Effect Of Friction Research Articles

Technical Note: Dynamic Duopolistic Competition with Sticky Prices

Steven Heston of the R.H. Smith School of Business at the University of Maryland, College Park, and Bo Hu of the Costello College of Business, George Mason University, resolve a puzzle about industrial competition in “Dynamic Duopolistic Competition with Sticky Prices.” Previous papers analyze the effect of frictions on competition in continuous time, such as sticky prices or transactions costs. Those papers conclude that miniscule frictions have a large impact on market prices and quantities. However, Heston and Hu show that these conclusions are an artifact of the continuous-time math. Heston and Hu use discrete-time models to analyze the effect of frictions that are small per unit of time. These models show the effect of small frictions is small.

Analysis and numerical simulation of a generalized compressible Cahn–Hilliard–Navier–Stokes model with friction effects

We propose a new generalized compressible diphasic Navier–Stokes Cahn–Hilliard model that we name G-NSCH. This new G-NSCH model takes into account important properties of diphasic compressible fluids such as possible non-matching densities and contrast in mechanical properties (viscosity, friction) between the two phases of the fluid. The model also comprises a term to account for possible exchange of mass between the two phases. Our G-NSCH system is derived rigorously and satisfies basic mechanics of fluids and thermodynamics of particles. Under some simplifying assumptions, we prove the existence of global weak solutions. We also propose a structure preserving numerical scheme based on the scalar auxiliary variable method to simulate our system and present some numerical simulations validating the properties of the numerical scheme and illustrating the solutions of the G-NSCH model.

A perspective on mechanoluminescence and multipiezo in ferroelectric materials

The discovery of innovative mechanoluminescence materials of SrAl2O4 and ZnS, which emit repeatable light [repeatable mechanoluminescence (ML), hereafter simply ML] even by soft touch, has trigged intense research interest in material/device/system development for applications across various fields. This perspective presents an overview of the crystal structures, mechanisms, and ML behaviors of most promising systems, namely, SrAl2O4-, ZnS-, LiNbO3-, and Sr3Sn2O7-based ferroelectric materials. These multipiezo materials, which simultaneously exhibit intrinsic piezoluminescence (true elastic deformation induced ML and no friction effect) and piezoelectricity, show distinct and valuable characteristics by integrating mechanical force, electric field, and light for stress sensing and other applications. Recent studies indicated the critical role of crystal structure, doping, and piezoelectric properties in achieving robust and reliable ML performance. These findings suggest that ML materials hold substantial promise for applications in stress/force sensing, structural health monitoring, mechanically activated lighting, and advanced imaging techniques. Further investigation and advancement of multipiezo materials could yield breakthroughs, further augmenting their usefulness across various industries and scientific domains. Exploring ferroelectric ML materials offer new prospects for developing advanced materials with unique electro-mechano-optical properties.

The Effect of Periodic Friction and Upsetting Pressure on Rotary Friction Welding Process

The Effect of Periodic Friction and Upsetting Pressure on Rotary Friction Welding Process

Modeling and experimental research on adjustable ejector in fuel cell gas circulation system

Fuel cells can be made to operate under a variety of conditions by implementing adjustable ejectors in their anode gas circulation systems. Based on a quasi-two-dimensional model and considering factors such as friction and variable area effects, a theoretical model of ejectors with needles was established to predict their primary and secondary flow rates. Theoretical calculations were used to analyze the variations in internal parameters and flow losses along the ejector, explain the reasons and laws behind the effect of needle position on ejector performance, and explore the control mechanism of different needle shapes on ejector flow rates. Finally, flow control experiments were conducted on three types of adjustable needle shapes–oblique straight, quadratic, and parabolic–to validate the precision of the adjustable ejector theoretical model and the controls of different shapes on the ejector flow rates. The research indicates that the relative errors of the quasi-two-dimensional model in predicting primary and secondary flow rates are within ± 5 % and + 20 % to −5%, respectively. Both the primary and secondary flow rates were impacted by the needle position variation, though the impact on the secondary flow was weaker. The parabolic shape was optimal for the linear control of primary flow rates, followed by the oblique straight shape. The quadratic shape was the weakest, although the quadratic-shaped needle had a wider range of flow rate control. Modeling and experimental research on the adjustable ejector contributes to understanding the influence of the needle on the ejector performance under different working conditions, broadening the application range of the ejector, and providing a basis for flow control in the fuel cell system

