**Holding Torque Characteristics of Stepper Motors**

When the coil of the stepping motor is through direct current, the relationship between the electromagnetic torque of the loaded rotor (the recovered electromagnetic torque generated by balancing the load torque is called static torque or static torque) and the rotor power angle is called angle-still. Torque characteristics, this is the static characteristics of the motor. As shown below:

Since the rotor is a permanent magnet and the resulting air gap magnetic density is sinusoidal, the theoretical static torque curve is a sine wave. This angle-stationary torque characteristic is an important indicator of the ability of the stepping motor to generate electromagnetic torque. The larger the maximum torque, the better, and the closer the torque waveform is to the sinusoid, the better. In fact, there is cogging torque under the magnetic pole, which causes the combined torque to be distorted. For example, the cogging torque of the two-phase motor is 4 times harmonic of the static torque angle period, and is added to the sinusoidal static torque. The torque shown is:

TL=TMsin[(θL/θM)n/2]

Wherein TL and TM each represent a load torque and a maximum static torque (or a holding torque), and the corresponding power angles are θL and θM, and the change of the displacement angle determines the positional accuracy of the stepping motor. According to the above formula:

θL=(2θM/n)arcsin(TL/TM)

The step angle θs of the PM permanent magnet stepper motor and the HB hybrid stepping motor is described in the previous lesson: θs=180°/PNr, and the angle is changed to the mechanical angle (radian), then it becomes the following formula:

Θs=n/(2Nr)

The above formula Nr is the number of rotor teeth or the number of pole pairs, so the two-phase motor θM = θs.

The load torque is the load of the electromagnetic torque (such as the spring force or the lifting force of the heavy object, etc.), if the motor is to move in the forward and reverse direction, it will produce an angular deviation of 2θL. To improve the positional accuracy, θL is small, therefore, based on For the θL=(2θM/n)arcsin(TL/TM), a stepping motor with a maximum static torque Tm and a small step angle θs should be selected, that is, a high-resolution motor. According to the equation θs=n/(2Nr), the smaller the θs is, the larger the Nr is.

In addition, the rotor structure of the high-resolution stepping motor is roughly classified into three types: PM type, VR type, and HB type, and HB type resolution is the best.

Due to the relationship between the PM type stator magnets and the claw-level structure, the increase in the number of stator poles is limited by machining. The surface of the HB type rotor has no teeth, and the N pole and the S pole are alternately magnetized on the surface of the rotor. Therefore, the pole number is the pole logarithm Nr. Similarly, the increase of the rotor pole Nr is also limited by the magnetizing mechanism. When the number of teeth of the VR type rotor is the same as that of the HB type, the same Nr is used because the permanent magnet is not used, but the step angle θs is twice the HB type, and since there is no permanent magnet pole, the maximum torque Tm is smaller than the HB type.

When the two-phase stepping motor has an outer diameter of about 42 mm, Nr = 100 teeth and a step angle of 0.9 °, which is the highest resolution in actual use. As Nr becomes larger and the reactance increases, the torque will decrease at high speeds. Therefore, a motor with Nr = 50 and a step angle of 1.8 is widely used. For the HB type structure, the step angle accuracy of the full step state is 3%, the stepping motor running angle θ=nθs, there is no cumulative error in each step of operation, and the speed of the motor is large enough to increase n (θs small) ) to improve positional positioning accuracy.