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    Misalignment Diagnosis, Vibration Response & Resulting Spectral Patterns 

    by François (Frank) Gagnon.

    © Copyright 2016 by François Gagnon. All Rights Reserved.

    ABSTRACT / There is nothing new in stating that misalignment and imbalance remain the two most

    common causes of machinery vibration and problematic amplitudes, from mild to severe, depending on

    context. Analysts, especially beginners, often request a recipe to detect and diagnose misalignment

    without fail. We have strong elements, in terms of waveform shape, spectral contents and phase

    analysis, but the list of factors influencing machine and structure behavior is quite extensive, as this

    paper will demonstrate. Literature on various vibration spectral patterns resulting from misalignment

    abounds, but yields highly conflicting conclusions, for reasons we will explore, comment and review.

    Key words: misalignment, parallel, angular, vibration response, FFT spectral contents, diagnosis.

    Author’s Note: where units are converted for the reader’s convenience, assume the metric, rms or Hz

    units are close approximations provided for convenience. Author bio on last page. DO read Appendices

    and references sections.

    Extensive documentation is available on the consequences of misalignment as 1X, 2X and/or 3X RPM

    spectral peaks (1X and 2X are more common, but 2X clearly predominant in terms of how many times

    we may come across it, as seen in Appendix 1), and references to phase analysis abound as support to

    the misalignment diagnosis, nobody can say with complete certainty how a specific case of

    misalignment will behave or “play out” without prior observation. 

    There are also considerations for impulses or impacting within the coupling when the misalignmentcondition reaches from important to extreme severity, and we recognize this behavior as a harmonic

    series visible in the FFT spectrum, but this series is the byproduct of inadequacies of the FFT to interpret

    spike or impulse behavior within the time waveform measurement.

    The question arises as to the reasons why, in spite of the by now enormous quantities of data amassed

    through decades of Condition Monitoring and Vibration Analysis, we still do not have a comprehensive

    reference book and full understanding of every relevant detail, causal relationships and resulting

    waveforms and spectra. Waveform shaped like Ms or Ws may arise from sources other than

    misalignment since all we require are a mix of 1X, 2X and/or 3X RPM to obtain similar “shapes”.

    While we proceed to explore the reasons why, readers who wish to participate in detailing their findings

    may send in their conclusions to the author [email protected]. Given enough examples, we will

    assemble a booklet and the participants will receive evolving copies of same as material filters in. All

    corporate references will be removed, but the contributors will receive credit for their input (unless you

    prefer not to be mentioned). Data received will be commented with respect to units (metric, US, peak,

    RMS) to facilitate comprehension. This also implies amplitude units should be visible (pk, rms, mm/s,

    ips), to avoid dimensionless consideration.

    mailto:[email protected]:[email protected]:[email protected]:[email protected]

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    Ideally, this effort would include:

    - a machine picture, and machine details (type, function, motor HP or kW, RPM, or RPM range for VFDs,

    coupling type, any other)

    - data on all 3 axes (time waveform and FFT spectra, or DFT), unless of no pertinence

    - confirmed misalignment type and quantity / severity when data was collected (what was found)

    - when MISdiagnosed, the reasons why (what was found to contribute to or emulate misalignment)

    A Quick 5 Whys (to explain a continued lack of such a resource) 

    Why? The list of variants is too long, and nobody has done the groundwork, meaning the full data set is

    not accessible in relation to machine-type, function, component type, prevailing conditions, and

    resulting vibration waveforms and spectral patterns.

    Why? Lack of budget, limited access to a wide variety of machines, limited awareness (of the problem or

    issues, or of factors in play), failure to recognize the influence of such details, unavailability of adequate

    measuring equipment, changes in technology, lack of training… Ex: (please correct the author if wrong

    and even better, send a reference title) we don’t even have good samples of  relative phase for 2X and

    3X when misalignment is present. Obtaining those would have been relatively easy from complexspectra, when performing cross-channel phase measurements, without having to do a full ODS

    (Operating Deflection Shape) analysis and animation.

    Why? While a relatively comprehensible and usable fuzzy-logic set of criteria exists, meaning that we

    have a general understanding of resulting vibration behavior, we seem to accept no further need to

    develop specifics for each potential variant. Thus, each case must be analyzed or treated individually.

    Why? Nobody committed the funds and resources to delve on the matter and reach appropriate

    conclusions or quantification, meaning a comprehensive rule-base for case assessment and diagnosis or

    analytics. Also, few people have the opportunity to work on a wide variety of machines or understand

    the nuances, and unless an algorithm and heuristic are considered, there is no foreseeable commercial

    benefit (aside from knowledge, and better / improved diagnoses).Why? No money, and publication makes for some small, limited notoriety, but little payback for

    completing the exercise. The knowledge, while usable, would thus only serve a single individual or a few

    participating professionals. Whereas within proprietary software, some return and commercial

    advantage would indeed be achieved, and prove beneficial.

    Factors Affecting Misalignment-Caused Vibration Response 

    The obvious (or perhaps not so evident) comprehensive (as complete as the author could make it; feel

    free to comment and add any missing item) list of influencing factors in play on misalignment response

    include:

    misalignment type (parallel, angular, combined), severity (may be quite divergent for one misalignmenttype versus the other if both are present) , variable thermal growth on the vertical but also on the much

    more disregarded horizontal, thermal cycling (may not put you back in your original starting position),

    load effects (positional shift), coupling type & stiffness & mass & number of elements (jaws, grids, bolts,

    shear pins, etc.), condition of elements, insert or spider type (design, material), lubrication condition

    (dry, partial, saturated, grit, contamination), universal joint (sometimes seen on paper machines), spacer

    or presence of a jackshaft (intermediate shaft extension), skewed flanges, torque transmission error,

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    rotor imbalance and severity (an imbalance will sometimes introduce or partly behave as misalignment),

    machine design (horizontal or vertical? Height, length, width, overhang or between bearings, rotor mass

    and its distribution, structural stiffness of motor, of machine frame, of rotors, of coupling, isotropy

