Shaft Centerline Plot

A shaft centerline plot shows where the average position of a rotating shaft lies relative to a bearing, casing or probe reference. It is usually built from the DC or slowly varying components of two orthogonal proximity-probe gap signals at one bearing plane.

If the probes are scaled to displacement, the mean shaft position can be written as:

where x_c and y_c are mean shaft-position coordinates in the probe coordinate system. The plot may show a single operating point, a speed trend during startup or coastdown, or a time trend during load and temperature changes.

Engineering Role

Shaft centerline plots help engineers understand how the rotor sits inside its available bearing clearance. They are especially useful for sleeve-bearing machines, turbines, compressors, generators, large pumps, marine shafting and high-speed test rigs where oil-film lift and thermal growth change rotor position.

Typical uses include:

• checking whether the shaft lifts into a plausible oil-film position during startup;
• identifying abnormal bearing loading, preload, misalignment or thermal movement;
• assessing rub risk by comparing mean position with clearance limits;
• separating DC position movement from AC vibration amplitude;
• confirming whether orbit data were plotted after removing a meaningful DC offset;
• documenting position changes during commissioning, trip testing, sea trials or condition monitoring.

The plot does not prove the machine is healthy by itself. It must be interpreted with bearing design, probe orientation, installed gap, clearance, speed, load, oil temperature, shaft rotation direction and vibration evidence.

Converting Gap Voltage to Position

For each proximity-probe channel, a change in DC gap voltage is converted with the calibrated sensitivity:

The sign depends on the probe system convention and the installed probe direction. Many proximity systems produce a more negative voltage as the target moves closer to the probe, so the engineer must document whether a voltage change means the shaft moved toward or away from each probe.

When the bearing radial clearance is known, the mean position can be compared with an approximate clearance fraction:

where c is the radial running clearance. This ratio is only meaningful when the coordinate origin, probe directions and clearance reference are stated.

Coordinate Origin and Remaining Clearance

The coordinate origin should be explicit. It may be the bearing geometric center, a cold static shaft position, a probe zero reference or a chosen commissioning baseline. Different origins can make the same shaft movement look acceptable or concerning.

For clearance review, the centerline radius is:

If the AC orbit has maximum radius a_{orbit} in the same coordinate frame, an approximate remaining radial clearance is:

This simplified screen assumes the clearance envelope is circular and the orbit radius is measured from the same centerline point. Real bearings may have preload, lemon-bore geometry, pad tilt, thermal distortion or anisotropic clearance, so the result should be treated as a release screen, not a bearing-design proof.

A centerline plot is most useful when it is reviewed together with orbit amplitude. A shaft centered in the bearing can still have an unsafe AC orbit, and a shifted shaft can be acceptable if the remaining clearance and temperature evidence are adequate.

Worked Example: Estimate Shaft Lift from DC Gap Change

A compressor has two orthogonal proximity probes at the drive-end bearing. Both channels have calibrated sensitivity:

During startup, after applying the documented sign convention, the DC gap changes correspond to:

Convert each channel to mean shaft-position shift:

The resulting centerline shift magnitude is:

If the bearing radial running clearance is:

then the shift is:

or about 27.8\% of the radial clearance.

Engineering comment: this is a plausible order of shaft lift for a sleeve-bearing machine, but it is not automatically acceptable. The engineer checks whether the motion direction agrees with rotation and load, whether the final position leaves adequate clearance margin, whether the probes stayed in their linear range and whether the AC orbit remains small relative to the remaining clearance.

Distinction from Related Terms

Shaft centerline plot is not an orbit plot. A shaft centerline plot shows mean or slowly varying position. An orbit plot shows dynamic X-Y motion about that position.

Shaft centerline plot is not runout. Runout is a repeatable once-per-revolution measurement contribution caused by geometry, target effects or setup. A centerline plot is usually based on averaged or low-frequency position.

Shaft centerline plot is not electrical runout. Electrical runout can bias or contaminate the probe signal. The centerline plot is the diagnostic display built after the measurement chain has been scaled and validated.

Shaft centerline plot is not bearing clearance. Clearance is the available radial space. The centerline plot shows where the shaft is operating inside that space.

Shaft centerline plot is not shaft alignment. Alignment compares shaft axes or coupling positions between machines. A centerline plot tracks rotor position inside a bearing or casing reference during operation.

Validation and Common Mistakes

A defensible shaft centerline plot states probe locations, probe angles, sensitivity, installed gap voltage, sign convention, coordinate origin, bearing clearance, shaft rotation direction, speed, load, temperature, oil condition, filtering, sampling or averaging method and whether runout compensation was applied.

Common mistakes include:

• removing DC gap information before reviewing shaft position;
• plotting voltage directly without applying calibrated sensitivity and sign convention;
• comparing centerline movement from different machines without normalizing by bearing clearance;
• interpreting probe bracket movement as shaft movement;
• ignoring thermal growth, oil-film lift, bearing preload or alignment changes;
• mixing compensated and uncompensated data on the same plot without labeling;
• treating a centered shaft as automatically safe when the AC orbit or subsynchronous motion is large.