Study on dry friction vibration model based on energy method

Purpose This study aims to establish the friction vibration model. Design/methodology/approach The friction vibration experiment was carried out on a pin disk friction tester. The causes of friction vibration are discussed, and the friction vibration model is established based on the energy method. Findings The experimental and simulation results show that the main cause of friction vibration is the nonlinear change of friction coefficient; degree of the friction vibration has a positive relationship with the friction relative velocity and normal contact positive pressure; the proposed friction vibration model is highly consistent in chaotic attractor and time-frequency distribution map and can well predict friction vibration. Originality/value The proposed friction vibration model is highly consistent in chaotic attractor and time-frequency distribution map and can well predict friction vibration.

Lubricated Soft Normal Elastic Contact of a Sphere: A New Numerical Method and Experiment

An important problem in lubrication is the squeezing of a thin liquid film between a rigid sphere and an elastic substrate under normal contact. Numerical solution of this problem typically...

Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement

The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground. According to the Carvallo-Whipple configuration, the unmanned bicycle is reduced to four rigid bodies, namely, rear wheel, rear frame, front fork, and front wheel, which are connected by perfect revolute joints. The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point, and these forces are described by the Hunt-Crossley contact force model and the LuGre friction force model, respectively. According to the characteristics of flat and curved pavements, calculation methods for contact forces and their generalized forces are presented. The dynamics of the system is modeled by the Lagrange equations of the first kind, a numerical solution algorithm of the dynamic equations is presented, and the Baumgarte stabilization method is used to restrict the drift of the constraints. The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies. The feasibility of the proposed model is demonstrated by simulations under different motion states.

Experimental and Numerical Analysis on Mesoscale Mechanical Behavior of Coarse Aggregates in the Asphalt Mixture during Gyratory Compaction

Compaction is a critical step in asphalt pavement construction. The objective of this study is to analyze the mesoscale mechanical behaviors of coarse aggregates in asphalt mixtures during gyratory compaction through experiments and numerical simulation using the Discrete Element Method (DEM). A novel granular sensor (SmartRock) was embedded in an asphalt mixture specimen to collect compaction response data, including acceleration, stress, rotation angle and temperature. Moreover, the irregularly shaped coarse aggregates were regenerated in the DEM model, and numerical simulations were conducted to analyze the evolution of aggregate interaction characteristics. The findings are as follows: (1) the measured contact stress between particles changes periodically during gyratory compaction, and the amplitude of stress tends to be stable with the increase of compaction cycles; (2) the contact stress of particles is influenced by the shape of aggregates: flat-shaped particles are subjected to greater stress than angular, fractured or elongated particles; (3) the proportion of strong contacts among particles is high in the initial gyratory compaction stage, then decreases as the number of gyratory compactions grows, the contacts among particles tending to homogenize; (4) during initial gyratory compactions, the normal contact forces form a vertical distribution due to the aggregates’ gravity accumulation. The isotropic distribution of contact forces increases locally in the loading direction along the axis with a calibrated internal angle orientation (1.25°) in the earlier cyclic loading stage, then the local strong contacts decrease in the later stage, while the strength of the force chains in other directions increase. The anisotropy of aggregate contact force networks tends to weaken. In other words, kneading and shearing action during gyratory compaction have a positive impact on the homogenization and isotropy of asphalt mixture contact forces.

Solutions of a singular integro-differential equation related to the adhesive contact problems of elasticity theory

Exact and approximate solutions of a some type singular integro-differential equation related to problems of adhesive interaction between elastic thin half-infinite or finite homogeneous patch and elastic plate are investigated. For the patch loaded with vertical forces, there holds a standard model in which vertical elastic displacements are assumed to be constant. Using the theory of analytic functions, integral transforms and orthogonal polynomials, the singular integro-differential equation is reduced to a different boundary value problem of the theory of analytic functions or to an infinite system of linear algebraic equations. Exact or approximate solutions of such problems and asymptotic estimates of normal contact stresses are obtained.

