Contact Stiffness Model Research Articles

DEM analysis of geobag wall system filled with recycled concrete aggregate

This paper investigates numerically a novel geobag wall system using recycled concrete aggregate. The analysis of the performance of the geobag wall system as a flexible retaining wall to support an embankment was conducted employing the discrete element method (DEM) code PFC2D. The slope soil was simulated as bonded balls utilizing the contact-bond model, and the recycled concrete aggregate was treated as unbonded balls based on the linear contact stiffness model. The geotextile of the geobags was set as ball clusters with the parallel bond model. The corresponding parameters of the slope soil, aggregate, and geotextile were derived from biaxial tests, large-scale direct shearing tests, tensile tests, and modified shearing tests. These parameters were calibrated by contrasting the measured data with the numerical results. Utilizing the calibrated parameters, numerical models were established for slopes strengthened by the geobag wall systems, which had been investigated in a series of experimental indoor 1-g model tests. The numerical results were contrasted with the measured data in terms of settlement, horizontal displacement, soil pressure, and crack distribution. Additionally, the coordination numbers, porosities and displacement vectors of the DEM models were also investigated. The modeling methods and results presented in this paper can provide researchers with more insights into the DEM modeling of geobag wall systems and recycled concrete aggregate.

Simple Contact Stiffness Model Validation for Tie Bolt Rotor Design With Butt Joints and Pilot Fits

Abstract Tie bolt rotors for centrifugal compressors comprise multiple shaft components that are held together by a single tie bolt. The axial connections of these rotors—including butt joints, Hirth couplings, and Curvic couplings—exhibit a contact stiffness effect, which tends to lower the shaft bending frequencies compared to geometrically identical monolithic shafts. If not accounted for in the design stage, shaft bending critical speed margins can be compromised after a rotor is built. A previous paper had investigated the effect of tie bolt force on the bending stiffness of stacked rotor assemblies with butt joint interfaces, both with and without pilot fits. This previous work derived an empirical contact stiffness model and developed a practical finite element modeling approach for simulating the axial contact surfaces, which was validated by predicting natural frequencies for several test rotor configurations. The present work built on these previous results by implementing the same contact stiffness modeling approach on a real tie bolt rotor system designed for a high pressure centrifugal compressor application. Each joint location included two axial contact faces, with contact pressures up to five times higher than previously modeled, and a locating pilot fit. The free-free natural frequencies for different amounts of tie bolt preload force were measured, and the frequencies exhibited the expected stiffening behavior with increasing preload. However, a discontinuity in the data trend indicated a step-change increase in the contact stiffness. It was shown that this was likely due to one or more of the contact faces becoming fully engaged only after sufficient tie bolt force was applied. Finally, a design calculation was presented that can be used to estimate whether contact stiffness effects may be ignored, which could simplify rotor analyses if adequate contact pressure is used.

A Novel Micro-Contact Stiffness Model for the Grinding Surfaces of Steel Materials Based on Cosine Curve-Shaped Asperities.

Contact stiffness is an important parameter for describing the contact behavior of rough surfaces. In this study, to more accurately describe the contact stiffness between grinding surfaces of steel materials, a novel microcontact stiffness model is proposed. In this model, the novel cosine curve-shaped asperity and the conventional Gauss distribution are used to develop a simulated rough surface. Based on this simulated rough surface, the analytical expression of the microcontact stiffness model is obtained using contact mechanics theory and statistical theory. Finally, an experimental study of the contact stiffness of rough surfaces was conducted on different steel materials of various levels of roughness. The comparison results reveal that the prediction results of the present model show the same trend as that of the experimental results; the contact stiffness increases with increasing contact pressure. Under the same contact pressure, the present model is closer to the experimental results than the already existing elastic–plastic contact (CEB) and finite-element microcontact stiffness (KE) models, whose hypothesis of a single asperity is hemispherical. In addition, under the same contact pressure, the contact stiffness of the same steel material decreases with increasing roughness, whereas the contact stiffness values of different steel materials under the same roughness show only small differences. The correctness and accuracy of the present model can be demonstrated by analyzing the measured asperity geometry of steel materials and experimental results.

Investigation of normal and tangential contact stiffness considering surface asperity interaction

PurposeThis paper aims to propose a normal and tangential contact stiffness model to investigate the contact characteristics between rough surfaces of machined joints based on fractal geometry and contact mechanics theory considering surface asperities interaction.Design/methodology/approachThe fractal geometry theory describes surface topography and Hertz contact theory derives the asperities elastic, elastic-plastic and plastic contact deformation. The joint normal and tangential contact stiffness are obtained. The experiment method for normal and tangential contact stiffness are introduced.FindingsThe relationship between dimensionless normal contact load and dimensionless normal and tangential contact stiffness are analyzed in different plasticity index. The results show that they are nonlinear relationships. The normal and tangential contact stiffness are obtained based on theoretical and experimental methods for milling and grinding machined specimens. The results indicate that the present model for the normal and tangential contact stiffness are consistent with experimental data, respectively.Originality/valueThe normal and tangential contact stiffness models are constructed by using the fractal geometry and the contact mechanics theory considering surface asperities interaction, which includes fully elastic, elastic-plastic and fully plastic contacts deformation. The present method can generate a more reliable calculation result as compared with the contact model no-considering asperities interaction.

