Normal Contact Stiffness Model Research Articles

A Fractal Prediction Method for Contact Stiffness of Helical Gear Considering Asperity Lateral Contact and Interaction

The normal contact stiffness (NCS) on rough surfaces has a significant impact on the dynamic characteristics of helical gear. Aiming at the problem of inaccurate calculation of the NCS model under the traditional Hertz theory of smooth surfaces, a fractal prediction model of helical gear contact stiffness considering asperity lateral contact and interaction between asperities is proposed in this paper. The variation formula of asperity and the correction coefficient of a tooth contact surface under asperity lateral contact and interaction are derived, and the influence of micro-elements on normal load and NCS is qualitatively analyzed. The results show that the NCS of considering the interaction and lateral contact of asperity is closer to the experimental results; the contact surface correction coefficient increases with the increase of curvature radius and load. The NCS of a tooth surface increases with the increase in fractal dimension D or the decrease in roughness amplitude G. The influence of asperity lateral contact and interaction decreases with the increase in D and the decrease in G. The NCS of the helical gear decreases under the lateral contact and interaction of the asperity, which is critical for exact estimation of the NCS of contact surfaces in gear.

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.

Normal contact stiffness model for fractal surfaces considering scale dependence and friction behavior

The normal contact stiffness on rough surfaces has a significant impact on the interfacial dynamic characteristics of mechanical joints. Based on the fractal geometry theory, this work improves the contact stiffness modeling by considering the complete contact characteristics of multiple asperities and frictional factor. First, to include the property that the critical contact areas of asperities are scale-dependent, the model for the contact stiffness is formed on each scale and the relationship between total stiffness and load on rough surfaces is obtained by the summation of all length scale asperities. Second, friction factor is taken into account in the revised normal contact stiffness model, where a contact friction coefficient is introduced into the equation to incorporate the effects of friction force. Moreover, the influences of fractal dimension D and fractal roughness G on normal contact stiffness and friction coefficient are investigated. Through the comparison of numerical and experimental results, the revised model is shown to be more reasonable and presents higher consistency of the stiffness versus load curve than the original model. It is therefore concluded that a complete and more accurate model for normal contact stiffness is proposed in this work with precise modeling of scale-dependent contact characteristics and friction behavior taken into account, which is critical for exact estimation of rigidity of contact surfaces in industrial applications.

A Normal Contact Stiffness Statistical Model of Joint Interface considering Hardness Changes

Based on Kogut and Etsion’s finite element contact model (KE model) and citing the hardness geometric limit proposed by Jackson et al., the deformation stage of an asperity is re-divided, and a normal contact stiffness model of joint interface is established by using a statistical theory. The simulation results show that the normal contact stiffness of joint interface is a nonlinear function of the mean surface separation and decreases with the increase of the mean surface separation under different plasticity indexes. By comparing the normal contact stiffness model of joint interface considering hardness changes with the normal contact stiffness model of joint interface without considering hardness changes, it is found that, with the increase of the plasticity index, the difference between calculated results becomes larger.

A CONTINUOUS SMOOTH CONTACT STIFFNESS MODEL FOR JOINT SURFACE CONSIDERING SUBSTRATE DEFORMATION

The contact stiffness of the joint surface directly affects the static and dynamic mechanical properties of the machine tool and the level of accuracy retention. In the process of elastic, elastoplastic and fully plastic contact deformation, based on the idea that asperity contact state variables have continuous and smooth characteristics, a single asperity normal contact stiffness model is established through Hermite polynomial interpolation function. Considering the effect of substrate deformation, the elastic contact substrate deformation is introduced in the three deformation stages of asperity. A continuous smooth joint surface stiffness model considering substrate deformation is established by statistical methods. The differences between GW, ZMC, KE, and Brake models are compared with the proposed model, and the influence of surface roughness on contact stiffness is revealed. The research shows that the contact stiffness and contact load obtained by considering the substrate deformation are smaller than those of ignoring the substrate deformation. The influence of substrate deformation increases rapidly as the surface roughness decreases. In addition, the contact load and surface roughness are the two main factors that affect the contact stiffness of the joint surface. The contact stiffness increases with the increase of the load or the decrease of the surface roughness.

