SHEAR AND NORMAL STIFFNESS OF MIXED LIQUID-SOLID CONTACTS R S Dwyer-Joyce Department of Mechanical Engineering, University of Sheffield, Sheffield, S1 3JD M Gonzalez Valadez Department of Mechanical Engineering, University of Sheffield, Sheffield, S1 3JD ABSTRACT When a wave of ultrasound strikes an interface between two bodies some proportion of the wave amplitude is reflected. A rough surface interface with a low real area of contact will reflect more ultrasound. This is the case for both normal and shear modes of ultrasound. If the ‘gaps’ in the contact are filled with liquid, then more of a longitudinal wave is transmitted through the interface. However, the shear wave should remain unaffected, since it is virtually all reflected at a solid liquid boundary. It is the stiffness of the interface that controls the response. Measurements of reflection can readily be used to determine the interface stiffness. In this work a series of experiments has been performed to measure the reflection of both normal and shear ultrasound from both dry and wet rough contacts. This gives information about the normal and shear stiffness of dry contacts. When the layer is flooded with a liquid the stiffness of the liquid part alone can be deduced. This can be used to determine the film thickness in mixed lubrication. The shear stiffness was found to reduce with the application of a liquid; this is caused by the presence of asperity micro-slip at the interface. INTRODUCTION In boundary or mixed lubrication surfaces may not be completely separated by the oil layer. In such conditions, load will be partially supported by the contacting surface asperities and partially by the lubricant film. The proportion of solid contact controls the friction and influences the wear experienced by the machine elements. In this work, ultrasound is used to examine the nature of the mixed liquid-solid contacts under pressure. Shear and longitudinal ultrasonic pulses have been reflected from mixed liquid solid interfaces. The recorded reflections are used to investigate the contact conditions and to determine the proportion of solid contact. Ultrasound has proved to be a useful method to study the in-situ characterisation of dry [1,2] and lubricated [3] surfaces in contact. The reflection coefficient (the proportion of the wave amplitude reflected), R depends on the stiffness of the interface, K according to a simple spring model: 2 2 1 1         + = z K R ω where ω is the angular frequency of the ultrasonic wave (ω=2πf), and z is the acoustic impedance of the media either side of the interface. This relationship is applicable for both normal and shear ultrasonic waveforms. Lubricated contact p p p p K liquid K solid = Figure 1. Modelling of a mixed contact by means of two springs in series. For a mixed liquid solid this stiffness will have two components (see figure 1): solid liquid total K K K + = The liquid part is given by: h B K = σ and 0 = τ K where, B is the bulk modulus of the liquid and h is the liquid film thickness. The subscripts σ and τ stand for normal and shear respectively. The solid stiffness part is governed by the surface deflection under traction: z u p K d d − = σ and x u q K d d − = τ where p and q are the normal and shear tractions, and u z and u x are the normal and tangential surface displacements. 1 Copyright © 2005 by ASME Proceedings of WTC2005 World Tribology Congress III September 12-16, 2005, Washington, D.C., USA WTC2005-63793