
t
N
• Calculation of motor-shaft conversion load torque (TL)
D
F
T
W
F
D
(Generally, the friction force can be calculated as:
F= Mg [N], where
: Coefficient of friction
: Mass of motion part [kg]
: Acceleration of gravity (g≈9.8 [m/s
T
L
T
W
Z
1
Z
2
G
A - 6
Speed (rotation speed)
N
Motor
t
A
J
M
: Acceleration torque [N·m]
A
: Motor-shaft conversion load inertia [kg·m
L
2
: Motor-rotor inertia [kg·m ]
M
: Efficiency of transfer part (η≤1)
: Acceleration time [s]
A
: Motor rotation speed [r/min]
D
T [N·m]=F· × 10
W
2
T
W
: Load torque (Load-shaft conversion) [N·m]
: External force [N]
: Diameter of cylinder [mm]
2
])
G
T [N·m] =T ·
L W
Z
2
Motor
Z
1
T
L
: Motor-shaft conversion load torque [N·m]
: Load torque (Load-shaft conversion) [N·m]
: Number of motor-side gear teeth
: Number of load-side gear teeth
: Gear ratio (Speed reduction ratio) =Z
High-function General-purpose Inverter 3G3RX-V1 User's Manual (I578-E1)
• Calculation of combined torque and effective torque
[r/min]
t
1
T
A
[N·m]
0
[N·m]
Time
0
T
1
[N·m]
0
2
]
· Effective torque T
∑ (T
=
∑t
2
T
1
=
· Maximum torque
–3
Motor selection
Based on the above calculation results, select the motor capacity
using the following formulae.
Select the larger of the two calculated values as the motor capacity.
Also, when selecting a motor, take into consideration the errors in
calculation and modeling. Select a motor whose capacity is at least
approximately 20% larger.
• Motor capacity conversion to effective torque
2π ·T
Motor capacity [kW] =
• Motor capacity required for maximum torque output
2π ·T
Motor capacity [kW] =
* The above calculation formulae assume that the maximum
motor toque is 150% of the rated torque.
Inverter Capacity Selection
Select an inverter that can be used with the motor you
selected based on the result of motor capacity selection.
Basically, select an inverter which fits the maximum
applicable motor capacity of the selected motor.
After selecting an inverter, check if it meets the both of the
following conditions. If not, select an inverter that has a
one class larger capacity and check again.
Rated motor current ≤ Rated output current of inverter
Max. continuous torque output time for application ≤ 1 min
/Z
1 2
Note 1. In the light load mode, the overload capacity of the inverter is 150%
of the rated torque for 5 seconds. Use the 5-seconds rating when
determining the maximum continuous torque.
2. If you want to use 0-Hz sensorless vector control, need a holding
torque at a rotation speed of 0 (r/min), or frequently require 150% of
the rated torque or more, use an inverter with a one class larger
capacity than the one selected by the above method.
N
t t t
2 3 4
1 cycle 1 cycle 1 cycle
T
L
T
2
T
4
T
3
[N·m]
RMS
2
· t )
i i
i
2 2 2
· t + T · t + T · t + T · t
1 2 2 3 3 4 4
t + t + t + t
1 2 3 4
T
[N · m] =T =T +T
MAX 1 A L
· N
RMS
– 3
×10 N: Maximum rotation speed
60
·N
MAX
– 3
×10 N: Maximum rotation speed
60×1.5
Time
Time
Time
Time
/ r [ m ] n i
/ r [
m ] n i