Contact Area Ratio Research Articles

An Isogeometric analysis based method for frictional elastic contact problems with randomly rough surfaces

The problem addressed in this paper concerns the frictional contact between an elastomer and a rigid body with randomly rough surfaces. The work is accomplished on the basis of two crucial elements: a framework for generating random geometries and a robust frictional contact algorithm, both of which are realised in the approach of Isogeometric analysis (IGA) for its high accuracy and robustness. For the former, a new Isogeometric framework for random geometry modelling is proposed, which combines the random field generation based on Karhunen–Loève expansion theory with Non-Uniform Rational B-Spline (NURBS) interpolation method. For the latter, a mortar-based frictional contact algorithm in 2D large deformation regime is adopted incorporating a modified closest point projection method for detection of contact. Numerical experiments are conducted with several settings such as ‘rough–smooth’, ‘smooth–rough’ and ‘rough–rough’ contact, depending on which side of the contact pair the randomly rough surface belongs to. The ratio of the global coefficient of friction to the prescribed local one and the ratio of true contact area to the nominal contact area are characterised under these settings, and factors like the root mean square roughness and correlation length of the random surface and the external traction are discovered to have a significant influence on the two ratios.

Study on Sliding Wear Characteristics of Non-Gaussian Rough Surface in Mixed Lubrication

Under mixed lubrication, when there is direct rough contact between two contact surfaces, surface wear occurs, altering surface morphology, which in turn changes their lubrication state. The tribological performance of materials can be improved with in-depth understanding of the coupling mechanism linking surface wear and lubrication. A numerical model was established to predict the lubrication state and wear characteristics of the surface wear process based on non-Gaussian surface reconstruction technology and a mixed elastohydrodynamic lubrication sliding wear model. The evolution of wear characteristics in Gaussian and non-Gaussian rough surfaces was investigated, and the effect of surface skewness and kurtosis on lubrication and wear characteristics was discussed. The results indicated that as the wear cycle increases, the contact area and contact load ratios of the rough surfaces decrease before gradually stabilizing, while the coefficient of friction and maximum flash temperature rise and then gradually decrease. Increasing surface skewness and kurtosis increases the probability of wear, leading to increased accumulated wear, friction coefficient, and maximum flash temperature rise.

Effect Mechanism and Performance Evaluation of Flange Contact Thermal Resistance in an Aero-Engine

According to the discontinuous structural characteristics of a gas turbine, by considering the contact thermal resistance of the rough surface, a contact thermal resistance measurement experiment was conducted in this study. The main objectives of this work were to investigate the influence mechanism and change law of the contact thermal resistance characteristics on flange installation. Furthermore, this study conducted a theoretical analysis of contact thermal resistance and the calculation of a typical flange mounting edge based on actual operating conditions. The research results show that the contact thermal resistance of a typical flange mounting edge increases with an increase in flange clearance under different tightening torques, which is essentially proportional to the flange clearance. As the flange clearance increases, the unit contact thermal conductivity firstly decreases rapidly. Then, as the flange clearance reaches 0.4 mm, the decreasing rate of unit contact thermal conductivity tends to flatten. In addition, the contact thermal resistance of the typical flange mounting edge decreases with the increase in the tightening torque under different flange clearances. Furthermore, the contact area ratio is not related to the material, and the contact thermal resistance under actual working conditions can be calculated using the unit contact area.

Modeling and analysis of sliding wear based on fractal surface reconstruction in line contact mixed lubrication

In mixed lubrication, the direct rough contact between the two contact surfaces causes material wear and lead to the variation of the surface micro-topography. In turn, the variation of the micro-topography affects the lubrication state between the two contacting surfaces. For the better comprehension of the interaction of lubrication and wear on rough surfaces in mixed lubrication, in this paper, a coupled model of fluid flow, rough contact, and surface wear was established, with fractal theory being applied to predict the changes in surface microtopography. Furthermore, the effects of fractal dimension, roughness direction, contact load and slide-roll ratio on the surface contact area ratio, accumulated wear, film thickness and friction coefficient are analyzed. The results demonstrated that surfaces with large fractal dimension have denser roughness peaks, resulting in larger contact areas and more severe wear. Transverse roughness surfaces exhibit better lubrication and wear performance compared to longitudinal and isotropic surfaces. In addition, increasing the contact load and slip-roll ratio increases the contact area ratio, resulting in lower lubricating performance and increased wear.