Normal fractal contact stiffness model among three disks of rod-fastening rotor system with considering friction and the asperities interaction

PurposeThe purpose of this study is to develop a normal contact stiffness (NCS) model among three disks of the assembled rotor system, which systematically considers the friction coefficient, the asperities interaction and the elastoplastic contact regime.Design/methodology/approachBased on the revised fractal theory, considering the friction effect, the elastoplastic contact regime and the asperities interaction in a simple way, the total NCS among three disks of the rod-fastening rotor bearing system is established. Effects of fractal dimension and roughness, friction coefficient, asperities interaction and material properties on the normal stiffness are investigated by simulations and the relevant comparisons are given for examining the reasonability of the proposed model.FindingsNCS will decrease when asperities interaction and friction are included. As the load increases, the influences of asperities interaction and friction on stiffness become serious. NCS will be enhanced when the elastoplastic regime is considered.Originality/valueA comprehensive NCS model is developed. It provides a theoretical basis for the modeling of the NCS for multi-interfaces.

A three-dimensional fractal model of the normal contact characteristics of two contacting rough surfaces

According to the common characteristics of elastic mechanics and plastic mechanics expressions, a new model of asperity elastic–plastic contact is developed. The proposed model can solve the problem of discontinuous, leap, and non-monotone contact load and mean contact pressure and contact area in three separate phases, i.e., a perfectly elastic phase, elastoplastic phase, and fully plastic phase. The analytical model of normal contact stiffness considering the influence of the contact area distribution of the asperity and the elastoplastic deformation mechanism on the characteristics of the joint surface is further established by the fractal theory. In addition, the input energy of the asperity in the elastoplastic deformation stage is separated into stored energy and dissipated energy by introducing the loading and unloading model of the asperity. The analytical model of normal contact damping considering the deformation process of asperities and the elastoplastic deformation mechanism is further established. The effects of normal contact load, fractal dimension, fractal roughness, and plastic index on the normal contact stiffness and damping of the joint surface are studied by numerical simulation. The comparison of different models shows that the elastoplastic contact deformation mechanism has an obvious effect on the normal contact stiffness and damping. The normal contact stiffness and damping considering the elastoplastic deformation mechanism are greater than the normal contact stiffness and damping considering only the elastic and plastic states. Finally, the rationality of the present model is verified through model comparison and experimental comparison.

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.

Normal contact stiffness model considering 3D surface topography and actual contact status

Abstract. A normal contact stiffness model considering 3D topography and elastic–plastic contact of rough surfaces is presented in this paper. The asperities are generated from the measured surfaces using the watershed segmentation and a modified nine-point rectangle. The topography parameters, including the asperity locations, heights, and radii of the summit, are obtained. Asperity shoulder–shoulder contact is considered. The relationship of the contact parameters, such as the contact force, the deformation, and the mean separation of two surfaces, is modelled in the three different contact regimes, namely elastic, elastic–plastic and fully plastic. The asperity contact state is determined, and if the contact occurs, the stiffness of the single asperity pair is calculated and summed as the total normal stiffness of two contact surfaces. The developed model is validated using experimental tests conducted on two types of specimens and is compared with published theoretical models.

Fractal Prediction Model of Normal Contact Stiffness of Micro-pitting Gear

Fractal Prediction Model of Normal Contact Stiffness of Micro-pitting Gear

A multi-scale stiffness fractal model of joint interfaces

Stiffness characterization of mechanical interfaces is quite crucial for the analysis of several tribological behaviors. The stiffness of different machine tools varies greatly, particularly for computer numerical control machine. Therefore, this research aims at providing an assessment of influence factors for stiffness of joint interfaces theoretically. Based on fractal roughness parameters independent of scale and contact mechanics theory, the contact area of joint interface is studied, and the multi-scale normal contact stiffness model and multi-scale tangential contact stiffness model are proposed. Meanwhile, the problem of the deformation of any contact asperity is considered as three separate regimes. The laws of area-displacement and force-displacement under elastic-plastic regime are established. The transition which is in the deformation mechanism of asperity from elastic to plastic is consistent with classical contact mechanics. The analysis of numerical calculation results indicates the approximate linear relation among dimensionless normal load and key parameters. Moreover, these key parameters have been divided into two main categories for the multiscale model of joint interfaces, one is fractal parameters such as fractal dimension D and fractal roughness parameter G, and the other is interfacial parameters. In addition, tangential load and friction factor are two important factors to the tangential stiffness.

