Friction Coefficient Model Research Articles

Non-Newtonian dynamics modelled with non-linear transport coefficients at the mesoscale by using dissipative particle dynamics.

We derive the algorithms for the dynamics of the standard dissipative particle dynamics model (DPD) for a velocity-dependent friction coefficient. By introducing simple estimators of the local rate of strain we propose an interparticle friction coefficient that decreases for high deformation rates, eventually leading to the macroscopic shear-thinning behaviour. We have derived the appropriate fluctuation-dissipation theorems that include the correction of the spurious behaviour due to the coupling of the non-linear friction and the fluctuations. The consistency of the model has been numerically investigated, including the Maxwell-Boltzmann distribution for the particle velocities as well as the comparison with the standard linear model for various stresses. The shear-thinning behaviour is clearly reported. Finally, along with the important methodological aspects related to the derivation of the algorithms for non-linear interparticle friction, we introduce a novel two-step algorithm that permits us the integration of the dynamic equations of the DPD model without the explicit derivation of the corrective terms due to the spurious behaviour.

A Fractal Prediction Model for the Friction Coefficient of Wet Clutch Friction Plates

The motion state of the friction plate in a wet friction clutch is investigated by analyzing the causes of friction coefficient formation. This study establishes static and dynamic friction coefficient models for the friction plate based on a fractal model. The fractal dimension and scaling coefficient are studied to understand the fractal characteristics and variation patterns of the surface morphology of friction pairs during engagement. The MM6000 friction and wear testing machine is utilized for experiments, measuring surface morphology changes due to wear and changes in the engagement motion state of the friction plate. The theoretical content is compared and analyzed to verify the accuracy of the friction coefficient prediction model for the friction pair. Experiments are conducted on paper-based friction materials under different bonding pressures, and the relationship between bonding times and surface morphology changes is established. A comparative experiment between the joint motion state and dynamic simulation is performed, concluding that the micro convex contact model has certain accuracy in predicting the contact state of friction plates under various working conditions.

Iterative Convergence for Solving the Exit Plastic Zone and Friction Coefficient Model of Ultra-thin Strip Rolling Force

Iterative Convergence for Solving the Exit Plastic Zone and Friction Coefficient Model of Ultra-thin Strip Rolling Force

A novel friction coefficient model parameters identification method for needle-tissue insertion procedure

Abstract In endoscopic liver vascular insertion surgeries, during the process of angiographic operation, the success of vascular staining depends on precise needle insertion control which heavily relies on experienced surgeons. Endoscopic vascular insertion surgical navigation system shows the potential to improve position precision, however it relies on needle-tissue interaction model and parameter identification to provide essential information for improving needle insertion accuracy, in which the friction coefficient is important parameters but difficult to determine. In this paper, a novel needle-tissue friction coefficient identification method was proposed with unknown tissue Young's modulus under endoscopic liver surgery scenarios. A modified friction coefficient model was proposed including the adhesion and elastic friction component to describe needle-tissue dynamic interaction process which can predict the friction coefficient more precisely. The proposed parameter estimation method based on the modified friction model can simultaneously estimate friction coefficient and Young's modulus. The proposed method was demonstrated by the friction coefficient measurement experiment. The results showed that the friction coefficient model prediction results agreed well with expected value. The proposed method can be applied to provide essential tissue-needle interactive information to improve needle insertion precision in the endoscopic liver vascular insertion surgery scenarios.

Research on friction and meshing efficiency of ADC12-POM gear pair considering off-line meshing

Metal-plastic gear pairs, due to their combination of the advantages of both materials, have been widely promoted and applied in many industries. However, research on their transmission performance is not yet complete, especially regarding the tribological properties of metal-plastic gear pairs. The study focus on ADC12-POM gear pairs. Based on the principle of potential energy, the study considers significant elastic deformation during POM meshing, resulting in obvious off-line meshing. Consequently, the study establishes a stiffness model for ADC12-POM gear pairs with off-line meshing. Using this stiffness model and a load distribution model, to calculate the tooth surface load distribution coefficient for the gear pairs. Building upon previous research on friction coefficient models, the study develop a friction coefficient model that accounts for off-line meshing and compare it with the friction coefficient model that does not consider off-line meshing. To validate the accuracy of the friction coefficient model, the study design and create an efficiency test rig for ADC12-POM gear pairs, conducting theoretical and experimental studies on gear mesh efficiency. The study analyzes the distribution of mesh efficiency along the meshing line and its relationship with the friction coefficient. By comparing experimental measurements with theoretical calculations, the study verifies the proposed friction coefficient model, providing a theoretical basis for the study of metal-plastic gears.

