Contact Stiffness Of Surfaces Research Articles

A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory

A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems.

A Joint Surface Contact Stiffness Model Considering Micro-Asperity Interaction

A Joint Surface Contact Stiffness Model Considering Micro-Asperity Interaction

Research on contact stiffness of tenon jointed turbine bladed disk under time-varying load

Abstract Tenon-jointed turbine blades will be impacted by airflow and centrifugal force during the high-speed rotation of the engine. The surface contact stiffness of the tenon and tenon groove will change with complex external loads. Through the analysis of the micro-morphological characteristics of the contact surface of the tenon joint bladed disk, the contact characteristics of the asperities on the rough surface are determined. At the same time, to solve the problem that the traditional microscopic contact stiffness calculation formula cannot be applied to the tangential displacement load, the periodic piecewise tangential stiffness expression is derived based on external loads of the normal force and the equivalent tangential force. Furthermore, this paper studies the properties of the tangential stiffness curves under different external load frequency ratios and phase differences. An increase in the frequency ratio will decrease the step value of the piecewise function and make it tend to a smooth transition. The change of the phase difference will directly change the monotonicity and fluctuation of the stiffness curve. The macro and micro theoretical analysis methods of contact characteristics have been established.

Analysis, Modeling and Experimental Study of the Normal Contact Stiffness of Rough Surfaces in Grinding

Grinding is the most important method in machining, which belongs to the category of precision machining processes. Many mechanical bonding surfaces are grinding surfaces. Therefore, the contact mechanism of grinding a joint surface is of great significance for predicting the loading process and dynamic characteristics of precision mechanical products. In this paper, based on the collected grinding surface roughness data, the profile parameters and topography characteristics of the asperity were analyzed, the rough surface data were fitted, the asperity profile was reconstructed, and the parabola y = nx2 + mx + l of the cylindrical asperity model was established. After analyzing the rough surface data of the grinding process, the asperity distribution height was fitted with a Gaussian distribution function, which proved that asperity follows the Gaussian distribution law. The validity of this model was confirmed by the non-dimensional processing of the assumed model and the fitting of six plasticity indices. When the pressure is the same, the normal stiffness increases with the decrease in the roughness value of the joint surface. The experimental stiffness values are basically consistent with the fitting stiffness values of the newly established model, which verifies the reliability and effectiveness of the new model established for the grinding surface. In this paper, a new model for grinding joint surface is established, and an experimental platform is set up to verify the validity of the model.

Introduction study on the influence of residual stress on contact stiffness of joint surface

The effects of residual stress on material properties can be divided into two main categories: its influence on material strength, such as fatigue, and its influence on harmful deformation, such as dimension deviation during or after processing. To investigate the effects of residual stress on the mechanical properties of material components, we select a simple structure that underwent loading and unloading cycles. In our finite element numerical simulation, we establish both a macroscopic solid model and an asperity model. Three different models are chosen, and load-displacement curves are obtained. The effects of residual stress on the stiffness of the contact surface are analyzed. Our results show that residual stress has a significant impact on the stiffness of the joint surface, from macroscopic to microscopic perspectives. Specifically, stiffness increases with residual stress when it is tensile stress.

Theoretical and Experimental Study on Normal Contact Stiffness of Plane Joint Surfaces With Surface Texturing

Effects of surface texturing on normal contact stiffness have been investigated by experiments in previous research studies; however, there are relatively few theoretical models in this regard. This article aims to investigate the influence of surface texturing on the normal contact stiffness in theory and experiment. In the present research, a rough surface with surface texturing is divided into two parts, the textured zone and the remaining zone, and their theoretical models of normal contact stiffness are established respectively, considering surface morphology and material properties. For the textured zone, microtextures are modeled theoretically based on the three-dimensional topographic data obtained via a laser profilometer. For the remaining zone, the surface topography is characterized based on fractal theory, and a calculation model is established considering the elastoplastic deformation of surface asperities. In the experiment, the normal contact stiffness of specimens is obtained through the self-developed experimental platform. The proposed theoretical model is appropriate through the comparison of test results and theoretical predictions. The research results show that the effect of surface texture on the contact stiffness is related to the surface roughness, Sa. For the joint surfaces with Sa > 2.69 μm, the normal contact stiffness can be effectively increased through proper surface texturing.

