Rayleigh Wave Interactions with Tribological Contacts Eng Seng OOI Thesis submitted for the degree of Doctor of Philosophy Department of Mechanical Engineering University of Sheffield March 2015 Summary The use of ultrasonic reflectometry is a proven method of condition monitoring machine systems. The working principles are simple. A burst of ultrasonic signal is sent to the interface of interest where reflection of the signal takes place. The manner in which reflection takes place depends on the properties of the interface. As such, the reflected signal carries information regarding the interface that can be extracted with proper techniques. However, the use of ultrasonic reflectometry in condition monitoring is not without its limitations. Conventional ultrasound techniques make use of ultrasonic bulk waves that travel through the body of a given material. Problems arise when the medium through which the wave travels is attenuative. This prevents any passage of ultrasonic signals as most of the energy will be absorbed by the material. In addition, most components have complex designs, requiring that the signal pass through multiple interfaces before reaching the interface of interest. Reflections occur at these intermediate interfaces, reducing the overall energy content of the signal. In order to overcome these issues, the use of Rayleigh wave as an alternative is researched in the work carried out here. Instead of having to travel through the bulk of the material, Rayleigh waves function by propagating along the free surface of the said material, thereby circumventing the existing issues with the use of conventional bulk waves. The research here was carried out to seek an understanding of how Rayleigh waves interact with a contact interface. This was performed on three separate fronts. First, a novel analytical model was developed by modelling the contact interface as a series of springs. It is discovered that the stiffness of the springs are directly proportional to the reflection coefficient of the Rayleigh wave incident upon the interface. The implication of this finding is that rough interfaces will have a lesser reflection coefficient (due to decreased stiffness), with a perfectly smooth interface giving the maximum reflection coefficient obtainable from a particular interface. This was then followed by studies performed using both finite element simulations as well as experimental work. Data from all three studies (analytical model, finite element simulations and experimental work) were compared against each other and it was shown that a good agreement exists between all three methods. Exploratory work on lip seals were performed in order to research the potential of using Rayleigh wave as a condition monitoring tool. By measuring the delay in the time of arrival of a Rayleigh wave pulse reflected from the sealing zone, it is possible to measure the extent of misalignment that is present in a lip seal. Axial misalignments of the lip between 6mm to 8mm were successfully measured. Additional work in measuring the degradation of a lubricating film via evaporation was qualitative in nature, with the amplitude of the reflected pulse slowly decreasing as the layer of fluid at the sealing zone diminishes via evaporation. i Contents Summary ........................................................................................................................................ i Contents ........................................................................................................................................ ii Acknowledgements ....................................................................................................................... v Nomenclature ............................................................................................................................... vi 1 Introduction ................................................................................................................................ 1 1.1 Problem Statement ............................................................................................................... 1 1.2 Aims and Objectives ............................................................................................................ 2 1.3 Thesis Layout ...................................................................................................................... 2 2 Background of Ultrasonic Techniques ....................................................................................... 4 2.1 Introduction .......................................................................................................................... 4 2.2 Ultrasonic Physics ................................................................................................................ 4 2.3 Common Applications of Ultrasonic Waves........................................................................ 5 2.4 Ultrasonic Applications in Tribology .................................................................................. 8 2.4.1 Ultrasound Theory ..................................................................................................... 12 2.5 Practical Aspects of Ultrasonic Applications in Tribology ................................................ 14 2.6 Conclusions ........................................................................................................................ 16 3 Background of Rayleigh Waves .............................................................................................. 17 3.1 Introduction ........................................................................................................................ 17 3.2 Rayleigh Wave Generation ................................................................................................ 20 3.3 Properties of Rayleigh Waves ............................................................................................ 25 3.3.1 Attenuation Due to Absorption and Scattering .......................................................... 25 3.3.2 Attenuation Due to Geometric Spreading .................................................................. 26 3.4 Rayleigh Waves in Practice ............................................................................................... 26 3.5 Engineering Applications of Rayleigh Waves ................................................................... 28 3.6 Conclusions ........................................................................................................................ 30 4 Rayleigh Wave Reflection – Literature Review ...................................................................... 31 4.1 Introduction ........................................................................................................................ 31 4.2 Sources of Rayleigh Wave Reflection ............................................................................... 31 4.2.1 Reflections Due to Changes in Material Topography ................................................ 32 4.2.2 Reflections Due to Surface Changes of the Medium ................................................. 36 4.3 Conclusions ........................................................................................................................ 38 ii 5 An Analytical Model of Rayleigh Wave Reflection from an Interface ................................... 39 5.1 Fundamental Rayleigh Wave Equations ............................................................................ 40 5.2 Response of the Interface Due to Incident Wave Components WI and UI ......................... 40 5.3 Deriving Reflection Coefficient ......................................................................................... 42 5.4 Interface Stiffness .............................................................................................................. 43 5.4.1 Stiffness Due to Asperity Interactions ....................................................................... 45 5.4.2 Stiffness Due to Bulk Deformation ............................................................................ 48 5.4.3 Tangential Stiffness.................................................................................................... 49 5.4.4 Prediction of R from Kσ, τ ............................................................................................ 50 5.5 Analytical Results .............................................................................................................. 50 5.5.1 Stiffness and Reflection Coefficient .......................................................................... 50 5.5.2 Relationship between Reflection Coefficient and Stiffness. ...................................... 52 5.6 Discussion .......................................................................................................................... 53 5.7 Conclusions ........................................................................................................................ 54 6 A Finite Element Study of Rayleigh Wave Reflection from an Interface ............................... 55 6.1 Background ........................................................................................................................ 55 6.2 Geometry of the Model ...................................................................................................... 56 6.3 Meshing.............................................................................................................................