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A novel hysteretic constitutive model (HCM) with four parameters was proposed to reproduce the nonlinear elasticity and dry friction characteristics of metal–rubber isolators (MRIs). The HCM accurately characterized the nonlinear hysteretic behavior due to its intrinsic relationship with the geometric properties of the hysteresis loop. A physics-based parameter estimation strategy was developed to provide reasonable initial iteration values. Three MRIs with different design stiffnesses were tested to investigate their hysteretic behavior under various excitation levels. The HCM accurately reproduced the entire experimental hysteresis loops using only a subset of the experimental data. This exhibited higher precision and scalability compared to the classical dynamic model. Friction damping forces were employed to distinguish the stick-slip states of the three MRIs. Additionally, the identified parameters were used to simulate the steady-state vibration response of a complex MRI system. The resulting frequency response functions (FRFs) agreed well with the experimental data. The proposed model can effectively capture the amplitude-dependent effects in MRI systems with various design stiffnesses, enabling more accurate predictions of vibration responses.

A two-mass oscillator with one mass lying on the driving belt with dry Coulomb friction is considered. A numerical method for finding all limit cycles and their parametric investigation, based on the analysis of fixed points of a two-dimensional map, is suggested. As successive points for the map we chose points of friction transferred from stick mode to slip mode. These transfers are defined by two equalities and yield a two-dimensional map, in contrast to three-dimensional maps that we can construct for regularized continuous dry friction laws.

We study complex dynamics of a cutting process, a recently developed frictional model of cutting process in [Rusinek et al., 2014] to gain better insight into the mechanics of frictional chatter and the factors affecting it. The new model takes into account the forces acting on the tool face as well as on the tool flank. We first present nonlinear dynamic behavior using bifurcation diagrams for nominal cutting depth and cutting velocity as the bifurcation parameters. Finally, the influence of the various forces on the tool flank on the system dynamics has been systematically studied. This has been performed by comparing the bifurcation diagrams with and without the forces on the flank. These flank forces have been found to largely have a stabilizing effect. These forces however increase the complexity of the solutions and are responsible for some instabilities in the low cutting velocity regime.

In this paper, we study a four-parameters piecewise-smooth dry friction oscillator from Control theory. Using Filippov's convention, we prove the existence of a codimension-1 bifurcation which gives rise to a normally hyperbolic set composed by a family of attracting cylinders. This bifurcation exhibits interesting discontinuous oscillation phenomena. We also present consistent numerical simulations.

In this paper, we investigate the multiple stick-slip chaotic motion of an archetypal self-excited smooth and discontinuous (SD) oscillator driven by moving belt friction, which is constructed with the SD oscillator and the classical moving belt. The friction force between the mass and the belt is modeled as a Coulomb friction for this system. The energy introduction or dissipation during the slip and stick modes in the system is analyzed. The analytical expressions of homoclinic orbits of the unperturbed SD oscillator are derived by using a special coordinate transformation without any pronominal truncation to retain the natural characteristics, which allows us to utilize the Melnikov’s method to obtain the chaotic thresholds of the self-excited SD oscillator in the presence of the damping and external excitation. Numerical simulations are carried out to demonstrate the multiple stick-slip dynamics of the system, which show the efficiency of the prediction for stick-slip chaos of the perturbed self-excited system. The results presented herein this paper demonstrate the complicated dynamics of stick-slip periodic solutions, multiple stick-slip chaotic solutions and also coexistence of multiple solutions for the perturbed self-excited SD oscillator.

ZrO₂-Al₂O₃ laminated ceramics of 3 layers were prepared by dry-pressing and pressureless sintering, and their mechanical properties and toughening mechanisms were studied. Furthermore, their tribological behaviors and wear mechanisms under dry friction and water lubrication conditions were also investigated, and compared with those of monolayer ZrO₂-Al₂O₃ ceramics under the same conditions. The results show that the bending strength, fracture toughness and hardness of the laminated ceramics are all better than those of the monolayer ceramics, moreover the friction factor and wear rate of the laminated ceramics are clearly lower than those of the monolayer ceramics. The excellent mechanical properties of the laminated ceramics, especially toughness, result mainly from effects of residual stress in the specially-designed layer, interface structure and phase transformation together. Good tribological properties of the laminated ceramics are supposed due to the high toughness and low shearing stress in the wear surface. The friction and wear of the composites are effectively decreased by water lubrication because of the transformation of the main wear mechanisms from abrasive and adhesive wear under dry friction to tribo-chemical and fatigue wear under water lubrication.

Nitriding is usually used to improve the surface properties of steel materials. In this way, the wear resistance of steels is improved. We conducted a series of studies in order to investigate the microstructural, mechanical and tribological properties of salt bath nitrided AISI 4140 steel. The present study has two parts. For the first phase, the tribological behavior of the AISI 4140 steel which was nitrided in sulfinuz salt bath (SBN) was compared to the behavior of the same steel which was untreated. After surface characterization using metallography, microhardness and sliding wear tests were performed on a block-on-cylinder machine in which carbonized AISI 52100 steel discs were used as the counter face. For the examined AISI 4140 steel samples with and without surface treatment, the evolution of both the friction coefficient and of the wear behavior were determined under various loads, at different sliding velocities and a total sliding distance of 1000 m. The test results showed that wear resistance increased with the nitriding process, friction coefficient decreased due to the sulfur in salt bath and friction coefficient depended systematically on surface hardness. For the second part of this study, four artificial neural network (ANN) models were designed to predict the weight loss and friction coefficient of the nitrided and unnitrided AISI 4140 steel. Load, velocity and sliding distance were used as input. Back-propagation algorithm was chosen for training the ANN. Statistical measurements of R², MAE and RMSE were employed to evaluate the success of the systems. The results showed that all the systems produced successful results.

In this paper, the dynamics of a two-degree-of-freedom block-on-belt system subjected to both dry friction and external excitations is studied. The dry friction in the system follows the classical Coulomb's law, and the external excitations consist of two harmonic forces with different frequencies. In the study, a new two-dimensional (2-D) map is developed, which reduces the system without losing its essential dynamic features and greatly simplifies the investigation. On the basis of the 2-D map, bifurcation analysis and the computation of Poincaré sections and Lyapunov exponents can be carried out straightforwardly. Numerical simulations are performed, in which the proposed 2-D map is proved to be very effective and provide a powerful tool to understand the dynamical behavior of the system. Numerical results show that the system possesses rich dynamics characterized by periodic, quasi-periodic and chaotic attractors. Furthermore, it is found that the two-frequency excitation has significant influence on the dynamical behavior of the system.

The prediction of damping remains an important research challenge in structural dynamics. This paper deals with the energy losses caused by friction in assembled structures. From previous analytical works and experimental studies of the bending vibrations of a clamped–clamped beam with original positions of the interfaces, the objective of this work is to compute the damping of the structure taking into account the local properties of the joints. The purpose is to understand and analyze the contribution of the surface defects on the damping due to the joints based on multi-spherical contacts governed by Hertz' and Mindlin's theories. A design of experiments based on the model parameters is proposed and the final results are compared to the experimental's ones.

A novel dry friction modeling and its impact on differential equations computation and Lyapunov exponent estimation are studied in this paper. A brief review of some existing standard friction laws is presented and a novel continuous friction model taking into account some elements of the mentioned classical friction models is proposed. Its advantages are illustrated and discussed with the use of classical differential equation of motion of a 1-DOF system with dry friction and harmonic excitation. The behavior of the mentioned system is monitored via standard tools, i.e. time series, phase portraits, bifurcation diagrams as well as the Lyapunov exponents.