# How to Measure Step Error?

This technical article describes the most accurate way to describe step error that is most meaningful to the step motor user. The traditional way to specify step accuracy is in the form of a percentage by taking the full step error divided by the fundamental step angle of the motor. Let’s understand this and see how we can convince the industry to measure in terms of actual step error in degrees or better yet, in arc-minutes.

The traditional method of using percentage error stems from applications that frequently used motors at full-stepping in order to generate the best torque. However, in today’s industry, most applications operate at ½ stepping or micro-stepping. Step accuracy during full stepping no longer serves the purpose for today’s needs.

Step accuracy is inherent in a motor’s mechanical design. Micro-stepping increases the step resolution but not step accuracy. Micro-stepping a motor without good step accuracy does not provide smooth motion.

Micro-stepping is controlled by the motor’s current ratio of the phases from the motor driver. The current ratio table is built based on a sinusoidal torque curve of step motors. See a visual understanding of how microstepping works in regards to the input current to the two motor phases.

A motor that does not have a sinusoidal torque curve cannot follow the micro-stepping position. Since not every motor can produce a sinusoidal torque curve and the current ratio cannot be perfect from electronics control, a step motor cannot maintain the same accuracy as full stepping when compared to micro-stepping.

Laboratory studies show that the step error may double or quadruple from full stepping to 1/64 stepping. A motor with good step accuracy at full stepping does not automatically provide good step accuracy at micro-stepping. Assuming that a perfect micro-stepping motor can keep the absolute step error regard-less of the number of micro-stepping, 5% step error of a full step becomes 10% of a ½ step and 20% of a ¼ step. The percentage of the micro-step size will be up to 100% or more at a high number of micro-stepping. Therefore, reporting the step error at the % of full step is meaningless.

For instance, a standard step motor with +/- 1.5% step error of full step seems to be very good. It turns out to be +/- 4.2% (not 3% = 2 × 1.5%) errors of half step, and it becomes +/- 180% (not 96% = 64 × 1.5%) errors of 1/64 step at micro-stepping.

Not knowing if the application uses 1/2 stepping, 1/4 stepping, 1/8 stepping, 1/16 stepping, 1/32 stepping or 1/64 stepping, ATO redefined the step accuracy in arc-minutes based on 1/64 stepping (1 arc-minute is 1/60th of a degree). Be-cause anything higher than 1/64 stepping has very little impact to the application in terms of smooth motion & noise. Meanwhile, a motor with good step accuracy at 1/64 stepping automatically pro-vide good step accuracy at larger stepping than 1/64. As a step motor user, we do care about the absolute step error based on our operating mode. Specifying step error as the % of full-step is meaningless, because the percentage of error gets much worse at higher micro-stepping. ATO’s 0.9° step motor specifies +/- 1.5 arc-minutes error at 1/64 stepping. It has +/- 0.4 arc-minute error at full step and +/- 0.6 arc-min error at half-stepping. 0.4 arc-minute translates to 0.37% of 1.8° or 0.72% of 0.9°. It is much better than the industry standard of 1.5% of 1.8°, which is considered good for most step motor manufacturers. It is the time for ATO to share with everyone about what truly good step accuracy is.

Microstepping has been clearly defined as full-stepping, 1/2 stepping and 1/4 stepping in the industry. Rather than saying 1/8 stepping or finer stepping, most engineers started saying 8 micro-stepping or more micro-stepping. Here is the table for a clear communication:

## Stepping Modes

Full Stepping = 1 Microstepping
1/2 Stepping = 2 Microstepping
1/4 Stepping = 4 Microstepping
1/8 Stepping = 8 Microstepping
1/10 Stepping = 10 Microstepping
1/16 Stepping = 16 Microstepping
1/32 Stepping = 32 Microstepping
1/64 Stepping = 64 Microstepping
1/128 Stepping = 128 Microstepping
1/256 Stepping = 256 Microstepping

The step errors can range from ±1.5 arc-minutes up to ±5 arc-minutes for size 17, 0.9-degree motors, and from ±3 arc-minutes up to ±12 arc-minutes for 1.8-degree motors during micro-stepping. Stepper motors perform the best in both the 0.9-degree and the 1.8-degree arenas. It is because we design a sinusoidal torque motor. This is one of the reasons that ATO’s 0.9-degree motors are the most popular in precision motion applications.

An accurately superior motor is also mechanically more efficient. Vibration, from inaccurate stepping wastes energy and results in a net loss of power from the electro-mechanical system. High accuracy motors deliver more energy to the load than more powerful but less accurate motors. The next time you see step error defined as a percentage, first be sure you know how it is defined. Is it a percentage of the full step or at a certain microstepping? Furthermore, what’s the actual error in degrees? The most effective way to call out step error is in arc-minutes (or degrees), and to specify the error at a specific step resolution, like 16x or 64x microstepping.