Analysis of load distribution and contact stiffness of the single-nut ball screw based on the whole rolling elements model

This paper aims to investigate the load distribution and contact stiffness characteristics of the single-nut ball screw pair (SNBSP). First, the transformed relationship of coordinate systems is established. Then, the whole rolling elements load distribution model of the SNBSP is presented. Based on this, the whole rolling elements contact stiffness model is obtained. Applying the Newton–Raphson iterative method to solve the model, the normal force of rolling elements and the contact angles between balls and raceway surface are determined. The calculation results are reasonably consistent with those of the half pitch model. Then, the local contact stiffness and global contact stiffness are obtained. Furthermore, the effects of axial load and structural parameters of the SNBSP on the normal contact force, contact angle, and local and global contact stiffness are discussed using numeric analysis. Finally, a dynamic model of the z-axis feed system with time-varying axial stiffness is established, and the accuracy of the model is verified by experiments.

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.

Influences of wear on dynamic characteristics of angular contact ball bearings

Wear between balls and races has significant effects on the dynamic characteristics of bearing, which is the main reason to cause bearing failure. Some existing contact stiffness models were established to study the dynamic characteristics of bearing. However, the wear of bearing has been rarely investigated due to the complexities of contact load and wear mechanism. This paper presents a new dynamic wear simulation model of angular contact ball bearings mounted in pairs to solve this problem. A final contact stiffness model is established based on the wear model. The effects of running distance, horizontal load, preload, initial contact angle, number and diameter of balls on wear performances are analyzed. A generalized time-varying and piecewise-nonlinear dynamic model of angular contact ball bearings is established to perform an accurate investigation on its dynamic characteristics, especially considering the coupling effects of wear and rolling contact. The effects of wear on the contact stiffness and nonlinear dynamic characteristics are analyzed according to the dynamic model. Additionally, the variations of the contact stiffnesses and frequency responses with different preloads are discussed and the results indicate that parameter selection has significant effects on the wear and nonlinear response.

Characteristics analysis of rotor model with support–foundation looseness fault considering elastic–plastic contact

In this paper, the nonlinear response characteristics of a single degree of freedom lumped mass model with a new support looseness fault are analyzed. In this model, a new nonlinear contact stiffness model between the support and foundation is considered, which considers the elastic–plastic deformation of the contact parts. The nonlinear response of the system is obtained by numerical integration methods. The nonlinear results are compared with an asymmetric model and a piece-wise contact model. By comparing three different looseness fault models, the mechanism of generating multi-frequencies and fractional frequencies is analyzed. The result shows that plastic deformation makes the displacement amplitude increase rapidly; odd harmonics appear in symmetric stiffness model due to the modulation of symmetric shock forces; however, harmonic response appears in asymmetric stiffness model; when the contact number is odd, the frequency components contain odd or even order fractional frequencies at supercritical speeds due to the incompatibility of contacts on the upper and lower surfaces; when the contact number is even, multiple frequency components appear at subcritical frequencies.

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

Dynamic axial contact stiffness analysis of position preloaded ball screw mechanism

This article establishes an axial contact stiffness model of position preloaded ball screw mechanism based on Hertz contact theory. The analysis of dynamic axial contact stiffness is one of the foundations of the research on the dynamic characteristic of the ball screw feed drive system. The model takes into account the coupling relationship between the contact angle and the normal contact force, as well as the coupling relationship between the elastic deformation and the contact deformation coefficient. The static and dynamic axial contact stiffness characteristics of the preloaded ball screw mechanism are studied. The numerical analysis result shows that the static contact stiffness of the preloaded ball screw mechanism increases with the increase in the preload and decreases with the increase in the axial load. The dynamic contact stiffness of the preloaded ball screw mechanism increases with the increase in the screw’s rotational speed. The variation range of dynamic contact stiffness increases with the increase in axial load under the same preload. And the variation range of dynamic contact stiffness decreases with the increase in preload under the same axial load. The axial contact stiffness model established in this article can be used to analyze either static or dynamic contact stiffness of position preloaded ball screw mechanism.

