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In order to analyze the evolution of normal contact stiffness under loading and unloading, an accurate elastic-plastic contact finite element model between rigid plane and fractal surface is established by introducing the equivalent metal matrix deformation in terms of the modified Weierstrass-Mandelbrot function. The effects of the fractal dimension, scale parameter, material properties on the normal contact stiffness were discussed. A method for evaluating the normal contact stiffness was proposed to analyze the evolution of the normal contact stiffness. Numerical simulation shows that there is a positive power function relationship between the normal contact stiffness and the load of fractal surface. Under the same load, at the fractal dimensions (D) of 2.4-2.7 and scale parameters (G) of 1.36×10-13-1.36×10-10 m, the loading normal contact stiffness increases with the increasing of fractal dimension and tangent modulus, but decreases with the increasing of scale parameter. The unloading normal contact stiffness increases with the material strengthening, and the variation amplitude is positively correlated with the fractal dimension, and negatively correlated with the scale parameters and tangent modulus.

Contact surfaces do not make contact perfectly because such surfaces have a lot of asperities. The real contact area is much smaller than the nominal contact area, and the real contact areas has a non-uniform distribution because of the waviness in the contact surface. The contact stiffness is influenced not only by the deformation of the asperities, but also by the distribution of the real contact areas. In general, a contact surface with a uniform distribution of the real contact areas has greater contact stiffness. However, this requires a grinding finish and costs more than the cutting finish. In this study, a method for uniformly distributing the real contact areas easily, is proposed to improve the contact stiffness of a contact surface finished by cutting. The method is called the cutter mark cross (CMC) method. The allowable waviness in the CMC method is shown. In addition, the effect of the CMC method is investigated by experimentation. The results show that the real contact areas can be distributed uniformly using the CMC method. The horizontal and vertical contact stiffness can also be improved.

One of the most important grinding parameters is the real depth of cut which is always lower than its programmed value. This is because in reality abrasive grains of the grinding wheel are not fixed but attached to a bonding material which is deformed during the process. In this study we investigate the effect of the contact stiffness between a single abrasive grain and the workpiece on the depth of cut and the grinding process characteristics via three-dimensional Molecular Dynamics (MD) simulations. Contact stiffness has been modelled by attaching a single trapezoid abrasive grain to a spring in the normal grinding direction. MD experiments have been repeated due to the stochastic nature of the grinding process in favour of statistical accuracy. Various grinding speeds have been considered while the case of a rough abrasive-workpiece interface has been investigated as well using fractal models. Our results indicate that the trajectory followed by the abrasive grain is not a straight line, as in the case of a rigid abrasive, but a curved one, asymptotically converging towards the equilibrium point which corresponds to the selected value of the spring stiffness. This behaviour alongside the grinding velocity and rough abrasive-workpiece interface have been found to affect the grinding forces, friction coefficient, morphology of the ground surface and subsurface temperature. The present MD model has also been proven to be capable of capturing the thermal softening phenomenon at the abrasive-workpiece interface.

We calibrate the lateral mode AFM (LFM) by determining the position-sensitive photodetector (PSPD) signal dependency on the lateral tip displacement, which is analogous to the constant-compliance region in normal-force calibration. By stick-slip on stiff, amorphous surfaces (silica or glass), the lateral tip displacement is determined accurately using the feedback loop control of AFM system. The sufficiently high contact stiffness between the Si AFM tip and stiff, amorphous surfaces substantially reduces the error of PSPD signal dependency on the lateral tip displacement. No damage or modification of the AFM probe is involved and only a clean silicon or glass wafer is needed.

Subsurface imaging of Au circuit structures embedded in poly(methyl methacrylate) (PMMA) thin films with a cover thickness ranging from 52 to 653 nm was carried out by using contact resonance atomic force microscopy (CR-AFM). The mechanical difference of the embedded metal layer leads to an obvious CR-AFM frequency shift and therefore its unambiguous differentiation from the polymer matrix. The contact stiffness contrast, determined from the tracked frequency images, was employed for quantitative evaluation. The influence of various parameter settings and sample properties was systematically investigated by combining experimental results with theoretical analysis from finite element simulations. The results show that imaging with a softer cantilever and a lower eigenmode will improve the subsurface contrast. The experimental results and theoretical calculations provide a guide to optimizing parameter settings for the nondestructive diagnosis of flexible circuits. Defect detection of the embedded circuit pattern was also carried out, which indicates the capability of imaging tiny subsurface structures smaller than 100 nm by using CR-AFM.