Prediction of the tribological characteristics of non‐Gaussian rough surfaces during sliding wear in mixed lubrication

AbstractIn mixed lubrication, material wear is inevitably caused due to solid contact. Simultaneously, the surface morphology after wear will affects the lubrication performance. To understand this coupling process, virtual surface reconstruction technology and mixed lubrication sliding wear model were applied to predict the evolution of wear characteristics and lubrication characteristics during wear in this study. The effects of the roughness root mean square (RMS), roughness direction and wavelength ratio on the contact area ratio, the contact load ratio, accumulated wear, film thickness and the friction coefficient were analysed. The results indicated that the contact area ratio and the contact load ratio and the friction coefficient decreased and average film thickness increased with the increase in the number of the wear cycles. In addition, a surface with low‐roughness RMS, longitudinal roughness texture and high‐wavelength ratio is suitable for improving lubrication performance and reducing wear.

A simulation study on stress-seepage characteristics of 3D rough single fracture based on fluid-structure interaction

This paper expounds on the process of deformation and seepage field change of single coarse fracture under normal stress and puts forward a numerical simulation framework based on fluid-structure coupling method to reasonably link contact deformation of fracture surface with seepage field change. The geometric model of a three-dimensional rough single fracture surface with controllable JRC is established based on the random surface generation method. The numerical test model of radiation flow of single fracture in rough rock is constructed, which is consistent with the laboratory test. Through carrying out numerical simulation tests of different JRC and normal stress conditions, this paper discusses the phenomenon and intrinsic nature of the influence of JRC on fracture seepage characteristics. The increase in eddy current intensity and eddy current area ratio is the inherent characteristics of the seepage field characteristics after JRC increases. With the rise of energy loss, the macroscopic seepage flow decreases. In addition, with the advantage of the fluid-structure interaction method, the fracture deformation characteristics under different normal stresses are reflected by the ratio of the contact area. The correlation among fracture surface deformation, velocity vector, and seepage pressure are analyzed. Finally, the cubic polynomial correlation between gap width ratio and contact area ratio is established and verified. It is of positive significance to quantify the influence of coarse single fracture contact ratio on deformation-seepage coupling characteristics under normal stress.

Dynamic photoelastic experimental study on the influence of joint surface geometrical property on wave propagation and stress disturbance

Rock joints significantly affect the dynamic response of rock masses and the stability of underground structures . In this study, the dynamic photoelastic test was conducted to investigate the influence of joints on the stress field and wave propagation . The photoelastic equipment as well as the Split Hopkinson Pressure Bar (SHPB) were adopted for the test. The specimen sandwiched between the input and output bars was composed of two polycarbonate plates. One side of the plates was uneven with a few notches, while other sides were smooth and flat. The artificial joints were simulated by the contact of the uneven and flat sides of the two plates. The relation between the stress wave propagation and the stress field around the joint was studied when the joint has different contact area ratios, joint thicknesses, and joint surface distributions. The test results show that compared to the joint thickness, the joint contact area ratio and the joint surface distribution have a significant influence on the wave propagation and stress field near the joint. The transmitted wave is highly correlative with the stress field. This work provides a beneficial attempt to reveal the stress field disturbance and the effect of joint geometrical properties on wave propagation from the photoelastic test.

Analysis of the Microstructure and Macroscopic Fluid-Dynamics Behavior of Soft Soil after Seepage Consolidation

The purpose is to study the microstructure and macroscopic fluid-dynamic behavior of soft soil after it has been subjected to a seepage consolidation procedure. First, the microscopic pore structure of soft clay is quantitatively studied by a scanning electron microscope technique. Second, the average contact area rate of soil particles is obtained employing statistical analysis applied to microscopic images of soft soil, and the macroscopic porosity of soft clay is determined through an indoor geotechnical test. Finally, mathematical relationships are introduced by fitting the results of the test. The results show that the unmodified empirical equation for the permeability coefficient of coarse-grained soil produces large errors in calculations related to cohesive soils. By contrast, the permeability coefficient calculated by the empirical equation modified by the average contact area ratio theory is in good agreement with the measured average value of the indoor test.

