Eccentricity Error Control for Magnetic Encoder Disks

Why Eccentricity Is the “Hidden Killer” of Magnetic Encoder Accuracy

In industrial servo systems, robot joints, and precision motion control, magnetic encoders have become a mainstream angle-feedback solution because of their compact structure and strong contamination resistance. However, one easily underestimated problem is this: eccentricity between the disk and the shaft introduces a sinusoidal periodic error once per revolution, directly eroding the system’s effective accuracy.

The data are intuitive: for a magnetic ring with a diameter of 60 mm, a radial runout of only 0.05 mm introduces an angular error of about ±0.1°. In multi-track vernier architectures, this error is further coupled into the absolute-position decoding result, causing power-on position jumps or periodic angular offsets.

Eccentricity error control therefore becomes a systems engineering task that must run through the entire chain of magnetic encoder design, from magnetic ring selection and magnetization process to installation and commissioning, and signal compensation.

I. Where Eccentricity Errors Come From: Three Levels of Error Sources

Eccentricity error does not have a single source. It is jointly composed of geometric eccentricity, magnetization eccentricity, and harmonic distortion at the signal level.

Geometric eccentricity is the most direct source. The fit clearance between the magnetic ring bore and the shaft, as well as the perpendicularity deviation between the magnetic ring end face and the shaft shoulder, can cause the geometric center of the magnetic ring to deviate from the rotation axis. When the disk rotates, the air gap between the sensor and the track changes periodically, appearing as a first-order sinusoidal error component in the output signal.

Magnetization eccentricity is a problem unique to multi-track disks. In a dual-track vernier architecture, the magnetic poles of the inner and outer tracks must be strictly concentric. If the centers of the two tracks shift during the magnetization process, or if the positioning accuracy of the magnetization head is insufficient, the pole alignment relationship between the coarse track and the fine track will vary non-monotonically over the full circumference, directly causing absolute-position jumps in vernier decoding.

Harmonic distortion is the “second-order effect” of eccentricity. Eccentricity makes the magnetic field distribution at the sensor position no longer an ideal sine wave; instead, second-order, third-order, and higher harmonics are superimposed. At the signal-processing level, these harmonics appear as amplitude mismatch, phase shift, and non-orthogonality errors. Even with differential Hall detection, they are difficult to eliminate completely.

II. Influence of Material Selection on Eccentricity Error Sensitivity

Injection-molded ferrite and rubber magnet are the two mainstream materials for dual-track disks, and they differ significantly in the generation mechanism and sensitivity of eccentricity errors.

Injection-molded ferrite is formed by mixing magnetic powder (usually strontium ferrite) with a thermoplastic resin (such as polyamide) and then injection molding it. The magnetic powder volume content is usually controlled between 60% and 80% to balance magnetic performance and injection fluidity. Its advantages are relatively high remanence and good temperature stability, but the melt flow direction during injection molding affects the orientation alignment of the magnetic powder. If the gate location or mold flow design is improper, non-uniform magnetic powder orientation directly translates into pole pitch error after magnetization, which is further amplified under eccentricity. Encoders injection-molded with a disk gate have better magnetic performance than those using a four-point pin gate.

Rubber magnet uses an elastomer as the matrix and is filled with ferrite magnetic powder. It has good flexibility and lower cost. One interesting characteristic of rubber magnet is that it has a natural tolerance to sensor eccentricity. Early studies showed that even when the magnetic field detection element is significantly eccentric, a rubber magnet encoder can still output a good-quality sinusoidal signal, with almost no change in amplitude or waveform. This means the rubber magnet material itself has stronger “immunity” to eccentricity error. The cost, however, is that rubber magnet has lower remanence than injection-molded ferrite, so at the same number of pole pairs, the signal amplitude is weaker, and the requirements for air gap control are actually stricter.

Therefore, material selection is essentially a trade-off between eccentricity sensitivity and signal strength: rubber magnet is suitable for applications with looser assembly tolerances but lower speeds; injection-molded ferrite is suitable for scenarios requiring high resolution but with strict control over assembly precision.

III. Magnetization Process: The “Inherent Source” of Eccentricity Error

Magnetization of dual-track disks is a precision process. A typical magnetization method is axial multipole magnetization, using pulse technology to magnetize pole by pole. For a dual-track structure, the numbers of pole pairs of the inner and outer tracks must be carefully matched according to the vernier principle—for example, combinations such as 64 poles on the outer ring and 62 poles on the inner ring—to produce a unique absolute position code within one revolution.

There are three main sources of eccentricity in the magnetization step:

Concentricity error between the magnetization head and the disk. The positioning accuracy of the magnetization head directly determines the offset of the track center. When the axis of the magnetization head deviates from the designed axis of the disk, the magnetized pole distribution itself deviates from an ideal concentric circle.

