Gear Noise and Vibration Episode 2 Part 7 potx

As far as noise is concerned, the use of a coupling is usually advantageous since those couplings which use rubber blocks as the torque transmitting units have flexibility for both torsi

Fig 16.12 Sketch of vibration responses and paths.

In practice, because measuring inside the gearbox is very difficult, it

is probably better to rely on T.E excitation when running or to estimate the internal resonances The reciprocal theorem is of limited help since, although

it may help for cross receptances P13 and p23, it does not assist access for Pj2

or the local responses Pn and P22 which need access inside the box in zero space In some cases the wheel is so massive and its support is so stiff that wheel response may be ignored, simplifying the algebra considerably

16.7 Coherence

Whichever method (b), (c) or (d) is used for measuring a transfer function with a transfer function analyser, it is worthwhile checking coherence

if there is any possibility of background noise, whether mechanical or electrical The idea of coherence is that if we take a single transfer function measurement we can deduce a transfer function However, we do not know how much of the output is really due to the input and how much is due to random external (or internal) disturbances

Repeating the test many times and getting exactly the same result in both amplitude and phase would suggest that there is little random effect Any variation would suggest randomness Coherence analysis routines carry out this check and compare how much of the measured output power (at a

Vibration Testing 261

particular frequency) can be attributed to the consistent transfer function A coherence of 1 suggests that output is firmly connected to input but < 0.5 suggests that random noise is dominating the measurements Any results with coherence < 0.8 should be viewed with suspicion Even if there are two vibrations whose coherence is 1 it is not necessarily true to say that the output

is "due to" the input since both vibrations may have been generated by another unknown input In particular a panel vibration may not be caused by the vibration at a bearing housing because both may have been caused by vibration from another bearing or even from a separate slave drive To carry out a coherence check it is necessary to take multiple tests, typically eight It is not possible to get a meaningful result from a single test because it is necessary to check whether the result is consistent over time

Extra care should be taken when impact testing because even though the responses may be consistent from test to test there is a greater likelihood of non-linearity This in turn will lead to false deductions since a high response

at one frequency may in fact be due to excitation at, say, one-third of the frequency encountering a non-linearity

Couplings

17.1 Advantages

Couplings in a system are rarely fitted initially with a thought to their effect on noise The most common requirement is that the coupling must accommodate misalignments which may be due to manufacturing or assembly errors but are often due to the effects of differential thermal growth, which can

be surprisingly large A temperature difference of 40°C can easily occur between a turbine casing and a gearbox and if the centre height is 1 m the corresponding differential expansion is 0.4 mm (16 mil) Axial growth can also present problems since a motor gearbox combination in a medium-sized (400 kW) installation with a distance of 4 m between foundation attachment points and a temperature rise of 50°C can expand axially by 2 mm

As far as noise is concerned, the use of a coupling is usually advantageous since those couplings which use rubber blocks as the torque transmitting units have flexibility for both torsional and lateral vibrations The steel diaphragm type of coupling, usually used in pairs with a short torque shaft in between, is torsionally stiff but laterally flexible

Toothed gear couplings are short and light and have lateral flexibility and, in theory, axial flexiblity but like diaphragm couplings have high torsional stiffness

In most installations the transmission of gear noise along the input or output shafts is not important as there is likely to be a large inertia for load or driver and so vibrations will be absorbed by the inertia Typically this occurs

on a car where any torsional vibrations from the gearbox encounter either the high inertia of the engine or of the wheels In the case of the wheels there is also the filtering effect of the propshaft flexibility to attenuate vibration

The exceptions to this occur when there is a large propeller or turbine which can act as a very effective radiator of noise On naval ships the propeller has a large surface and the vibration frequencies are high so that any vibration will radiate powerfully and betray the ships position Under these circumstances it is critical that some form of very flexible coupling is used for isolation of both lateral and axial vibration

A similar requirement occurred recently with the installation of wind turbines for "renewable energy" purposes Early designs did not consider that

