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Selection Steps

  1. Determine system (machinery/ application).
  2. Determine operating mode (speed, acceleration/deceleration time, positioning time).
  3. Calculate speed of rotation (n), inertia (J) and torque (T).
  4. 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 Option 1 Option 2 Option 3
      Closed loop stepping motor 50 100 200
      Stepping motor 30 40 50
      DC brushed servomotor 3 5 10
      DC brushless servomotor 3 5 10
      DC brushless torque motor 10 20 30
      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.
  5. Calculate additional acceleration/deceleration torque (MA).
  6. Calculate maximum momentary torque and calculate effective torque
    Acceleration torque (N∙m): \(M_1=M+M_A\)
    Uniform torque (N∙m): \(M_2=M\)
    Deceleration torque (N∙m): \(M_3=M-M_A\)
    Effective torque/Root mean square torque (N∙m): $$M_{RMS} = \sqrt{\frac {1} {\left(t_1+t_2+\cdots+t_n\right)} \left (t_1 \cdot {M_1}^2+t_2 \cdot {M_2}^2+ \cdots +t_n \cdot {M_n}^2\right)}$$
  7. 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.
  8. Rated torque and maximum torque should be calculated if required.

Selection Diagram



Power and Torque

The relationship between power and torque is: $$M=9550\cdot\frac{P}{n}$$ where
M: Torque (N∙m)
P: Power (kW)
n: Speed of Rotation (rpm)

Also, power can be calculated by: $$P=F\cdot v$$ where
F: Force (N)
v: Velocity (m/s)

In many cases, when force is friction force: $$F=\mu mg$$ 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 Speed of Rotation $$n=\frac{60}{p}\cdot v$$
Inertia $$J_B={\frac{1}{8}\cdot m}_B\cdot{D_B}^2$$ $$J_W=m_W\cdot\left(\frac{p}{2\pi}\right)^2$$ $$J_L=J_B+J_W$$
Torque $$M=F\cdot\frac{p}{2\pi\eta}$$ $$M_A=\frac{2\pi n}{60t_1}\cdot\left(\frac{J_L}{\eta}+J_M\right)$$
Lift Speed of Rotation $$n=\frac{60}{\pi D}\cdot v$$
Inertia $$J_1=\frac{m_1D^2}{8}$$ $$J_2=\frac{m_2D^2}{4}$$ $$J_L=J_1+J_2$$
Torque $$M=F\cdot\frac{D}{2\eta}$$ $$M_A=\frac{2\pi n}{60t_1}\cdot\left(\frac{J_L}{\eta}+J_M\right)$$
Belt Speed of Rotation $$n=\frac{60}{{\pi D}_1}\cdot v$$
Inertia $$J_1=\frac{m_1{D_1}^2}{8}$$ $$J_2=\frac{m_2{D_2}^2}{8}\cdot\frac{{D_1}^2}{{D_2}^2}$$ $$J_3=\frac{m_3{D_1}^2}{4}$$ $$J_4=\frac{m_4{D_1}^2}{4}$$ $$J_L=J_1+J_2+J_3+J_4$$
Torque $$M=F\cdot\frac{D_1}{2\eta}$$ $$M_A=\frac{2\pi n}{60t_1}\cdot\left(\frac{J_L}{\eta}+J_M\right)$$
Rack and Pinion Speed of Rotation $$n=\frac{60}{pz}\cdot v$$
Inertia $$J_W=m_W\cdot\left(\frac{pz}{2\pi}\right)^2$$ $$J_L=J_P+J_W$$
Torque $$M=F\cdot\frac{pz}{2\pi\eta}$$ $$M_A=\frac{2\pi n}{60t_1}\cdot\left(\frac{J_L}{\eta}+J_M\right)$$
Four-Wheel Vehicle Speed of Rotation $$n=\frac{60}{\pi D}\cdot v$$
Inertia $$J_W=\frac{1}{8}\cdot m_1\cdot D^2\cdot4$$ $$J_V=m_2\cdot\left(\frac{D}{2}\right)^2$$ $$J_L=J_W+J_V$$
Torque $$M=F\cdot\frac{D}{2\eta}$$ $$M_A=\frac{2\pi n}{60t_1}\cdot\left(\frac{J_L}{\eta}+J_M\right)$$
Table Speed of Rotation $$n$$
Inertia $$J_1=\frac{1}{8}\cdot m_1\cdot{D_1}^2$$ $$J_2=\frac{1}{8}\cdot m_2\cdot{D_2}^2$$ $$J_3=\frac{1}{8}\cdot m_3\cdot{D_3}^2+m_3\cdot r^2$$ $$J_L=J_1+J_2+J_3$$
Torque $$M=F\cdot\frac{d}{\eta}$$ $$M_A=\frac{2\pi n}{60t_1}\cdot\left(\frac{J_L}{\eta}+J_M\right)$$