We present an investigation through numerical analysis (FEM) of the solution of the contact problem in friction clutch systems during engagement manoeuver. The case of high contact pressure between the sliding elements of a clutch system (flywheel, friction clutch and pressure plate) has been also considered. A finite element model of a dry friction clutch system (single disc) to estimate the distributions of the contact pressure between the contact elements of the clutch system under different working conditions has been developed and the main findings are discussed. Furthermore, the effect of modules of elasticity (contact stiffness) on the distribution of contact pressure of the mating surfaces was investigated. Also, the results encompass the deformations of the contacting surfaces for different cases. This work could provide a fundamental intermediate step to obtain a partial solution to the thermos-elastic problem in order to compute the thermal-driven deformations and stresses in the automotive clutches and brakes under different working conditions. We present an investigation through numerical analysis (FEM) of the solution of the contact problem in friction clutch systems during engagement manoeuver. The case of high contact pressure between the sliding elements of a clutch system (flywheel, friction clutch and pressure plate) has been also considered. A finite element model of a dry friction clutch system (single disc) to estimate the distributions of the contact pressure between the contact elements of the clutch system under different working conditions has been developed and the main findings are discussed. Furthermore, the effect of modules of elasticity (contact stiffness) on the distribution of contact pressure of the mating surfaces was investigated. Also, the results encompass the deformations of the contacting surfaces for different cases. This work could provide a fundamental intermediate step to obtain a partial solution to the thermos-elastic problem in order to compute the thermal-driven deformations and stresses in the automotive clutches and brakes under different working conditions.

This paper presents the effect of grinding wheel contact stiffness on the plunge grinding cycle. First, it proposes a novel model of the generalized plunge grinding system. The model is applicable to all plunge grinding operations including cylindrical, centerless, shoe-centerless, internal, and shoe-internal grinding. The analysis of the model explicitly describes transient behaviors during the ramp infeed and the spark-out in the plunge grinding cycle. Clarification is provided regarding the premise that the system stiffness is composed of machine stiffness and wheel contact stiffness, and these stiffnesses significantly affect productivity and grinding accuracy. The elastic deflection of the grinding wheel is accurately measured and formulas for representing the deflection nature under various contact loads are derived. The deflection model allows us to find the non-linear contact stiffness with respect to the normal load. The contact stiffnesses of four kinds of grinding wheels with different grades and bond materials are presented. Both cylindrical grinding and centerless grinding tests are carried out, and it is experimentally revealed that the time constant at ramp infeed and spark-out is significantly prolonged by reducing the grinding force. It is verified that a simulation of the grinding tests using the proposed model can accurately predict critical parameters like forces and machine deflection during plunge grinding operations. Finally, this paper provides a guideline for grinding cycle design in order to achieve the required productivity and grinding accuracy.

Friction joints are one of the fundamental means used for the assembly of structural components in engineering applications. The structural dynamics of these components becomes nonlinear, due to the nonlinear nature of the forces arising at the contact interface characterised by stick-slip phenomena and separation. Advanced numerical models have been proposed in the last decades which have shown some promising capabilities in capturing these local nonlinearities. However, despite the research efforts in producing more advanced models over the years, a lack of validation experiments made it difficult to have fully validated models. For this reason, experimental techniques which can provide insights into the local dynamics of joints can be of great interest for the refinement of such models and for the optimisation of the joint design and local wear predictions. In this paper, a preliminary study is presented where ultrasound waves are used to characterise the local dynamics of friction contacts by observing changes of the ultrasound reflection/transmission at the friction interface. The experimental technique is applied to a dynamic friction rig, where two steel specimens are rubbed against each other under a harmonic tangential excitation. Initial results show that, with a controlled experimental test procedure, this technique can identify microslip effects at the contact interface.

