Stepper motor selection calculation method

Stepper motor selection calculation method

A stepper motor is an electromagnetic actuator that converts digital input pulses into rotational or linear incremental motion. Each time a pulse is input, the motor shaft steps by one step angle increment. The total rotation angle of the motor is proportional to the number of input pulses, and the corresponding rotation speed depends on the input pulse frequency.

Stepper motor is one of the key components in mechatronics products and is usually used for positioning control and fixed speed control. Stepper motors have the characteristics of low inertia, high positioning accuracy, no cumulative error, and simple control. Widely used in mechatronics 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 stepper motor, you must first calculate the load torque of the mechanical system. The torque-frequency characteristics of the motor can meet the mechanical load and have 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 moment Mjmax has a large load torque.

When selecting a stepper motor, the step angle should match the mechanical system so that the pulse equivalent required by the machine tool can be obtained. In order to have a smaller pulse equivalent during the mechanical transmission process, firstly, the lead of the screw can be changed, and secondly, it can be accomplished through subdivided driving of the stepper motor. But subdivision can only change its resolution, not its accuracy. 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 to match the inertia frequency characteristics of the stepper motor with a certain margin, so that the highest speed continuous operating frequency can meet the requirements of the machine tool. The need to move quickly.

Selecting a stepper motor requires the following calculations:

• Calculate 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 the stepper motor (o/pulse) S ---Screw pitch (mm) Δ---(mm/pulse)
• Calculate the inertia Jt of the worktable, screw rod and gear converted to the motor shaft.
  Jt=J1+（1/i2)[(J2+Js）+W/g（S/2π)2] (1-2) In the formula, 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 --- Workbench weight (N) S ---Screw pitch (cm)
• Calculate the total torque M output by the motor
  M=Ma+Mf+Mt (1-3) Ma=（Jm+Jt).n/T×1.02×10ˉ2 (1-4) In the formula, Ma ---motor starting acceleration torque (N.m) Jm, Jt---motor's own inertia and load inertia (Kg.cm.s2) n---the required speed of the motor (r/min) T---motor speed-up time (s) Mf=(u.W.s)/(2πηi)×10ˉ2 (1-5) Mf---guide rail friction converted to motor torque (N.m) u---friction coefficient η---transmission efficiency Mt=(Pt.s)/(2πηi)×10ˉ2 (1-6) Mt---cutting force converted to motor torque (N.m) Pt---maximum cutting force (N)
• Load starting frequency estimation. The starting frequency of the motor controlled by the CNC system has a great relationship with the load torque and inertia. Its estimation formula is:
  fq=fq0[(1-(Mf+Mt))/Ml)÷(1+Jt/Jm)] 1/2 (1-7) In the formula, fq---load starting frequency (Hz) fq0---no-load starting frequency Ml---motor output torque (N.m) determined by torque frequency characteristics at starting frequency If the load parameters cannot be determined accurately, they can be estimated as fq=1/2fq0.
• Calculation of the maximum operating frequency and speed-up time. Since the output torque of the motor decreases as the frequency increases, at the highest frequency, the output torque based on the torque-frequency characteristics should be able to drive the load with sufficient margin.
• Load moment and maximum static moment Mmax. The load torque can be calculated according to equations (1-5) and (1-6). When the motor is at the maximum feed speed, the motor output torque 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 execution motors in motion control systems. During the motor selection process, the converted torque (T-fold) exerted by the load on the motor shaft through the mechanical transmission system must first be calculated. The calculation process of the converted torque (T-fold) is introduced below for several common mechanical transmission methods.
  1. Lifting heavy objects T-fold= (m×g×D)/(2×i) [N.m] 2. Screw nut transmission T fold= 1/I((F×t)/(2×π×η)+Tb) [N.m] F=F0+μmg [N] 3. Timing belt or rack and pinion transmission T fold=(F×D)/(2×i ×η) [N.m] F=F0+μmg [N]