The basic characteristics of a stepper motor include its static characteristics, continuous motion characteristics (dynamic characteristics), starting characteristics, and braking characteristics (transient characteristics). These will be described in detail below:
Static torque characteristics
When a stepper motor 's coils are energized with direct current, the relationship between the electromagnetic torque of the loaded rotor (the restoring electromagnetic torque generated by balancing the load torque is called the static torque) and the rotor power angle is called the angle-static torque characteristic, which is the motor's static characteristic. See the diagram below:
Because the rotor is a permanent magnet, the resulting air gap magnetic flux density is sinusoidal, so theoretically the static torque curve is a sine wave. This angle-static torque characteristic is an important indicator of a stepper motor's ability to generate electromagnetic torque; the larger the maximum torque, the better, and the closer the torque waveform is to a sine wave, the better. In reality, there is cogging torque under the magnetic poles, which distorts the resultant torque. For example, the cogging torque of a two-phase motor is a fourth harmonic of the static torque angle period. Added to the sinusoidal static torque, the torque shown in the diagram above would be:
TL = TMsin[(θL/θM)π/2]
Where TL and TM represent the load torque and maximum static torque (or holding torque), respectively, and the corresponding power angles are θL and θM. The change in this displacement angle determines the positional accuracy of the stepper motor . According to the above formula:
θL=(2θM/π)arcsin(TL/TM)
The step angle θs of PM-type permanent magnet stepper motors and HB hybrid stepper motors were discussed in previous lessons, namely: θs = 180°/PNr. Converting the angle to mechanical angles (radians), it becomes the following formula:
θs=π/(2Nr)
In the above formula, Nr is the number of rotor teeth or pole pairs, so for a two-phase motor, θM = θs.
For loads with electromagnetic torque (such as spring force or the lifting force of a heavy object), if the motor needs to move in both directions, it will produce an angular deviation of 2θL. To improve positional accuracy, θL needs to be small. Therefore, according to the formula θL=(2θM/π)arcsin(TL/TM), a stepper motor with a large maximum static torque Tm and a small step angle θs should be selected, i.e., a high-resolution motor. According to the formula θs=π/(2Nr), to make θs smaller, Nr should be larger.
In addition, the rotor structure of high-resolution stepper motors is generally divided into three types: PM type, R type, and HB type, among which the HB type has the best resolution.
Due to the claw-like structure of the stator poles in the PM type, the increase in the number of stator poles is limited by machining. The HB type rotor has no teeth on its surface; the N and S poles are alternately magnetized on the rotor surface, therefore the number of poles is equal to the number of pole pairs Nr. Similarly, the increase in the rotor pole Nr is also limited by the magnetization mechanism. When the R type rotor has the same number of teeth as the HB type, although it has the same Nr, it does not use permanent magnets, but the step angle θs is twice that of the HB type, and due to the absence of permanent magnet poles, the maximum torque Tm is smaller than that of the HB type.
When the outer diameter of a two-phase stepper motor is around 42mm, Nr=100 teeth and the step angle is 0.9°, which is the highest resolution in practical applications. As Nr increases, the reactance also increases, leading to a decrease in torque at high speeds. Therefore, motors with Nr=50 and a step angle of 1.8° are widely used. For the HB type structure, the step angle accuracy in full-step mode is ±3%, the stepper motor running angle θ=nθs, and there is no cumulative error in each step. If the motor speed is high enough, n (smaller θs) should be maximized to improve position accuracy.
Dynamic torque characteristics
Dynamic torque characteristics include drive pulse frequency-torque characteristics and drive pulse frequency-inertia characteristics.
Pulse frequency-torque characteristics
The pulse frequency-torque characteristic is an important feature for selecting a stepper motor. As shown in the figure below, the vertical axis represents the dynamic torque, and the horizontal axis represents the response pulse frequency, which is expressed in pps (pulse per second).
As shown in the figure, the dynamic torque generation of a stepper motor includes two torques: pull-out torque and pull-in torque. The former is called pull-out torque, and the latter is called starting torque. The pull-in torque ranges from zero to the maximum self-starting pulse frequency or maximum self-starting frequency range. The area enclosed by the pull-in curve is called the self-starting region. The motor starts and runs synchronously in both forward and reverse directions. The operating region is between the pull-in and pull-out regions. Within this region, the motor can run synchronously and continuously with a corresponding load. Load torques exceeding this range will prevent continuous operation, resulting in pull-out. Stepper motors use open-loop drive control, and there should be a margin between the load torque and the electromagnetic torque, which should be 50% to 80%.
The out-of-step torque and pull-in torque are equal at 0pps. The load-carrying capacity decreases as the control pulse frequency increases. At the start of operation, the control pulse frequency should be increased slowly to utilize the high torque at low speeds, providing the necessary acceleration torque for the motor during low-speed operation and reducing acceleration time. The smaller the inductance of the stepper motor stator coils, the greater the maximum response pulse frequency, thus enabling the conversion from slow acceleration drive to fast acceleration drive operation.
Pulse frequency-inertia characteristics
When a stepper motor starts rapidly with an inertial load, it must have sufficient starting acceleration. Therefore, if the load inertia increases, the starting pulse frequency will decrease. For this reason, both factors must be considered when selecting a stepper motor.
The vertical axis of the graph below represents the maximum self-starting frequency, and the horizontal axis represents the load inertia. The curves show the relationship between the load inertia and the maximum self-starting pulse frequency. This example uses a PM-type claw-pole stepper motor (two-phase, step angle 7.5°). Under load PL, the relationship between the maximum self-starting pulse frequency PL and the load inertia Jc is as follows:
In the formula, JR represents the rotor inertia of the stepper motor, and Ps represents the maximum self-starting frequency under no-load conditions.
