B. W. Drinkwater

A Study of the Interaction between Ultrasound and a Partially Contacting Solid--Solid Interface

The measurement of the reflection of ultrasonic waves from a partially contacting solid-solid interface can be used to study the contact conditions at that interface. This paper describes measurements and predictions of the reflection of ultrasonic waves from partially contacting aluminium-aluminium interfaces, performed in the low frequency regime where the wavelength of the ultrasound is large compared to the size of the gaps. The proportion of the incident wave which is reflected at the interface (the reflection coefficient) was measured as a function of frequency with a single wideband ultrasonic transducer. When load was applied across the interface three regions of contact can be seen; no contact, partial contact and perfect contact. In the no contact region the measured reflection coefficient was unity at all frequencies. In the partial contact region the measured reflection coefficient increased with frequency. No measurements were taken in the perfect contact region in which the reflection coefficient is known to be zero at all frequencies as this state is the same as a continuous piece of aluminium. The reflection coefficient variation with frequency was modelled using a spring model, good agreement between experiments and predictions being achieved. Reflection coefficient measurements were then used to study the contact between two aluminium surfaces under repeated loading and unloading cycles. Plastic flow on first loading was evident while subsequent loading cycles revealed largely elastic behaviour. Both elastic and plastic statistical contact models, as well as a numerical contact model, were used to predict the variation of interfacial stiffness with pressure. These models agreed qualitatively with the experimentally determined stiffness variations and the predicted stiffness was within an order of magnitude of the measured value in all cases.

The measurement of lubricant-film thickness using ultrasound

Ultrasound is reflected from a liquid layer between two solid bodies. This reflection depends on the ultrasonic frequency, the acoustic properties of the liquid and solid, and the layer thickness. If the wavelength is much greater than the liquid–layer thickness, then the response is governed by the stiffness of the layer. If the wavelength and layer thickness are similar, then the interaction of ultrasound with the layer is controlled by its resonant behaviour. This stiffness governed response and resonant response can be used to determine the thickness of the liquid layer, if the other parameters are known. In this paper, ultrasound has been developed as a method to determine the thickness of lubricating films in bearing systems. An ultrasonic transducer is positioned on the outside of a bearing shell such that the wave is focused on the lubricant–film layer. The transducer is used to both emit and receive wide–band ultrasonic pulses. For a particular lubricant film, the reflected pulse is processed to give a reflection–coefficient spectrum. The lubricant–film thickness is then obtained from either the layer stiffness or the resonant frequency. The method has been validated using fluid wedges at ambient pressure between flat and curved surfaces. Experiments on the elastohydrodynamic film formed between a sliding ball and a flat surface were performed. Film–thickness values in the range 50–500 nm were recorded, which agreed well with theoretical film–formation predictions. Similar measurements have been made on the oil film between the balls and outer raceway of a deep–groove ball bearing.

Operating Limits for Acoustic Measurement of Rolling Bearing Oil Film Thickness

An ultrasonic pulse striking a thin layer of liquid trapped between solid bodies will be partially reflected. The proportion reflected is a function of the layer stiffness, which in turn depends on the film thickness and its bulk modulus. In this work, measurements of reflection have been used to determine the thickness of oil films in elastohydrodynamic lubricated (EHL) contacts. A very thin liquid layer behaves like a spring when struck by an ultrasonic pulse. A simple quasi-static spring model can be used to determine the proportion of the ultrasonic waves reflected. Experiments have been performed on a model EHL contact between a ball and a flat surface. A transducer is mounted above the contact such that the ultrasonic wave is focused onto the oil film. The reflected signals are captured and passed to a PC for processing. Fourier analysis gives the reflection spectrum that is then used to determine the stiffness of the liquid layer and hence its thickness. In further testing, an ultrasonic transducer has been mounted in the housing of a deep-groove ball bearing to measure the film generated at the outer raceway as each ball passes. Results from both the ball-flat and ball bearing measurements agree well with steady-state theoretical EHL predictions. The limits of the measuring technique, in terms of the measurable rolling bearing size and operating parameters, have been investigated.