A MODIFIED COMPLETE NORMAL CONTACT STIFFNESS MODEL OF A FRACTAL SURFACE CONSIDERING CONTACT FRICTION

This paper presents a modified complete normal contact stiffness model of a fractal surface considering contact friction. We use this model to study the influence of fractal dimensions and fractal roughness on normal contact stiffness. The fractal micro-contact model of an asperity and the complete length scale contact model of fractal surface (both contrasting classical mechanics) are revised. The influence of frictional resistance at micro-contact interfaces on normal contact stiffness is also considered. Predictions of the new model are found to be in greater agreement with the results of the experiments than the predictions of the original model. The study analyzes the influence of fractal dimensions and fractal roughness on the normal contact stiffness. With the increase of these two fractal parameters, their influences on the normal contact stiffness are opposite and are different under high pressure and low pressure.

A normal contact stiffness model of machined joint surfaces considering elastic, elasto-plastic and plastic factors

Considering the rough surface as a fractal model makes the research of contact parameters more practical. In the fractal model of the machined surface, the parameters describing the surface topography are independent of the measurement resolution. Based on the elastic, elasto-plastic and plastic deformations of a single pair of contact asperities, a normal contact stiffness model using the fractal model for surface topography description is proposed in this paper. The specimens machined by milling and grinding methods are used to verify the proposed contact stiffness model based on the fractal theory. The experimental and theoretical results indicate that the proposed contact stiffness model is appropriate for the machined joint surfaces.

A Normal Contact Stiffness Model of Joint Surface Based on Fractal Theory

Based on the fractal theory, a normal contact stiffness model is established. In the model, the asperity is initially in elastic deformation under contact interference. As the interference is increased, a transition from elas... | Find, read and cite all the research you need on Tech Science Press

Normal Stiffness model of bolted joint based on the modified three-dimensional elastic-plastic contact fractal model

Bolted joints have a significant effect on the dynamical behaviour of assembled structures. Accurate contact stiffness model of bolted joint is crucial in predicting the dynamic performance of bolted structures. In this research, a modified three-dimensional fractal model of normal contact stiffness is presented to more accurately predict the dynamic characteristic of a bolted assembly. In the present model, while the contact deformation exceed the critical value the elastic-plastic contact is used to take the place of Hertz elastic contact in the traditional M-B model, and revise the drawback that elastic-plastic contact occurs before elastic contact in existing elastic-plastic fractal models. As the increase of contact force, the plastic deformation of single asperity is considered again, which is omitted in the two type fractal models. An experimental set-up with two T-shaped specimen is designed conducted to verify the efficiency of the proposed model. Comparing with the ZX elastic-plastic fractal model, the present model can predict contact stiffness and dynamic performance more accurately, particularly, while for higher contact loads. The results show that the modified elastic-plastic fractal contact model can be used to more accurately predict the stiffness and dynamic characteristic of bolted structures in the machine tools.

Fractal Model of Normal Contact Stiffness between Two Spheres of Joint Interfaces with Simulation

The contact stiffness of joint surface plays a significant role in the overall static and dynamic characteristics of mechanical systems. When considering joint interfaces with two rough surfaces, the traditional model based on Hertz contact theory between a sphere and a plane is difficult to use, especially for increasingly complex engineering surfaces. In order to overcome the weakness, here we propose a new contact stiffness model in view of the influence of domain extension factor between two rough surfaces. We study the deformation mechanism and the critical contact parameters. Subsequently, we analyze evolution of the elastic-plastic contact involving three distinct stages ranged from complete elastic through elastic-plastic to fully plastic deformation. Our fractal model is more universal than the traditional model based on some strict assumptions which simplify the contact of two rough surfaces to a rough surface and a rigid plane. In fact, the traditional model could be regarded as a special case in our new model. Simulations show that non-dimensional normal contact stiffness increases with dimensionless contact total load under the mechanism of elastic-plastic transition when the fractal dimension is between 1.1 to 1.5. The results indicate that contact stiffness of our fractal model is appropriate and the theoretical contact stiffness is consistent with the experiment data. DOI: http://dx.doi.org/10.5755/j01.mech.23.5.19356