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noise would be a problem as the installations were meant to be away from dwelling houses They made the mistake of connecting the propellor directly

to a gearbox which was chosen for low cost rather than low vibration The result was that the relatively large vibrations at 1/tooth and harmonics were transmitted straight through to the propellor This acted as a remarkably efficient loudspeaker with a very large surface area and produced a gear whine which could be heard miles away The eventual solution was not only to use high quality gears and reduce propellor dynamic flexibility but to isolate the propellor from the gearbox with a soft rubber torsional coupling In addition,

of course, the gearcase had to be effectively isolated from the supporting tower which could also act as a noise radiator At the other end of the drive there was no problem as the high inertia of the generator absorbed all vibration very effectively

17.2 Problems

The problems associated with rubber couplings are usually at low frequencies where either the torsional flexibility of the coupling gives a torsional resonance at a frequency too near the running speed or the mass of the coupling brings whirl speeds down into the operating range This effect on whirl speed can of course also occur with diapraghm couplings

It is difficult to carry out accurate predictions because the properties of rubber couplings are not well documented This is partly due to production variations which give a surprising spread of rubber hardness which can vary some ± 20% so that it is possible to find a "soft" unit which is stiffer than a

"hard" unit of the same design, hi addition the characteristics of the filled natural rubber which is usually used vary at low amplitudes both in the stiffness and the damping factor as well as varying with frequency Typically dynamic stiffness may be 40% higher than the figures quoted by the manufacturer (as they are given for low frequency response)

Reliable information can be obtained by using a back-to-back rig to give an exact replica of operating conditions as indicated in Fig 17.1 High drive torque is applied statically, then the intermediate ring is oscillated torsionally at the correct (low) level using two opposed exciters mounted tangentially and is measured using two tangential accelerometers It is necessary to mass correct for the moment of inertia of the intermediate ring

Torsional couplings, like conventional vibration isolators, may also have been designed and installed with the main objective being to isolate I/rev and 2/rev vibration and so may be ineffective for the much higher frequencies

of gear noise

Couplings 265

I

sandwich plate coupling ;coupling w,.

torque arm

accelerometer

sandwich plate I

accelerometer

Fig 17.1 Back-to-back test rig for torsional stiffness under working torque.

The high static torque is applied by the torque arm, which is then locked

reverse drive block

working

block

reverse drive block

Fig 17.2 Sketch of axial view of coupling with axes offset

17.3 Vibration generation

Couplings are capable of producing unexpected results by injecting torsional excitation or modulating existing gear noise

The most common problem occurs when a simple rubber block coupling is used to connect two shafts which are slightly offset The effect is shown diagrammatically in Fig 17.2

If there are four rubber blocks the load should be taken by two of the blocks in each direction With offset, the load is not taken evenly by the two blocks and with hard rubber or low loads, one of the blocks takes all the torque and there is clearance on the other block for half of the rev then the other block drives for the other half of the rev The resulting error is as shown in Fig 17.3 and with an amplitude peak-to-peak equal to the offset acting at block radius Alternatively manufacturing tolerances can give once per rev errors

Couplings 267

1 revolution

Fig 17.3 Torsional transmission error with offset.

Assembly of a drive motor onto a worm and wheel gearbox with conventional tolerances can easily involve an offset and runout of 100 jam and this can appear as either a I/rev or 2/rev effect according to the type of error

Any attempt to measure T.E under these circumstances will give (at 1/tooth or 2/tooth) an apparent gear error of the order of the offset and so possibly a factor of 10 larger than the true gear errors This effect can occur to

a limited extent with higher numbers of blocks but will be small if all the blocks are under sufficient load to be in contact all the time so that the system remains linear

Diaphragm couplings are preferably radially symmetric and so will not inject torsional vibrations into a drive but the trailing link type of coupling needs to have more than two links to be self centering and so to be satisfactory when used at each end of a torque shaft

Gear tooth couplings can produce some very unexpected results They are radially symmetric and so we would expect a smooth drive with no injection of extra frequencies They will in practice run vibration free when they are perfectly aligned and also when they are badly misaligned Vibration problems can arise when they are only slightly misaligned