Numerical and experimental study on water-sediment flow in a lateral pumping station forebay

Multiple vortex flow patterns are commonly observed in lateral pumping station forebays, particularly in basins with high sediment concentrations. These patterns can lead to pump blockage, sediment deposition, and other issues that disrupt pump station operations. The water-sediment two-phase flow in lateral pumping station forebays is significantly influenced by the start-up combination, yet our understanding remains limited. To address this, the mixture multiphase flow theory is introduced to describe water-sediment dynamics, and the mathematical model is validated with experimental data. By analyzing the characteristics and formation mechanisms of large vortex and multiple small vortex regions in the original scheme, nine different start-up combination schemes were proposed. The research results indicate that, due to the narrow channel and slope effect in the lateral forebay, some of the gravitational potential energy of the water-sediment mixture is converted into kinetic energy upon entering the forebay, thereby increasing the velocity in the main flow area. Additionally, due to the friction and dissipation effects of the two sidewalls, a pressure difference is generated in the main flow area, resulting in the formation of multi-level vortices. Furthermore, the various types of proposed start-up combinations can optimize the flow patterns in the forebay to a certain extent. The preferred scheme improved the uniformity of flow velocity by 18.63% and increased the deviation angle by 17.62°, resulting in a 75.47% reduction in vortex area compared to the original scheme. These research results provide theoretical guidance for optimizing start-up combinations and reorganizing flow field structures to achieve hydrodynamic dredging effects.

Frictional Axial Resistance of Clamped Split Pocket Mechanism Steel Structural Joint: An Experimental Study

The Clamped Split Pocket Mechanism (CSPM) prefabricated joint system was developed for a single-story steel instant house, designed to be compact and rapidly constructed without modifying the end of the beam and column element member. The CSPM bolted joint system was proposed as an optimal solution for post-disaster housing, especially after earthquakes. Despite its potential, the frictional tensile resistance behavior of the CSPM bolted joint system has not been previously studied, necessitating experimental investigation. This study examined the frictional tensile resistance behavior of the CSPM joint system by monitoring the effective friction coefficient under axial tension force. The experiments considered both the strong and weak axes of the joint and utilized two configuration types of specimens (L and T) with varying bolt pretensions of 2.5, 5, 7.5, and 10 kN. Results indicated that the effective friction coefficient of the CSPM bolted joint system ranged from 0.19 to 0.26, correlated to bolt pretension. Increased bolt pretension resulted in larger surface deformation of the split pocket, triggering a not uniform frictional tensile resistance across the steel surfaces of the split pocket joint. From this study, the achieved effective friction coefficients could guide the design of minimum pretension forces for clamps in prefabricated steel instant houses. Doi: 10.28991/CEJ-2024-010-09-07 Full Text: PDF

Unified gear tribo-dynamic of transient mixed lubrication and nonlinear dynamics and its experimental validation

The rapid development of electric drives technology presents new challenges in the domain of vibration and noise suppression within gear trains. Dynamics modeling serves as a crucial method for studying vibration and noise; however, a deficiency exists in adequately considering the interaction between tribology and the dynamics of gear drives in current research endeavors. This article proposes a unified tribo-dynamic approach to facilitate a more realistic and accurate linkage analysis of transient mixed lubrication, friction, flash temperature, stiffness, backlash, and dynamics in gear drives. The TPMD approach is proposed to reduce convergence elapsed time. The meshing stiffness and backlash under transient mixed lubrication are developed and used as additional crucial bridges for the interactions in tribo-dynamic, supplementing the traditional consideration of friction. Gear vibration tests are carried out in both LOA and OLOA directions to validate the accuracy of the proposed model. Comparative analyses with conventional models highlight the advancements of the proposed model. The lubricated meshing stiffness, influenced by the combined effects of dynamics and tribology, exhibits characteristic fluctuations and is significantly lower than the Hertzian meshing stiffness. Tribological characteristics in tribo-dynamic differ notably from quasi-static conditions due to gear vibrations. The proposed tribo-dynamic model reveals higher DTE and vibration in the LOA direction compared to traditional dynamics. The intricate effects of friction, meshing stiffness, and backlash on vibration depend on factors like surface roughness, torque, and rotational speed.