Research on fractal model of normal contact stiffness for mechanical joint considering asperity interaction

The normal contact stiffness of mechanical joint has immediate impact on dynamic characteristics and machining precision of machine tools. A fractal contact stiffness model considering the effect of asperity interaction is proposed in this paper. On the basis of elastic theory, the deformation of a given asperity is deduced. The relationship between contact stiffness, normal load and contact area is derived from Hertz contact theory and fractal theory. The effect of asperity interaction on contact stiffness is studied by comparing with fractal model. The fractal smoothness is defined from relation between fractal parameters and surface roughness. It is concluded that with the increase of the fractal dimension D and the decrease of fractal roughness parameter G, the contact stiffness of the joint increases, and the effect of asperity interaction becomes greater. The fractal smoothness also affects the normal contact stiffness and the effect of surface smoothness can be offset by the asperity interaction. Experiment shows that the proposed model is more in line with the actual load-stiffness relationship. The model reveals the factors that affect stiffness of the joint, which can provide a theoretical basis for improving the rigidity and precision of integrated machineries.

A new fractal model of elastic, elastoplastic and plastic normal contact stiffness for slow sliding interface considering dynamic friction and strain hardening

The deflection properties of elastic stage, elastoplastic stage and plastic stage of elastomer were analyzed. Taking account of the kinetic friction force in friction interface and strain hardening in slow sliding interface, the elastic, elastoplastic and plastic normal contact stiffness model for harsh surface was established, which revised the Majumdar-Bhushan fractal model and made it more perfect. In the combination of macro and micro perspective, the effects of coarse surface fractal variables, kinetic friction force in the friction interface, material characters of the friction couples on the contact status and contact property were discussed by the study of digital analysis. Results imply that the normal contact stiffness improves with the increasing real contact area and normal contact load, and reduces with the augment of kinetic friction coefficient. When the kinetic friction coefficient is smaller than 0.3, the normal contact stiffness comprises a linear decrease with the increment of kinetic friction coefficient. When the kinetic friction coefficient is bigger than 0.3, the normal contact stiffness has an exponential decrease with the increasing kinetic friction coefficient.

Research on fractal model of normal contact stiffness between two spheroidal joint surfaces considering friction factor

In order to precisely calculate normal contact stiffness (NCS), this paper discusses the fractal model to calculate NCS for spheroidal contact bodies considering friction factor. The numerical results show that the relationship between NCS and normal load is direct or inverse ratio decided by the value of fractal dimension; as fractal dimension, material propertied parameters and curvature radius increase, NCS adds; as friction coefficient and roughness amplitude rises, NCS falls instead; It is effective to increase NCS by choosing the internal contact, improving surface quality of contacts and raising the yield strength of the softer material.

A modified normal contact stiffness model considering effect of surface topography

The contact stiffness of joint surfaces is an important factor influencing the static and dynamic characteristics of the mechanical equipment. In the present research, a modified normal contact stiffness model of two rough surfaces is proposed. First, the stiffness model of a single asperity contact pair is obtained based on shoulder-shoulder contact in conjunction with the elastic-plastic contact model proposed by Jackson and Green. Second, the topographies of contact surfaces are analyzed, and the locations of asperities and the statistical distributions of asperity heights and radii are acquired experimentally. The asperities are then generated using Monte Carlo method with the information to simulate the real contact. Finally, the asperities contact state is determined and if the contact occurs, the stiffness of the single asperity pair is calculated and summed as the total normal stiffness of two contact surfaces. The proposed stiffness model is validated by experiments with the errors less than 10%.