scholarly journals Linear and Nonlinear Normal Interface Stiffness in Dry Rough Surface Contact Measured Using Longitudinal Ultrasonic Waves

2021 ◽  
Vol 11 (12) ◽  
pp. 5720
Author(s):  
Saeid Taghizadeh ◽  
Robert Sean Dwyer-Joyce
Keyword(s):  
Rough Surface ◽  
Contact Pressure ◽  
Ultrasonic Wave ◽  
Bulk Material ◽  
Nonlinear Differential Equations ◽  
Small Deformation ◽  
Ultrasonic Waves ◽  
Solid Contact ◽  
Interfacial Stiffness ◽  
Linear And Nonlinear

When two rough surfaces are loaded together contact occurs at asperity peaks. An interface of solid contact regions and air gaps is formed that is less stiff than the bulk material. The stiffness of a structure thus depends on the interface conditions; this is particularly critical when high stiffness is required, for example in precision systems such as machine tool spindles. The rough surface interface can be modelled as a distributed spring. For small deformation, the spring can be assumed to be linear; whilst for large deformations the spring gets stiffer as the amount of solid contact increases. One method to measure the spring stiffness, both the linear and nonlinear aspect, is by the reflection of ultrasound. An ultrasonic wave causes a perturbation of the contact and the reflection depends on the stiffness of the interface. In most conventional applications, the ultrasonic wave is low power, deformation is small and entirely elastic, and the linear stiffness is measured. However, if a high-powered ultrasonic wave is used, this changes the geometry of the contact and induces nonlinear response. In previous studies through transmission methods were used to measure the nonlinear interfacial stiffness. This approach is inconvenient for the study of machine elements where only one side of the interface is accessible. In this study a reflection method is undertaken, and the results are compared to existing experimental work with through transmission. The variation of both linear and nonlinear interfacial stiffnesses was measured as the nominal contact pressure was increased. In both cases interfacial stiffness was expressed as nonlinear differential equations and solved to deduce the contact pressure-relative surface approach relationships. The relationships derived from linear and nonlinear measurements were similar, indicating the validity of the presented methods.

Effects of Friction on Contact of Transverse Ground Surfaces

1994 ◽  
Vol 116 (3) ◽  
pp. 430-437 ◽  
Author(s):  
J. B. Mann ◽  
T. N. Farris ◽  
S. Chandrasekar
Keyword(s):  
Rough Surface ◽  
Contact Pressure ◽  
Smooth Surface ◽  
Bulk Material ◽  
Elastic Half Space ◽  
Material Surface ◽  
Asperity Contact ◽  
Hertz Contact ◽  
Effective Stresses ◽  
Subsurface Stress

The two-dimensional plane-strain sliding contact of a smooth rigid roller on a transverse ground rough surface is analyzed. The rough surface is idealized as an elastic half-space with periodic roughness modeled as cylindrical ridges oriented transverse to the sliding direction. The contact problem is solved using a numerical iterative method in which each asperity contact is treated as a micro-Hertz contact, and the exact treatment of asperity interaction is included. The subsurface stress field is calculated using Westergaard stress functions. The subsequent analysis compares the rough surface stress fields with the corresponding smooth Hertz contact to evaluate the influence of surface roughness and friction on the subsurface stress distributions. The results show that the real area of contact is less than the corresponding smooth surface Hertz contact area, and the magnitude of the actual localized maximum contact pressure is always greater than the corresponding smooth surface contact pressure. The asperity level subsurface effective stresses are greater in magnitude than the maximum subsurface stress due to the macro-Hertz contact for low coefficients of friction, and for high coefficients of friction the maximum effective stresses occur on the bulk material surface.

