# Selection and calculation method of stepping motor

Technology

Stepping motor is an electromagnetic actuator that can convert digital input pulses into rotation or linear incremental motion. Each input of a pulse motor shaft steps a step angle increment. The total rotation angle of the motor is proportional to the number of input pulses, and the corresponding speed depends on the input pulse frequency.

Stepping motor is one of the key components in mechatronics products, usually used for positioning control and constant speed control. The stepping motor has the characteristics of low inertia, high positioning accuracy, no accumulated error, and simple control. Widely used in mechatronics products, such as: CNC machine tools, packaging machinery, computer peripherals, copiers, fax machines, etc.

When choosing a stepper motor, you must first ensure that the output power of the stepper motor is greater than the power required by the load. When selecting a power stepper motor, first calculate the load torque of the mechanical system. The torque-frequency characteristic of the motor meets the mechanical load and has a certain margin to ensure its reliable operation. In the actual working process, the load torque at various frequencies must be within the range of the torque-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 with the mechanical system, so that the pulse equivalent required by the machine tool can be obtained. In order to have a smaller pulse equivalent in the process of mechanical transmission, one is to change the lead of the screw rod, and the other is to complete the subdivision drive of a stepper motor. But subdivision can only change its resolution, not its accuracy. The accuracy is determined by the inherent characteristics of the motor.

When selecting a power stepper motor, the load inertia of the mechanical load and the starting frequency required by the machine tool should be estimated, so that it matches the inertial frequency characteristics of the stepper motor and there is a certain margin, so that the highest speed continuous operating frequency can meet the machine tool The need to move fast.

### The following calculations are required to select a stepper motor:

(1) Calculate the gear reduction ratio

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 worktable, screw and gear to the motor shaft Jt on the inertia.

Jt=J1+(1/i2)[(J2+Js)+W/g(S/2π)2] (1-2)
where Jt — 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 output by the motor M

M=Ma+Mf+Mt (1-3)
Ma=(Jm+Jt).n/T×1.02×10ˉ2 (1-4)
where Ma — motor start Accelerating torque (Nm)
Jm, Jt—motor’s own inertia and load inertia (Kg.cm.s2)
n—motor speed (r/min)
T—motor speed-up time (s)
Mf=(uWs)/(2πηi)×10ˉ2 (1-5)
Mf—the torque of the motor converted from the friction of the guide rail (Nm)
u—friction coefficient
η—transmission efficiency
Mt=(Pt.s) /(2πηi)×10ˉ2 (1-6)
Mt—cutting force converted to motor torque (Nm)
Pt—maximum cutting force (N)

(4) Estimated load starting frequency. The starting frequency of the motor controlled by the numerical control system has a great relationship with the load torque and inertia.

The estimation formula is

fq=fq0[(1-(Mf+Mt))/Ml)÷(1+Jt/Jm)] 1/2 (1-7) In the
Ml—Motor output torque (Nm) determined by the torque-frequency characteristics at the starting frequency.
If the load parameters cannot be accurately determined, it can be estimated according to fq=1/2fq0.

(5) Calculation of the highest operating frequency and speed-up time .

Since the output torque of the motor decreases with the increase of the frequency, at the highest frequency, the output torque of the torque-frequency characteristic should be able to drive the load and leave enough margin.

(6) Load moment and maximum static moment 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 output torque of the motor determined by the torque-frequency characteristics is greater than the sum of Mf and Mt, and there is a margin. Generally speaking, the sum of Mf and Mt should be less than (0.2 ~ 0.4) Mmax.

Stepper motors and AC servo motors are the two most commonly used executive motors in motion control systems. In the process of motor selection, you must first calculate the converted torque (T-fold) of the load to the motor shaft through the mechanical transmission system.

The following describes the calculation process of the converted torque (T-fold) for several common mechanical transmission methods.

1. T-fold for lifting weight = (m×g×D) /(2×i) [Nm]

2. T-fold for screw nut drive = 1/I((F×t)/(2×π ×η) +Tb) [Nm] F=F0+μmg [N]

3. Synchronous belt or rack and pinion drive
T-fold=(F×D)/( 2×i×η) [Nm] F=F0+μmg [N] 