    (meaning equal in all radial directions), comparative masses, function, shafts’ lengths, bearing type and

    preload if any, lubrication type and film thickness, sheave eccentricity, pendulum or inverted pendulum

    effects, open sections favoring distortion, etc.), rigid or flexible rotor, slender rotor,

    attachments to driven machine (ducts, piping, residual stress, thermal stress, mass, stiffness, isolation or

    lack thereof, such as collapsed flexible joints, etc.), expansion / contraction effects of pipes, ducts or

    their supports, belt tightness,

    base, floor, foundation stiffness, mass, pendulum or inverted pendulum, water table, level or plumb

    issues, sprung or soft foot, shim stacks, shim size (relative to each other and relative to motor or

    machine foot size), isolation springs or pads, inertial blocks, length& mass, single or dual bases, grout,

    voids or cavities (in cement, grout or underlying floor, sometimes from erosion or chemical attack),

    comparative position (building corners are stiffeners, when compared to middle of the plate floor), floor

    stiffness, anchorages and attachments (bolts, etc.), bolt-bound, stripped bolts or lodgings / nuts,

    damaged adjustments, lost or inadequate dowel pins, indoor/outdoor and seasonal changes, integrity or

    state of any and all of the previous

    geographical location (oddly enough, due to variants in design requirements: a design std rule-of-

    thumb1 states a minimum of 3:2 to 2:1 for the inert mass to rotating mass relationship, but in seismic

    prone areas, the rule is void, changing to 6:1 to 8:1), so, design imperatives with respect to rotating

    versus inert mass ratio, and/or rotating mass to casing mass ratio, often a key factor for flexible rotors

    such as steam turbines,

    structural stiffness alterations (looseness, broken welds, loose anchorage, shorn anchorage, etc.),

    mechanical power transmitted (3HP? 30? 100? 3,000?), transmission error, stability, presence of gears,

    RPM, or RPMs, VFDs, reduction or overdrive (especially large reductions as introducing massive

    mechanical power output),

    component stiffness, distance between components, shaft overhangs, shaft bend, shaft kink,

    component condition (such as wear, defects, damage, impacting, rubs, etc.),

    nonlinearities and discontinuities,

    rotating mass (inertial effects, possible gyroscopic effects, shifting radial reaction by 90 degrees, or in

    extreme cases, for an inertia flywheel or similar rotor, autogyration)

    resonant effects (amplification, but also an amount of phase shift, up to, but not necessarily as much as,

    90 degrees, at a perfect resonance), other causes of vibration tied to design or problems,

    eccentricity can influence phase, albeit not in the same fashion as (whole or partial) resonance,

    critical speed effect (rotor bow, proximity to first or 2nd lateral modes),

    bent shaft from idleness,

    structure and/or load temperature (steam, for instance), rotor function load, and thermal bow,

    torsional issues if any are present (misalignment can augment an otherwise benign torsional effect),

    1 Making exception of highly sophisticated rotor or machine designs, such as aeroderivative gas turbines, meaning

    aircraft engines possibly used in industrial applications, or similar stringent requirements.

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    About Thermal Growth, Thermal Gradients & Dynamic / Load Reactions 

    There is an important nuance at work: the hot/cold alignment really only deals with thermal growth,

    and what this writer calls dynamic misalignment should only consider reactions to dynamic load

    SEPARATE from thermal expansion / cryogenic or cooling contraction. "Hot" holds unavoidable ties with

    process flows and quasi static loads from piping and casing growth or contraction, while the machine is

    still really hot, which is transient state at best once the power is shut off.

    A few of the many course participants who heard this over the years do report beneficial results in

    aiming for a compromise alignment when certain of the prevailing conditions or environments we

    describe hereafter can shift the alignment over time.

    In hazardous areas, where risks involve flammable or explosion, hot work permits would be required to

    closely install a laser and target across a span, in parallel to a shaft, while the machine operates. The

    specifics in terms of industrial facility environments vary, and the possibility may simply not exist in

    certain environments, a decidedly limiting factor. Still, IF and WHEN the machine is critical and exposed

    to load and thermal or seasonal variations, this approach may prove worthwhile.

    In terms of mostly parallel alignment, if a laser is mounted (properly and safely) so as to measure off a

    target mounted exactly in parallel to the shaft at the bearing center height, and preferably right next to

    the guard, and the laser then zeroed, we will then enable quantification of dynamic-load effect. Ideally,

    from 100% (or nominal / usual) load, and if at all possible, progressively unloading the motor / driven

    machine tandem, and then turning off. The variations, plotted for load %, equal dynamic load reaction.

    Some machines just get powered off with no such unloading ramp, but this method properly documents

    the variations linked to load. No need to mention the importance of stability for any such temporary

    assembly: care is needed so the results must remain valid as the machine coasts down, possibly crossing

    some rotor critical speed or structural resonance and thus shaking the laser. Relative motion is possiblefrom laser to target, and if a resonant amplification is perceived, it should be noted.

    Once those positional changes are measured / quantified, immediately zero again, and shrinkage (or

    growth for cryogenic or cold applications) then takes over to further move the machine components.

    Thus, only if & when possible / feasible, the difference between dynamic reaction and thermal variations

    can be established and offsets implemented accordingly.

    Consider the cases where the machine is either located outdoors, or its suction or discharge piping

    extend outside. Since realigning will hardly be doable twice a year, the "not so ideal but pragmatic"

    target will be in Spring / Fall, with extremes in Winter / Summer. Not so dramatic in the Caribbean, butclearly a consideration if ambient delta T is significant / huge (from -30

    oF to 90

    oF, meaning -30

    oC to 30

    oC

    or similar). So, we face the inevitability of hopefully reasonably mitigated unavoidable misalignment.

    Not a typical approach, and diverges from ideal mounting practice. But it can serve us in extreme cases.

    Not always feasible due to access, and also possibly limited by alignment-device brand & model.

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    For critical machines, so exposed to seasonal temperature fluctuations, if steps are not taken to aim for

    the middle ground, one of the seasonal extremes may yield much higher and possibly damaging or even

    destructive vibration amplitudes. Triggering machine protection warnings or alarms has been seen,

    though not machine shutdown / trip.

    Seen for air-separation plants in northern climes: long-term overall amplitude trends resemble a sine

    wave. The sine amplitude, from a lower threshold amplitude to a higher one, over LONG time may be

    sharper or flatter depending on the scope of the temperature gradient. This may be linked in part to

    alignment variations for some machines. On air compressors, colder air aspiration also means a portion

    of the liquefaction work has been done for you. From the previous, we can also assert that trending

    upwards does not always mean deteriorating machine health, but may simply be tied to prevailing

    operational parameters. Elsewhere, a large nitrogen compressor had alarms in spring and late fall, as the

    ground thawed or froze.

    Another apparently absurd consideration, but of some import when high-precision is absolutely

    required: sun exposure. In one application, feed sealing for a rotary kiln required extremely tighttolerances. Sunlight exposure of the jacket (kiln outer skin) had to be considered. Facetiously, white

    paint or covers do much to eliminate such considerations for pipes and the like, but would just peel off a

    kiln. More seriously, where sunlight exposure does occur, dark colors (dark brown, black) for an

    elongated component may introduce a variant.

    To conclude this small section, such methods have been used successfully to partially resolve a handful

    of difficult cases. Partially, since some misalignment may be deemed incurable.

    Field Consideration / Machine Start or Restart & Alignment 

    A machine (usually) starts COLD (at ambient temperature, unless it was only turned off for a very short

    time period), and proper offset should have been implemented to take thermal growth into account.