A novel cohesive interlayer model considering friction

To understand the influence of friction on the shear-slip behavior of heterogeneous brittle composites, a novel cohesive interlayer model that can effectively capture the friction effect was proposed based on the classical Park-Paulino-Roesler model. Meanwhile, the unified potential energy function governing the interface tangential and normal behaviors was introduced to realize the mechanical interaction between Mode I fracture and Mode II fracture, and a smooth friction growth function was added in the elastic deformation stage for calculating the accurate contact pressure and friction force. Furthermore, the capability of the proposed model in addressing unloading and reloading was improved, and the fracture energy can vary accordingly during cyclic loading. To verify the effectiveness of the proposed model, it was examined by modelling the shear behavior of a masonry wallette. The results show that the relative error of the proposed model is 14.92% which is much lower than those of the other three pre-existing models when calculating the displacement corresponding to peak shear stress. Meanwhile, in terms of peak shear stress and initial displacement at residual stage, the relative errors of the proposed model are only 1.82% and 5.04%, respectively, indicating the high accuracy. Besides, the tangent stiffness determined by the second-order integration of the potential energy function is also continuous and smooth, which ensures the effective convergence of the proposed cohesive model.

Analytical investigation on load sharing characteristics and speed difference of coaxial reverse closed differential herringbone gear transmission system with floating gear and errors

To investigate the influence of gear floating on the load sharing characteristics of the Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS) and the rotational speed difference between the upper and lower rotors, a dynamic Bending-Torsional-Axial-Pendular (BTAP) model of the CRCDHGTS was established using the centralized parameter method, which considers various excitation factors such as gear floating, errors, Time Varying Meshing Stiffness (TVMS), gyroscopic effect, and tooth friction. It considers the interaction between the closed-stage gear set and the differential-stage gear set, treating the herringbone gear as a symmetric helical gear connected through a receding slot. The dynamic model was solved using the Runge-Kutta method to obtain the dynamic meshing forces for each gear pair under single and combined floating modes. The Dynamic Load Sharing Coefficient (DLSC) of the system, which characterizes the Load Sharing Performance (LSP), was deduced. The load sharing characteristics of different floating modes were analyzed, as well as the influence of different floating displacement on the DLSC. The motion path of the gear floating was also determined. Additionally, the impact of manufacturing error and assembly error of each component on the DLSC under combined floating mode was analyzed. Finally, the influence of gear floating on the output rotation speeds of the upper and lower rotors of the system was investigated. The results indicate that both free-floating of the center gear and combined floating can effectively improve the LSP of the system. When the system adopts combined floating mode, the DLSC of inner and outer meshing changes between 0.91 and 1.09, demonstrating a significant improvement in the LSP. The DLSC of the system increases with the increase in error, with the eccentricity error having a greater impact on the DLSC compared to the assembly error. The optimal floating value for the sun gear is between 0.6 mm and 0.8 mm, while for the planetary gear, it is between 0.4 mm and 0.6 mm. The rotational speed difference between the upper and lower rotors can be controlled within 1r/min. These research findings provide a theoretical basis for further analysis of the dynamic stability and reliability of the system.

Performance analysis of quantum harmonic Otto engine and refrigerator under a trade-off figure of merit

Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.

Effect of vibratory probe compaction method on bearing capacity of loess investigated via random finite element analysis

Probabilistic analyses using random fields are increasingly performed in geotechnical fields; however, they focus on random fields in natural soils. Comparatively, few studies have been conducted regarding random field variations in improved ground. An innovative technique for treating loess–the pneumatic vibratory probe compaction method is used in this study. The effects of different construction techniques on the spatial variability of improved ground and bearing capacity are investigated by varying the pneumatic injection pressure and treatment interval. To determine the posteriori parameter of the effective friction angle of a loess random field, Bayes' theorem and the transitional Markov chain Monte Carlo algorithm are applied. Subsequently, a random finite element analysis is performed. Based on the results, the maximum increase in bearing capacity and the minimum dispersion are achieved at a jet pressure of 0.6 MPa under a treatment interval of 1.4 m. Furthermore, the probability of failure is reduced to the lowest possible level.

