  #### Technical Knowledge Stepper motor selection and calculation method
Release Date : 2019-03-08 10:30:26
Stepper motor selection calculation method

A stepper motor is an electromagnetic actuator that converts a digital input pulse into a rotary or linear incremental motion. Each step of the pulse motor is stepped by one step angle increment. The total angle of rotation of the motor is proportional to the number of input pulses, and the corresponding speed depends on the input pulse frequency. Stepper motors are one of the key components in mechatronics and are often used for position control and constant speed control. Stepper motor has low inertia, high positioning accuracy, no cumulative error, and simple control. Widely used in electromechanical integration products, such as: CNC machine tools, packaging machinery, computer peripherals, copiers, fax machines, etc.

When selecting a stepper motor, first ensure that the output power of the stepper motor is greater than the power required by the load. When selecting a power stepping motor, the load torque of the mechanical system must first be calculated. The torque frequency characteristic of the motor satisfies the mechanical load and has a certain margin to ensure reliable operation. In the actual working process, the load torque at various frequencies must be within the range of the moment frequency characteristic curve. Generally speaking, a motor with a large maximum static torque Mjmax has a large load torque.

When selecting a stepper motor, the step angle should be matched to the mechanical system so that the pulse equivalent required by the machine can be obtained. In order to make a smaller pulse equivalent in the mechanical transmission process, the lead of the screw can be changed, and the second can be done by the subdivision drive of the stepping motor. However, subdivision can only change its resolution without changing its accuracy. Accuracy is determined by the inherent characteristics of the motor. When selecting a power stepping motor, the load inertia of the mechanical load and the starting frequency required by the machine tool should be estimated to match the inertial frequency characteristics of the stepping motor with a certain margin, so that the highest speed continuous working frequency can satisfy the machine tool. The need for fast moving.

The following calculations are required to select a 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---stepping angle of the stepping motor (o/pulse)
S --- screw pitch (mm)
Δ---(mm/pulse)

(2) Calculate the inertia Jt of the table, the screw and the gears converted to the motor shaft.

Jt=J1(1/i2)[(J2 Js)W/g(S/2π)2](1-2) where Jt --- is converted to the inertia on the motor shaft (Kg.cm.s2)
J1, J2 --- Gear inertia (Kg.cm.s2)
Js ---- screw inertia (Kg.cm.s2) W---table weight (N)S --- screw pitch (cm)

(3) Calculate the total torque of the motor output M

M=Ma Mf Mt(1-3)
Ma=(Jm Jt).n/T×1.02×10ˉ2(1-4)
In the formula Ma --- motor starting acceleration torque (Nm) Jm, Jt --- motor inertia and load inertia (Kg.cm.s2) n --- the required speed (r / min) of the motor T -- - Motor speed up time (s) Mf = (uWs) / (2πηi) × 10 ˉ 2 (1-5)
Mf---rail friction is converted to the torque of the motor (N.m)
u---coefficient of friction
η---transfer efficiency
Mt=(Pt.s)/(2πηi)×10ˉ2(1-6)
Mt---cutting force is converted to motor torque (N.m)
Pt---maximum cutting force (N)

The starting frequency of the control system of the CNC system is closely related to the load torque and inertia. The estimation formula is fq=fq0[(1-(MfMt))/Ml)÷(1 Jt/Jm)] 1/2(1- 7) where fq---loading starting frequency (Hz) fq0---no-load starting frequency Ml---motor output torque (Nm) determined by the moment frequency characteristic at starting frequency, if the load parameter cannot be accurately determined, then Can be estimated by fq = 1/2fq0.

(5) Calculation of the highest frequency and acceleration time of the operation.

Since the output torque of the motor decreases as the frequency increases, at the highest frequency, the output torque of the moment frequency characteristic should be able to drive the load with sufficient margin.

(6) Load torque and maximum static torque Mmax.

The load torque can be calculated according to formula (1-5) and formula (1-6). When the motor is at the maximum feed speed, the motor output torque determined by the moment frequency characteristic is greater than the sum of Mf and Mt, and the margin is left. In general, the sum of Mf and Mt should be less than (0.2~0.4) Mmax. 