    Upon reaching nominal RPM, initial measurements’ vibration amplitudes should be rougher, and ease as

    the machine warms up and temperature stabilizes. Starting smooth and finishing rough shows a

    problem (no offset). Starting rough and improving up to a still undesirable amplitude plateau might

    indicate not enough compensation. And then, starting rough, followed by easing and THEN seeing

    amplitudes move back up in value (likely overshooting with too much offset compensation?).

    Imbalance Extremes 

    As analysts, we often think in terms of acceleration or velocity, and displacement takes a backseat

    unless low-frequency applications are considered or proximity probes are involved in turbomachinery’s

    sleeve bearings. We might remind ourselves that the displacement from a severe imbalance acts as a

    form of or contributor to dynamic misalignment. The net impact of such a rotating force will be tied to

    the stiffness of the machine structure as well as to the actual location of the imbalance: away from the

    coupling end may only mean a short “attempted” travel of the shaft end. 

    Different amplitude parameters or units skew our data or our perception of same. When considering the

    possibility of imbalance contributions to misalignment, peak-peak displacement units should be

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    remembered, as well as the frequency under consideration. A 3.2 Mils p-p displacement (80microns p-p)

    for a 3580 RPM 1X (appr. 60Hz) is equivalent to 0.6 ips pk (10mm/s rms). Those 3.2 Mils become 0.3 ips

    pk (or 5mm/s rms) for 1780 RPM (appr. 30Hz). For 0.3 inch/sec pk at 880 RPM (appr. 15Hz), the

    displacement becomes 6.4 Mil p-p (160microns p-p). In that last case, the unbalanced rotor’s shaft will

    try to pull itself out of line by 3.2 thousandths (of an inch), and half a turn later, by that same 3.2 Mils to

    the other side. Will this result in an artificial instance of momentary misalignment? It might. All those

    factors we listed earlier may determine if this will be the case or not. See Appendix 2 for a brief

    exploration of moving the imbalance vector along a machine train.

    Having prior knowledge of the expected misalignment limit or tolerance for a shaft can provide some

    notion of how important any such displacement effect might become in terms of rotor behavior.

    From Dec 2002 Maintenance Technology  

    A decent reference, but not entirely inagreement with the Ludeca tolerance

    chart (below).

    0.001”= 25,4 microns or 0,0254 mm 

    This author always felt the use of RMS displacement values was especially convoluted, and establishing

    correlates with alignment is a glaring example.

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    Working Machines vs. Test Rotors & Test Lab

    Reading various papers on the topics of misalignment and vibration response, spectral contents and the

    like, we need to maintain a discerning mindset as authors may unintentionally lead us astray, even if

    only with a paper title where the plural “rotors” is used in lieu of “a rotor” or “a rotor model”. The

    catalog of factors of influence included in this paper should make it amply clear that experimental work

    on a specific rotor or mathematical model and whatever conclusions may be derived from same are

    usually ONLY and strictly applicable to that very same rotor, as opposed to being descriptive or

    pertinent to the behavior of all rotors. 

    Trusting in a few laboratory test rotors fails to deliver GENERAL dominant rules for parallel and angular

    misalignment, or increasing or exaggerated amounts of one, the other or both. The effort yields specific

    rules for a given rotor. A test rotor2 is NOT (or rarely is) a machine. In most laboratory scenarios, the

    rotor is designed to 1) turn, at fixed or variable RPM, and 2) vibrate or not, according to imbalance and

    introduced misalignment. A machine, by definition, performs a task or function to accomplish a set goal.

    This involves considerably higher motor power (and commensurate energy consumption). Limited

    budgets are in part responsible for the use of limited power. And in most cases, due to the very absenceof a machine function, the transmitted mechanical power poorly reflects a real machine’s behavior. 

    Such statements do not invalidate rotor lab experiments. The data and conclusions derived from

    experimentation remains extremely useful to expand our comprehension, but, a caveat serves us well

    to prevent the generalized application or expectation to all rotors. Also, many tests are executed with

    the introduction of measured or quantified imbalance, but such imbalance is applied to a thin-disk

    located between bearings. The possible incidence of couple-imbalance disappears, and the frequent

    placement of the disk between supporting bearings, as opposed to at or near the coupling, also alters

    responses compared to what might be observed in the field or plant-floor.

    Slight oddity, but one that requires our attention, most experiments involving angular misalignment, or

    the angular portion of combined misalignment, seem to always rely on the angularity being on the

    vertical. We regularly mention horizontal or vertical parallel offset, but we also seem to instantly assume

    that angularity will be tied to cases of vertical “slant”. We have little comparing HV reactions for V

    angular to HV reactions for H angular, or any differences for axial response to either H or V angular.

    There are certainly machine and/or base designs propitious to horizontal angularity, and given the usual

    differences between structural horizontal and vertical stiffness, the end-result response or behavior

    might diverge from our expectations. Angular misalignment can be introduced with ease on the vertical,

    and readily quantified, whereas doing so in the horizontal, or simultaneously on both axes, requires a lot

    of work and is rife with the prospect of error. In the field, a pump’s suction or discharge may well be

    horizontal, and the cause for the motor-to-pump angularity may be exaggerated stress from that pipe.

    Under undue stress, bases or other components may swivel, twist or otherwise get misshapen.

    On a demo rotor, the inert mass MAY fit the rule-of-thumb, but the stiffness ratio (machine to base,

    base to "foundation", meaning a table) are not representative of plant-floor machinery reality, and the

    2 Technical nuance, “rotor” refers to the “rotary part of a machine”, and is not a machine itself  

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    demo rotor base is often laid on top of a table, or attached to same with clamps. “Real world” masses in

    play become entirely different due to floor anchors, inertia blocks, steel and cement structures.

    Some rotor supports use frames or pedestals for bearing locations, and those will be especially weak in

    the axial direction, favoring a sharper or more severe axial response. Longer rotors also mean a much

    higher probability of stiffness discrepancies along the machine train.

    The most common industry workhorse is the 100 HP (75kW), 4-pole asynchronous motor. Nowadays, it

    may or may not be fitted with a VFD control. There is a considerably larger park of smaller motors, but

    spread between 1, 5, 10, 30, 50 or 75HP (this last, 50kW), and a smaller random population of large

    motors, that could be 400HP (300kW) or 5,000 (3,750kW). Largest asynchronous motor seen: 13KHP.

    Not to be confused with synchronous motors. For that last type, largest seen: 40,000 HP (30 MW).

    Apparently ABB makes motors to 80,000HP (60MW), but this consultant has neither come across nor

    dealt with that specific model.

    This portrait of the motor population by HP (or kW) does have a direct tie-in to Condition Monitoring.