Ultrasonic Test on Recycled Concrete: Relationship among Ultrasonic Waves Velocity, Compressive Strength and Elastic Modulus

2014 ◽  
Vol 894 ◽  
pp. 45-49 ◽  
Author(s):  
Luisa Pani ◽  
Lorena Francesconi
Keyword(s):  
Compressive Strength ◽  
Elastic Modulus ◽  
Ultrasonic Wave ◽  
Ultrasonic Test ◽  
Ultrasonic Waves ◽  
Recycled Concrete ◽  
Recycled Aggregates ◽  
Experimental Program ◽  
Static Modulus ◽  
Cylindrical Samples

In this paper an experimental program has been carried out in order to compare compressive strength fcand elastic static modulus Ecof recycled concrete with ultrasonic waves velocity Vp, to establish the possibility of employing nondestructive ultrasonic tests to qualify recycled concrete. 9 mix of concrete with different substitution percentage of recycled aggregates instead of natural ones and 27 cylindrical samples have been made. At first ultrasonic tests have been carried out on cylindrical samples, later elastic static modulus Ecand compressive strength fchave been experimentally evaluated. The dynamic elastic modulus Edhas been determined in function of ultrasonic wave velocity Vp; furthermore the correlations among Ed, Ec, fce Vphave been determined. It has been demonstrated that ultrasonic tests are suitable for evaluating different deformative and resisting concrete performances even when variations are small.

Design Optimization of Ultra-Low Flying Head-Disk Interfaces Using an Improved Elastic-Plastic Rough Surface Model

2006 ◽  
Vol 128 (4) ◽  
pp. 801-810 ◽  
Author(s):  
Allison Y. Suh ◽  
Sung-Chang Lee ◽  
Andreas A. Polycarpou
Keyword(s):  
Rough Surface ◽  
Contact Pressure ◽  
Surface Model ◽  
Successful Implementation ◽  
Contact Conditions ◽  
Friction Forces ◽  
Interfacial Forces ◽  
Elastic Plastic ◽  
The Mean ◽  
Improved Model

Sub-5nm flying head-disk interfaces (HDIs) designed to attain extremely high areal recording densities of the order of Tbit∕in2 are susceptible to strong adhesive forces, which can lead to subsequent contact, bouncing vibration, and high friction. Accurate prediction of the relevant interfacial forces can help ensure successful implementation of ultra-low flying HDIs. In this study, an improved rough surface model is developed to estimate the adhesive, contact, and friction forces as well as the mean contact pressure relevant to sub-5nm HDIs. The improved model was applied to four different HDIs of varying roughness and contact conditions, and was compared to the sub-boundary lubrication rough surface model. It was found that the interfacial forces in HDIs undergoing primarily elastic-plastic and plastic contact are more accurately predicted with the improved model, while under predominantly elastic contact conditions, the two models give similar results. The improved model was then used to systematically investigate the effect of roughness parameters on the interfacial forces and mean contact pressure (response). The trends in the responses were investigated via a series of regression models using a full 33 factorial design. It was found that the adhesive and net normal interfacial forces increase with increasing mean radius R of asperities when the mean separation is small (≈0.5nm), i.e., pseudo-contacting interface, but it increases primarily with increasing root-mean-square (rms) surface height roughness between 2 and 4nm, i.e., pseudo-flying interface. Also, increasing rms roughness and decreasing R, increases the contact force and mean contact pressure, while the same design decreases the friction force. As the directions of optimization for minimizing the individual interfacial forces are not the same, simultaneous optimization is required for a successful ultra-low flying HDI design.

Linear and Nonlinear Differential Equations

1984 ◽  
Vol 52 (7) ◽  
pp. 670-670 ◽  
Author(s):  
I. D. Huntley ◽  
R. M. Johnson ◽  
Fred Brauer
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Linear And Nonlinear

scholarly journals High Frequency Ultrasonic Wave Propagation in  Anisotropic Materials

2021 ◽  
Author(s):  
◽  
Andrew Paul Dawson
Keyword(s):  
Wave Propagation ◽  
Ultrasonic Wave ◽  
High Frequency ◽  
Guided Wave ◽  
Ultrasonic Waves ◽  
Tissue Characterisation ◽  
Ultrasonic Wave Propagation ◽  
Matching Layer ◽  
Fibrous Tissues ◽  
Wave Modes