An Analytical Model for the Normal Contact Stiffness of Mechanical Joint Surfaces Based on Parabolic Cylindrical Asperities.

The analytical results of normal contact stiffness for mechanical joint surfaces are quite different from the experimental data. So, this paper proposes an analytical model based on parabolic cylindrical asperity that considers the micro-topography of machined surfaces and how they were made. First, the topography of a machined surface was considered. Then, the parabolic cylindrical asperity and Gaussian distribution were used to create a hypothetical surface that better matches the real topography. Second, based on the hypothetical surface, the relationship between indentation depth and contact force in the elastic, elastoplastic, and plastic deformation intervals of the asperity was recalculated, and the theoretical analytical model of normal contact stiffness was obtained. Finally, an experimental test platform was then constructed, and the numerical simulation results were compared with the experimental results. At the same time, the numerical simulation results of the proposed model, the J. A. Greenwood and J. B. P. Williamson (GW) model, the W. R. Chang, I. Etsion, and D. B. Bogy (CEB) model, and the L. Kogut and I. Etsion (KE) model were compared with the experimental results. The results show that when roughness is Sa 1.6 μm, the maximum relative errors are 2.56%, 157.9%, 134%, and 90.3%, respectively. When roughness is Sa 3.2 μm, the maximum relative errors are 2.92%, 152.4%, 108.4%, and 75.1%, respectively. When roughness is Sa 4.5 μm, the maximum relative errors are 2.89%, 158.07%, 68.4%, and 46.13%, respectively. When roughness is Sa 5.8 μm, the maximum relative errors are 2.89%, 201.57%, 110.26%, and 73.18%, respectively. The comparison results demonstrate that the suggested model is accurate. This new method for examining the contact characteristics of mechanical joint surfaces uses the proposed model in conjunction with a micro-topography examination of an actual machined surface.

Dynamics analysis of width-varying microcantilevers: Interplay between eigenfrequencies, contact stiffness and interaction forces

In this study, the resonance-frequency dependence and modal sensitivity of the flexural vibration modes of overhang/T-shaped microcantilevers to the interaction force and surface stiffness variations were analysed, and a closed-form expression was derived. The Euler–Bernoulli beam theory was used to develop the overhang/T-shaped models, and a characteristic formula representing the dependence of cantilever frequencies on the overhang dimensions was obtained. The results of the derived expression were analysed using numerical simulations to investigate and compare the effects of the overhang width, length, repulsive and attractive forces, and surface contact stiffness on the flexural mode of overhang/T-shaped cantilevers. Furthermore, a closed-form expression for the modal sensitivities of the width-varying cantilever was derived, and the modal sensitivities were compared using numerical simulations. Finally, the effects of the interaction forces and contact stiffness on the frequency response and sensitivities of different cantilevers based on their stiffness and geometrical parameters were verified experimentally. This study can open new paths for designing, fabricating, and using width-varying cantilevers in sensing and imaging applications, particularly for cantilever array systems.

Fractal Model of Contact Thermal Stiffness

The continuity, self-similarity, and self-affinity of a microscopic contact surface can be described by the Weierstrass–Mandelbrot (W–M) function in fractal theory. To address the problems that the existing normal contact load fractal model does not take into account the effect of thermal stress and is not applicable to the temperature variation in the joint surface of the giant magnetostrictive ultrasonic vibration systems, a fractal model of thermal–elastic–plastic contact normal load fractal is established based on fractal theory. The model is an extension of the traditional model in terms of basic theory and application scope, and it takes into account the effects of temperature difference, linear expansion coefficient, fractal dimension, and other parameters. Finally, the effect of the temperature difference at the joint surface on the normal load of the thermoelastic contact is revealed through numerical simulations. The results show that the nonlinearity of the contact stiffness of the thermoelastic joint surface is mainly related to the surface roughness and the fractal dimension, while the effect of the temperature change on the joint surface properties within a certain range is linear.