    PdM is most financially rewarding where continuous processes are involved, meaning chemical, paper,

    metals and oil (refining or petrochemical). Power generation is excluded from motors, because its large

    machines are of a different type. For misalignment concerns, though, those large machines will be

    extremely important. As would the mostly sleeve bearing assets such as steam turbines, compressors

    and others found in the other industrial sectors. From the US DoE’s United States Industrial Electric

    Motor Systems Market Opportunities Assessment , the following tables show motor population

    distribution by size (or power), and by energy-consumption. The document is either 1998 or 2002, but

    little or no variation or departure from those percentages would have been expected between that

    study and the present, save perhaps a high proliferation of VFDs. Also, that same source states that 42%

    of motors drive pumps, the most common industrial machine, and some 19% drive fans.

     

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    Conclusions (from literature; see Appendix 1 and References) 

    From our literature and textbooks, we know and generally accept that misalignment will:

    - typically generate a mix of 1X, and/or 2X and/or 3X RPM in our FFT spectra,

    - “mix” in the previous statement means “any permutation thereof ” 

    - the exact response or behavior will depend on a long list of factors, including the type and severity of

    misalignment

    - more severe amplitudes will appear from sharper misalignment, but the relationship is typically non-

    linear and said relationship will depend on the various factors already listed, although it is possible to

    observe proportionality in some cases, or to see linearity over a limited range of misalignment severity

    - from the previous, due to a frequent lack of proportionality between misalignment severity and

    vibration amplitudes, quantifying the misalignment or its severity remains challenging in a significant

    percentage of cases

    - misalignment extremes (or for that matter, any other cause of extreme amplitudes, reactions or

    dynamic loads) may show behavior quite different from that of a more reasonable severity

    - the behavior from misalignment acting on an unbalanced rotor differs from that of misalignment acting

    alone Reference [11] partly covers those variants. Also see Appendix 2 on same topic.

    - as a generic statement, most looseness acts in the vertical, but vertical predominance can also mean a

    sharp vertical offset misalignment

    - other frequencies may appear, namely a) # of components within the coupling, and harmonics of

    same, b) multiple harmonics of 1X if sharp reactions occur due to severe misalignment, such as springing

    back or even impulses, c) evidence of rubbing or friction, characterized by 0.5X3 and/or 1.5X, but those

    are scarcer and typically tied to certain specific machine configurations or coupling types, and d) a

    subharmonic or subharmonic series linked to rubbing, mostly seen for elastomeric coupling inserts.

    - Phase analysis is deemed useful in confirming the misalignment diagnosis. Reference [4] demonstrates

    this at length. This writer would call phase analysis essential in this context. Accessibility or execution

    challenges of the past have mostly disappeared with the advent and wide availability of cross-channel

    phase. The 180o (and margin for error) out-of-phase behavior is a strong support to our diagnosis.

    - Given the presence of several forcing frequencies (Ff), or the wide-band excitation effect of impulses,

    we can expect one or more natural frequencies (Fn) of the structure or one of its components to show

    mild (or greater) resonant amplification. This reaction occurs anywhere (depending on Fn locations). It

    may add amplitude at or near a harmonic of running speed frequency.

    If, and likely ONLY if, test data has ever been conducted on a specific machine, or the machine has been

    modeled, we can assume that our misalignment predictions and diagnosis become very highly accurate

    when identical or closely related problems or faults appear.

    3 From experience, few instructors or reference works explain 0.5X adequately. The mathematical aspect does not

    instantly reveal its implication: 0.5X means the phenomenon occurs once per 2 rotations, which would fit well with

    a scenario of action-reaction such as a bouncing contact and then having time complete more than a full shaft

    rotation before returning to that same contact. Alternately, we may at times find an explanation in vibrating string

    theory, an area of study which is sorely neglected in CM/VA, yet finds its greatest pertinence in flexible and slender

    rotors. As to 1.5X, the reader will likely have concluded that the physical manifestation could be a harmonic of

    0.5X, with the contribution to 1X lost or covered up by usual 1X concerns, or 1.5X may well be a 3X vibration

    manifest every 2 turns of the shaft. The actual mechanism is case-dependent.

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    A Few Additional Considerations 

    Coupling Tolerance 

    Coupling manufacturers and vendors state acceptable tolerances, in terms of allowable misalignment,

    by type. What do those tolerances say? What do they mean? Such references ONLY define how much

    the coupling can withstand and still transmit mechanical power without quick or immediate failure ofthe coupling itself. It has nothing to do with a permissible quantity of misalignment on your machine.

    Belt-Drives 

    The purpose of this paper is not to address sheaves in particular, but on that topic, a few observations…

    Sheave misalignment can be marginally more forgiving than coupling misalignment, but other failure-

    types are possible. Sheaves exhibit a high-probability of eccentricity due to their manufacturing process.

    They are cast-iron pieces, with some machining. In fact, reports of 0.001” eccentricity by inch of

    diameter have been heard. So a 10” (25cm) sheave might be off by as much as 0.010” (250microns) 

    Unless using notched or toothed belts, 1:1 drive to driven is never seen, due to the almost inevitableslight belt slippage on the driven pulley/sheave. Since RPMs will still be very close in terms of value, both

    amplitude and phase interactions occur in spite of the small differentiation of RPM values. The rising

    and falling amplitudes are then accompanied by a wide phase fluctuation.

    Note: In such a case, the ratio can still be extremely close, such as 1:0.995, which then calls for

    Synchronous Time Averaging to separate the frequencies, or extremely high resolution. Interaction of

    the waveforms may still occur, though, meaning sympathetic or beat vibration. Such beat interaction

    can make balancing a challenge.

    An electric motor may have axial float or play to enable magnetic centering. When pursuing tight belt-

    drive alignment tolerances, the motor rotor’s position during alignment must be representative of

    working position.

    Seen: belt "tugging" from belt vibration can result in fatigue shearing of a shaft at the bearing entrance

    point (usually front of motor), and this is more readily seen on reciprocating machines. Longer shaft

    segment overhang from bearing to sheave may be a contributor. It is best to keep the overhang short.

    Belt dressing spray: a quick-fix solution to squealing belts and to slip, belt dressing can also be hazardous

    where an electric motor is operating at borderline due to ambient temperature, power transmitted or

    other undesirable circumstances (lower voltage, or unclean power, etc.). One case reported motor

    failure upon spaying the belts. Not quite the dressing’s fault, but certainly a tie-in to sudden increasedpower under already harsh working conditions.

    As to configuration, we might call them "elongated" or "parallel", and base mounting might be deemed

    shared (common structure) or independent.

    Gyroscopic Effect, Moment of Inertia & Effect on Response Direction 

    Readers will forgive the informal approach and utter lack of mathematical expression: the idea is to

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    make the phenomenon vivid, not to express it through formulae. As this is not a textbook, see Coriolis

    effect, gyroscopes and the like, even on Youtube, for complete explanations.

