How much angular error does 5 μm of disc eccentricity cause? Sources, measurement and control of eccentricity
In a single-readhead encoder, disc eccentricity e produces a once-per-revolution sinusoidal angular error with an amplitude of about e divided by the reading radius r. This article gives worked examples and explains where eccentricity comes from, how to measure it, and how to control it in manufacturing and assembly.
2026-10-02 · Langfang Jingzheng Optoelectronic Technology Co., Ltd.
In a single-readhead encoder, disc eccentricity e produces a once-per-revolution sinusoidal angular error with an amplitude approximately equal to e divided by the reading radius r (in radians):
Δθ ≈ e ÷ r (rad), 1 rad ≈ 206265″
With a reading radius of 20 mm:
| Eccentricity e | Angular error amplitude |
|---|---|
| 1 μm | approx. 10″ |
| 3 μm | approx. 31″ |
| 5 μm | approx. 52″ |
| 10 μm | approx. 103″ |
For comparison: one count of a 17-bit encoder is 360° ÷ 2¹⁷ ≈ 9.9″. On a disc with a 20 mm reading radius, 1 μm of eccentricity already produces an error of one count. Averaging two symmetrically placed readheads cancels this first-harmonic error, but adds cost and size.
Where eccentricity comes from
- The disc itself: the center of the graduation pattern does not coincide with the center of the bore
- Assembly: the disc is not properly centered when bonded or pressed onto the hub
- Shaft system: radial runout of the shaft
How to measure it
- Disc as shipped: using a vision measuring machine, take multiple points around the circumference and fit the graduation circle and the bore circle separately; the distance between the two centers is the eccentricity of the pattern relative to the bore
- After assembly: add a centering reference ring to the disc and observe the radial runout of the ring under a microscope over one revolution; half of the runout is the eccentricity
- Complete encoder: compare against a higher-accuracy angular reference and look at the once-per-revolution sinusoidal component of the error curve
How to control it
- Machine the bore referenced to the graduation pattern, rather than drilling the hole first and then applying photolithography. For laser bore machining, first align to the pattern center using machine vision, then cut the hole
- Keep a centering reference ring on the disc for centering during assembly
- Use a dedicated fixture for assembly; center the disc under a microscope before bonding and re-measure after curing
- In your RFQ, state the pattern-to-bore concentricity requirement and whether a reference ring is needed
This article was compiled by the engineering department of Langfang Jingzheng Optoelectronic Technology Co., Ltd. Jingzheng Optoelectronics manufactures glass encoder discs, reflective metal encoder discs, PC encoder discs and custom encoder discs. Website: www.encoderdisk.cn; phone: 0316-8933331.