Accuracy
Encoder Disc Eccentricity: How Much Error Does 5 µm Cause?
Short answer
With one readhead, eccentricity e gives a once-per-revolution sinusoidal angular error of about e ÷ r radians. At a 20 mm reading radius, 5 µm of eccentricity is about 52″, and 1 µm already equals one count of a 17-bit encoder.
The rule of thumb
Δθ ≈ e ÷ r (rad), with 1 rad ≈ 206,265″
At a reading radius of 20 mm:
| Eccentricity e | Angular error amplitude |
|---|---|
| 1 µm | ≈ 10″ |
| 3 µm | ≈ 31″ |
| 5 µm | ≈ 52″ |
| 10 µm | ≈ 103″ |
For comparison, one count of a 17-bit encoder is 360° ÷ 2¹⁷ ≈ 9.9″. Two diametrically opposed readheads averaged together cancel this first-harmonic error, but add cost and size.
Where eccentricity comes from
- The disc: the graduation pattern center does not coincide with the bore center.
- Assembly: the disc is not centered when bonded or pressed onto the hub.
- The shaft: radial runout of the shaft system.
How to measure it
- Disc as shipped: on a vision measuring machine, fit the graduation circle and the bore circle from multiple points; the distance between centers is the pattern-to-bore eccentricity.
- After assembly: watch the radial runout of a centering reference ring under a microscope over one revolution; half the runout is the eccentricity.
- Complete encoder: compare against a higher-accuracy angle reference and look at the once-per-revolution sinusoidal term of the error curve.
How to control it
- Machine the bore referenced to the pattern — not drill first and pattern later. For laser bore machining, align to the pattern center with machine vision before cutting.
- Keep a centering reference ring on the disc for assembly.
- Use a dedicated fixture; center under a microscope before bonding and re-measure after curing.
- State the pattern-to-bore concentricity requirement and whether a reference ring is needed in your RFQ.