    From the spinning top to the toy gyroscope, the latter exhibiting a rotor with its mass highly

    concentrated at its outer radius or periphery, we can draw simple observations from childhood play or

    high-school physics experiences. The gyro usually comes with a little stand. When reaching the end of its

    cycle, the whole gyro rotor turns slowly around the stand while being suspended in mid-air, supported

    at one end by the stand, and at its other end by... nothing.

    What can we conclude? Other than the dynamic reaction, nothing is acting to turn the rotor around the

    pedestal, so that is part of the gyro effect. For a rotor in the field, that would mean a horizontal rotor

    (usually solely vertical static load) applying a horizontal radial load to one of its bearings.

    More importantly, and quite empirically, if the

    gyro remains suspended in mid-air, supported

    only at one end, we can conclude that the gyro

    effect can reach at least HALF of the static load

    (linked to rotor mass).

    If the rotor static load applied to the bearing gets

    "suspended", the shaft can do whatever it wants,

    meaning, the dynamic loads will command the

    shaft unhampered. As a note, a side effect is

    underloading of rolling-element bearing, leading

    to overheating, lack of lubricant film formation

    and early failure.

    Admittedly, the gyroscope rotor is purposely designed with greater peripheral mass, meaning a higher

    Moment of Inertia, to favor the “spinning top” effect. An equivalent mass distribution would be harder

    to find in real-world rotors.

    Thermal Bow, Critical Speed Deformation & Bent Shaft 

    This is a case where both imbalance and misalignment will be present, but the root-cause is the bow,

    which may otherwise be called an elastically (non-plastic, non permanent) bent shaft.

    The characteristic behavior will be 180 out-of-phase axial measurements, but on sleeve bearings, this

    may be challenging to measure or perceive. Radial phase (H with H, V with V) should be in-phase or

    having little phase discrepancy. And misalignment also occurs between driver and driven rotors.

    Those same symptoms can be introduced by a critical speed event (a resonance of the rotor) for the first

    lateral mode, when any forcing frequency (Ff) matches or closely approximates the critical speed value

    (Fn). How close the match needs to be to create deformation is dependent on damping.

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    On certain machines, maintaining slow rotation or having a prolonged period of same may be needed to

    either avoid an elastic deformation or to remove it if the shaft remained in the same position for too

    long. That would qualify as a temporarily bent shaft, can be removed with turning the shaft, and will

    show symptoms as described in the previous paragraph. Those symptoms appear for a plastically (or

    permanently) bent shaft.

    Critical Speed or Natural Frequency Excitation 

    2X RPM or 3X RPM component of a rotor’s vibration response, often from misalignment, can match a

    natural frequency Fn. The same can occur with a critical speed (a natural frequency) of the rotor. And as

    many have found out the hard way, having a VFD controller to move the RPM around can make such

    occurrences much more probable. For example, an overhung single-eye pump impeller driven by a 2-

    pole motor will typically have a first critical speed in the (roughly) 2300-2800 CPM range. A VFD will

    enable a match with RPM and of course the ensuing resonant amplification and rotor deformation.

    See reference [14] for a primer on Critical Speed matters.

    Misalignment Induced Vibration Response 

    As previously mentioned, several individuals and organizations conducted simulations and tests to

    document the effects of misalignment and the expected behavior resulting from same.

    What has mostly been left unsaid about these efforts is that conclusions drawn from such endeavors

    ARE applicable to the (exact or identical) test-rig or machine used in testing, but NOT NECESSARILY

    applicable to any other machine as a generalization. In fact, it is likely that altering any factor on the

    actual initial machine used in testing will yield changes in behavior.

    Stiffness, masses, configuration, power transmitted, function, base, foundation, lengths and distances,

    motor design, rotor design, actual RPM(s), misalignment severity, misalignment type, shimming, softfoot, coupling type, number of components in coupling, actual machine condition (such as any other

    interfering factor, bearing damage, looseness, other) and other factors (temperature, pressure,

    de/stabilizing effects, etc.) play a role in the final outcome.

    From [12], the following are examples of behavior patterns observed with

    the stated coupling type on a specific rotor-type, but is NOT meant to say

    "this behavior ALWAYS matches this type".

    The previous explains WHY we would rather state a fuzzy-logic approach

    instead of hard-set rules. An expectation of 1X, 2X and/or 3X in ANY

    permutation, plus number of coupling-component X RPM and harmonics,plus a possibility of multiple harmonics due to shocks or amplitude

    extremes, is likely the best "expected behavior" description.

    For those poor souls who worked exclusively in displacement units, back

    in the "old days", the previously described behavior might have gone

    unseen (3X 4-pole, or 3X 2-pole, means higher frequencies AND lower

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    displacement amplitudes at those frequencies). To a lesser extent, the same might be said of proximity

    probes.

    Long-span alignment: for mills, multiple rotors, kilns or line-shafts where still extant, alignment is not

    merely considered at the coupling or alternately, support locations. Some clutches can make the

    alignment of individual components quite challenging. Care must be taken to have support rolls (on akiln), dryers (on a paper machine), parallel and on the level (for some) or on a straight-line incline

    (where necessary by design). A long-range laser or theodolite may be needed to avoid having a winding

    snake instead of a straight-line.

    As to piping growth or shrinkage under normal process operation, or even masses, these will not be

    present when attempting to align a machine. This can result in severe static loads as pipes are pulled to

    match flanges with, for instance, a pump casing. Breakage can occur at the flange or casings can get

    fractured (pump casings are often cast, and are thus brittle or fragile). Upon tension release, the come-

    along or chain blocks used to impose a positional match will transfer static load to the casing.

    Checking Your Work  (the vibration pen rationale)

    This may work for certain machine configurations, such as belt-drives, but since the millwright will not

    be camping for 2 hours next to the machine, we can instantly grasp the inherent fallacy of solely

    measuring overall amplitudes right at the restart moment: for machines with any significant thermal

    growth, the latter is NOT achieved for some time, and the amplitudes SHOULD be higher until the

    machine components expand to their final position. A good example is the NEMA electric motor

    reception test, upon purchase or repair, where depending on size, the shop floor (as opposed to

    installed in the plant) unloaded reception test requires a prolonged period of operation sometimes

    measured in HOURS before the motor is deemed “warmed up” and stabilized,yet, the motor will never

    reach full-load temperatures. As a note, there are now pens that do allow for 800-line FFT spectrum

    collection to be downloaded to a PC.

    On the topic of LOOSENESS 

    True, there are several possible frequency components to looseness. And the analyst should ALWAYS

    endeavor to report WHERE the looseness occurs. IRD Mechanalysis may have been the original source of

    the so-called Type A, B and C looseness, which are descriptive. In the same order, 1X, then 2X, and then

    multiple harmonics (from banging, hammering, spikes). Keep in mind multiple harmonics from impacts

    are mostly fictitious (save for the fundamental) and the spectral peaks arise from a picket-fence effect.