Research on Normal Contact Stiffness of Rough Joint Surfaces Machined by Turning and Grinding

In order to accurately obtain the contact stiffness of rough joint surfaces machined by turning and grinding, a research simulation is carried out by using the finite element method. Based on the surface modeling method under the combined machining mode, the three-dimensional (3D) solid model is constructed. Then, the finite element results of the normal contact stiffness were obtained through contact analysis. The comparative analysis was carried out with the analytical results of the KE model and the experimental results. The comparison results show that three results have the same trend of change. However, the maximum relative error of the finite element results is 6.03%, while that of the analytical results for the KE model is 60.07%. After that, the finite element results under different machining parameters are compared. The normal contact stiffness increases with the increase in the turning tool arc radius, grinding depth, and fractal dimension, but decreases with the increase in the turning feed rate and scale coefficient. The rationality of the results is explained by the distribution of the asperities and the contact deformation law of the asperities on the rough surface.

Simulation and experiment of secondary contact stiffness of rough surface

Simulation and experiment of secondary contact stiffness of rough surface

Loss Characterization of Giant Magnetostrictive Material Under Compressive Stress

The properties of giant magnetostrictive material (GMM) are very sensitive to external compressive stress. Knowledge of these key properties is of essential importance in practical applications such as high-power underwater transducers. Although the parameters of GMM have been extensively studied, characterization and analysis of magnetic, elastic, and piezoelectric losses under different compressive stresses are rarely reported due to the difficulty in experimentally realizing the ideal mechanical free or clamped boundary conditions. In this study, we designed a longitudinal transducer for complex parameters characterization of GMM. We successfully characterize the key three losses in GMM using a multi-degree-of-freedom (MDOF) lumped parameter equivalent circuit model (LECM), meticulously incorporating the surface contact damping, stiffness, and structural losses. MDOF LECM provides a novel idea for loss characterization of GMM under compressive stress. In contrast to prior-art parameters characterization based on the distributed parameter equivalent circuit model (DECM), the proposed characterization based on MDOF LECM shows apparent superiority in terms of global sensitivity. The intensive losses of GMM for ten-time characterizations show high stability and are all positive. Statistical analysis of intensive losses’ dependency on the compressive stress is performed. A longitudinal transducer is designed for experimental verification. Finally, 95% prediction and confidence intervals for the variation trend of the intensive losses in relationship with compressive stress are obtained.

TECHNOLOGICAL SUPPORT OF CONTACT RIGIDITY OF MACHINE PARTS

The theoretical provisions on establishing the relationship between the geometric characteristics of the surfaces of contacting parts, as well as the physical and mechanical characteristics of the material of these surfaces on their contact stiffness, including the contact stiffness of the surfaces of parts of high-load gas turbine engine components, are presented. The analysis of dependencies on the relationship of contact stiffness and pliability of surfaces with the technological conditions of their processing by various types of cutting process (turning, milling, grinding) is given.

A revised contact stiffness model of rough curved surfaces based on the length scale

Based on the continuity of length scale for asperities, a complete model of normal stiffness between curved fractal surfaces considering friction factor is proposed. Through the coupling of critical base diameter and contact area, deformation modes of all asperities are determined, and contact stiffness of the whole rough surface is derived by double integral. Accordingly, effects of contact load, surface topography, friction factor, size parameters and material properties on the contact stiffness are investigated. Results show that contact stiffness depends sensitively on the fractal dimension, and exhibits nonmonotonic characteristics as fractal roughness varies across scales. Finally, predicted values of normal stiffness are compared with existing contact models as well as experimental data.