Modeling of Seismic Energy Dissipation of Rocking Foundations Using Nonparametric Machine Learning Algorithms

The objective of this study is to develop data-driven predictive models for seismic energy dissipation of rocking shallow foundations during earthquake loading using multiple machine learning (ML) algorithms and experimental data from a rocking foundations database. Three nonlinear, nonparametric ML algorithms are considered: k-nearest neighbors regression (KNN), support vector regression (SVR) and decision tree regression (DTR). The input features to ML algorithms include critical contact area ratio, slenderness ratio and rocking coefficient of rocking system, and peak ground acceleration and Arias intensity of earthquake motion. A randomly split pair of training and testing datasets is used for initial evaluation of the models and hyperparameter tuning. Repeated k-fold cross validation technique is used to further evaluate the performance of ML models in terms of bias and variance using mean absolute percentage error. It is found that all three ML models perform better than multivariate linear regression model, and that both KNN and SVR models consistently outperform DTR model. On average, the accuracy of KNN model is about 16% higher than that of SVR model, while the variance of SVR model is about 27% smaller than that of KNN model, making them both excellent candidates for modeling the problem considered.

Effect of lubricant selection on the wear characteristics of spur gear under oil-air mixed lubrication

The helicopter transmission system generally employs oil injection lubrication, while the tooth surface often operates under mixed lubrication. In the case of mixed lubrication, the relationship among the fluid flow, rough contact, and material wear renders it quite difficult to establish a predictive model for wear and lubrication coupling. The present study involved, in consideration of the effect of tooth surface micro-morphology, establishing a coupling analysis model for the wear characteristics of involute gear mixed lubrication. The effects of the mixture of squalane base oil and 15% (by weight) polyisoprene(SQL+PIP), polyalphaolefin oil (PAO6) and mineral SN100 on the distribution of lubrication performance parameters and the wear characteristics were analyzed. The results revealed that the film thickness of SQL+PIP was higher than that of PAO6 and SN100, and the coefficient of friction is lower. In addition, the increase in lubricant viscosity was conducive to reducing the contact area and load ratios of direct rough contact, which was, in turn, beneficial to reducing wear.

Study on a New Static Sealing Method and Sealing Performance Evaluation Model for PEMFC

The long-term stability and durability of seals are critical for various instruments and types of equipment. For static sealing, an important sealing state, there are currently two representative sealing methods, namely, pre-compressing static sealing and adhesive static sealing. In this paper, the characteristics and shortcomings of these sealing methods are summarized. At present, some static sealing requirements are urgent and difficult. For example, the deterioration of the sealing performance is an important factor which limits the service life of proton exchange membrane fuel cells and redox flow batteries. Therefore, a new method of static sealing whose sealing materials are rubber elastomers is proposed, named alterable static sealing. Then, its sealing processes are proposed. Furthermore, the actual contact area ratio r is used as the standard for sealability. Based on the mathematical model of pre-compressing static sealing, the influence of interface bonding was considered, and the mathematical model of alterable static sealing was established. Moreover, the compensatory effect of alterable static sealing on the static sealing capacity of rubber elastomers was proved.

Fractal variation of three-dimensional surface topography during sliding wear under mixed elastohydrodynamic lubrication

The surface morphology variation of the friction pair during the wear process directly affects the local lubrication effect and contact strength, and this variation is difficult to quantify in mixed lubrication. In this study, a numerical simulation and characterization model method of sliding wear surface morphology evolution based on deterministic elastohydrodynamic lubrication (EHL) model and surface three-dimensional morphology fractal method is established. The effectiveness of the lubrication model is verified by the film thickness measurement, and the actual surface wear coefficient is obtained through the wear experiment. On this basis, the variation of surface morphology and fractal parameters in the sliding wear process is investigated, and the effect of contact load and sliding speed on surface lubrication characteristics and fractal parameters is analyzed. The results show: wear will cause the higher wave peaks on the ground surface to be gradually worn away and the fine structure of the surface is reduced, and the fractal dimension of the morphology is therefore reduced. In addition, the contact area ratio and contact load ratio, as well as the coefficient of friction and surface evolution under different loads and sliding speeds are consistent.