    If the system can FOLLOW, looseness will most often be seen as 2X. This most likely occurs from 2

    events per rotation when the system "lands" and when it reaches its vertical stop. Otherwise, 1X will bethe dominant identifier. BOTH in the vertical direction (unless the machine structure ties the rotor down

    horizontally or on a slant). Often seen with soft foot / inadequate assembly cases.

    An inability to complete an event cycle during a single rotation, perhaps due to inertia, may allow for 2

    rotations before the event occurs anew. And that is 0.5X. On significant masses, the 0.5X is either

    unusual, or often so low in amplitude as to be difficult to perceive.

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     Appendix 1/ Misalignment Diagnostics Review from References

    In [1], Edwards, Lees and Friswell refer to… Sekhar and Prabhu (1995) discussed the effect of coupling

    misalignment on the vibration of rotating machinery. Shaft misalignment can be a major cause of vibration, due to

    reaction forces generated in the shaft couplings. It is generally accepted that a significant 2X vibration response is

    a major feature of bearing misalignment. A finite element model of the rotor-coupling-bearing system was

    developed and the effect of misalignment was introduced through a coupling-co-ordinate system. The model

    agrees well with empirical results, where the 1X response is not nearly as significantly affected as the 2X . By using

    this model it is therefore possible to predict the vibration response due to misalignment at the various harmonics -

    valuable in terms of both fault diagnosis and machinery design. Note: emphasis / bold is this writer’s hand iwork.

    From [2], Bloch & Geitner show a simplified model for parallel misalignment, and how the forced

    excursion provoked by the misalignment might produce 2X RPM vibration.

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    In [3], the authors clearly document the sharp rise in 1X and 2X amplitudes with increasing coupling misalignment for

    parallel and then for angular. For THEIR test rotor at that time, and graphed for 2 different RPMs.

    Take note of the significant difference in amplitude progression, where the 2X response to misalignment evolves

    much more rapidly for parallel misalignment as compared to angular misalignment.

    The authors conclude “The 2X vibration response clearly shows the characteristicsignature of misaligned shafts” 

    ,

    In [4], we see a case for which the authors’ rotor, fitted with a jaw coupling, clearly shows the 3X amplitude increases

    at their motor inboard horizontal as more severe misalignment is introduced.

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    From [5], the evolving amplitudes at 1X, 2X and 3X for increasing angular misalignment. Take note that

    the amplitude scale is in m/s2, or the equivalent of 1/10th of a g per division.

    For the specific rig or test rotor, fitted with a specified coupling, the 3X RPM amplitude increases as

    misalignment gets more severe. As a passing note, this writer (Gagnon) prefers to use peak velocity forthis frequency range. Something can be said of preserving a transducer’s native units (accelerometer)

    without integration, but this also skews the data in certain ways, alters our perception of amplitude

    severity, inflates the relative importance of higher frequencies and since a large percentage of analysts

    deal with CM data in velocity, relying on such units offers an easier correlate from experiments to field

    data machine behavior.

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    Appendix 2

     A Brief Exploration of the Consequences of Moving the Unbalance Vector Location Along a Machine Train 

    NOTE: use of this picture does not imply that the components are more, nor less, susceptible to

    imbalance or misalignment than any other commercially available components.

    Imbalance Location & Dynamic Load 

    We can imagine sliding the exact location of a punctual imbalance along the length of a direct-drive

    assembly. The response will vary since the (imaginary) point of application alters the lever effect, and

    thus, the reaction. This is merely meant as a thinking tool.

    Motor rear Fan: if the fan is out of balance, the reaction may be measurable on the ENTIRE motor if the motor is of

    small-size, but the reaction would otherwise be mostly localized at the rear of the motor. An exception

    can be found in cases where the motor base has low stiffness and allows the motor to pitch (as in

    pitch/roll/yaw) axially. The shaft may orbit at the inboard location, but the bearing benefits from the

    rotor length as a lever to control such movement.

    Still at the back, but in front of the bearing, as opposed to behind it:, provokes a reaction in both

    bearings, especially as we move towards the center, at which point we would expect reaction to be

    almost equal in amplitude in both outboard and inboard positions, presuming equal stiffness, with due

    consideration for the added mass/stiffness of the coupling and its influence at the inboard location.

    Special case: a tilted rotor or 2 distinct imbalance vectors will generate some axial vibration

    Special case 2: eccentric rotor (seen electrically) or bent shaft (180 out of phase axial measurements,

    plus electrical 2X Fl vibration)

    Special case 3: hot spot, causing a raised segment of the rotor, which then gets resolved dynamically as

    imbalance + 2X Fl (thermography useful in diagnosis). Usually signifies an urgent need for motor repairs.

    Worst case CAN deform the rotor to imitate a bent shaft.

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    Special case 4: the bent shaft, a fairly rare occurrence on a motor unless a long overhang at the inboard,

    a stiff coupling and severe loads contributed to that bend. A thermally induced bent shaft IS possible. A

    bend (as opposed to a kink, which is a localized deformation) introduces imbalance, some misalignment

    and some air-gap eccentricity.

    Motor front A highly localized imbalance at the front can be resolved balancing at the sheave or coupling, but the

    question remains: WHY is it locally out of balance? Often from improper key-size relative to keyway.

    Note: when considering rules applicable to response, one must seriously think about the inherent

    differences between a 10HP, 50HP, 100HP or 500+HP motor in terms of length, mass, stiffness, and how

    these relate to the base, and also, the foundation or support of said base.

    Coupling type, overhang distance to coupling 

    A severe imbalance manifest at the FRONT will introduce a parallel misalignment. A severe couple

    imbalance causing pitching may introduce a minor angular misalignment. Seen in the past: magnetic

    couplings, allowing for variable-speed (RPM), may introduce significant localized masses on both driver

    and driven shafts. This can affect rotor dynamics behavior. As they are unsupported, these may also

    have much lower natural frequencies (Fn), and each shaft with its coupling half behaves like a

    pendulum.

    Coupling 

    An imbalance vector at the coupling means equal phases to either side of it, if it is the only acting force,

    or if it is the dominant force in terms of a resulting vector, whereas amplitudes may differ (normally,

    slightly) due to differences in stiffness from motor to driven rotor. A coupling can only introduce a

    couple-effect if both coupling-halves are out of balance, the coupling is elongated and the imbalance

    locations are diametrically opposed (or close to it). Rare case.

    Couplings come in 2 states: working and locked. Locked usually means damage. Furthermore, it could be

    dry. Consider the difference in friction coefficient between lubricated steel-steel contact, and dry steel-

    steel contact (presuming of course that the components are made of steel), and then kinetic (sliding)

    versus static friction. Lubricated steel in movement will thus show friction = 0.03 (appr.), whereas dry

    sliding would see friction = 0.4. This next statement is an expedient fallacy, but serves to illustrate the

    mechanics in play. Imagine a 100HP (75kW) full-load motor: to maintain axial sliding movement in the

    (hopefully well lubricated) coupling, we must overcome the load from torque, so we might imagine that

    the axial load would be equivalent to 3% of 100HP. Or 3HP reciprocating motion at the coupling. IF the

    lubricant persists between the steel parts (while said lubricant gets centrifuged outwards, heats up,etc.). Should lubricant disappear, or grit appear from wear, we have a possibility of much greater axial

    thrust.

