# Step angles and accuracy

Aug. 1, 2005
For every system design, engineers must determine how much accuracy is necessary. All components put into the system affect this accuracy, even back to

For every system design, engineers must determine how much accuracy is necessary. All components put into the system affect this accuracy, even back to the motor. In step motors, accuracy increases when the steps are smaller. This is because one revolution is sliced into more careful, numerous steps, leaving less room for error. For example, a 0.9° stepper delivers more accuracy than a 1.8° stepper.

One common misconception is that 1.8° motors running at half steps generate the same accuracy as 0.9° steppers running at full steps. Another is that torque is lost by using a 0.9° stepper. These are false assumptions, and an understanding of mechanical design features can explain why.

### Q & A

Q: Why doesn't half-stepping increase accuracy?

A: A controller running a 1.8° stepper at half steps does not achieve greater accuracy because as step resolution increases, so does the likelihood of step error. What improves accuracy is increasing the number of rotor teeth. This is why 0.9° step motors with 100 rotor teeth are more accurate than 1.8° step motors, which contain only 50 teeth.

Torque stiffness also affects accuracy, operating somewhat like a spring. The greater the stiffness, the lower the motor oscillation — or the rotor springing back and forth — between steps. This is represented mathematically as dT/d_ = NTOsin(N_), where dT = change in torque, d_ = change in angle, N = number of rotor teeth, and TO = maximum holding torque.

Q: What else affects accuracy?

A: The magnitude of variation in the airgap is another factor when it comes to accuracy. On today's step motors, airgap measurements (taken between the rotor and stator) are typically 0.002 ± 0.0002 in. If the variation is allowed to double, and the motor is manufactured with a yield of 0.002 ± 0.0004 in., the step error doubles as well. Having more poles in the motor, however, can mitigate the effect of airgap variations.

As the number of poles in a motor increases, the space between them decreases, as does the amount of airgap variation from one pole to the next. By comparison, 1.8° steppers contain eight poles that are 45° apart, while 0.9° steppers have 16 poles 22.5° apart. Another advantage of having more poles is that fewer coils are needed in each winding to generate a given torque, effectively reducing inductance.

Q: Is there a rule of thumb to choosing a step motor?

A: Yes, generally speaking, 0.9° steppers work best for high speeds and high-accuracy applications. Conversely, 1.8° steppers deliver greater torque, but less accuracy. Also available are 0.9° step motors with a patented 12-pole design. These more advanced motors combine characteristics of both 0.9° and 1.8° motors to deliver high accuracy and increased torque.

This month's handy tips provided by Mindy Lin of Lin Engineering Inc. For more information, visit www.linenginering.com or call (408) 919-0200.

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