An Analytical Model for Almost Conformal Spherical Contact Problems: Application to Total Hip Arthroplasty with UHMWPE Liner

Due to its high relevance for designing ball joints in mechanical engineering and (artificial) hip joints in biomechanics, the almost conformal elastic contact between a sphere and a spherical cup represents an important contact problem of current research. As no closed-form analytical solution to the problem has been found to date, full computational methods such as the finite element method are needed for analysis. However, they often require incredibly long, unacceptable calculation times, making parameter studies hardly practicable. For this reason, approximate analytical and semi-analytical models are applied, capable of predicting quantities of interest with sufficient accuracy. In the present work, a very simple model based on a radially directed Winkler foundation is presented, which provides (approximate) closed-form analytical solutions for both the pressure distribution and the dependencies between macroscopic contact quantities such as normal force and indentation depth. To ensure an optimal mapping of a specific contact problem, only the foundation modulus must be defined in a suitable way. As an example, the proposed model has been successfully adapted to adequately simulate the frictionless normal contact for hard-on-soft hip implants. For this purpose, the foundation modulus was approximated with the aid of a finite element analysis instead of adopting it from already well-established models, as the latter produce clearly erroneous results for large liner thicknesses and large Poisson’s ratios. By a comparison with extensive parameter studies of finite element simulations, it is demonstrated that the proposed model provides acceptable results for all commonly used hard-on-soft hip implants. On this basis, the influence of geometrical changes of the femoral head and the acetabular cup on the maximum pressure as well as the half-contact angle is discussed, and consequences on the wear behavior are deduced.

Calibration of a finite element model of Prescale film for wheel-rail normal contact area measurements

This article presents the latest of a series of research activities aimed to determine the deviation originated when Prescale pressure measurement film is used to measure the size and shape of the wheel-rail contact area. Despite being an attractive solution due to the simplicity of the measurement procedure, it is well known that the contact interaction is altered by the presence of the film. Consequently, characterizing and filtering out the systematic measurement error is a fundamental requirement for accurate quantitative assessments. Nevertheless, the complexity of the wheel-rail contact problem, which lacks an analytical solution, hinders the direct determination of correction values. The approach presented here builds on error corrections for simpler Hertzian geometries to calibrate a film model for further use in the wheel-rail contact scenario. The results highlight the marked dependency of the measurement error on wheel and rail roughness and underline the importance of including the film into finite element models that are validated by comparison with experimental observations.

A simple discrete-element model for numerical studying the dynamic thermal response of granular materials

This paper aims to investigate the influence of periodicity temperature change on the properties of dry granular materials in macroscopic and microscopic. A series of cyclic thermal consolidation tests have been carried out based on the discrete element method (DEM) that incorporate particles’ volumetric thermal expansion coefficient. The simulation of the direct shear test was carried out on the samples after thermal cycling. Results showed that thermally-induced volumetric strain accumulation of the specimen can be calculated by the DEM model, based on the PFC2D software. The lateral pressure degraded concomitantly thanks to decreases in particles’ horizontal contact during periodic thermal cycling. In addition, the shear dilatancy level decreases during the shearing process with the number of thermal cycles. Both the size and anisotropy of the normal contact force and contact number and the force chain are affected by the temperature cycle. Finally, the results of this paper have a certain reference for the engineering practice, such as thermal piles or others, when granular materials are subjected to thermal cycling.

Study of a parabolic cylinder elastic-plastic contact model

Based on Hertz contact theory, two parabolic cylinder normal contact models are established. The effect of contact angle on normal approach, actual contact area, and normal contact stiffness are investigated, and the effect of the distance from the focus to the directrix (focus distance) on the mechanical characteristics of the models is further analyzed. The parabolic cylinder contact model was verified by simulation analysis and comparison with cylinder contact model. The results demonstrated that the contact angle, focal distance, and load have significant effects on the mechanical properties of the model. The simulation data are basically consistent with the contact model data, and the parabolic cylinder contact model and cylinder contact model have the same change trend. The results verify the correctness of the parabolic cylinder contact model and reveal the variation of the mechanical properties of the contact model.