Chaotic dynamic analysis of electrical contact resistance measured in sliding current-carrying friction

This work explores the dynamic laws of electrical contact resistance (ECR) signals measured in the sliding current-carrying friction tests based on chaos theory. It is found that ECR time series have a chaotic nature, strongly verified by the positive largest Lyapunov exponent λ1. The chaos may originate from the combined friction effects on short and long timescales. Phase space analysis indicates that the ECR phase trajectory adheres to the “convergence–stability” evolution law over time, which pertains closely to energy dissipation. Hence, the chaotic attractor exists during current-carrying friction. Strikingly, wear surfaces confirm that the ECR phase trajectory evolution process corresponds to the stages of “formation–keeping” of the chaotic attractor, and also agrees with the electrical wear stages of “running-in–steady-state”. Further, the chaos quantifier variation is consistent with the phase space analysis results to identify wear transition quantitatively.

Discrete and continuum modelling of rock-ice avalanches: vertical segregation and its feedback on flow mobility

Rock-ice avalanches are rapid, catastrophic mass flows consisting of massive rock and ice particles in alpine regions. Varying material properties of rock and ice particles cause them to spontaneously mix and segregate during the flow. However, the impacts of segregation on the mobility remain poorly understood and are overlooked in current rock-ice avalanche models. Here, we address modeling of segregation and its mobility feedback from both discrete and continuum points of view. Using the discrete element method, we simulate rock-ice avalanches, and the segregation that occur therein, as steady gravity-driven flows of particles different in size, density, and surface friction. Segregation results in sharp particle concentration gradients which, when coupled with the large surface friction difference between rocks and ice, lead to transitions in the flow kinematic profiles. We reveal that rocks and ice contact probabilities are key to modelling the effective friction and volume fraction of the mixture flows. Continuum equations are proposed to model the concentration dependence of the pressure, while segregation-induced flow velocity profiles are modelled using the non-local granular fluidity framework that accounts for microscopic frictional interactions. The findings are expected to promote more sophisticated modeling of rock-ice avalanches necessary for hazard risk reduction and mitigation.

Characterization of Friction within a Novel 3 mm Wristed Robotic Instrument

Surgical robotic tools are being developed for a variety of surgical procedures that are executed within small workspaces. Novel designs of miniaturized cable-actuated surgical tools for cleft palate repair have previously been developed. However, the behavior and significance of friction within these tools are largely unknown. A study was conducted to investigate the friction in a pulleyless 3 mm diameter wristed instrument. The wrist utilizes cable guide channels that allow for miniaturization at the cost of increased friction. An experimental rig was developed to measure friction within the wrist link mechanism when the tool is positioned at various pitch angles. A strong relationship between the cable tension and the tool’s pitch angle was found as a result of friction. The cable tension increased as the pitch angle approached extreme values (percent increases in the cable tension of 33% and 67.3% at a pitch of 90° and −90°, respectively). However, the resultant cable tension was below the failure strength of the cable, indicating that the design is feasible. The results of this study would be useful to those considering the design of miniature robotic surgical tools that are cable-driven. Significant tool reduction can be achieved by employing static guide channels for the cables, forgoing the use of additional moving components like pulleys while maintaining cable tension well within its break strength. Future work in the design and optimization of novel miniaturized wrist mechanisms should consider frictional effects and their impact on mechanism function.

Efficient numerical analysis of in-plane compression-induced defects in thick multi-ply woven textile preforms during double diaphragm forming

To gain adoption in the composites manufacturing sector, forming process models must be assessed for their suitability in analysing representative preform architectures processed in industrial production environments. A computationally efficient, mutually constrained Shell-Membrane (S-M) finite element approach is developed to predict the anisotropic, non-linear deformation of a woven textile preform in a Double Diaphragm Forming (DDF) process. Formability of a thick, multi-ply aerostructures preform is numerically investigated and experimentally correlated using a high-volume, industrial forming process. The effects of fibre orientation, preform thickness, and inter-ply friction on defect formation are investigated. The process model identifies in-plane axial fibre compression as the primary mechanism leading to macroscopic buckling defects and infers the underlying defect morphology. Defect formation is shown to be weakly correlated with the state of the fabric shear strain field. The study concludes that buckling defects are mitigated by reducing tangential contact friction between preform plies.