Modeling of frictional contact systems with high accuracy needs the knowledge of several contact parameters, which are mainly related to the local phenomena at the contact interfaces and affect the complex dynamics of mechanical systems in a prominent way. This work presents a newer approach for identifying reliable values of the normal contact stiffness between surfaces in contact, in both sliding and sticking conditions. The combination of experimental tests, on a dedicated set-up, with finite element modeling, allowed for an indirect determination of the normal contact stiffness. The stiffness was found to increase with increasing contact pressure and decreasing roughness, while the evolution of surface topography and third-body rheology affected the contact stiffness when sliding.

This paper investigates the effects of fretting wear on frictional contacts. A high frequency friction rig is used to measure the evolution of hysteresis loops, friction coefficient and tangential contact stiffness over time. This evolution of the contact parameters is linked to significant changes in natural frequencies and damping of the rig. Hysteresis loops are replicated by using a Bouc-Wen modified formulation, which includes wear to simulate the evolution of contact parameters and to model the evolving dynamic behaviour of the rig. A comparison of the measured and predicted dynamic behaviour demonstrates the feasibility of the proposed approach and highlights the need to consider wear to accurately capture the dynamic response of a system with frictional joints over its lifetime.

Instrumented indentation test is a non-conventional hardness test, relevant for performing both hardness measurement and estimating the elastic modulus. The indentation modulus, which depends on the contact stiffness, estimates the elastic modulus. To evaluate contact stiffness, the literature requires fitting force–displacement curve according to mathematical models, which are hardly representative of the curve. This research aims at proposing alternatives, which estimate contact stiffness directly from experimental data. Proposed methods are applied to nano-indentations performed on a reference material and a high-speed bearing steel; indentation modulus is evaluated along with uncertainty contribution of contact stiffness. Comparison with standard methods is provided.

A state-dependent contact model including nonlinear contact stiffness and nonlinear contact filtering is used to calculate contact forces and rail vibrations with a time-domain wheel-track interaction model. In the proposed method, the full three-dimensional contact geometry is reduced to a point contact in order to lower the computational cost and to reduce the amount of required input roughness-data. Greens functions including the linear dynamics of the wheel and the track are coupled with a point contact model, leading to a numerically efficient model for the wheel-track interaction. Nonlinear effects due to the shape and roughness of the wheel and the rail surfaces are included in the point contact model by pre-calculation of functions for the contact stiffness and contact filters. Numerical results are compared to field measurements of rail vibrations for passenger trains running at 200 kph on a ballast track. Moreover, the influence of vehicle pre-load and different degrees of roughness excitation on the resulting wheel-track interaction is studied by means of numerical predictions.

This paper focuses on an experimental investigation of the mechanical behavior of bolted joints. A new test apparatus to measure friction hysteresis was designed to provide a reliable experimental database for the calibration of contact models. This apparatus uses a piezoelectric actuator to provide the contact interfaces with stable oscillatory relative displacement. The friction force and the bolt preload were continuously measured during the test, using a load cell and a force washer, respectively. The relative motion between the interfaces was measured using a single laser vibrometer. The influence of the bolt preload and excitation amplitude on friction hysteresis was investigated. A numerical model was developed to extract the tangential contact stiffness from the measured data.

The present paper is devoted to a theoretical analysis of sliding friction under the influence of in-plane oscillations perpendicular to the sliding direction. Contrary to previous studies of this mode of active control of friction, we consider the influence of the stiffness of the tribological contact in detail and show that the contact stiffness plays a central role for small oscillation amplitudes. In the present paper we consider the case of a displacement-controlled system, where the contact stiffness is small compared to the stiffness of the measuring system. It is shown that in this case the macroscopic coefficient of friction is a function of two dimensionless parameters—a dimensionless sliding velocity and dimensionless oscillation amplitude. In the limit of very large oscillation amplitudes, known solutions previously reported in the literature are reproduced. The region of small amplitudes is described for the first time in this paper.

Instrumented indentation tests enable evaluation of several material parameters. Preliminary investigations underlined the influence of contact stiffness in the nano-range. ISO 14577-1 recommends two methods for contact stiffness evaluation, which, however, present shortcomings mainly related to the disregard of actual shape of unloading indentation curve. Given the relevance not only at the extent of material characterization, but also at testing machine calibration, alternative evaluation procedures have been developed, showing better agreement with experimental data and lower uncertainty in the evaluation of contact stiffness. In this work, shortcomings of standard and alternative methods in the evaluation of material parameters are highlighted, and innovative procedures are proposed to overcome them.