An ultrasonic approach for contact stress mapping in machine joints and concentrated contacts

The measurement of pressure at a contact in a machine part is important because contact stresses frequently lead to failure by seizure, wear or fatigue. While the interface might appear smooth on a macroscale, it consists of regions of asperity contact and air gaps on a microscale. The reflection of an ultrasonic pulse at such a rough contact can be used to give information about the contact conditions. The more conformal the contact, the smaller is the proportion of an incident wave amplitude that will be reflected. In this paper, this phenomenon has been used to produce maps of contact pressure at machine element interfaces. An ultrasonic pulse is generated and reflected at the interface, to be received by the same piezoelectric transducer. The transducer is scanned across the interface and a map of reflected ultrasound (a c-scan) is recorded. The proportion of the wave reflected can be used to determine the stiffness of the interface. Stiffness correlates qualitatively with contact pressure, but unfortunately there is no unique relationship. In this work, two approaches have been used to obtain contact pressure: firstly by using an independent calibration experiment, and secondly by using experimental observations that stiffness and pressure are linearly related. The approach has been used in three example cases: a series of press fitted joints, a wheel/rail contact and a bolted joint.

A study of the transmission of ultrasound across real rough solid-solid interfaces

A link between reflection coefficient, surface roughness and interfacial pressure is described for the case of elastic contact, the example chosen being contact between rubber and metal or plastic. This case is of practical interest for the dry coupling of ultrasonic transducers using a rubber contact tip. Real measured surface profiles are used in a numerical elastic contact model to predict the size and distribution of contacts and gaps between two contacting bodies under a given load. In addition to this modelling, reflection coefficients from rubber-solid interfaces have been measured at varying contact pressures. From the combination of the contact model and these experimental results, the variation of reflection coefficient with size and distribution of contacts and gaps (percentage contact) can be found. Results are presented for contact between surfaces of different roughness. These results are then compared with the predictions of various simple quasi-static models of the interface such as the Balk and Thompson representation

An Ultrasonic Wheel Probe Alternative to Liquid Coupling

Ultrasonic testing involves the generation of waves in a transmitting transducer, the passage of the waves from this transducer into the testpiece, passage through the testpiece often involving one or more reflections, and return to either the transmitting transducer (pulse-echo mode) or a separate receiving transducer (pitch-catch mode).

High frequency measurements of the contact between machine elements using ultrasound

This paper describes a study of the experimental interaction of ultrasound with real rough surfaces, and the modeled interaction of ultrasound with an infinite array of holes, using Finite Element Analysis, in an attempt to discover the limit of applicability of the quasi-static spring model. The relationship between reflected amplitude of the scattered wave, and the size of the hole acting as reflector, was found and used to create a finite element independent scatter model. This was compared to the quasi-static model and it was found that the two models diverge at a ka value of approximately 0.6.

Towards an ultrasonic mapping of the contact pressure within an engineering component

A technique has been developed by which the stiffness of an interface can be measured by the reflection of ultrasound from that interface. Ultrasound is an ideal measurement medium, because it is non-invasive and has good transmission through most solids, irrespective of their electrical, magnetic, optical or surface properties. Interface stiffness is a function of both contact pressure and surface roughness. The technique has been used to scan across some typical model engineering contacts. Stiffness scans are presented for several Hertzian ball-on-flat contacts, between 650 and 480 microns in diameter. Due to the finite focal diameter of the 25MHz ultrasonic transducer, the measured profile is significantly blurred. These measured profiles are compared to theoretical pressure profiles and mathematical convolutions of these pressure profile. Good agreement is found between the measured and convoluted profiles. With future mathematical analysis, this data should provide a true measurement of the contact pressures within an engineering component.

Ultrasonic characterization of the contact of components in machine elements

This paper describes a study of the use of ultrasound to measure the pressure between two machine elements in contact. Relationships between ultrasonic reflection coefficient and pressure have been found both empirically and via a numerical contact model. These relationships were then used to calculate the contact pressure distribution, over a ball-flat contact. Excellent agreement was found between the calculated contact pressure distribution and that predicted by Hertzian contact theory.

The stiffness of graphite-graphite joints: Ultrasonic investigation and modelling

Large assemblies of graphite blocks are a feature of many nuclear reactors, and the seismic response of these assemblies are determined by the blocks’ static and dynamic behavior. The load-deflection relationship of these blocks can be influenced by surface roughness effects and is dependent on the nature of the interface between blocks. Ultrasonic reflection coefficient measurements are used to investigate the stiffness distribution of this interface under various loading conditions. A quasi-static model of the interface was adopted, allowing the interfacial stiffness to be measured as a function of applied load, sound frequency, surface roughness and graphite composition, for which issues of high attenuation and granular scattering were addressed and overcome. This method was also used to study the distribution of the load across large face areas. Cyclical loading of the graphite-graphite interface has also been carried out—giving information on the elastic/plastic nature of the contact and an insight i...