Alignment error between the two tracks. Dual tracks require stepwise magnetization (first magnetizing one track, then the other), and the alignment accuracy between the two magnetization steps is critical. If secondary clamping introduces additional eccentricity, the two tracks will be “offset in their own ways,” and the vernier decoding error curve will no longer be a single sinusoid but will exhibit complex modulation.

Demagnetization and thermal effects. The temperature coefficient of ferrite remanence is about -0.19%/°C. Temperature changes alter the amplitude ratio of the two signals, thereby affecting the stability of absolute decoding. If the demagnetization aging treatment after magnetization is insufficient, residual magnetic domain switching can also introduce slow drift during subsequent use.

The current direction of process optimization has shifted from “back-end compensation” to “front-end control”: segmented alignment magnetization, closed-loop servo-controlled magnetization, and other schemes are gradually replacing traditional one-time magnetization, reducing magnetization-derived errors at the source.

IV. Mechanical Installation: Dual Constraints of Coaxiality and Air Gap

The installation step is the key node at which eccentricity error changes from a “potential risk” into an “actual error.” The commonly accepted engineering guidelines in the industry are very clear:

• Coaxiality: The coaxiality between the magnetic ring and the shaft should be controlled within ≤0.05 mm. For high-resolution code disks with more than 64 magnetic poles, radial runout should be further tightened to ≤10 μm.

• Air gap: The air gap between the sensor and the magnetic ring surface should be stabilized within 0.5–1.5 mm.

These two indicators are interrelated. The smaller the air gap, the higher the magnetic field strength picked up by the sensor and the better the signal-to-noise ratio, but the more severe the magnetic flux variation caused by eccentricity; the larger the air gap, the lower the sensitivity to eccentricity, but the lower the signal amplitude, which places higher demands on the chip’s automatic gain control (AGC) capability.

In a dual-track architecture, air gap control has an additional special constraint: both tracks are sensitive to the air gap at the same time. If the disk has axial tilt, the air gaps from the inner and outer tracks to their respective sensors will be inconsistent, causing amplitude mismatch between the two signals and reducing the accuracy of vernier decoding. Therefore, in addition to radial coaxiality, end-face perpendicularity also needs to be strictly controlled. In patent practice, the coaxiality between the outer diameter surface and the inner diameter surface of a fixed component is usually specified as 0.05 mm or less.

For high-precision applications, a practical engineering practice is to use a lever dial indicator to measure the actual radial runout of the disk after assembly, so as to verify assembly quality rather than relying only on design tolerances.

V. Signal-Level Eccentricity Compensation: From Passive Control to Active Correction

Even if materials and assembly are optimized to the extreme, residual eccentricity still exists. Signal-level compensation is the last line of defense and is currently the most active area of technological iteration.

Self-calibration algorithms are the current mainstream chip-level solution. The NOVOSENSE NSM350x series uses a differential Hall detection architecture combined with a dual-track vernier magnetic ring and integrates a client-side self-calibration function. It collects an error curve through one full revolution, builds a lookup table (LUT) for real-time angle correction, and can simultaneously eliminate the effects of component mismatch, mechanical structure deviation, installation eccentricity, and non-uniform magnetization of the magnetic ring.

The Lissajous figure fitting method is a more “lightweight” correction strategy. This method uses the quadrature sampling signals of the magnetic encoder to plot a Lissajous figure. Under ideal conditions, the figure should be a perfect circle; eccentricity and harmonic distortion cause the figure to degenerate into an ellipse or shift. By using least-squares fitting to identify correction parameters, amplitude error, gain error, and non-orthogonality error can be corrected in real time, restoring the corrected Lissajous figure to a circle. This method has simple testing conditions, and once the correction parameters are obtained, real-time correction can be achieved, making it suitable for rapid deployment in production line final inspection.

Neural network methods represent a more cutting-edge exploration. Some studies use a radial basis function neural network (RBFNN) combined with a third-order phase-locked loop to perform harmonic suppression on the non-ideal signal components of an eccentric magnetic absolute encoder. The advantage of RBFNN is that it does not require pre-selecting the harmonic orders to be suppressed; the system can adaptively identify and compensate for low-order and high-order harmonic components caused by eccentricity.

One fact that must be clearly recognized is that algorithmic compensation is not omnipotent. If magnetization eccentricity is too large, causing the alignment relationship between tracks to lose monotonicity over the full circumference, no post-processing algorithm can recover the correct absolute position from the distorted signal. Therefore, front-end process control remains the foundation, and algorithmic compensation is the icing on the cake.

VI. Engineering Quick Reference: Key Parameters for Eccentricity Error Control

Eccentricity error control is not a “special cure” for any single step. It is a systems engineering task spanning magnetic powder mixing, injection orientation, magnetization alignment, assembly concentricity, and signal correction. For multi-track vernier architectures, it is especially necessary to manage inter-track magnetization concentricity as an independent control indicator separate from single-track precision—its importance is no less than the magnetization quality of any single track itself. In material selection, the eccentricity tolerance of rubber magnet is an underestimated card and is worth prioritizing in scenarios with limited assembly conditions.