A methodology for tuning the stiffness of machine tool supports is described based on a stiffness model using the contact stiffness approach. Using this model, the mathematical relationship between the load of the support and its stiffness is established. The relationship is separated into three regions. When the total stiffness of all supports is maximized, the load must be tuned so that the stiffness–support load relationship is in the critical region, whereby the contact stiffness is slightly larger than the bulk stiffness. Correspondingly, a placement method of supports is proposed that increases their stiffness without anchor bolts. The effectiveness of the proposed method is verified in two experiments. In the first experiment, the natural frequency of a small machine tool prototype is compared for several placements of three supports. The lowest natural frequency of the machine tool under the proposed placement scheme is maximized. In the second experiment, the proposed method is applied to increase the lowest natural frequency of a horizontal milling machine. The lowest natural frequency with a distinct arrangement of three supports is increased by 15–55%, compared to other popular placements of these three supports. The experimental results show that the proposed placement method is effective for enhancing the stiffness of machine tool supports.

The stiffness of micron-sized sphere–plate contacts was studied by employing high frequency, tangential excitation of variable amplitude (0–20 nm). The contacts were established between glass spheres and the surface of a quartz crystal microbalance (QCM), where the resonator surface had been coated with either sputtered SiO2 or a spin-cast layer of poly(methyl methacrylate) (PMMA). The results from experiments undertaken in the dry state and in water are compared. Building on the shifts in the resonance frequency and resonance bandwidth, the instrument determines the real and the imaginary part of the contact stiffness, where the imaginary part quantifies dissipative processes. The method is closely analogous to related procedures in AFM-based metrology. The real part of the contact stiffness as a function of normal load can be fitted with the Johnson–Kendall–Roberts (JKR) model. The contact stiffness was found to increase in the presence of liquid water. This finding is tentatively explained by the rocking motion of the spheres, which couples to a squeeze flow of the water close to the contact. The loss tangent of the contact stiffness is on the order of 0.1, where the energy losses are associated with interfacial processes. At high amplitudes partial slip was found to occur. The apparent contact stiffness at large amplitude depends linearly on the amplitude, as predicted by the Cattaneo–Mindlin model. This finding is remarkable insofar, as the Cattaneo–Mindlin model assumes Coulomb friction inside the sliding region. Coulomb friction is typically viewed as a macroscopic concept, related to surface roughness. An alternative model (formulated by Savkoor), which assumes a constant frictional stress in the sliding zone independent of the normal pressure, is inconsistent with the experimental data. The apparent friction coefficients slightly increase with normal force, which can be explained by nanoroughness. In other words, contact splitting (i.e., a transport of shear stress across many small contacts, rather than a few large ones) can be exploited to reduce partial slip.

The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane. In contrast to previous works we analyze the influence of the stiffness of the tribological contact in detail and also consider the case of large oscillation amplitudes at which the contact is lost during a part of the oscillation period, so that the sample starts to “jump”. It is shown that the macroscopic coefficient of friction is a function of only two dimensionless parameters—a dimensionless sliding velocity and dimensionless oscillation amplitude. This function in turn depends on the shape of the contacting bodies. In the present paper, analysis is carried out for two shapes: a flat cylindrical punch and a parabolic shape. Here we consider “stiff systems”, where the contact stiffness is small compared with the stiffness of the system. The role of the system stiffness will be studied in more detail in a separate paper.

Ultrasound Atomic Force Microscopy (US-AFM) has been used for subsurface imaging of nanostructures. The contact stiffness variations have been suggested as the origin of the image contrast. Therefore, to analyze the image contrast, the local changes in the contact stiffness due to the presence of subsurface features should be calculated. So far, only static simulations have been conducted to analyze the local changes in the contact stiffness and, consequently, the contrast in US-AFM. Such a static approach does not fully represent the real US-AFM experiment, where an ultrasound wave is launched either into the sample or at the tip, which modulates the contact stiffness. This is a time-dependent nonlinear dynamic problem rather than a static and stationary one. This letter presents dynamic 3D ultrasound analysis of contact stiffness in US-AFM (in contrast to static analysis) to realistically predict the changes in contact stiffness and thus the changes in the subsurface image contrast. The modulation frequency also influences the contact stiffness variations and, thus, the image contrast. The three-dimensional time-dependent ultrasound analysis will greatly aid in the contrast optimization of subsurface nanoimaging with US-AFM., 11 pages, 5 figures

