Angular Encoder Accuracy and Bearing Selection: How Runout and Vibration Reach the Feedback Signal

The bearing is part of the measurement chain

An angular encoder reports the relative angle between scale and readhead, and on a conventional rotary stage the only thing that should ever change that angle is commanded rotation. The bearing is the mechanical promise that this is true. Every micrometre of radial runout shifts the rotor laterally relative to the stator, every micrometre of axial float changes the readhead gap, and both appear in the feedback as angle terms the encoder cannot distinguish from real rotation. The datasheet accuracy of the scale is therefore a ceiling the assembled axis approaches, never a guarantee it inherits.

The conversion is brutally geometric. Angle error in radians equals radial displacement divided by the effective radius at which the scale measures, so a five-micrometre runout on a fifty-millimetre radius is already one hundred microradians, twenty arc-seconds, while the same runout on a two-hundred-millimetre ring is five arc-seconds. Small-diameter rotary modules suffer most, which is exactly where miniature bearings with relaxed runout grades are most tempting. Writing the runout budget in micrometres at the scale radius, before choosing a bearing, turns a vague accuracy hope into a selectable grade.

Runout signatures: what the harmonics tell you

Runout is diagnosable from its shape. A pure centre offset between scale rotation axis and bearing axis produces a once-per-revolution sinusoid in the angle error, the classic eccentricity signature, and it repeats identically every revolution. Raceway imperfections and rolling element errors add harmonics at multiples of the revolution frequency and at ball-pass frequencies that depend on the bearing geometry and speed. Plotting angle error against angle over several revolutions, then examining the spectrum, separates static geometry from dynamic bearing behaviour in a single measurement session.

The repeatable part is treatable and the rest must be bought. A stable eccentricity signature can be mapped and compensated in the drive or controller, often recovering a large fraction of the error, and the accuracy verification protocol should record the spectrum before and after compensation. What compensation cannot fix is instability: a signature that changes with temperature, load orientation or re-assembly indicates the mounting or bearing itself is not settled, and no table will follow it. Repeatable first, compensated second, is the only order that survives a production floor.

Vibration at speed: interpolation jitter and lost counts

At standstill, bearing imperfections are geometry; at speed they become excitation. Ball-pass frequencies, motor cogging and imbalance modulate the readhead gap, and the readhead's gain control chases the modulation, adding amplitude noise exactly where the interpolator is most sensitive. The visible result is position jitter, velocity ripple and, in the worst case, miscounting when the Lissajous trajectory is disturbed enough to cross its decision boundaries. Because the excitation is frequency specific, these faults appear and disappear across the speed range in narrow bands.

This is why a speed sweep belongs in acceptance testing. Sweep the axis through its full operating range while recording jitter and signal quality, and mark the bands where degradation appears; compare those bands against the calculated ball-pass and structural frequencies. Countermeasures differ by diagnosis: raceway and preload issues improve with bearing quality or preload adjustment, while a resonance band calls for bracket stiffening, damping or a speed exclusion programmed into the motion profile. The encoder supplier can usually contribute signal diagnostics, but only if the vibration evidence is measured on the assembled axis and shared.

Choosing among crossed roller, angular contact and air bearings

Crossed roller bearings are the default for precision rotary stages: high stiffness, low runout in compact sections and predictable preload behaviour. Their limitations are speed and cleanliness sensitivity; grease behaviour and roller skidding at high speed can add vibration, and contamination in the raceway shows immediately in the feedback. Duplex angular contact ball bearings allow preload tuning across a wider speed range and suit faster rotary tables, but individual raceway quality varies more, so the runout budget must be checked against the actual grade, not the series name.

Air bearings remove mechanical contact and its ball-pass signature entirely, offering nanometre-level runout and the quietest possible feedback environment for metrology-grade rotary tables. The price is stiffness and infrastructure: they need clean, dry, filtered air, tolerate less overload, and shift the design burden to the structure around them. The selection logic is therefore budget-driven rather than preferential: convert the angle budget to micrometres at the radius, add the speed range and environment, and the bearing class usually chooses itself.

• Crossed roller: default precision choice, check speed and contamination limits
• Angular contact duplex: faster axes, verify raceway grade against the runout budget
• Air bearing: metrology-grade runout, requires clean air supply and structural care

Mounting strategy: where runout becomes repeatability

A good bearing in a bad mounting produces a repeatable-looking error that is neither. Thin ring scales are sensitive to clamping stress, so the ring scale mounting plan, datum faces, bolt sequence and torque discipline, decides whether the scale keeps its manufactured form after assembly. The readhead bracket deserves equal attention: a cantilevered bracket with a resonance near the ball-pass frequency converts bearing vibration into gap modulation, while a stiff, damped bracket mounted to the stator structure keeps the readhead observing rotation rather than participating in it.

Temperature couples the mounting to accuracy as well. Asymmetric bearing and housing geometry shifts the rotor centre as the axis warms, and readhead gap changes with it, so symmetric designs and materials with matched expansion keep the harmonic signature stable across the working day. After any disassembly the verification is not optional: the angle error spectrum must be re-recorded, because clamping stress and centre position are exactly the terms that re-assembly changes.

Acceptance evidence for a rotary axis

Four measurements close the loop between bearing and feedback. First, assembled-axis angle error against a reference over full revolutions, recording the harmonic spectrum, on a calibrated divider or equivalent method. Second, a speed sweep capturing jitter and velocity ripple across the operating range, with any degraded bands identified and explained. Third, amplitude and quality-index stability across a warm-up cycle, which exposes thermal centre shift and gap drift. Fourth, repeatability of the angle error spectrum after a controlled disassembly and re-assembly, which validates the mounting plan itself.

Each measurement maps to a specification clause, and together they transfer ownership of the coupling term. If the harmonics are stable, error mapping can shrink them; if jitter bands exist, they are either engineered out or excluded in the profile; if the spectrum survives re-assembly, the mounting is sound. An axis delivered with this evidence can be maintained by measurement instead of by folklore, which is the practical difference between a rotary stage that keeps its accuracy and one that is periodically rediscovered.