A new diagnostic technique for asperity contact

J. D. Smith

Investigations into high frequency gear vibration have given a diagnostic technique which shows asperity interactions. Smith shocks are generated at the contacts and can be detected using high frequency accelerometers to give a measure of the number and intensity of the contacts.

Keywords: asperities, contact, gears, wear, Smith shocks

Introduction

In the tribology of surfaces which are lubricated but which wear, there is great interest in the exact mechanism of the metallic contact between the surfaces. The wear may be beneficial, as in running in to give better surfaces, or it may be harmful and lead to scuffing, scoring or pitting.

The contact loads between the surfaces may be at low pressures, of the order of 5 MPa as in a conventional hydrodynamic bearing, or may rise to 1500 MPa, as in highly loaded gear teeth. In the first case the surface deformations are small and the surfaces can be assumed to be effectively rigid. In the- la t te r case there is elastohydrodynamic lubrication in which the oil film is of constant thickness, typically about 1 p~m and there is elastic (Hertzian) deformation of the surfaces. In either case it is customary to estimate the oil film thickness assuming that the surfaces are smooth and to measure the surface roughnesses to give the peak positive metal heights relative to the average position of the surfaces, shown as a and b in Fig 1. The ratio between the 'asperity heights' and the nominal film thickness gives a measure of the likelihood of contact between the asperities. The ratio is called A and is

Fig 1 Sketch o f asperity contact, h is the mean oil film thickness and a and b are the asperity heights above the surface mean levels

Engineering Department, University of Cambridge, Trumpington Street, Cambridge CB2 I PZ, UK.

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often expressed in terms of the Centre Line Average (CLA) roughness rather than the peak heights which, for an unworn ground surface would be about three times the CLA value. A simple expectation would be that as soon as the sum of the asperity heights on the two surfaces exceeded the film thickness, as in Fig 1, then asperity contact and wear would occur. In practice the situation is much more complex and, as yet, not fully resolved since the directional properties of the surface roughnesses are very important for the oil film thickness. In addition, the local elastic deformations of the asperities caused by local pressure variations give suppression of peak heights 1.2.

For research and for monitoring components, in practice it would be a great advantage to know when asperity contact occurs and to have a measure not only of the rate at which contacts occur but also their intensity. So far, this information has not been available but a new technique being developed for gear monitoring appears to provide this combination.

Existing methods

Optical methods of detecting asperity contact necessi- tate the use of a transparent surface which is a severe practical limitation. The associated video scanning techniques which would be necessary to catch dynamic effects can operate fast but are expensive.

Electrical contact methods are used with limited success. Typically, in a disc testing machine, one rotating (disc) surface is isolated electrically by mount- ing its rolling bearings in insulating rings and driving through a plastic or rubber coupling and the other surface is earthed. Measurement of the resistance across the contact should indicate whether a metal-to- metal asperity contact is 'shorting' the isolated surface to earth. In practice, the results are rarely clear-cut. One technique is to use a DC voltage between the surfaces and to detect any current flow. The voltage that can be used is, however, rather small since it is too easy to break down the oil film. The permitted voltage gradient in oil is of the order of 2 kV mm 1. If the nominal oil film thickness is 1 ~m and it is assumed, arbitrarily, that a film of less than 0.1 ~m

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J. D. Smi th--A new diagnostic technique for asperity contact

represents contact then the voltage should be less than 100 mV and, as currents should be kept low to prevent damage to the oil, high impedances are desirable. The system will have a capacitance of the order of 1000 pF and the combination of resistance and capacitance gives a fairly slow response. This relatively slow response time would allow detection of slow moving contacts but, if a relative sliding speed of 10 mm s ' is used with asperity peak widths of the order of 1 ~m, the contact time is 0.1 ms and so a simple direct current system will not be fast enough for detection. There is an additional problem that the resistance of a relatively large area of oil film, perhaps 0.2 ~m thick, may be of the same order as the resistance of a point contact between surfaces of a metal such as steel, which has significant resistivity. This can make the establishment of a sharp dividing criterion between 'contact' and 'non-contact ' difficult.