A three-step model for the performance-based numerical simulations of the fire response of steel–RC two-layered beam-like composite structures is presented and validated. The first step consists of the determination of the evolution of temperatures in the structure׳s surroundings. Moisture and the heat transfer through the RC layer and the conduction of heat over the steel layer are obtained in the second step. In concrete, the transfer of water vapour, dry air, and free water is discussed as well as the evaporation and liquefaction phenomena and the dehydration of concrete and its thermal and mechanical degradation. Within the framework of the third step, a geometrically and materially non-linear mechanical response of the structure is proposed accounting for interlayer slips and uplifts as well as for various material-related phenomena such as the material hardening/softening and creep. The governing equations are solved numerically. An efficient, novel strain-based finite element formulation is introduced for the mechanical analysis. Due to its generality and consideration of several different possible non-linear material, geometrical, and interlayer contact phenomena and their couplings the model can be of a use to a broader fire science community for exploring the impact of different physical parameters on the results of the addressed numerical simulations, thereby providing directions for further research. In the paper a case of such a study is also demonstrated exploring the contribution of the steel sheet and the flexibility of the interlayer connection of a standard trapezoidal steel–RC slab to its ultimate fire resistance. A reasonable contribution of the sheet is proved if the stiffness ratio between the integrated and the external tensile reinforcement of the RC plate is low provided that the contact connection is sufficiently stiff.

The development of steam turbine's blades is closely related to the computer modelling of their vibrations. In this work, a numeric method that (i) implements the calculation of nonlinear vibrations (ii) makes use of the cyclic symmetry of the bladed disk and (iii) models structural contact elements between blades is presented. The cyclic symmetry properties of the bladed disk are used for the calculations of its natural frequencies and mode shapes, then, these are employed in the analysis of its nonlinear vibrations. The contact elements reinforce the bladed disk and act as friction dampers in case of its exceeding excitation. Contact areas between blades are modeled via coupling elements implementing dry Coulomb friction. The method is demonstrated on the particular case of the bladed disk equipped with the LSB48 blades and excited by travelling-wave of two nodal diameters. Finally, the accuracy of the mathematical model and the concept of a contact stiffness are discussed.

It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one dimensional (1D) elastic foundation model. Using this 1D mapping we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness $K$ and compare it with the result of an analytical study. We attribute the failure of the elastic foundation model to the neglect of the long-range elastic coupling between the asperity contact regions., 5 pages, 4 figures, 29 references

The stiffness of machine tool supports should be properly designed for reducing both the ground disturbance vibration and the drive disturbance vibration. However, the stiffness cannot be easily calculated from the geometry and material properties of the support. In this paper, a 3D stiffness model of a machine tool support is proposed using contact stiffness. The stiffness in each direction is assumed to be determined by the contact stiffness at the interfaces and the bulk stiffnesses of the supports and the floor. The contact stiffness model proposed by Shimizu et al. is expanded to determine the contact stiffness in the normal and tangential directions of an interface. In the proposed model, the contact stiffness is obtained by multiplying the unit contact stiffness by the real contact area. The contact stiffness of concrete is experimentally investigated to estimate the stiffness between machine tool supports and the floor, and it was observed to be the primary determinant of the stiffness of interfaces between metal and concrete. Moreover, the unit contact stiffness of concrete is discovered to be less than 1/10 of those of the metals that were used for the study. The natural frequency and vibration mode shape of a model machine tool bed are also experimentally measured and used to verify the proposed stiffness model. The comparison of the results obtained from the two procedures shows that the natural frequency and vibration mode shape of a machine tool bed can be predicted using the proposed stiffness model.