    To launch the movement would be harder since we then consider static friction.

    Driven-rotor (DR) inboard / DR center / DR outboard 

    Vector location progression more or less emulates the previous description of moving the vector(s)

    along, but in reverse from the motor (from front or inboard to back / outboard).

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    Eccentricity: if the rotor is in contact or interaction with solids, any eccentric effect becomes huge. This

    may be the case for electromagnetic, or liquid interaction as well. Unless severe pressures or high-

    density fluids are involved, aerodynamic (or gas) interactions is more forgiving.

    Between bearings / Overhung Rotor Considerations 

    For direct-drive overhung rotors, the static load is greater at the bearing closest to the drivenrotor, roughly 2:1. Gravity pulls the rotor downwards, and the bearing (and bearing cap especially)

    closest the coupling must pull the shaft down to maintain equilibrium.

    The dynamic response to imbalance involves a RATIO between the static load (and in some cases, quasi

    static loads introduced by the rotor's function) and the imbalance vector.

    Thus, an imbalance vector acting in the farthest plane of the overhung rotor has considerable effect on

    the inboard bearing (closest to the coupling): the imbalance gets leverage from the overhang length,

    and since the static load is lesser at that location, the response from the imbalance is more readily

    influenced (meaning a greater amplitude). Lower force, greater reaction, due to leverage.

    Belts alter the previous portrait. The belt tension becomes a significant static load contributor.

    For the pictured fan, the rotor sits between

    bearings, and thus, static loads are approximately

    equal at each bearing location (presuming even

    mass distribution and equal shaft lengths to

    either side of rotor center of gravity) and are

    applied downwards.

    Excessive vibration amplitude 

    If and when the amplitude is disproportionately huge, anything goes: knocking in the coupling, bearings

    knocking in the pillow (plummer) block, imbalance introducing misalignment, etc.

    Note: in such cases, appropriate questioning to grasp HOW we got there, and how quickly, can be of

    considerable help in establishing an accurate diagnosis.

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    References, with Some Commentary

    [1] Edwards, Lees and Friswell, Fault Diagnosis of Rotating Machinery  (Shock & Vibration Digest, Vol 30

    Number 1, 1998

    [2] H.P. Bloch and F.K. Geitner, Practical Machinery Management for Process Plants 2: Machinery failure

    analysis and troubleshooting, Gulf Publishing Company, 1986

    [3] Sekhar A.S. and Prabhu B.S., Effects of Coupling Misalignment on Vibrations of Rotating Machinery ,

    Journal of Sound and Vibration, 1995 

    [4] P N Saavedra and D E Ramírez, Vibration analysis of rotors for the identification of shaft

    misalignment Part 2: Experimental validation, Proceedings of the Institution of Mechanical Engineers,

    Part C: Journal of Mechanical Engineering Science 2004

    [5] G.R. Rameshkumar, B.V.A. Rao, K.P. Ramachandran, Coast Down Time Analysis to Analyze

    the Effect of Misalignment in Rotating Machinery , International Journal of Engineering and Advanced

    Technology (IJEAT), April 2012, where the authors examine the changes in CDT (Coastdown Time),

    essentially a parallel to start-up time performance sometimes recommended (by us) in

    consulting for large electric motors, recording the TWF, preferably for both current AND

    vibration. In the presence of constant or comparable conditions, an increasing start-up time

    points to deteriorating motor condition and warrants further investigation. Given the presence

    of a working blower on their set-up, the authors actually study a machine per say.[6] Lees, AW, Misalignment in Rigidly Coupled Flexible Rotors, Society of Experimental Mechanics, IMAC

    XXV Proceedings, 2007, where Dr. Lees states “…the misalignment has introduced cross couplingbetween torsional and lateral motion which implies that any synchronous variations in torque will bereflected in twice per revolution lateral vibration” and alluding to earlier work, “The 2X excitation is clear ”.

    Whereas an excerpt of his conclusions affirm “It has been shown that the linear model generatesresponses at harmonics of shaft speed .”, and “The harmonics are caused by an interaction of torsionaland flexural effects” 

    [7]] Redmond, I., Shaft Misalignment and Vibration - A Model , Society of Experimental Mechanics, IMAC

    XXV Proceedings, 2007. From his simplified model, Redmond concludes that:

    The equations provide insight to the situation where only shaft angular misalignment is present and,surprisingly, demonstrate that in these circumstances system vibration does not occur. The resultingstatic displacements lead to static loading of the supports and dynamic loading of the rotating elements.The presence of coupling skew, or rotating angular misalignment, leads to the introduction of an angulardisplacement-forcing function at a frequency corresponding to the rotor speed.

    The system equations show clearly that parallel misalignment introduces a static displacement in additionto fundamental-frequency (1X) lateral and torsional excitation components. A discrete second-harmonic(2X) torsional excitation term is also evident in the system force vector. The magnitude of this term isdirectly proportional to the support anisotropy and disappears for isotropic supports.

    The above effects are demonstrated through numerical analysis of the equations of motion for a range ofmodel parameters where it is confirmed that:

    •   Both angular and parallel misalignment introduce a static loading, or preload, to the system.

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    •    Angular misalignment alone produces only static system displacements. The introduction of transmitted

    torque reduces the shaft misalignment angle leading to greater imposed static forces.

    •   The presence of an angularly skewed coupling produces 1X shaft lateral response when isotropic

    supports are employed. The introduction of support anisotropy leads to 2X shaft axial response and 2Xloading of the rotating elements.

    •  

     

    Parallel misalignment alone produces both static and dynamic, multi-harmonic system response. The presence of parallel offset introduces torsional response occurring mainly at fundamental and secondharmonic frequencies. The resulting speed oscillations couple through to the system lateral motions and produce multi-frequency support and rotating element forces. Parallel misalignment also induces shaftaxial motion which is dominated by 1X and 2X response. Support anisotropy plays a major role indetermining system dynamic response, with greater divergence of support orthogonal stiffness valuesleading to increased dynamic response. Increasing the parallel offset results in an increase of the 1X and2X system dynamic response. The coupling angular stiffness is very influential in controlling the systemresponse, as would be expected, so that a reduction in this parameter leads to reduced dynamicresponse, for a given parallel offset.

     As far as the author is aware there is nothing in the literature outlining the relationship of angular and parallel misalignment with rotor vibration as demonstrated in this paper, particularly with respect to the

    importance of support anisotropy and lateral-torsional coupling in producing parallel misalignment-related2X vibration and the inability of angular misalignment alone to produce shaft vibration. 