Influence of dynamic loads in joints on dimensional stability

In small arms manufacturing the lock dimensional chain final link precision is secured with manual file fitting and removing the tolerance intentionally left on the recoil lugs. The manual process reduces the contact stiffness of the lock components, and the final link dimension (between the cylindrical gauge end that simulates a cartridge, and the breeching lock face) set during the assembly is distorted when the breech lock components are exposed to shot impact loads. For this reason, the cylindrical cartridge dummy used for the initial assembly is sized to allow for subsequent plastic deformation at the breech lock component interfaces. The deformation value is determined experimentally on an ad hoc basis. Polynomial expressions have been obtained experimentally for the interface plastic deformation vs. relative positioning errors and surface finish relation for parts made of typical military steel grades. To study the relation between the interface surface machining methods and contact stiffness flat specimens, 50RA steel quenched to HRC 40…45 (the roughness Rz is 10…15 μm) were machined as follows: peripheral pregrinding; flank milling; file crosswise (at 45°) movements. The results generated after processing the measurements made with a HOMMEL TESTER W55 instrument show that finish flank milling yields the best results.

Технологическое обеспечение эксплуатационных свойств плоских поверхностей скольжения

There are shown experimental investigations of wear-resistance, contact stiffness and anti-friction properties of flat surfaces at their relative sliding. A technological support of quality parameters in flat friction surfaces after their sput-tering and strengthening is described.

Analysis of complex modal instability of a minimal friction self-excited vibration system from multiscale fractal surface topography

In order to reveal the stability and nonlinear characteristics of the friction self-excited vibration system from the perspective of microscopic multiscale fractal surface topography, a minimal two-degree-of-freedom mathematical model of the disc brake system is established in this paper. Considering the fractal characteristics of rough surface topography, the fractal contact stiffness of contact surfaces is introduced into the system model from the perspective of microscopic contact, and the effects of two important surface fractal parameters, fractal dimension D and fractal roughness G, on the stability and nonlinearity of the system are analyzed. Further finite element analysis and brake noise test improve the analysis of system stability and noise intensity by different surface topographies. The results show that the system stability can be improved with the increase of fractal dimension within a certain range, and the system will be in a stick state with the further increase of fractal dimension. With the increase of fractal roughness, the unstable modal coupling region of the system is increasing, which can reduce the stability of the system. The unstable region of the system is dependent on fractal dimension and fractal roughness, and has different sensitivity to them.

New analytical model of elastic-plastic contact for three-dimensional rough surfaces considering interaction of asperities

The contact calculation of three-dimensional real rough surfaces is the frontier field of tribology and surface science. In this study, we consider the interaction and elastic-plastic deformation characteristics of asperities and further, propose an analytical contact calculation method for rough surfaces considering the interaction of asperities. Based on the watershed algorithm, the rough surface is segmented and the asperities are reconstructed into ellipsoids. According to the height relationship between the asperities, the definition of the deformation reference height of the matrix between each couple of asperities is provided. Subsequently, the calculation formula of the substrate deformation is provided according to the local contact pressure considering the elastic-plastic deformation of the asperity, and the contact state under a specific load is determined using the iterative correction method. The results correspond with those of finite element numerical calculation and the study reveals the following: (1) compared with the results obtained without considering the asperity interaction, contact area, distance, and stiffness will be reduced by 6.6%, 19.6%, and 49.5%, respectively, when the influence of asperity interaction is considered; (2) the interaction of the asperities has the greatest influence on the surface contact distance and stiffness. Under the same load, the existence of asperity interaction will reduce the contact distance, area, and stiffness; (3) considering the interaction of the asperities, the higher asperity will bear more load, but it will simultaneously reduce the contact of the surrounding area and increase that of the distant area. The calculation method proposed in this study has the advantages of high calculation efficiency and accuracy, thus, providing the calculation basis and method for subsequent studies on service performance of rough surfaces, such as the calculation of contact stiffness and fatigue performance analysis of rough surfaces.

Statistical Model of Normal Contact Stiffness of Fixed Joint Surface during Unloading after First Loading

Based on Kogut and Etsion’s model (KE model), a statistical method is used to establish a model of normal contact stiffness of fixed joint surface during unloading after first loading. Simulation results show that, for the elastoplastic contact, normal contact stiffness of joint surface is the nonlinear function of mean surface separation during loading and unloading and decreases as the separation increases. For different plasticity indexes, the normal contact stiffness of joint surface varies differently following the change of mean surface separation during loading and unloading.

Evolution Behavior Analysis of Normal Contact Stiffness of Fractal Surface under Loading and Unloading

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.