Stepper motor torque calculation formula

Calculation formula of stepping motor torque

Abstract: Calculation of moment of inertia and torque on output shaft of stepping motor: torque=force * arm
The radius of the wheel can be calculated as 0.8cm if the wheel is 5 cm long. Required torque
=20*0.8=16kg. cm。 The speed required for lifting heavy objects shall be converted into speed unit RPM (per minute
Now we have all the important parameters of the motor
Calculation of moment of inertia and torque on output shaft of stepping motor:
Moment=force * arm The wheel you put on is 5cm long for a circle, and the radius of the wheel can be calculated as 0.8cm. place
Required torque=20 * 0.8=16kg.cm. How much speed is required for lifting heavy objects, which is converted into speed units
RPM
Now we have all the important parameters for selecting the motor. You just need to find the speed you want to output
16kg. Cm torque stepping motor. It is better to multiply by a safety factor of 1.2, the output torque
It is required to reach about 20kg.cm.
When selecting the power stepping motor, the load inertia of the mechanical load and the starting frequency required by the machine tool should be estimated
To make it match with the inertial frequency characteristic of the stepping motor, there is still some margin, so that it can be connected at the highest speed
The continuous working frequency can meet the needs of rapid movement of the machine tool.
The following calculations are required to select the stepper motor:
(1) Calculate the reduction ratio of the gear
According to the required pulse equivalent, the gear reduction ratio i is calculated as follows:
i=( φ. S)/(360. Δ)  (1-1) Where φ －－- Step angle of stepping motor (o/pulse)
S - - screw pitch (mm)
Δ－－- (mm/pulse)
(2) Calculate the inertia Jt of the workbench, screw rod and gear converted to the motor shaft.
Jt=J1+（1/i2）[(J2+Js)+W/g（S/2π）2） （1-2）
Where, Jt --- inertia converted to motor shaft (Kg. cm. s2)
J1, J2 --- gear inertia (Kg. cm. s2)
Js -------- Inertia of screw rod (Kg. cm. s2) W -------- Weight of worktable (N)
S --- Screw pitch of screw rod (cm)
(3) Calculate the total torque M of motor output
M=Ma+Mf+Mt （1-3）
Ma=（Jm+Jt）.n/T × one point zero two × ten ˉ 2 （1-4）
Where, Ma -- motor starting acceleration torque (N.m)
Jm, Jt --- motor inertia and load inertia (Kg. cm. s2)
N --- the required speed of the motor (r/min)
T --- Motor speed raising time (s)
Mf=(u.W.s)/(2π η i) × ten ˉ 2 （1-5）
Mf --- torque converted from guide rail friction to motor (N.m)
U - - friction coefficient
η－－- Transfer efficiency
Mt=(Pt.s)/(2π η i) × ten ˉ 2 （1-6）
Mt - - cutting force converted to motor torque (N.m)
Pt - - maximum cutting force (N)
(4) Load starting frequency estimation. Starting frequency, load torque and inertia of motor controlled by numerical control system
It has a lot to do with, and its estimation formula is
fq=fq0[(1-(Mf+Mt))/Ml]÷(1+Jt/Jm)] 1/2 （1-7）
Where, fq - - starting frequency with load (Hz)
Fq0 --- no-load starting frequency
Ml --- motor output torque determined by torque frequency characteristics at starting frequency (N.m)
If the load parameters cannot be accurately determined, it can be estimated as fq=1/2fq0
(5) Calculation of the highest frequency of operation and speed rise time. As the output torque of the motor varies with the frequency
The output torque of torque frequency characteristics shall be able to drive the load at the highest frequency
Sufficient margin shall be reserved.
(6) Load moment and maximum static moment Mmax. The load torque can be calculated according to Formula (1-5) and Formula (1-6)
It is calculated that when the motor is at the maximum feed speed, the motor output torque determined by the torque frequency characteristic is greater than Mf
Sum with Mt, with allowance. In general, the sum of Mf and Mt should be less than (0.2 ～ 0.4)
Mmax.