Another complication arises if the oil is operating under realistic conditions and is not clean. A 1 p~m gap between the surfaces, bridged by a 1 ~m metallic debris particle, will conduct just as well as a proper 'asperity' and so it is not possible to differentiate between the two cases. Although a solution is to use clean oil, this may give unrealistic testing conditions and involves very fine filtering of the oil, ideally to about 0.1 ~m.

An alternative approach to the contact problem is to use an alternating voltage, possibly in a bridge circuit. This approach can be very sensitive and noise-free but is again limited in response speed. The major problems are again the unclear distinction between contact and non-contact and the effects of oil contamination bridging the gap.

Shocks

During investigations on torsional gear vibration measurement techniques, gears were run under load with accelerometers fitted on the rotor. This is unusual due to the difficulty of mounting the accelerometers and of transmitting signals from accelerometers which are only generating about 10 pC of charge; normally, accelerometers are mounted on bearing housings. Test results obtained by Vergottis in 1983 showed some vibration at frequencies of the order of 30 kHz- - the resonant frequency of the accelerometers. However, the vibrations were not regular from tooth to tooth and did not occur at all under some operating conditions.

Detailed investigations, theoretically and practically, eliminated other possible causes such as 'pitch circle impulse '~ and 'engagement impulse '4. This left metallic contact as a possibility and further tests confirmed that this hypothesis fitted the observed facts. Estimation of elastohydrodynamic oil film thicknesses at the gear contact gave values of the order of 1 ~m, typical for the high pressures encountered in gear contacts. Surface roughnesses were high, initially of the order of 3 i~m so that there would have been much asperity contact. The major contribution to the CLA roughness was at relatively long wavelengths compared with a contact width of less than 100 ~m and the surface was

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ridged from the manufacturing process at right angles to the sliding direction so that there was additional hydrodynamic action over the ridges. The surfaces ' r an - in ' and the roughness value then halved but the lubrication was probably still dominantly not hydrodynamic.

The test which gave final confirmation that the shocks were due to asperity contact involved testing soft (ie non-hardened) surfaces at a given torque level, doubling the torque level for a while to 'run in' the surfaces, ie to remove or deform some of the higher asperities, and then returning to the original torque level. The observed vibrations increased when the torque was increased, as would be expected, then reduced below the initial levels when the torque was returned to the original level.

Observed vibrat ions

The basic hypothesis is that an asperity contact generates a Smith shock which travels to the accelerometer(s). In practice, it was found that it was preferable to use accelerometers with a higher resonant frequency than normal but not so high that the charge output from the accelerometer dropped to undetectable levels.

Testing of the accelerometers was carried out by dropping small (3 ram) ball bearings onto the gear and matching roughly the amplitude and character of response obtained when running. Figure 2 shows a vibration trace obtained. Similar traces can be obtained by hitting with an instrumented hammer but these are less repeatable and tend to give longer pulses. The trace obtained is not the simple exponentially decaying vibration expected but an extremely complex shape, presumably due to multiple reflections of the initial pulse within the rotor, resulting in a series of pulses of varying amplitude arriving at the accelerometers at varying times. The accelerometers then 'ring' at their natural frequency of 50 kHz. The standard check of a 25 mm drop gives an estimated pulse duration of 15 ~s and a peak force of the order of 2 N ; the corresponding amplitude at the accelerometers is about _+ 1.4 g. Although the original pulse may be only 15 p~s long the complexity of reflections gives a trace lasting about a millisecond.

Of interest is the very short time that is required for the pulse, much less than 1 ms, suggesting that the shocks from the gears have a pulse rise-time of the order of 10 its. With sliding and rolling velocities in the tooth contact of the order of 500 mm s ~ and asperities perhaps some 5 ~m wide at the top, the contact time between asperities is of this order.

