Stepper motor selection calculation method
Stepper motor is a kind of electromagnetic actuator which can convert the digital input pulse into rotating or linear incremental motion. Each input pulse motor shaft steps a step Angle increment. The total rotation Angle of the motor is directly proportional to the number of input pulses, and the corresponding speed depends on the input pulse frequency. Stepper motor is one of the key components in mechatronics products, and is usually used as positioning control and constant speed control. The stepper motor has 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 of all, ensure that the output power of the stepper motor is greater than the power required by the load. When choosing a power stepper motor, the load torque of the mechanical system must be calculated first, and the torque frequency characteristics of the motor can meet the mechanical load and have a certain margin to ensure its reliable operation. In the real working process, the load torque under various frequencies must be within the range of the torque frequency characteristic curve. Generally speaking, the maximum static moment Mjmax is large, and the load moment is large.
When selecting the stepper motor, the step Angle should be matched with the mechanical system, so that the pulse equivalent required by the machine can be obtained. In order to have a smaller pulse equivalent in the mechanical transmission process, the lead of the lead screw can be changed, and the second can be completed by the subdivision drive of the stepper motor. However, subdivision can only change its resolution, not its accuracy. The accuracy is determined by the inherent characteristics of the motor. When selecting the 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 inertia frequency characteristics of the stepper motor and has a certain margin, so that the highest speed continuous working frequency can meet the needs of the rapid movement of the machine tool.
(1) Calculate the gear reduction ratio
According to the required pulse equivalent, gear reduction than I calculated as follows: I = (phi. S)/(360. Δ) (1-1) type of phi - interval Angle of stepper motor (o)/pulse S -- lead screw pitch (mm)
Δ-- (mm/ pulse)
(2) Calculate the inertia Jt of the table, screw and gear converted to the motor shaft.
Jt = J1 (1 / i2) [J2 (Js) W/g (S / 2 PI) 2] (1-2) in Jt - convert to the motor shaft of inertia (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 M output by the motor
M=Ma Mf Mt(1-3)
Ma=(Jm Jt).n/T×1.02×10ˉ2(1-4)
Type of Ma - (N.m) of motor starting and accelerating torque Jm, Jt - motor's moment of inertia and load inertia (Kg. Cm. S2) n - motor required to achieve speed (r/min) T - motor acc time (s) Mf = (U.W.S)/(2 PI eta I) x 10 ˉ 2 (1-5)
Mf-- Guideway friction converted to motor torque (N.m)
u-- coefficient of friction
η- transfer efficiency
Mt = (Pt) s)/(2 PI eta I) x 10 ˉ 2 (1-6)
Mt-- Cutting force converted to motor torque (N.m)
Pt-- Maximum cutting force (N)
(4) 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, and its estimation formula is fq=fq0[(1-(Mf Mt))/Ml)÷(1 Jt/Jm)] 1/2(1-7) fq-- Load starting frequency (Hz)fq0-- no-load starting frequency Ml-- Motor output torque (N.m) determined by the moment frequency characteristic under the starting frequency If the load parameter cannot be accurately determined, it can be estimated according to fq=1/2fq0.
(5) Calculation of the maximum frequency of operation and the time of acceleration.
Since the output torque of the motor decreases with the increase of frequency, the output torque of the torque frequency characteristic should be able to drive the load at the highest frequency, and leave enough 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 torque frequency characteristic is greater than the sum of Mf and Mt, and there is a margin. In general, the sum of Mf and Mt should be less than (0.2~0.4)Mmax.
