Selection Steps
- Determine system (machinery/ application).
- Determine operating mode (speed, acceleration/deceleration time, positioning time).
- Calculate speed of rotation (n), inertia (J) and torque (T).
- Select a motor temporarily.
- The inertia of the selected servo motor is more than a certain ratio of a load Inertia.
Load/Motor inertia ratio
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Option 1
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Option 2
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Option 3
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Closed loop stepping motor
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50
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100
|
200
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Stepping motor
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30
|
40
|
50
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DC brushed servomotor
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3
|
5
|
10
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DC brushless servomotor
|
3
|
5
|
10
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DC brushless torque motor
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10
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20
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30
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Note: For large inertia (> 20kg∙m2), DC brushed motors and DC brushless motors usually use ratio of 3 or 5.
- 80% of the Rated Torque of the selected servo motor is more than the load torque of the servomotor shaft conversion value.
- Calculate additional acceleration/deceleration torque (MA).
- Calculate maximum momentary torque and calculate effective torque
Acceleration torque (N∙m): M1=M+MA
Uniform torque (N∙m): M2=M
Deceleration torque (N∙m): M3=M−MA
Effective torque/Root mean square torque (N∙m):
MRMS=√1(t1+t2+⋯+tn)(t1⋅M12+t2⋅M22+⋯+tn⋅Mn2)
- Confirm motor selection requirements and verify selected motor.
The maximum torque of the motor is larger than M1;
The rated torque of the motor is larger than M and MRMS;
The rated speed of the motor is larger than n.
- Rated torque and maximum torque should be calculated if required.
Power and Torque
The relationship between power and torque is:
M=9550⋅Pn
where
M: Torque (N∙m)
P: Power (kW)
n: Speed of Rotation (rpm)
Also, power can be calculated by:
P=F⋅v
where
F: Force (N)
v: Velocity (m/s)
In many cases, when force is friction force:
F=μmg
where
µ: Friction Coefficient (N∙m)
m: Mass (m/s)
g: Gravity Acceleration (m/s2)
External force is positive when it is against the direction of operation.
Formulas for different machinery
Screw
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Speed of Rotation
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n=60p⋅v
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Inertia
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JB=18⋅mB⋅DB2
JW=mW⋅(p2π)2
JL=JB+JW
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Torque
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M=F⋅p2πη
MA=2πn60t1⋅(JLη+JM)
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Lift
|
|
Speed of Rotation
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n=60πD⋅v
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Inertia
|
J1=m1D28
J2=m2D24
JL=J1+J2
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Torque
|
M=F⋅D2η
MA=2πn60t1⋅(JLη+JM)
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Belt
|
|
Speed of Rotation
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n=60πD1⋅v
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Inertia
|
J1=m1D128
J2=m2D228⋅D12D22
J3=m3D124
J4=m4D124
JL=J1+J2+J3+J4
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Torque
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M=F⋅D12η
MA=2πn60t1⋅(JLη+JM)
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Rack and Pinion
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Speed of Rotation
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n=60pz⋅v
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Inertia
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JW=mW⋅(pz2π)2
JL=JP+JW
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Torque
|
M=F⋅pz2πη
MA=2πn60t1⋅(JLη+JM)
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Four-Wheel Vehicle
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|
Speed of Rotation
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n=60πD⋅v
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Inertia
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JW=18⋅m1⋅D2⋅4
JV=m2⋅(D2)2
JL=JW+JV
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Torque
|
M=F⋅D2η
MA=2πn60t1⋅(JLη+JM)
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Table
|
|
Speed of Rotation
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n
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Inertia
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J1=18⋅m1⋅D12
J2=18⋅m2⋅D22
J3=18⋅m3⋅D32+m3⋅r2
JL=J1+J2+J3
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Torque
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M=F⋅dη
MA=2πn60t1⋅(JLη+JM)
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