A superalloy traditionally offers excellent mechanical strength, resistance to thermal creep deformation, good surface stability and resistance to corrosion or oxidation. However, a superalloy often also needs performance in terms of fretting resistance. Experimental results regarding fretting wear and contact properties of the superalloy René 80 are illustrated and discussed. The widespread applications of superalloys in jointing with friction as in the jointing of a turbine blade, is the main motivation for characterizing their fretting behaviour. The fretting experiments were performed at 100 Hz for two temperatures (600, 800 °C), and two sliding amplitudes (30, 60 µm). These temperatures and strokes are typical at the medium stage of a low-pressure gas turbine. Wear volume and the contact properties such as friction coefficient and tangential contact stiffness were measured and analysed. Results show that the lowest friction coefficient was measured at the temperature of 800 °C. This temperature hence appears to be an optimum working condition for the fretting wear of René 80. With regard to wear mechanism, a fundamental role of the sliding amplitude was found. In particular, the ratio between the sliding amplitude and the characteristic contact length has a significant influence upon the oxide growth on contact surfaces.

International audience; In a range of energy systems, interfacial characteristics at the finest length scales strongly impact overall system performance, including cycle life, electrical power loss, and storage capacity. In this letter, we experimentally investigate the influence of surface topology on interfacial electro-mechanical properties, including contact stiffness and electrical conductance at rough surfaces under varying compressive stresses. We consider different rough surfaces modified through polishing and/or sand blasting. The measured normal contact stiffness, obtained through nanoindentation employing a partial unloading method, is shown to exhibit power law scaling with normal pressure, with the exponent of this relationship closely correlated to the fractal dimension of the surfaces. The electrical contact resistance at interfaces, measured using a controlled current method, revealed that the measured resistance is affected by testing current, mechanical loading, and surface topology. At a constant applied current, the electrical resistance as a function of applied normal stress is found to follow a power law within a certain range, the exponent of which is closely linked to surface topology. The correlation between stress-dependent electrical contact and normal contact stiffness is discussed based on simple scaling arguments. This study provides a first-order investigation connecting interfacial mechanical and electrical behaviour, applicable to studies of multiple components in energy systems.

In this paper, the dynamic behavior of a cantilever beam impacting two flexible stops as well as rigid stops is studied both experimentally and numerically. The effect of contact stiffness, clearance, and contacting materials is studied in detail. For the numerical study of the system, a finite element model is created and the resulting differential equations are solved using a Time Variational Method (TVM). To achieve higher computational efficiency, the Newton-Krylov method is used along with TVM. Experimental results validate the contact model proposed for predicting the first mode system dynamics. A new nonlinear force estimation function has been proposed based on measured accelerations, which enables the understanding of the impact dynamics. � 2011 Springer Science+Business Media B.V.

Contact interface is one of the most important factors in a mechanical contact because it is the place where friction, sound, and heat originate. It is therefore inevitable that modeling various phenomenon related to contact dynamics requires a proper representation of the contact interfaces. One of the methods in representing the behavior of two surfaces in contact is by using the parameter of contact stiffness. In this study, the effect of surface texture on contact stiffness is analyzed. the texture was used in order to reduce the randomness of surface roughness. the soft material was chosen to achieve a pure elastic contact thus preventing plastic deformation to the asperities. the analysis was conducted by using an indentation method employing a steel ball with a relatively small indentation force. the result show contact stiffness values of the textured surfaces were smaller than that of smooth surface. This is particularly observed at low normal load at which total deformation of the surface is relatively small compared to the asperities height. This decrease in the contact stiffness value of the textured surfaces can be related to the reduction in the real contact area.

Nanostructured silicon carbide coatings were synthesized on Si(111) using Pulsed Laser Deposition (PLD) technique in Ultra High Vacuum (UHV). The PLD grown coatings possessing a nanocomposite architecture were characterized by Atomic Force Acoustic Microscopy (AFAM). The contact stiffness of such a coating was quantitatively evaluated from force-distance curves after due calibration with PZT and elemental Si. AFAM based metrology was used to map contact stiffness. Elastic constant for nanosturctured SiC coating of 150 nm thickness is found to be about 30 x 1010 N/m2. Contrast inversion procedure could reproducibly indicate hard and soft zones on the specimens. The latter showed stiffer zones due to pinning by nano-sized SiC particles. Copyright � 2009 American Scientific Publishers.

