Does Resolver Mounting Eccentricity Affect Angular Accuracy?

A resolver is one of the most commonly used high-precision angular position sensors in motor control systems, playing a key role especially in drive motors for new energy vehicles, industrial servo systems, and aerospace. Its operating principle is based on electromagnetic induction—the stator windings receive signals modulated by the rotor position, and a decoding algorithm then calculates the rotor angle.

Because a resolver is extremely sensitive to changes in the air-gap magnetic field, a seemingly small mounting deviation—eccentricity—can have a non-negligible impact on angle detection accuracy. So how large is the impact of eccentricity? Where do the errors come from? Can they be compensated for? This article attempts to clarify these questions.

Why Are Resolvers Afraid of Eccentricity?

A resolver is essentially a precision electromagnetic coupling device. Ideally, the rotor's center of rotation coincides exactly with the stator center, the air gap is uniformly distributed around the circumference, and the sine and cosine signals induced in the stator windings have symmetric amplitudes and orthogonal phases, so the decoded angle matches the true angle.

In actual installation, however, due to factors such as shaft machining tolerances, assembly process limitations, and thermal deformation, a radial offset—eccentricity—inevitably exists between the resolver stator and rotor. Once eccentricity occurs, the air gap is no longer uniform around the circumference: it becomes larger on one side and smaller on the other. The air-gap permeance then changes periodically, directly causing periodic fluctuations in the amplitudes of the output sine and cosine signals and destroying the symmetry and orthogonality of the ideal signals.

Forms of Eccentricity Error: Second and Third Harmonics

Air-gap non-uniformity caused by eccentricity manifests electrically as two main types of error components.

First type: fundamental modulation and second-harmonic error. Eccentricity causes the amplitudes of the sine and cosine signals to vary periodically with rotor position, and a second-harmonic component related to the rotational frequency appears in the decoded angle error. Studies show that the unequal-amplitude and non-orthogonal characteristics of the resolver's sine and cosine output signals produce mutually uncorrelated second-harmonic errors, which are one of the main sources of resolver angle measurement error. In the frequency spectrum, this error appears as the second harmonic of the resolver's rotational frequency and directly affects the position control accuracy of the servo system.

Second type: third harmonic and the fourth-order component of angle error. Eccentricity also introduces odd-order harmonics into the output signals, among which the third-harmonic component has the most significant effect. Technical analysis indicates that the third-harmonic component is correlated with the fourth-order component of the angle error, while the amplitudes of fifth and higher harmonics are already very small and can be ignored. In other words, how to suppress the third harmonic is key to improving resolver detection accuracy. Therefore, in the design stage, high-performance resolvers actively reduce the third-harmonic component by optimizing the shape of the rotor's outer circumference, rather than relying solely on ensuring mounting accuracy.

Relationship Between Eccentricity and Error: Approximately Linear but with Limits

A natural engineering question is: how much angular error will a given amount of eccentricity cause? This determines how mounting tolerances should be set.

Analysis of dual-channel resolvers has found that the resolver's mounting eccentricity and accuracy error are approximately linearly related. This means that within a certain eccentricity range, for each unit increase in eccentricity, the angular error increases roughly in a fixed proportion. This conclusion provides a direct quantitative basis for designing mounting tolerances.

However, the linear relationship does not hold unconditionally. Research by the Japan Society of Applied Magnetics shows that when the eccentricity ratio (the ratio of eccentricity to air gap) is controlled within 50%, a reasonable resolver design can keep the angle error within 10 arcminutes. But when eccentricity increases further, the nonlinear effects of the error become significant, and the increase in error may exceed what linear extrapolation would predict. Therefore, in actual engineering, eccentricity should be kept within the linear range allowed by the design as much as possible.

Compensation for Eccentricity: From Hardware to Software

Since eccentricity is unavoidable, engineers have developed various compensation methods.

At the hardware level, one effective method is to place a short-circuit winding in the direction orthogonal to the excitation winding. Research confirms that when the internal impedance of the short-circuit winding is optimally designed, it can effectively suppress the quadrature-axis flux component caused by shaft eccentricity, thereby significantly reducing the angle error. This is an "anti-eccentricity design" of the resolver itself and should be considered during product selection.

At the software level, the mainstream approach is to build a signal error model that includes amplitude error, DC offset, phase error, and harmonic components, use an online parameter identification algorithm to estimate the error parameters caused by eccentricity from actual measured signals, and then perform real-time compensation. Specifically, the actual measured values of the resolver's sine and cosine signals can be input into a signal flow network; through gradient iteration, the optimal error parameters caused by mounting, eccentricity, and tilt problems are identified; then online self-compensation is performed, and the compensated signals are used for angle calculation. The advantage of this type of method is that it requires no additional hardware changes and can adapt to situations where the eccentricity state drifts with operating conditions such as temperature and speed.

In actual engineering, hardware anti-eccentricity measures and software compensation are often used together: the former lowers the "noise floor" of the error, while the latter further reduces the residual error to a lower level.

Mounting Specifications: What Does 0.003 Inches Mean?

In resolver mounting engineering practice, the most commonly cited tolerance figure comes from the recommended values of mainstream resolver manufacturers: the radial eccentricity between the resolver stator and rotor mounting surfaces should not exceed 0.003 inches (about 0.076 mm). At the same time, the perpendicularity tolerance between the mounting shaft shoulder and the hole/shaft should be controlled within 0.0005 inches (about 0.013 mm), and the axial deviation should not exceed 0.015 inches.

This 0.003-inch radial eccentricity limit is not arbitrarily set; it is derived from the air-gap dimensions and accuracy requirements of a typical resolver. For a resolver whose air gap is usually on the order of 0.3–0.5 mm, an eccentricity of 0.076 mm is equivalent to 15%–25% of the air gap, which in most designs can keep the angle error within an acceptable range. However, manufacturers also point out that the specific tolerance should be adjusted appropriately according to the resolver size, air-gap clearance, and accuracy requirements.

For split-type resolvers—that is, resolvers whose stator and rotor are mounted separately onto the host machine—mounting accuracy is even more critical. The stator and rotor of a split-type resolver need to be mounted separately with the host machine, and assembly errors of either the stator or rotor can degrade the resolver's output accuracy. In such applications, the control of mounting structure design and assembly processes is often more decisive than the electrical accuracy of the resolver itself.

Conclusion

Resolver mounting eccentricity does affect angular accuracy. Its mechanism is that eccentricity causes non-uniform air-gap permeance and introduces second- and third-harmonic errors into the output signals. Within a reasonable range, eccentricity and angular error are approximately linear, but once the eccentricity ratio exceeds 50%, nonlinear effects become significant. Through hardware-level short-circuit winding design and software-level online parameter identification compensation, the impact of eccentricity can be offset to a certain extent, but the most fundamental safeguard is still tolerance control during installation. For high-precision applications, it is recommended to include resolver mounting eccentricity in the tolerance chain analysis at the design stage and to combine it with the mounting specifications recommended by the resolver manufacturer for process control, so as to obtain reliable angle detection accuracy at the system level.