Elastohydrodynamic film thickness response to harmonic vibrations

Transcription

1 Elastohydrodynamic film thickness response to harmonic vibrations Konstantinos KALOGIANNIS, Cristinel MARES, Romeo P. GLOVNEA School of Engineering and Design, Brunel University Kingston lane, Uxbridge, UB8 3PH United Kingdom and Stathis IOANNIDES SKF Research and Development Company BV Kelvinbahn 16, 343DT Nieuwegein, The Netherlands ABSTRACT Many machine components, which work in the Elastohydrodynamic (EHD) lubrication regime, including transportation bearings, reciprocating engines, geared transmissions also experience vibrations, which result in a rapid variation of contact load or entrainment speed. The bearings supporting the main spindle of machine tools are subjected to vibrations generated by the cutting process, the gearbox, geometrical inaccuracies and also vibrations from the surrounding environment. It is very important to understand how these vibrations affect the functioning of the bearings supporting the main spindle, in order to maintain the desired precision and accuracy of the cutting process. The present study uses optical interferometry to monitor the response of the EHD films to forced harmonic vibrations. The contact is formed between a transparent disc and a ball pressed one against the other at desired loads. The disc is coated with a thin chromium layer and a silica layer, on the face contacting the ball. White light is shown onto the contact through a specially built microscope. The interferometric fringes formed by the rays reflected by the chromium layer and by the ball s surface are captured by a high speed CCD camera. These images are subsequently analysed and converted to film thickness maps, according to calibration curves. Keywords: elastohydrodynamic lubrication, harmonic, vibrations, bearings, film thickness, optical interferometry. 1. INTRODUCTION Many practical machine components including gears, rolling element bearings, cams and constant velocity joints operate in the lubrication regime known as elastohydrodynamic lubrication (EHD). In this regime, lubricant film thickness and pressure depend on the coupled effects of surface motion, surface elastic deformation and the rheological response of the lubricant to the very high local pressures and shear stresses in the contact. Despite this complexity, EHD lubrication in steady-state conditions is now quite well-understood. Numerical and experimental studies agree quite closely and design rules have been developed to predict both film thickness and contact pressure [1-5]. Unfortunately EHD-lubricated contacts rarely operate in steady-state conditions. In many machine components, speed, load or geometry vary cyclically, in most vibrations are present, while all experience the unsteadiness of start and stop. Thus mechanisms like cams, gears and constant velocity joints are designed to perform over working cycles where load, geometry or entrainment speed change continuously. In rolling elements bearings the load varies very rapidly as the rolling element enters or exits the loading area. The effect of transient phenomena on the lubricant film behaviour in EHD contacts has received a merited attention during the past two decades. This was driven, on one hand by the progress made in the numerical techniques, and on the other hand by the development of fast imaging experimental methods. From the experimental point of view many studies

2 have focused on the effect of the variation of entrainment speed, the micro-geometry of the surfaces and of load. It has been shown that rapid variation of entrainment velocity is accompanied by a squeeze effect on the film, due to rapid decrease or increase of the film thickness, with two main consequences [6-8]. One is that the film thickness does not fall to zero together with a momentarily stop of the speed, which will cushion the surfaces against direct contact. The second consequence is that film perturbations formed in the inlet will travel through the contact, affecting the local pressure and possible affecting the fatigue life of the components. Early theoretical and experimental studies of elastohydrodynamically lubricated contacts applied to smooth surfaces and when the inlet geometry is constant in time. In practice real surfaces of machine components, are on a smaller or larger extent rough. Various experimental studies have shown that, depending on the average lubricant film thickness, the asperities are deformed inside the contact, at the same time creating a film perturbation, due to the alteration of the geometry in the inlet. It has also been found that even on small areas at the tip of asperities, mechanisms similar to those which take place at macro scale, allow the formation of micro-elastohydrodynamic films, which will still separate the metallic surfaces, even if the average film thickness is lass than the combined height of asperities [9, 1]. Wijnant and co-authors report a comparative, experimental and theoretical, study on the effect of vibrations upon the thickness of an EHD circular contact [11]. The main conclusion is the need to include both, squeeze and entrainment effects in analyses of vibrational components. The is no quantitative comparison in their analysis, and although the load is applied in a transient, in a step-like fashion and not in a repetitive way. They conclude that, for the analysis of vibrations of rolling elements bearings, it is more appropriate to derive models for individual EHD contacts and to apply those to dynamic models of bearings. Ciulli and Bassani [12] carried out an experimental study of the effct of vibrations and noise on lubricated non-conformal contacts. They conclude that there is a connection between the variation detected of the friction force and the fluctuations of the film thickness. It was difficult to extract any quantitative relations between vibrations and the behaviour of the film, as those vibrations were randomly created by inaccuracies of the experimental apparatus, and thus impossible to control. El Kilali and co-workers also described incipient results of their study on the behaviour of lubricated contacts under dynamic normal forces [13]. Sakamoto et al [14] measured the film thickness in both, static and rolling contacts, under pulsating loading. They show that film thickness fluctuations are dependent on the entrainment speed, but hardly depend on the slide/roll ratio. Glovnea and Spikes [15] studied the oscillations of the EHD film due to a sudden variation of the entrainment speed. As the two, contacting bodies together with the loading system and the lubricating film form an elastic/viscous system, when taken out form the quasi-equilibrium conditions, will respond by a showing dampened oscillations of the thickness of the film. To be noted that those oscillations can be considered free vibrations, as they take place under constant loading. In the present study an elastohydrodynamic film is established, under a constant load, and thereafter this load is varied in a controlled, sinusoidal fashion, thus a forced vibration system is obtained. 2. EXPERIMENT Experimental setup The method for measuring the EHD film thickness, used in this study is optical interferometry. In this method, initially developed in early sixties [4] and then extended to very thin film region [16], the contact is established between a transparent flat and highly reflective ball or roller. A schematic of the experimental apparatus is seen in Figure 1. The glass disc, one hundred millimetres in diameter, is coated with a semi-reflective chromium layer and a silica layer on the loaded surface. White light is directed through a microscope towards the contact, the reflected rays from the chromium and ball surfaces recombine to interfere constructively or destructively depending on their wavelength.

