Engineering · Learn · Motion
Positioning Accuracy & Error Budget
Your encoder says 0.001 mm. Why does the machine stop 0.05 mm away?
Encoder resolution is only one of five places where position error comes from. Gearbox backlash, flex in shafts and screws, the drive’s following error and the load itself all add to it. This page shows each source, how big it usually is, and how to add them up into one number you can compare with your tolerance. Figures are typical and indicative; datasheets and measurements win. Every drawing here is made for this page.
The encoder sits on the motor, so the drive can only correct what it can see. Everything after the encoder (gearbox, coupling, screw, frame and load) is invisible to the loop. That is why a very fine encoder does not guarantee an accurate stop, and why the biggest errors usually live in the mechanics.
| Encoder PPR | Gear ratio | Screw lead (mm) | Counts per motor turn | Smallest step at the load (mm) |
|---|
Smallest step = travel per load turn ÷ (PPR × 4 × gear ratio). The × 4 is there because the drive counts both edges of channels A and B. Rotary axis: 360° ÷ (PPR × 4 × gear ratio). Resolution is the finest step the drive can see, not the accuracy of the stop.
| Gearbox type | Typical backlash (arcmin) | In degrees | At the screw (mm, current lead) |
|---|
1 arcmin = 1/60 of a degree. Backlash is lost motion when the direction reverses; it is not noise, it is a fixed gap, so it adds in full whenever the axis reverses. A gearbox in front of a ball screw shrinks its backlash a lot (an angle times lead ÷ 360), but a gearbox driving a rack, a rotary table or a belt does not. Always check the datasheet value; it is quoted at the output shaft, often at a small test torque.
Following error is the gap between where the drive was told to be and where the encoder says it is. It is largest during acceleration and deceleration and shrinks to almost nothing once the axis has settled. Main causes: limited loop bandwidth, hard acceleration, large or changing inertia and poor tuning. S-curve (jerk-limited) profiles make it smaller and calmer.
Worst case is the plain sum: every error at its worst, in the same direction. RSS (root sum of squares) assumes the errors are independent and random, so they partly cancel; it is the more realistic estimate for many small random errors. Backlash, deflection and thermal growth are systematic, so treat them as worst case where they apply. Use worst case for safety-critical tolerances.
Repeatability is usually much better than accuracy, often several times finer. A repeatable offset can be removed by calibration (a position offset, screw pitch error compensation, backlash compensation, or always approaching from the same direction). Scatter cannot be calibrated away; it needs a stiffer, cleaner or better-controlled machine.
| System type | Typical accuracy (mm) | Typical repeatability (mm) |
|---|
System-level figures for a ball-screw or belt axis, not the motor shaft alone. Closed-loop vector is dominated by mechanics: ±0.1° to ±0.5° at the motor shaft is only a few micrometres at a 10 mm lead. Open-loop V/f has no position loop, so a stop is set by timers or sensors and varies with load. For the motor-side view see Induction Motor Position Control and VFD Control Methods.
All values are typical orders of magnitude, for learning and first estimates. Real accuracy is measured on the machine (for example to ISO 230-2) and depends on the encoder, drive tuning, gearbox, screw grade, structure, temperature and load.