    While the conclusion pertaining to the response, or lack thereof, triggered by the presence of angular

    misalignment contradicts much of the physical test measurements literature, as opposed to modeling,

    the author’s exploration of stiffness isotropy and anisotropy in terms of expected vibration reaction

    does expand the misalignment response knowledge-base. The comment does not seek invalidate

    Redmond’s conclusions about HIS model. 

    [8] Fakhfakh, Hili, Hammami, and Haddar,  Angular Misalignment Effect on Bearings Dynamical

    Behavior . Arabian Journal for Science and Engineering, June 2004

    The authors document the significant difference in response of a flexible versus a rigid coupling for, as

    the title suggests, angular misalignment. And the responses at 1X, 2X as well as response at their 

    system’s Fn, and some modulation sideband families spaced at 1X and 2X around the Fn. As a note in

    passing, the authors assumed this modulation was AM (amplitude modulation).

    [9] Chao-Yang Tsai and Shyh-Chin Huang, Vibrations of a Rotor System with Multiple Coupler Offsets,

    Transactions of the Canadian Society for Mechanical Engineering, Vol. 35, No. 1, 2011

    The authors conclude… “TMM (note: where TMM means Transfer Matrix Method) derivation and

    numerical results in the present studies revealed the offset induced the rotor’s lateral response at

    the same frequency as rotational speed (1X) and that was unlike most other research wheremultiple integer (n X) components were found. Though reference [17] obtained results similar to

    the present paper and concluded the absence of 2X components mainly due to no consideration of

     bearing non-linear effects and shaft asymmetries.” -  Note: Bold emphasis by Gagnon

    [10] Nakhaeinejad, M., Ganeriwala, S., Observations on Dynamic Responses of Misalignments,

    SpectraQuest Inc., Tech note, 2009, explore the vibration response differences with a number of test

    rotor and coupling variants.

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    [11] Patel, T.H. and Darpe, A.K., Vibration Response of Misaligned Rotors, JSV 325, 2009 

    [12] Unknown author, Turvac Corp., Why Shaft Misalignment Continues to Befuddle and Undermine Even

    the Best CBM and Pro-Active Maintenance Programs, maintenancerecources.com, Oct 2008

    [13] Lorenc, J.A., Changes in Pump Vibration Levels Caused by the Misalignment of Different Style

    Couplings, Proceedings 8th

     Pump Symposium, Texas A&M, 1991

    The author has a marked advantage with the use of a test bench at Gould Pumps, Inc., facilities. The

    pump is driven by a 100HP, 2-pole motor, with the pump at BEP. And tests ensue for steel couplings

    (flexing beam, grid, gear and disc) and elastomer (shear x 2, compression, flexing beam x 2). This is a

    good case to reinforce earlier discussion of test rotor versus actual machine.

    Of note, a) for one coupling, the initial aligned vibration amplitude at 5X (linked to one elastomeric

    coupling’s construction) DECREASED as misalignment increased, b) elastomeric couplings being more

    forgiving of misalignment, save for extremes, c) extremely sharp amplitude increases for metallic

    couplings once a threshold was reached, d) one case of 3X & 6X, due to coupling construction, and e)one example of a harmonic series corresponding to the most severe misalignment (see below).

    Note: the seemingly

    unaffected spectral

    contents in spite of

    increasing parallel

    misalignment severity,

    until a threshold value (the

    worst misalignment) is

    reached.

    [14] Swanson, E., Powell, C.D., Weissman, S., A Practical Review of Rotating Machinery Critical Speeds

    and Modes, Sound & Vibration, May 2006

    Other references deemed absorbed over time might be Buscarello, R., Berry, J., Eshleman, R., and B&K

    books are all noteworthy in that respect.

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    Author’s Bio / François (Frank) Gagnon

    Nearly 40 years in Condition Monitoring & Vibration Analysis,

    studied mechanical engineering, built, managed, executed and

    optimized dozens of CM programs in all industrial sectors, first

    instructed a course in ’84, participated in various committees,

    contract trainer for Entek IRD, TA and Update, has own curricula &

    audit process, instructs Intro through Level 3/Cat IV, plus Asset

    Management / Reliability and CM/VA Advanced & focused topics.

    Certification held or lapsed: ASNT VA Central Lvl 3 (equivalent to but

    more stringent than Cat IV), Entek/TA VA I, II, & III, VI Lvl 1.

    Resolved thousands of cases, multilingual, at ease in metric or US/Imperial, current in reliability & Asset

    Management tasks & PdM/Reliability integration, published papers (Shock&Vibration Digest, VI Annual

    Meeting Proceedings, CMVA Annual), managed projects, consulted / instructed in 25+ countries

    At the end of a training session, it is typical to tender an evaluation form, asking participants for

    feedback, opinion, suggestions. That may exceed the scope of a white paper, but any feedback is still

    welcome and appreciated. Send at [email protected] 

    Training Customized to your Needs / REMOTE Consulting & Support 

    Get an instructor who DID spend extensive time on the floor. 

    In pulp & paper, to touch upon one sector and its specific assets (not meant to be exhaustive): refiners,

    pulpers, agitators (not the political kind), fan-pump, headbox, forming table, fourdrinier, felt life, paper

    machine structures, dryer section, or Yankee dryer for tissue, presses, vacuum pumps, winder,

    conversion equipment, embossing rolls, break problems, quality or profile versus prior event, etc.

    Elsewhere, we will find roasters, grinders, mills, rolling or other, catalytic cracking compressors,

    centrifugal, screw and reciprocating compressors, root blowers, machine tools, gas, steam and hydraulic

    turbines (hydro are strange beasts), test benches, generators, DC motors, in-line or master/slave,

    alternators, diesel engines, excavators, shovels, digesters, batch mixers, rotary kilns, ball mills, SAG mills,

    crushers, shovels, excavators, pneumatic tools, synchronous & DC motors, asynchronous & VFDs, rolling

    mills, wire drawing machines, and the whole catalog of fans, ID or FD, blowers and pumps, canned,

    vertical, barrel, high-speed, high-pressure, boilers and combustion, etc.

    Courses / English, French, Spanish, Portuguese 

    Introduction (Cat. I), and Cat. II through IV, as per ISO 18432-2 compliant certification, or ASNT

    Advanced Topics

    PdM / CBM Program Management & Audits

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      6402 25th Avenue, Montreal, Quebec, Canada H1T 3L6

    Tel: 1 (514) 727 2084 / www.vibra-k.com / [email protected]

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    Time Waveform / Asynchronous Motors & VFDs / Machinery Acceptance Testing (New, Rebuilt,

    Procurement) / Phase Analysis ^ODS / Basic Modal & FEA

    Physical Asset Management Tasks / Exemplary Practices