Fractal modeling of normal contact stiffness for rough surface contact considering the elastic–plastic deformation

In this work, a new formulation of elastic–plastic contact model for the normal contact between rough surfaces is proposed based on the fractal theory. The surface topography is described using the modified one-variable Weierstrass–Mandelbrot fractal function. A new elastoplastic asperity contact model is developed based on the contact mechanics combined with the continuity and smoothness of mean contact pressure and contact load across different deformation regimes from elastic to elastoplastic, and from elastoplastic to fully plastic. The contact stiffness of a single asperity in the three deformation regimes of fully plastic, elastoplastic and elastic is derived, which changes smoothly at transit points between different deformation modes and overcomes the shortcoming of discontinuity derived from previous model. The contact stiffness and contact load of the whole surface in the three deformation regimes are formulated by integrating the micro-asperity contact. The difference between contact stiffness calculated from the plastic–elastoplastic–elastic three contact regimes and plastic–elastic two contact regimes is not obvious for surface with rougher topograph; however, for surface with smoother topograph, the two contact regimes predict a much smaller contact stiffness. The relationship of the normal contact stiffness and the normal contact force follows a power law function for the fractal surface contact considering three deformation regimes. The power exponent is nonlinearly dependent on the fractal dimension, which is different from the linear relationship for the purely elastic contact.

Dynamic identification of tangential contact stiffness by using friction damping in moving contact

Abstract Interactions at interfaces play a pivotal role in the mechanics of fractured materials as well as joint interfaces. Therein, the dry friction and stick-slip effects will serve as essential factors of a certain nature. Here, we focuses on the investigating of transition process from adhesion to sliding between two rough surfaces during reciprocating moving contact. A measurement system for friction damping is designed to identify the key parameters of tangential contact stiffness associated with the transition process. A tangential contact stiffness model is proposed to describe the mating rough surfaces by considering the effect of sticking and sliding. As a result, the tangential contact stiffness can be obtained through the compiled calculation procedure.

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.

A novel nonlinear contact stiffness model of concrete–steel joint based on the fractal contact theory

The heavy-duty machine tool is usually assumed in the concrete foundation, in which the machine tool-foundation joints have a critical effect on the working accuracy and life of heavy-duty machine tool. This paper proposed a novel contact stiffness model of concrete–steel joint based on the fractal theory. The topography of contact surface exist in concrete–steel joint has a fractal feature and can be described by fractal parameters. Asperities are considered as elastic, plastic deformation in micro-scale. However, the asperities of concrete surface will be crushed when the stress is larger than their yield limit. Then, the force balance of contact surfaces will be broken. Here, an iteration model is proposed to describe the contact state of concrete–steel joint. Because the contact asperities cover a very small proportion (less than 1%), the load on crushed asperities is assumed carried by other no contact asperities. This process will be repeated again and again until the crushed asperities are not being produced under external load. After that, the real contact area, contact stiffness of the concrete–steel joint can be calculated by integrating the asperities of contact surfaces. Nonlinear relationships between contact stiffness and load, fractal roughness parameter G, fractal dimension D can be revealed based on the presented model. An experimental setup with concrete–steel test-specimens is designed to validate the proposed model. Results indicate that the theoretical vibration mode shapes agree well with the experimental variation mode shapes. The errors between theoretical and experimental natural frequencies are less than 4.18%. The presented model can be used to predict the contact stiffness of concrete–steel joint, which will provide a theoretical basis for optimizing the connection characteristic of machine tool-concrete foundation.

Implementation of Hertz Contact Theory and Validation of Applicability of Hertz Contact Stiffness Model for Helical Gear using Multi Body Dynamics

Implementation of Hertz Contact Theory and Validation of Applicability of Hertz Contact Stiffness Model for Helical Gear using Multi Body Dynamics

A robust interaction control approach for underwater vehicle manipulator systems

In underwater robotic interaction tasks (e.g., sampling of sea organisms, underwater welding, panel handling, etc) various issues regarding the uncertainties and complexity of the robot dynamic model, the external disturbances (e.g., sea currents), the steady state performance as well as the overshooting/undershooting of the interaction force error, should be addressed during the control design. Motivated by the aforementioned considerations, this paper presents a force/position tracking control protocol for an Underwater Vehicle Manipulator System (UVMS) in compliant contact with a planar surface, without incorporating any knowledge of the UVMS dynamic model, the exogenous disturbances or the contact stiffness model. Moreover, the proposed control framework guarantees: (i) certain predefined minimum speed of response, maximum steady state error as well as overshoot/undershoot concerning the force/position tracking errors, (ii) contact maintenance and (iii) bounded closed loop signals. Additionally, the achieved transient and steady state performance is solely determined by certain designer-specified performance functions/parameters and is fully decoupled from the control gain selection and the initial conditions. Finally, both simulation and experimental studies clarify the proposed method and verify its efficiency.

Investigation of Contact Stiffness Model for Joint Surfaces Based on Domain Expansion Factor and Asperity Interaction

Investigation of Contact Stiffness Model for Joint Surfaces Based on Domain Expansion Factor and Asperity Interaction

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.