The closure behaviour of rock joints under impact loading

The dynamic properties of jointed rock and closure deformation behavior of rock joints under impact loading are of significant importance for a correct understanding of stress wave propagation or dynamic failure in the rock masses, so a serial of impact tests of the intact and joined samples was carried out based on a hammer-driven SHPB device. The cement mortar was used to make regular joint surface asperity for studying the effect of joint surface morphology on its deformation features and a dynamic B-B model was applied to describe closure curve characteristics. The test results demonstrate that the stress-strain curve of jointed rock is obviously influenced by joint roughness and the closure characteristic was affected by joint surface morphology. Specifically, the stress-strain curve of jointed rock exhibited some differences with the intact sample because of the existence of discontinuity and its roughness. the peak stress and elastic modulus of jointed rock were obviously low when compared to the intact samples. Rock joint under impact load exhibited hyperbolic deformation characteristics, and this behavior is not affected by joint surface morphologies. The dynamic initial stiffness increases and maximum allowance closure decrease with the increase of contact area ratio (CAR) and asperity inclination angle.

Application of machine learning algorithms to performance prediction of rocking shallow foundations during earthquake loading

The objective of this research is to develop preliminary predictive models for the performance of rocking shallow foundations using machine learning algorithms and supervised learning technique. Data from a rocking foundation database, consisting of dynamic base shaking experiments conducted on centrifuges and shaking tables, have been used for the development of multivariate linear regression (MLR) model using stochastic gradient descent optimization and distance-weighted k-nearest neighbors (k-NN) regression model. Seismic energy dissipation in soil, permanent settlement of foundation, and the maximum acceleration transmitted to the structure are considered as the performance parameters of rocking foundations, while the input features to machine learning algorithms include critical contact area ratio and rocking coefficient of soil-foundation system, and peak ground acceleration and Arias intensity of earthquake ground motion. It is found that both MLR and weighted k-NN models perform satisfactorily in capturing the complex relationships between the performance parameters and input features of rocking foundations, and that both models perform better than simple statistical models. Based on multiple k-fold cross validation tests across all performance parameters and the mean absolute percentage errors, it is found that the weighted k-NN model consistently outperforms the MLR model in terms of accuracy for the problem considered.

Mechanics Analysis of Rough Surface Based on Shoulder-Shoulder Contact

Proper methods and models for mechanical analysis of rough surface can improve the theory of surface contact. When the topography parameters of two rough surfaces are similar, the contact should be considered shoulder-shoulder rather than top-top. Based on shoulder-shoulder contact and fractal characteristics, the geometric model for asperity and contact mechanics model for rough surfaces are established, and the deformation of asperity, the real contact area and contact load of sealing surface are discussed. The effects of contact pressure p and topography parameters (fractal dimension D and fractal roughness G) on the variation of porosity and contact area ratio Ar/A0 are achieved. Results show that with the increase of p, larger D and smaller G corresponds to larger initial porosity but faster and larger decrease of porosity; with the increment of D, porosity increases first and then decreases, and smaller G corresponds to larger porosity reduction; as G becomes bigger, porosity increases, and larger D corresponds to larger porosity difference and change. With the addition of p, Ar/A0 increases, and the variation of Ar/A0 is closer to linearity and less at smaller D and larger G; with the increase of D, Ar/A0 increases gradually, and the growth rate is bigger at smaller G and bigger p; as G becomes bigger, Ar/A0 declines, and it declines more gently at smaller D and p. The influence of D on Ar/A0 is greater than that of G. The results can provide the theoretical basis for the design of sealing surfaces and the research of sealing or lubrication technologies of rough surfaces.