<p>The influence of highly regular, anisotropic, microstructured materials on high frequency ultrasonic wave propagation was investigated in this work. Microstructure, often only treated as a source of scattering, significantly influences high frequency ultrasonic waves, resulting in unexpected guided wave modes. Tissues, such as skin or muscle, are treated as homogeneous by current medical ultrasound systems, but actually consist of highly anisotropic micron-sized fibres. As these systems increase towards 100 MHz, these fibres will significantly influence propagating waves leading to guided wave modes. The effect of these modes on image quality must be considered. However, before studies can be undertaken on fibrous tissues, wave propagation in more ideal structures must be first understood. After the construction of a suitable high frequency ultrasound experimental system, finite element modelling and experimental characterisation of high frequency (20-200 MHz) ultrasonic waves in ideal, collinear, nanostructured alumina was carried out. These results revealed interesting waveguiding phenomena, and also identified the potential and significant advantages of using a microstructured material as an alternative acoustic matching layer in ultrasonic transducer design. Tailorable acoustic impedances were achieved from 4-17 MRayl, covering the impedance range of 7-12 MRayl most commonly required by transducer matching layers. Attenuation coefficients as low as 3.5 dBmm-1 were measured at 100 MHz, which is excellent when compared with 500 dBmm-1 that was measured for a state of the art loaded epoxy matching layer at the same frequency. Reception of ultrasound without the restriction of critical angles was also achieved, and no dispersion was observed in these structures (unlike current matching layers) until at least 200 MHz. In addition, to make a significant step forward towards high frequency tissue characterisation, novel microstructured poly(vinyl alcohol) tissue-mimicking phantoms were also developed. These phantoms possessed acoustic and microstructural properties representative of fibrous tissues, much more realistic than currently used homogeneous phantoms. The attenuation coefficient measured along the direction of PVA alignment in an example phantom was 8 dBmm-1 at 30 MHz, in excellent agreement with healthy human myocardium. This method will allow the fabrication of more realistic and repeatable phantoms for future high frequency tissue characterisation studies.</p>

scholarly journals Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu ◽  
Imtiaz Ahmad
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Models ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Compact Finite Difference Method ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
The Stability

Variational iteration method has been extensively employed to deal with linear and nonlinear differential equations of integer and fractional order. The key property of the technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The current study presents an improved algorithm to the variational iteration algorithm-II (VIA-II) for the numerical treatment of diffusion as well as convection-diffusion equations. This newly introduced modification is termed as the modified variational iteration algorithm-II (MVIA-II). The convergence of the MVIA-II is studied in the case of solving nonlinear equations. The main advantage of the MVIA-II improvement is an auxiliary parameter which makes sure a fast convergence of the standard VIA-II iteration algorithm. In order to verify the stability, accuracy, and computational speed of the method, the obtained solutions are compared numerically and graphically with the exact ones as well as with the results obtained by the previously proposed compact finite difference method and second kind Chebyshev wavelets. The comparison revealed that the modified version yields accurate results, converges rapidly, and offers better robustness in comparison with other methods used in the literature. Moreover, the basic idea depicted in this study is relied upon the possibility of the MVIA-II being utilized to handle nonlinear differential equations that arise in different fields of physical and biological sciences. A strong motivation for such applications is the fact that any discretization, transformation, or any assumptions are not required for this proposed algorithm in finding appropriate numerical solutions.

Contact Pattern Measurement by Means of Ultrasonic Waves: Art of Present and Some Improvements of its Performance

1983 ◽  
Vol 105 (2) ◽  
pp. 237-241 ◽  
Author(s):  
Yoshimi Ito ◽  
Shuzo Itoh
Keyword(s):  
Contact Pressure ◽  
Pressure Measurement ◽  
Ultrasonic Waves ◽  
Joint Surface ◽  
Contact Pattern ◽  
Good Characteristic ◽  
Focus Type ◽  
Type Transducer

To understand the contact characteristics of a joint surface, it is necessary and indispensable to measure the contact pressure. There have, however, been very few contributions to the method of measuring the contact pressure when comparing it with other methods to detect the properties of engineering surfaces. The contact pressure measurement by means of ultrasonic waves (ultrasonic contact pressure measurement) is surely an effective method as ascertained by earlier works, and thus in this paper some improvements of its performance by using a focus type transducer have been reported, also referring to its art of the present. The measurement using a focus type transducer shows a fairly good characteristic as compared with that using a conventional transducer, especially from the aspect of the resolution ability of the contact pattern.

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