Shaft Coupling Misalignment Bearing Overload Case Study

Shaft coupling misalignment is not only an assembly tolerance problem. It changes the load path through couplings, shafts, bearings, seals, baseplates and driven equipment. A machine can pass a no-load rotation check and still overload bearings after it warms up, because thermal growth moves shaft centerlines after the cold alignment record has been signed.

This case study follows a motor-pump train returned to service after maintenance. The first run shows high axial vibration, a strong 2x component, rising bearing temperature and coupling guard heat. The useful engineering task is to decide whether the machine can keep running, whether the vibration is imbalance or misalignment, how much bearing life is being consumed, and what evidence is required before release.

The case is simplified for engineering learning. Real work must follow the equipment manual, coupling vendor limits, alignment procedure, safety rules, lockout requirements, vibration standard, lubrication requirements, site reliability limits and qualified rotating-equipment judgement.

Case Context

A horizontal motor drives a process pump through a flexible spacer coupling. The pump was removed for seal replacement, reinstalled, aligned cold and returned to service. At operating temperature, the non-drive-end motor bearing runs hot, axial vibration is high, and the coupling guard is warmer than normal.

The central question is:

Is the machine train acceptable for unrestricted operation, or is coupling misalignment imposing bearing load that must be corrected before release?

The answer requires alignment geometry, thermal-growth correction, vibration evidence, bearing-life screening and validation after correction.

Field Data

Quantity	Symbol	Value
running speed	n	1780\ \text{rpm}
coupling spacer length	L_s	160\ \text{mm}
coupling effective lateral stiffness	k_c	1.5\times10^6\ \text{N/m}
measured cold vertical offset, motor high relative to pump	\Delta_{cold}	+0.22\ \text{mm}
expected motor vertical thermal growth	g_m	+0.18\ \text{mm}
expected pump vertical thermal growth	g_p	+0.05\ \text{mm}
measured face gap difference across coupling diameter	\Delta_f	0.16\ \text{mm}
coupling face measurement diameter	D_f	120\ \text{mm}
baseline radial load on reviewed bearing	F_{base}	1.20\ \text{kN}
bearing dynamic load rating	C	20.0\ \text{kN}
bearing life exponent for ball bearing screen	p	3
1x radial vibration		4.2\ \text{mm/s RMS}
2x radial vibration		5.8\ \text{mm/s RMS}
axial vibration		6.0\ \text{mm/s RMS}
bearing temperature rise above usual baseline		32\ \text{K}

The stiffness value is a simplified equivalent for screening. Real coupling reaction loads depend on coupling type, element stiffness, spacer geometry, angular and parallel offset, torque, speed, temperature and installation condition.

Field Evidence

The evidence supports misalignment more strongly than imbalance.

Evidence	Engineering interpretation
2x vibration is larger than 1x	misalignment or looseness is plausible
axial vibration is high	angular misalignment or thrust loading is plausible
phase is not stable enough for field balancing	imbalance is not the leading correction
bearing temperature rises after thermal soak	hot alignment is suspect
coupling guard is warmer than normal	coupling element is dissipating energy
pump hydraulic conditions are steady	hydraulic excitation is less likely
no new bearing defect frequencies dominate	bearing damage may be consequence, not root cause

The diagnosis should not be made from one spectral line. It should come from the agreement between alignment record, thermal growth, vibration pattern, bearing temperature and post-correction response.

Step 1: Convert Speed to Rotational Frequency

The shaft rotational frequency is:

With:

the result is:

The 2x component is:

Engineering Comment

The frequency check anchors the diagnosis. A 2x peak near 59.3\ \text{Hz} does not prove misalignment, but it is consistent with coupling geometry or looseness when axial vibration and bearing heating agree.

Step 2: Calculate Hot Vertical Offset

Cold alignment is not the operating alignment. The hot relative offset is:

Substitute the data:

If the intended hot offset is near zero, the motor should have been set cold by approximately:

Engineering Comment

The machine was aligned cold with the motor already high. Thermal growth made it worse. The cold alignment record is therefore not a release certificate; it must be interpreted against the expected operating temperature profile.

Step 3: Estimate Angular Misalignment Contribution

The angular slope from the face readings is:

Using:

gives:

The equivalent offset across the spacer length is:

Engineering Comment

Angular misalignment is often hidden when teams look only at rim offset. The coupling can see both parallel offset and angular bending. Both contribute to alternating loads and heating.

Step 4: Calculate Effective Misalignment

Use a first-pass combined offset:

Convert to metres:

Engineering Comment

This is a simplified scalar screen. A real alignment report should keep horizontal and vertical planes separate, include sign convention, feet moves, thermal targets, coupling type, shaft sag correction, runout, soft foot and measurement uncertainty.