Numerical investigation of seismic performance of bridge piers with spread footings considering pier plastic hinging and footing rocking, sliding, and settlement

In this study, we conducted numerical parametric analyses to investigate the seismic performance of a bridge pier with a spread footing on dense sandy ground. For the numerical model, we considered plastic hinging in the pier and foundation rocking, sliding, settlement, and embedment. The investigated parameters included pier height, footing width, excitation intensity and type, and footing embedment. With an increase in the pier height-to-foundation width ratio, the rocking response became more pronounced. The direction of the foundation’s permanent tilt was highly dependent on that of the maximum foundation rotation. Near-fault pulse-like ground motions destabilized a system easily. In addition, the maximum drift ratio of the pier and the maximum rotation and settlement of the footing were highly dependent on the minimum contact area. Thus, the ratio of minimum contact area to footing base area (minimum contact area ratio) is an important index for evaluating the performance and stability of the model. When the minimum contact area ratio exceeded 30%, the overall performance of the pier-footing system was suitable; by contrast, when it was below 30%, the drift ratio of the pier and rotation of footing dramatically increased, influencing the system stability.

Outcomes After Deepening Trochleoplasty and Concomitant Realignment in Patients With Severe Trochlear Dysplasia With Chronic Patellofemoral Pain: Results at 2-Year Follow-up.

Background:Abnormal patellofemoral joint stress appears to have major relevance in a subgroup of patients with patellofemoral pain (PFP).Purpose:To evaluate whether patients with chronic PFP and trochlear dysplasia–induced patellofemoral joint malalignment benefit from a deepening trochleoplasty procedure with the aim of improving patellotrochlear congruence.Study Design:Case series; Level of evidence, 4.Methods:Included were 15 patients (male/female, 1/14; mean age, 30.3 years [range, 19-51 years]) with 8.8 years (range, 1-20 years) of chronic PFP and severe trochlear dysplasia. All patients underwent correction of patellotrochlear malalignment with deepening trochleoplasty and concomitant realignment procedures. The Kujala score and a numerical analog scale (0-10) for intensity of pain were used to assess symptoms preoperatively and at 12 and 24 months postoperatively. Pre- and postoperative magnetic resonance imaging (MRI) scans from the patients were compared with the MRI scans of age- and sex-matched controls regarding the patellotrochlear contact area and contact ratio, patellar tilt, patellotrochlear index, and lateral trochlear inclination (LTI) angle.Results:The Kujala score increased from a mean of 55 (range, 15-81) preoperatively to 82.5 (range, 53-98) after 12 months (95% CI, –42.56 to –12.37; P < .001) and to 84.2 (range, 59-99) after 24 months (95% CI, –44.29 to –14.11; P < .001). The intensity of PFP decreased from 5.7 (range, 3-10) preoperatively to 1.4 (range, 0-4) after 12 months (95% CI, 2.57 to 5.96; P < .001) and had a mean of 1.6 (range, 0-6) after 24 months (95% CI, 2.44 to 5.75; P < .001). Preoperatively, parameters in the study group indicated significant patellotrochlear malalignment, which improved and normalized (except for the LTI angle) postoperatively compared with the values of the control group (P > .05).Conclusion:In a subgroup of patients with chronic PFP due to severe trochlear dysplasia, deepening trochleoplasty and concomitant realignment procedures significantly reduced pain and improved knee joint function while normalizing patellotrochlear congruence.

Hydromechanical Investigations on the Self-propping Potential of Fractures in Tight Sandstones