In a gear tooth coupling there are friction forces as sketched in Fig 17.4 and there will also be some bending elasticity in the drive shafts There are two extreme cases

Fig 17.4 Sketch of gear tooth coupling Friction forces are controlled by axial

velocity and thus generate a couple to bend the drive shafts out of the page

Near perfect alignment allows the coupling to lock up as the friction is sufficient to bend the shafts so that there is no relative axial motion at the meshing gear teeth and there is no vibration excitation apart from a I/rev bending on the shafts Significant misalignment gives continuous sliding at the coupling gear teeth and thus no significant vibration injection The problem arises with small misalignments which will initially bend the drive shafts because there is not sufficient force to overcome the axial friction at the teeth but after perhaps one-third of a revolution the friction will be overcome and there will be an axial slip at the teeth This effect will inject a disturbance into the drive at 3/rev, altering the shaft bending at this frequency and so disturbing any neighbouring gear mesh at this frequency This can lead to the modulation of the gear noise frequency so that noise occurs at tooth frequency plus or minus 3/rev Deliberate alteration of the misalignment may change the slip frequency higher or lower or it may disappear completely

As far as testing T.E is concerned it is much safer to test the gear drive separately without any couplings in place to get the basic gear information then, if the couplings are suspect, to test the complete assembly Unfortunately this must be done under load as otherwise the friction forces will not be correct

Failures

18.1 Introduction

Although this book is predominantly about gear noise, it is of interest

to discuss the various failure mechanisms to see which might be connected to noise and which are not As may be deduced from the comments in Chapter

15, there is in general not much connection

18.2 Pitting

Pitting arises from traditional Hertzian contact stresses giving failure

as a result of a fatigue process The standard theory [1] gives the results that for line contact, i.e., cylinder to cylinder with load P'/unit length, the maximum contact pressure p0, and the semi contact width b, will be

1 _ 1 1

Effective curvature ~R~~R~ + ~R~ where Rj and R.2 are the radii of curvature.

1 _ l ~ v l 1 ~ V

E 1 2

moduli and Poisson's ratio, and suffixes 1, 2 refer to the two bodies in contact The maximum shear stress is then tmax = 0.300 po at x = 0, z = 0.79b

This leads to a maximum shear stress occuring typically about 0.5 mm below the surface and giving fatigue cracks which, for traditional pitting, travel initially horizontally then curve upward toward the surface When they reach the surface a hemisphere of steel breaks out leaving the classical pit which is typically 1 mm diameter and 0.5 mm deep

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o o o 5

root

Fig 18.1 View of tooth flank with pitting.

The simple static theory suggests that pitting will be at its worst where stresses are highest because the effective radius of curvature is smallest, which is when contact is toward the root of the pinion but this is not what happens The pitting occurs initially very near but not exactly on the pitch line where sliding velocities are low and the typical pattern is sketched in Fig 18.1 In cases where a gear pair is significantly misaligned the pitting will concentrate on the highly loaded areas The result is an area of metal removal which is sometimes called spalling [2] Whether the term spalling should be used for this localised heavy pitting is debatable as it was formerly used for the rather different failure when the

"skin" of an inadequately carburised gear peels off, giving an effect labelled as case/core separation in the AGMA 1010 The flake pitting [2], which is sometimes encountered, is similar and may also be caused by faulty carburising

Pitting depends on fatigue and so is a relatively slow process which in most cases stabilises Occasionally the loadings are too high for the material and the pitting progresses and covers the whole gear surface but even this serious deterioration is unlikely to produce "gear" noise because as mentioned in Chapter

15 the frequencies are very high and tend to be reflected or to be absorbed before reaching panels which could radiate noise

18.3 Micropitting

Micropitting (sometimes called gray staining) has become more important recently, possibly as a result of greater use of case-hardened gears and changes in manufacturing techniques It has similarities to conventional pitting but occurs on a much smaller distance scale and occurs at slightly lower loads than pitting Unlike conventional pitting, it tends to spread and progress and may start anywhere on the flank