Step 5: Estimate Coupling Side Load

The coupling side load screen is:

With:

the result is:

Engineering Comment

The exact force distribution between motor and pump bearings depends on shaft spans and support stiffness. The screening result is still useful: the coupling can add a meaningful lateral load compared with the bearing’s normal radial load.

Step 6: Screen Bearing Life Impact

For a simplified ball-bearing life screen:

where P is equivalent dynamic bearing load.

Before misalignment:

With misalignment side load added conservatively:

Baseline life:

Misaligned life:

Convert revolutions to hours:

Baseline:

Misaligned:

Life reduction:

So the screening calculation indicates about a:

reduction in L_{10} life.

Engineering Comment

This is not a bearing vendor rating calculation. It is a decision screen. The real equivalent load may be lower or higher depending on bearing type, axial load, preload, lubrication, contamination, temperature and vibration. The important point is that a small alignment error can consume a large fraction of bearing-life margin because bearing life scales with load ratio cubed for this simplified ball-bearing model.

Step 7: Corrected Alignment Target

The corrected cold vertical target should offset expected thermal growth:

Assume the final laser alignment record gives:

Then:

Assume angular face error is reduced to:

Angular slope:

Angular contribution:

Combined offset:

Side load:

Engineering Comment

The corrected alignment does not claim perfection. It brings the expected hot offset and angular error into a range where coupling reaction load is small compared with the baseline bearing load.

Step 8: Post-Correction Bearing Screen

Corrected equivalent bearing load:

Corrected life:

Hours:

Engineering Comment

The bearing-life screen is no longer near the misaligned case. Release should still depend on measured vibration, temperature stabilization, coupling inspection and oil or grease condition. A calculation can justify the corrective target, but the machine must prove the correction while running.

Engineering Decision

The machine should not be returned to unrestricted service in the original condition. The evidence supports coupling misalignment amplified by thermal growth, with bearing overload risk.

The decision is:

Hold unrestricted release, correct cold alignment using the hot-growth target, verify soft foot and pipe strain, inspect the coupling element, run the machine to thermal steady state, and release only if vibration, bearing temperature and phase evidence are stable within the accepted limits.

The machine may be allowed a controlled short test run if required for diagnosis, but continued production operation should be treated as a reliability risk until the hot alignment and vibration response are validated.

Failure Modes and Controls

Failure mode	Evidence	Control
cold alignment ignores thermal growth	hot offset grows after startup	align to hot target, not only cold zero
angular misalignment remains after offset correction	high axial and 2x vibration	record face/angular values and coupling limits
pipe strain moves pump after alignment	alignment changes when flanges are loosened	perform pipe-strain check and support correction
soft foot distorts motor frame	alignment repeats poorly	soft-foot measurement and shim correction
coupling element damaged by prior run	heat and stiffness change persist	inspect and replace coupling element if needed
bearing already damaged	vibration improves but temperature remains high	bearing inspection, lubricant analysis and trend review

Risk Review

Risk item	Severity	Occurrence	Detection	RPN
continued operation with hot misalignment	8	4	5	160
bearing damage hidden by short no-load test	7	4	6	168
cold zero alignment used without thermal target	7	5	4	140
pipe strain mistaken for coupling alignment error	7	3	5	105

The controls should reduce occurrence and improve detection: hot-growth target, soft-foot check, pipe-strain check, loaded thermal run, vibration spectrum, bearing temperature trend and follow-up inspection.

Release Criteria

Release should require evidence, not only a new alignment printout.

Criterion	Required evidence
alignment geometry	cold alignment record includes hot-growth target, sign convention, angular and offset values
soft foot	measured and corrected before final alignment
pipe strain	flange loosening or support check does not move pump beyond tolerance
coupling condition	elastomer, grid, gear or spacer element inspected for heat damage and wear
vibration response	1x, 2x and axial vibration below site limits at operating speed and load
temperature response	bearing temperatures stabilize within alarm limits after thermal soak
bearing condition	no dominant bearing-defect frequencies or lubricant evidence of damage
operating trend	follow-up route or online trend confirms no rebound after restart

Transferable Lessons

Coupling misalignment is a system fault. It combines geometry, thermal growth, stiffness, bearing load, vibration and maintenance evidence.

The practical workflow is:

1. identify 1x, 2x, axial vibration and bearing temperature evidence;
2. compare cold alignment with expected hot growth;
3. calculate hot offset and angular contribution;
4. estimate whether coupling side load is significant;
5. screen bearing-life impact;
6. correct alignment using a hot target;
7. verify soft foot, pipe strain and coupling condition;
8. release only after vibration and temperature validate the correction.

This case is distinct from a rotor imbalance case. Imbalance primarily asks whether a 1x vector can be corrected with balance weights. Misalignment asks whether the machine train geometry, thermal movement and coupling stiffness are forcing bearings to carry loads they were not intended to carry.