The elastic contact problem, as implemented in some commercial software such as ANSYS, depends on the user choice of some parameters such as normal contact stiffness, penetration limit and contact algorithms. This work investigates the artificial neural networks (ANN) potential to predict the value of some parameters, avoiding the trial-and-error procedure to determine these values. Contact problems based on simple problems are used to train the neural network, so it can predict the normal contact stiffness for more complex problems. Some contact examples are evaluated, including the small end connecting rod contact problem, of great importance in automobile industry. HighlightsANN were applied to obtain the normal contact stiffness parameter instead of the traditional trial-and-error approach.Simplified 2D contact models were used to capture the main features of the original 3D contact problem.A correction factor is deduced to correctly correlate the 2D-3D contact solutions.Good agreement is obtained from the normal contact stiffness estimated from 2D models with the original 3D parameter.

International audience; Obtaining a surface with negligible roughness is very expensive, time consuming and unnecessary. The influence of surface roughness on the contact stiffness is of great importance. The extra cost associated with unnecessary surface finish can be limited by eliminating the unnecessary machining operations beyond the required surface finish. In this article, a simplified solution is presented to calculate the stiffness of rough contact between the workpiece and spherical locator; also, the effect of surface roughness on the stiffness and deformation of rough spherical contact is studied for different applied loads to find an ‘economic roughness’ under machining forces.

Underplatform dampers (UPDs) are still in use to reduce the vibration amplitude of turbine blades and to shift the position of resonant frequencies. The dynamics of blades with UPDs is nonlinear and the analysis is challenging from both the experimental and the numerical point of view. A key point in obtaining a predictive numerical tool is the choice of the correct contact parameters (contact stiffness and friction coefficient) that are required as input to the contact model. The paper presents different approaches to choose these parameters: the contact stiffness in normal and tangential direction are both calculated and measured. The calculation is based on the analytical models in literature, the measurements are carried out on a dedicated test rig. The friction coefficient is also measured. Test results of the forced response of the same bladed disk with UPDs are available for each blade, they come from an experimental campaign under controlled excitation and centrifugal force. The forced response of the bladed disk is not used as a mean to tune the contact parameters, but rather as a validation tool: the effect of the different choices of contact parameters in the code is highlighted by the comparison of the calculated and experimental forced response of the bladed disk.

The vibration of a violin bridge is a dynamic contact vibration with two interfaces: strings-bridge, and bridge feet-top plate. In this paper, the mobility of an isolated bridge under in-plane excitation is explored using finite element modeling based on the contact vibration model. Numerical results show that the dynamic contact stiffness in the two contact interfaces has a great impact on the bridge mobility. A main resonance peak is observed in the frequency range of 2-3 kHz in the frequency response of the isolated bridge when the contact stiffness is smaller than a critical threshold. The main resonance peak frequency is affected by the contact stiffness as well. In order to verify the numerical findings, a novel experimental system is then designed on the basis of a piezoelectric dynamometer for bridge mobility analysis. Experimental results confirm the impact of the dynamic contact stiffness on the bridge mobility.

Comparative studies of different discrete element models of a rock-type material are presented. The discrete element formulation employs spherical particles with the cohesive interaction model combining linear elastic behaviour with brittle failure. Numerical studies consisted in simulation of the uniaxial compression test. Two cylindrical specimens with particle size distributions yielding different degree of heterogeneity have been used. Macroscopic response produced by different discrete element models has been compared. The main difference between the compared models consists in the evaluation of micromechanical constitutive parameters. Two approaches are compared. In the first approach, the contact stiffness and strength parameters depend on the local particle size, while in the second approach, global uniform contact parameters are assumed for all the contacting pairs in function of average geometric measures characterizing the particle assembly. The size dependent contact parameters are calculated as functions of geometric parameters characterizing each contacting particle pair. As geometric scaling parameters, the arithmetic and harmonic means, as well as the minimum of the radii of two contacting particles are considered. Two different models with size dependent contact parameters are formulated. The performance of these models is compared with that of the discrete element model with global uniform contact parameters. Equivalence between the models with size dependent and uniform contact parameters has been checked. In search of this equivalence, different methods of evaluation of global uniform parameters have been studied. The contact stiffness has been evaluated in terms of the average radius of the particle assembly or in terms of the averages of the arithmetic and harmonic means of the contact pair radii, the geometric parameters used in the evaluation of the contact stiffness in the size-dependent models. The uniform contact strengths have been determined as functions of the averages of radii squares, squares of arithmetic radii means or squares of minimum radii of the contacting pairs. For the more homogenous specimen, the models with local size dependent parameters and models with global uniform parameters give similar response. The models with uniform parameters evaluated according to the averages of the geometric parameters used in the evaluation of local parameters ensure better agreement with the respective models with size-dependent parameters than the models with uniform parameters evaluated according to the particle radii. Simulations using the more heterogenous specimen reveal differences between the considered models. There are significant differences in stress-strain curves as well as in the failure pattern. The models with local size-dependent parameters are more sensitive to the change of heterogeneity than the model with global uniform parameters. © 2012 Elsevier Ltd. All rights reserved.