The hydromechanical properties of single self-propping fractures under stress are of fundamental interest for fractured-rock hydrology and a large number of geotechnical applications. This experimental study investigates fracture closure and hydraulic aperture changes of displaced tensile fractures, aligned tensile fractures, and saw-cut fractures for two types of sandstone (i.e., Flechtinger and Fontainebleau) with contrasting mechanical properties, cycling confining pressure between 5 and 30 MPa. Emphasis is placed on how surface roughness, fracture wall offset, and the mechanical properties of the contact asperities affect the self-propping potential of these fractures under normal stress. A relative fracture wall displacement can significantly increase fracture aperture and hydraulic conductivity, but the degree of increase strongly depends on the fracture surface roughness. For smooth fractures, surface roughness remains scale-independent as long as the fracture area is larger than a roll-off wavelength and thus any further displacement does not affect fracture aperture. For rough tensile fractures, these are self-affine over a larger scale so that an incremental fracture wall offset likely leads to an increase in fracture aperture. X-ray microtomography of the fractures indicates that the contact area ratio of the tensile fractures after the confining pressure cycle inversely correlates with the fracture wall offset yielding values in the range of about 3–25%, depending, first, on the respective surface roughness and, second, on the strength of the asperities in contact. Moreover, the contact asperities mainly occur isolated and tend to be preferentially oriented in the direction perpendicular to the fracture wall displacement which, in turn, may induce flow anisotropy. This, overall, implies that relatively harder sedimentary rocks have a higher self-propping potential for sustainable fluid flow through fractures in comparison to relatively soft rocks when specific conditions regarding surface roughness and fracture wall offset are met.

A method for tire wet grip performance evaluation based on grounding characteristics

The wet grip performance of tire is one of the important performances affecting vehicle safety. The steering, acceleration, and braking of the vehicle are directly affected by the grounding characteristics between the radial tire and the ground. In order to study the influence of grounding characteristics of the tire on wet grip performance, ten 205/55R16 tires produced by different manufacturers were selected and tested. The grounding characteristics of the tires were tested using an optical test rig for tire grounding pressure distribution, considering inflation pressure distribution, load and wheel alignment. The tire-road contact area was subdivided into five parts, and 69 parameters were used to describe the grounding characteristics. A software was proposed to process the test results automatically, and 69 grounding characteristic parameters of each tire were obtained. Correlation analysis on tire wet grip performance and grounding characteristics was used for selecting the principal parameters. Finally, eight grounding characteristic parameters related to tire wet grip performance was obtained. Among them are five grounding characteristic parameters (central area rectangle ratio, central area width, internal shoulder length-to-width ratio, external and internal shoulder contact area ratio, external and internal shoulder impression area ratio) which have high correlation to tire wet grip performance, and three grounding characteristic parameters (external shoulder width, external shoulder length-to-width ratio, external and internal shoulder width ratio) which have low correlation to the wet grip performance of the tire. The principal component analysis method was used to analyze the highly correlated grounding characteristic parameters, and the regression equation for evaluating tire wet grip performance was fitted. The comparison of experimental and fitted values show that the errors are within 4%. The result demonstrates that, the method for evaluating wet grip performance of the radial tire through tire-road grounding characteristics was achieved.

Investigation on the adhesive contact and electrical performance for triboelectric nanogenerator considering polymer viscoelasticity

The triboelectric nanogenerator (TENG) is a new mechanical energy harvesting technology in which the typical viscoelastic material polydimethylsiloxane (PDMS) is widely used. Micro-/nano-textures are often fabricated on the PDMS surface to enhance the electrical performance of TENG. As the contact region decreases to micro/nano scale, the adhesive forces become dominant. However, there is still a lack of contact mechanics model considering both material viscoelasticity and the adhesive forces to guide the surface texture design. In this paper, the explicit data-fitting formulas based on the fractional derivative Zener model are firstly derived to identify the viscoelastic constitutive parameters, which can not only avoid the influence of the initial contact point, but also ensure the accurate conversion between the creep compliance and the relaxation modulus function. Then a viscoelastic-adhesive contact model based on the fitted constitutive parameters is established, and the numerical algorithms such as bi-conjugate stabilized (Bi-CGSTAB) method and fast Fourier transform (FFT) technique are employed to analyze the effects of material viscoelasticity and texture sizes on the contact and electrical performance. It is shown that, compared with results from the elastic-adhesive contact model, the contact area ratio based on the viscoelastic-adhesive contact model is significantly larger, which is much closer to the experimental results. Among the selected sizes of pyramid texture, the higher electrical performance can be obtained from the textures with a smaller pitch and a larger width under the heavier applied load. This study can provide a theoretical reference for the design of viscoelastic surface texture of TENG.