A mathematical model for the dynamic angle of repose of a granular material in the rotating drum

This study introduces a mathematical model to predict the dynamic angle of repose exhibited by granular materials in a rotating drum. The model accounts for the effect of particle properties, particularly sliding and rolling friction, as well as process conditions, i.e., the Froude number. We show that the effects of particle properties can be modeled independently of the process conditions, resulting in a multiplicative model. The model is validated using experimental data taken at different Froude numbers, yielding favorable agreement between the predicted dynamic angle of repose and the experimental observations. The findings of this study hold significant implications for engineering disciplines, as they provide crucial insights for optimizing processes involving granular materials in various engineering applications.

The effect of load-dependent tyre friction and aerodynamic cross-flow forces on the g-g maps and minimum-lap-time of motorcycles

A three-dimensional quasi-steady-state free-trajectory method based on semi-analytical g-g maps has been recently proposed to simulate the minimum-time manoeuvring of road vehicles. A number of assumptions, such as identical tyre-road friction coefficients on front and rear tyres and negligible aerodynamic cross-flow forces (i.e. downforces and sideforces), were enforced in the case of motorcycles to keep the g-g maps semi-analytical. Such assumptions are lifted in this work and their effect on the g-g maps of single-track vehicles is analysed, together with the consequences on the related minimum-lap-time simulations. The examples of application are carried out on the Mugello circuit and compared with previous findings in the literature. It is found that different friction coefficients on tyres call for different braking strategies to extract the maximum performance of the vehicle (when compared against the case with equal friction coefficients), while aerodynamic downforces can reduce stoppie and wheelie problems, improve acceleration and braking performance and increase the maximum lateral acceleration achievable. However, if the resulting cross-flow force lies on the plane of the bike the maximum lateral performance could be reduced, depending on tyre properties.

Effect of Friction on Critical Cutting Depth for Ductile–Brittle Transition in Material Removal Mechanism

Abstract The material removal process takes place due to phenomena such as plastic deformation and brittle fracture. A long continuous chip is formed when the plastic deformation dominates, whereas a fracture-induced discontinuous chip is formed when the brittle fracture dominates. The means of material removal changes at a certain cutting depth for a particular material, the so-called transition depth of cut (TDoC). This article aims to predict the TDoC while including the effect of friction between the tool and workpiece. We propose a modification to a recently developed model (Aghababaei et al., 2021, “Cutting Depth Dictates the Transition From Continuous to Segmented Chip Formation,” Phy. Rev. Lett., 127(23), pp. 235502) to incorporate the effect of friction. The model predicts a transitional depth of cut as a function of tool geometry, material properties, and friction. The model is supported by performing orthogonal cutting experiments on different polymers such as polymethyl methacrylate (PMMA), polyoxymethylene (POM), and polycarbonate (PC). The model is also compared with existing models in the literature, where an improvement in the prediction of TDoC is shown. Moreover, the effect of the friction coefficient and rake angle on the TDoC is discussed. The results show that transitional cutting depth is reduced by increasing the friction coefficient. Alternatively, the TDoC reaches its maximum at an optimum rake angle, which is a function of the specific material being cut. The model aids in accurately predicting the TDoC, a crucial factor for optimizing various material removal processes.

A length-free phase field model for epoxy adhesive materials based on modified Drucker–Prager criterion

Characterizing the cracking behavior of epoxy adhesive material is of great importance for composite structures. Recently, the phase field model has emerged as the preferred method for predicting the crack propagation. This paper presents a length-free phase field model considering the characteristics of epoxy adhesive materials. The proposed model is formulated within a framework that decomposes the phase field fracture driving force, ensuring that it adequately considers the tension/compression asymmetry of the epoxy adhesive materials. The effects of hydrostatic pressure, deviational stress, and friction are incorporated into the model by employing a modified Drucker-Prager failure criterion. The failure criterion is included in the phase field model using the effective stress invariants. Furthermore, the internal length scale, previously considered to lack real physical meaning, is reformulated based on material strength. This model addresses the challenge of measuring the internal length of epoxy materials. It serves as a valuable reference for applying phase field models to epoxy materials. The accuracy of the model is validated through an L-shaped plate simulation, and an attempt using the model to predict the crack development in thick epoxy adhesive joints is undertaken. Several representative samples are simulated, including three double cantilever beams with different configurations. The numerical results demonstrate a good correlation with experimental data, highlighting the potential of the model in simulating the crack propagation in epoxy adhesive joints.