The article presents research on the problem of two gear contact in the car gearbox. Contact stiffness is evaluated for the whole period of mesh. Also, contact stresses are evaluated in the contact place. The presented method can be used for calculating spur gear. Article in Lithuanian Automobilio pavarų dėžės cilindrinių tiesiakrumplių krumpliaračių krumplių kontaktinės sąveikos tyrimas Santrauka Straipsnyje nagrinėjama automobilio pavarų dėžės dviejų krumpliaračių krumplių kontaktinė sąveika. Nustatytas kontaktinis standumas nuo krumplių sukabinimo pradžios iki sukabinimo pabaigos. Taip pat nustatyti kontaktiniai įtempiai kontakto vietoje. Pateikta skaičiavimo metodika gali būti taikoma projektuojant tiesiakrumples cilindrines pavaras. Reikšminiai žodžiai: pavarų dėžė, tiesiakrumplė cilindrinė pavara, kontaktas, modelis, kontaktinis standumas, kontaktiniai įtempiai.

Under-platform dampers are commonly adopted in order to mitigate resonant vibration of turbine blades. The need for reliable models for the design of under-platform dampers has led to a considerable amount of technical literature on under-platform damper modeling in the last three decades. Although much effort has been devoted to the under-platform damper modeling in order to avail of a predictive tool for new damper designs, experimental validation of the modeling is still necessary. This is due to the complexity caused by the interaction of the contacts at the two damper-platform interfaces with the additional complication of the variablity of physical contact parameters (in particularly friction) and their nonlinearity. The traditional experimental configuration for evaluating under-platform damper behavior is measuring the blade tip response by incorporating the damper between two adjacent blades (representing a cyclic segment of the bladed disk) under controlled excitation. The effectiveness of the damper is revealed by the difference in blade tip response depending on whether the damper is applied or not. With this approach one cannot investigate the damper behavior directly and no measurements of the contact parameters can be undertake. Consequently, tentative values for the contact parameters are assigned from previous experience and then case-by-case finely tuned until the numerical predictions are consistent with the experimental evidence. In this method the physical determination of the contact parameters is obtained using test rigs designed to produce single contact tests which simulate the local damper-platfom contact geometry. However, the significant limitation of single contact test results is that they do not reveal the dependence of contact parameters on the real damper contact conditions. The method proposed in this paper overcomes this problem. In this new approach a purposely developed test rig allows the in-plane forces transferred through the damper between the two simulated platforms to be measured, while at the same time monitoring in-plane relative displacements of the platforms. The in-plane damper kinematics are reconstructed from the experimental data using the contact constraints and two damper motion measurements, one translational and one rotational. The measurement procedures provide reliable results, which allow very fine details of contact kinematics to be revealed. It is demonstrated that the highly satisfactory performance of the test rig and the related procedures allows fine tuning of the contact parameters (local friction coefficients and contact stiffness), which can be safely fed into a direct time integration numerical model. The numerical model is, in turn, cross-checked against the experimental results, and then used to acquire deeper understanding of the damper behavior (e.g. contact state, slipping and sticking displacement at all contact points), giving an insight into those features which the measurements alone are not capable of producing. The numerical model of the system is based on one key assumption: the contact model does not take into account the microslip effect that exists in the experiments. Although there is room for improvement of both experimental configuration and numerical modeling, which future work will consider, the results obtained with this approach demonstrate that the optimization of dampers can be less a matter of trial and error development and more a matter of knowledge of damper dynamics.