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# Summary of commonly used calculation formulas for stepper motors

2020-09-12
1. Step angle:
Each time the stator winding of the Stepper Motor changes its power state, the angle at which the rotor turns is called the step angle.
The more the number of rotor teeth, the smaller the step angle; the more the stator phases, the smaller the step angle; the more the beat of the energization mode, the smaller the step angle.
Step angle θ=360°/(number of rotor teeth×number of running beats).
The step angle of the motor indicates the angle of rotation of the motor every time the control system sends a pulse signal. In other words, the angle that the rotor rotates for each input pulse electric signal is called the step angle, which is represented by θ.
Take a conventional two-phase and four-phase motor with a 50-tooth rotor as an example. The step angle is θ=360 degrees/(50×4)=1.8 degrees (commonly known as full step) in four-beat operation, and the step angle is θ=360 degrees/(50×8)=0.9 degrees in eight-beat operation. Half step).

Extended information
The stepping motor has a fixed resolution. For example, a stepping motor with a resolution of 24 steps per revolution has a step angle of 15°. The advantages of using a small step angle to complete a certain incremental movement in several steps are: the amount of overshoot during operation is small, the oscillation is not obvious, and the accuracy is high. When selecting, the accuracy and speed requirements of the system should be weighed.
The common ones are 3°/1.5°, 1.5°/0.75°, 3.6°/1.8°. For example, for a stepping motor (small motor) with a step angle of 1.8 degrees, the number of pulses used for one revolution is n=360/1.8=200 pulses.
The error of the step angle will not accumulate for a long time, and only corresponds to the number of input pulse signals. It can form an open-loop control system with a relatively simple structure and a certain precision, or a closed-loop system when higher precision is required.
The step angle can be measured directly by using precision angle measuring equipment such as a reading microscope and photoelectric encoder to measure the angle that each pulse has turned. Since the stepping motor receives a pulse signal, it must rotate a certain angle accordingly. In the inspection test, the method of preset pulse number Nf can also be used to check the number of steps per revolution to indirectly check whether the step angle is correct.

2. Related conclusions
⑴. Controlling the energization sequence of the stator windings of the stepping motor can control the direction of rotation of the stepping motor;
⑵, control the frequency of the pulse input to the Stepper motor can control the speed of the stepper motor;
⑶, control the number of pulses input to the stepper motor can control the angular displacement of the stepper motor.

3. The relationship between torque and speed
Speed formula: n=60f/P
(n=speed, f=power frequency, P=number of magnetic pole pairs)
Torque: The torque that makes a mechanical element rotate is called rotational torque, or torque for short. Mechanical components will produce a certain degree of torsional deformation under the action of torque, so torque is sometimes called torque.
Torque formula: T=9550P/n
T is the torque in N·m
P is the output power in KW
n is the motor speed, unit r/min
The specific derivation relationship is as follows:
1) Power = Force * Speed
That is: P=F*V Formula 1
2) Torque (T) = Torque (F) * Radius of action (R)
That is: T=F*R
Through the above formula, you can deduce
F=T/R formula 2
3) Linear velocity (V)=2πR*rotation speed per second (n seconds)=2πR*rotation speed per minute (n minutes)/60=πR*nminute/30 Formula 3
Substituting formulas 2 and 3 into formula 1, we get:
aP=F*V=(T/R )*(πR*n/30) =(π/30)*T*n
P=power unit W, T=torque unit Nm, n minutes=rotation per minute unit revolution/minute If the unit of P is changed to KW, then the formula is as follows: P*1000=π/30*T*n 30000/ π*P=T*n
30000/3.1415926*P=T*n
9549.297*P=T*n

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