Fig 2 Observed vibration due to ball impulse. Peak amplitude is 1.4 g and total trace time is 2 ms

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J. D. Smi th- -A new diagnostic technique for asperity contact

" " ' [ " " t . . =_aJ~.,~lL, . ~ , J ~ , l ~ . . k ] , L ~ n ~ L l e L ~ ,L -k . . . . . . . . . .

r jl' I - . . , , . , . , , . , , , ,

b

Fig 3 (a) Observed vibration at 13 Nm torque; and (b) observed vibration at 26 Nm torque. Both traces are 5 ms (1 tooth pitch) long for the same teeth and maximum amplitude is +-1 g for (a) and +-2 g for (b)

A question arises as to why these Smith shocks have not been noted previously and used for monitoring purposes or for contact research. The reason is that the bearings supporting a rotating system effectively filter out high frequency vibrations so that shock effects due to asperities are below ambient noise levels. A ball in a rolling bearing acts as a vibrating system with the mass of the ball restrained by the two supporting Hertzian contact stiffnesses. Typically, the natural frequency is of the order of 20 kHz, reducing as size increases, and the vibration well above this frequency is attenuated. Hydrodynamic oil films have a low compliance and, at the two interfaces between oil and steel, have modulus ratios of the order of 15 to 1. This high modulus ratio gives, predominantly, reflection of pulses rather than transmission through the interface.

Meshing of two 80 mm PCD 'industrial quality', ie rather rough, gears gave traces as shown in Fig 3(a), under light load (13 Nm torque) and Fig 3(b), under double the load. The traces were taken without stopping the test rig so that temperatures did not have time to vary. The effect of increased load can be seen in both the size of the bursts of vibration and the number of bursts. The traces show the same pair of teeth in contact with a time span of 5 ms.

Varying the speed produces much more complex effects which require further investigation. Some preliminary results were published without permission by a student 5 but due to the lack of experimental control were not reliable and led to incorrect deductions.

Deductions It appears that detection of the short pulses associated with metal-to-metal contact could be a sensitive method of determining when such contact occurs.

Contact between surfaces can occur without generating pulses if there is no relative motion at the contact so this approach will not be of use for static contacts.

A complication which can arise occurs if there is dirt present in the oil since if a metallic particle is large enough to bridge the gap between the surfaces, there will be a pulse generated. In a repetitive system such as a gear drive, debris effects will be intermittent and irregular whereas surface-to-surface contacts will occur regularly for some time until surface peaks have been worn away. A time-averaging technique will allow separation of the regular effects from the intermittent loose debris effects.

The observed pattern of vibration recorded from a single impact is sufficiently long, varied and compli- cated that it is extremely difficult to decide whether an observed response as in Fig 3 is due to a single large pulse or several small pulses. More sophisticated analysis techniques could, in theory, be used to separate out multiple pulses provided that transfer functions remain consistent. This latter provision will never strictly be true since pulses originate from different points on a surface and hence will have varying transfer functions.

Testing with an exact 1:1 ratio, as in these tests, is not typical and so non-synchronous tests will be needed to allow more general deductions.

It should be possible to reduce asperity contact frequency by increasing film thickness and reducing speed in a disc machine to allow observation of a single contact for comparison with test impulses. As yet, knowledge is very limited about the effects of speed but the sensitivity of the method suggests that it would be advisable to make provision for measurement of these shocks when designing any new lubrication test rigs.

Acknowledgements Thanks are due to the staff at Cambridge and in particular to Professor K. L. Johnson on the lubrication aspects and to Mr F. Dolman for his help on the rig design.

References 1. Johnson K.L. and Spence D.I. Determination of gear tooth

friction by disc machine. Tribology International, 1991, 24 (5), 269-275

2. Sutcliffe M.P.F. Traction measurements in mixed elastohydrodyn- amic lubrication with a controlled circumferential roughness. Proc. Inst. Mech. Eng. 1991, 205 C, 265-273

3. Soden A.G. Gear testing apparatus and a study of gear noise. VDI Zeit. 1933, March 4, 231

4. lshida K. On the friction noise and pitch circle impulse noise of a gear. JSME 'Gearing', Semi-international symposium, 1967, 161, paper 318

5. Echeverria-Villagomez J.S. Gearbox monitoring: a new approach. ISATA 25th Conference, Florence, 1992, paper 920862

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