# Motores paso a paso

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Industrial Circuits Application Note

Microstepping
This application note discusses microstepping and the increased system performance that it offers. Some of the most important factors that limit microstepping performance, as well as methods of overcoming these limitations, are discussed. It is assumed that the reader is somewhat familiar with stepper motor driving and the torque generationprinciples of a stepper motor. If not, chapter 1 and 2 of this book can be read to get the background information necessary. flux is rotated 90 and 45 electrical degrees, respectively every step of the motor. From the formula above we see that a pulsing torque is developed by the motor (see figure 1a, which also shows the speed ripple caused by the torque ripple). The reason for this is that fs -fr is not constant in time due to the discontinuous motion of fs. Generating a stator flux that rotates 90 or 45 degrees at a time is simple, just two current levels are required Ion and 0. This can be done easily with all type of drivers. For a given direction of the stator flux, the current levels corresponding to that direction are calculated from the formulas: IA = Ipeak × sin(fs) IB = Ipeak ×cos(fs) By combining the Ion and 0 values in the two windings we can achieve 8 different combinations of winding currents. This gives us the 8 normal
Load angle [degrees] Motor torque [% of Thold] 100.00 90.00 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 100.00 90.00 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 0.00

What is microstepping
Microstepping is a way of moving thestator flux of a stepper more smoothly than in full- or half-step drive modes. This results in less vibration, and makes noiseless stepping possible down to 0 Hz. It also makes smaller step angles and better positioning possible. There are a lot of different microstepping modes, with step lengths from 1⁄3-full-step down to 1⁄32-fullstep—or even less. Theoretically it is possible to use non-integerfractions of a full-step, but this is often impractical. A stepper motor is a synchronous electrical motor. This means that the rotor’s stable stop position is in synchronization with the stator flux. The rotor is made to rotate by rotating the stator flux, thus making the rotor move towards the new stable stop position. The torque (T) developed by the motor is a function of the holding torque (TH)and the distance between the stator flux (fs) and the rotor position (fr). T = TH × sin(fs - fr) where fs and fr are given in electrical degrees. The relationship between electrical and mechanical angles is given by the formula: fel = (n ÷ 4) × fmech where n is the number of full-steps per revolution. When a stepper is driven in fullstep and half-step modes the stator

1- and 2-phase-on stoppositions corresponding to the flux directions 0, 45, …, 315 electrical degrees (see figure 2a). If we have a driver which can generate any current level from 0 to 141% of the nominal 2-phase-on current for the motor, it is possible to create a rotating flux which can stop at any desired electrical position (see figure 2b). It is therefore also possible to select any electrical stepping angle—1⁄4-full-step (15 electrical degrees), 1⁄8full-step or 1⁄32-full-step (2.8 electrical degrees) for instance. Not only can the direction of flux be varied, but also the amplitude. From the torque development formula, we can now see that the effect of microstepping is that the rotor will have a much smoother movement on low frequencies because the stator flux, which controls the stable rotor stop position,is moved in a more-con-

full-step mode

Speed [full-steps/ms] 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 Load angle (fs-fr) Torque Speed 3.50 3.00 2.50 2.00 1.50 1.00 0.50

1/8-full-step mode

0.25

0.50 0.75 1.00 Time from first step [ms].

1.25

0.00 1.50

Figure 1. (A)—torque and speed ripple as function of load angle, full-step mode. (B)—torque and speed ripple as function...