3 High speed CCD camera Glass disc Microscope White light Steel ball White light Chromium layer Silica layer Load cell Glass disc Elastic beam Steel ball EHD film Constant loading system Figure 1. The experimental setup Piezo actuator As it has similar refractive index to the lubricant, the silica layer acts like a solid lubricant, increasing the separation between the two solid surfaces and thus allowing separations down to few nanometres to be measured. The principle of this method is seen in Figure 2. In the present experiment only the disc is driven by an electrical motor, while the ball is driven by the friction forces at the interface, giving a nominally pure rolling relative motion in the contact. The ball, 19.5mm diameter, is firstly statically loaded through a lever and plunger system, at a desired load. Between the lever and the plunger there is placed an elastic beam, calculated in such a way that its critical buckling load is well above the loads employed in these tests. The oscillatory motion is generated by a piezo-actuator which, on the push stroke creates a deflection which has the effect of diminishing the load acting on the contact. On the pull stroke the elastic forces in the beam act to restore the geometry of the beam and thus the load on the contact. In this way a sinusoidal, oscillatory load with values between 2N and 3N was applied to the elastohydrodynamic contact. Figure 2. The principle of optical interferometry Testing materials parameters and procedure The lubricant used in these tests is a polyalphaolefin with a viscosity of.43pas at the temperature of the tests. The entrainment speed, defined as the average of discs and ball speeds, is.15m/s. A graph of the steady state film thickness versus entrainment speed, used for the calibration purposes, is seen in Figure Entrainment speed [m/s] Figure 3. Steady state film thickness versus speed

4 The Hertzian pressure in the contact varied between.51gpa and.58gpa, while the frequency of the oscillations was set to 1Hz, 5Hz and 1Hz. The disc and ball were thoroughly cleaned with analar toluene and iso-propanol, dried and attached to the rig. The ball was loaded in static conditions to a load of 3N and images were captured, which were subsequently used to estimate the thickness of the silica spacer layer. Then the power source of the piezo-actuator was switch on and static contact images were captured at all three working frequencies. The disc and ball were thoroughly cleaned with analar toluene and iso-propanol, dried and attached to the rig. The ball was loaded in static conditions to a load of 3N and images were captured, which were subsequently used to estimate the thickness of the silica spacer layer. R,G,B values Red Green Blue Figure 4. Film thickness versus RGB, calibration curves In the next step, lubricant was added in the working chamber and the disc was set in motion, under steady loading conditions, after which the power source of the piezo-actuator was switched on again and images were recorded at 1, 5 and 1 Hz. The interferometric images of the contact were captured by a high speed CCD camera, at a rate of 3 frames per second and downloaded to a PC computer for analysis. 3. RESULTS AND DISCUSSION The coloured images, which are in fact maps of the thickness of the contact, were converted to film thickness values, for every pixel of those images, according to calibration curves seen in Figure 4. Figures 5a to 5e show profiles of the film thickness along the rolling direction, for the 1Hz tests. Only one in four measured points are shown, for the clarity of the graphs. It is well known that the elastohydrodynamic film thickness is established in the inlet of the contact and depends on the entrainment speed, lubricant viscosity and piezoviscosity coefficient inlet geometry and on a much lesser extent on the load. At the same time, due to the law of mass and flow conservation, any perturbation of the film thickness generated in the inlet will subsequently travel through the contact unchanged. Moreover, the flow is predominantly Couette, which means that the perturbations in the film travel at a velocity equal to the average velocity of the contacting surfaces. An increase of load has an effect of increasing the contact diameter and at the same time modifies the convergence in the inlet. This in turn will generate an enhanced film thickness perturbation, as shown in Figure 5b, which then travel along the contact. For the given load variation, frequency and lubricant properties, the enhanced film is no more than about 15nm thickness as it seen in Figure 5d. A constriction is then formed behind the enhanced film in order to balance the load and the pressure over the contact area, which in its turn will travel towards the exit of the contact. This sequence is reversed during the period when the load decreases and the cycle repeats itself. At the lower frequencies used in this tests 1Hz and 5Hz no significant film thickness variation has been detected. There may be three elements which coupled, can explain this behaviour. The average film is relative thick and as Sakamoto and co-workers have found [14], in thick film conditions the inlet film perturbation does not form. Secondly the load variation was relatively small and thirdly the frequency and thus acceleration was not large enough to significantly disturb the conditions of film formation.

5 a d b e c Figure 5. Film thickness along rolling direction for 1Hz For the present conditions the film thickness variation is relatively small, but they still create local fluctuations of the pressure in the contact, which affects, periodically the contacting elements surfaces. These fluctuations, which can be significant for larger load variations, may have a negative impact upon the contact fatigue durability of the elements. 4. CONCLUSIONS This paper show initial results of a wider study on the behaviour of elastohydrodynamic contacts subjected to vibrations.

6 Optical interferometry, coupled with high speed imaging, have been used to measure film thickness in contacts sinusoidally varied load conditions. The results show that for the largest frequency employed, 1Hz, film perturbations are formed in the inlet, due to the variation of load, which subsequently travel through the contact at the average speed of the surfaces. The film thickness variation is not very significant, but it generates fluctuations of the pressure, with potential effect upon the fatigue life of the contact. 5. REFERENCES [1] A.N. Grubin and I.E. Vinogradova, 1949, Fundamentals of the hydrodynamic theory of lubrication of heavily loaded cylindrical surfaces, (in Russian) Central Scientific Research Institute for Technology and Mechanical Engineering, Book No. 3, Moscow, D.S.I.R Trans. No. 337 [2] D. Dowson and G.R. Higginson, 1959, A numerical solution to the elastohydrodynamic problem, J. Mech. Eng. Sci., Vol. 1, pp [3] B.T. Hamrock and D. Dowson, 1977, Isothermal elastohydrodynamic lubrication of point contacts. Part III. Fully flooded results, Trans. ASME J. Lub.Tech., Vol. 99, pp [4] A. Cameron, and R. Gohar Theoretical and Experimental Studies of the Oil Film in Lubricated Point Contacts. Proc. Roy. Soc. London A291, 1966, pp [5] M.M.A. Safa, and R. Gohar Pressure Distribution under a Ball Impacting a Thin Lubricant Layer. Trans. ASME, J. of Tribology 18, 1986, pp [6] H. Nishikawa, K. Handa and M. Kaneta, 1995, Behavior of EHL Films in Reciprocating Motion, JSME International Journal, Series C, Vol. 38, No.3, pp [8] R.P. Glovnea and H.A. Spikes, 21, Elastohydrodynamic Film Collapse During Rapid Deceleration Part I: Experimental Results, ASME Trans. Journal of Tribology, 123, 2, pp [9] M. Kaneta, and H. Nishikawa, 1999, Experimental study on micro -elastohydrodynamic lubrication, Proc. IMechE., Vol 213, Part J, pp [1] J.W. Choo, A. V. Olver and H.A. Spikes, 27, The influence of transverse roughness in thin film, mixed elastohydrodynamic lubrication, Tribology International, 4, pp [11] Y.H. Wijnant, C.H. Venner, R. Larsson and P. Ericsson, 1999, Effects of structural vibrations on the film thickness in an EHL circular contact, Trans. ASME, J. Trib., 121, pp [12] E. Ciulli and R. Bassani, 26, Influence of vibrations and noise on experimental results of lubricated non-conformal contacts, Proc. IMechE., Vol. 22, Part J., pp [13] T. El Kilali, J. Perret-Liaudet and D. Mazuyer, 24., Experimental analysis of a high pressure lubricated contact under dynamic normal excitation force, Transient Processes in Tribology, Elsevier, pp [14] M. Sakamoto, H. Nishikawa and M. Kaneta, 24, Behaviour of point contact EHL films under pulsating loads, Transient Processes in Tribology, Elsevier, pp [15] R.P. Glovnea and H.A. Spikes, Oscillations Induced in EHD Films Thickness by a Step in Entrainment Speed, Lubrication Science, 15-4, 23, (15), [16] G.J. Johnston, R.C. Wayte and H.A. Spikes, 1991, The measurement and study of very thin lubricant films in concentrated contacts, Tribology Transactions 34, pp [7] J. Sugimura, W.R. Jr. Jones and H.A. Spikes, 1998, EHD Film Thickness in Non-Steady State Contacts. ASME Trans J. of Tribology 12, pp