A novel method to establish friction coefficient model for numerical simulation of inertia friction welding

The precise friction coefficient at interface determines the friction behavior in inertia friction welding (IFW), its model is the basis to precisely describe the friction behavior in the numerical simulation of IFW. To measure the friction coefficient related to the temperature, pressure, and sliding velocity, the IFW trials between 2219-O Al alloy and 304 stainless steel were conducted with the simultaneous measurement of temperature and angular velocity evolutions. Two types of friction coefficient models were established by considering whether the effects of temperature and friction pressure were independent. The S-(T&P) L model, which considered the couple effect of temperature and friction pressure, was recommended as the best suitable model with its very high accuracy and best simplicity. The proposed model was successfully used in simulating the temperature evolution of IFW between Al alloy and steel tubes. The effect of the influencing variables on the friction coefficient was also discussed.

Anisotropy Dependence of Material Deformation Mechanisms in Nanoscratching Monocrystalline BaF2: Experiments and Atomic Simulations.

Monocrystalline barium fluoride (BaF2), known for its exceptional optical properties in the infrared spectrum, exhibits anisotropy that influences surface quality and material removal efficiency during ultraprecision machining. This research explores the impact of anisotropy on the deformation and removal mechanisms of monocrystalline BaF2 by integrating nanoscratch tests with molecular dynamics (MD) simulations. Nanoscratch tests conducted on variously oriented monocrystalline BaF2 surfaces using a ramp loading mode facilitated the identification of surface cracks and a systematic description of material removal behaviors. This study elucidates the effect of crystal orientation on the ductile-brittle transition (DBT) of monocrystalline BaF2, further developing a critical depth prediction model for DBT on the (111) crystal plane to reveal the underlying anisotropy mechanisms. Moreover, nanofriction and wear behaviors in monocrystalline BaF2 are found to be predominantly influenced by scratch direction, crystal surface, and applied load, with the (110) and (100) planes showing pronounced frictional and wear anisotropy. A coefficient of friction model, accounting for the material's elastic recovery, establishes the intrinsic relationship between anisotropic friction and wear behaviors, the size effect, and scratch direction. Lastly, MD modeling of nanoscratched monocrystalline BaF2 reveals the diversity of dislocations and strain distributions along the (111) [-110] and [-1-12] crystal directions, offering atomic scale insights into the origins of BaF2 anisotropy. Thus, this study provides a theoretical foundation for the efficient processing of fluorine-based infrared optic materials exhibiting anisotropy.

Parametric optimization and case study of nanofluid flow between two parallel plates in the presence of Darcy Brinkman Forchheimer: Sensitivity analysis

Due to its vast industrial applications and thermal engineering, the investigation of the inconsistent heat and mass transfer that drives the flow of squeezing viscous nanofluids between two plates is an interesting topic. In this case study, we have investigated the heat transfer analysis of unsteady viscous nanofluid between two parallel plates by using Response Surface Methodology (RSM). The partial differential equations illustrating the flow model are converted to nonlinear ordinary differential equations by suggesting similarity transformations. The resulting dimensionless and nonlinear ODEs of temperature functions and velocity are solved using the well-known numerical technique bvp4c by transforming the problem into initial value problem from boundary value problem. The results found are consistent with this numerical solution. These numerical values are then used to optimize the different input parameters and to design an experimental model. RSM is used to develop an experimental model for skin friction coefficient. ANOVA tables are generated for input parameters and then sensitivity analysis is performed for output response. Further, the impacts of different parameters on temperature profiles and velocity are graphically explored. The results are compared with the results solved by HPM. The results concurred with this numerical solution. These findings considered much be useful in the application of polymer processing, power transmission, compression, temporary loading of mechanical parts, food processing, cooling water, gravity machinery, modeling of plastic transport in vivo, chemical processing instruments, and demolition due to freezing.

Hybrid modeling prediction of residual stresses in turned Ti6Al4V considering frictional contact

Residual stress plays a pivotal role in assessing the surface quality of machined components, influencing characteristics such as fatigue performance, corrosion resistance, and mechanical strength. Ti6Al4V, a critical material in the nuclear sector, the generation of residual stresses during machining has attracted significant attention. A model for variable friction coefficient model is proposed to accurately characterize the complex plastic deformation behavior of the material. This model takes into account variables such as the relative sliding velocity, contact pressure, and temperature. A subroutine has been developed using the VFRIC interface to enhance precise cutting simulation and modeling. Using the friction model, a new hybrid prediction model for surface residual stresses is developed by integrating finite element analysis and analytical methods. The reliability of both the hybrid and friction models is confirmed through the evaluation of cutting forces, chip morphology, and residual stress. The findings suggest that the novel friction model produces simulation results with higher accuracy compared to traditional Coulomb friction models. The variations in cutting force amount to 5.8% and 13.7%, the error in chip serration is 12.4%, and the deviation in predicting the maximum residual compressive stress is 10.3%. This study contributes to the advancement of friction models and methodologies used in predicting residual stress.

Prediction of mechanical efficiency of spur gear pairs based on tribo-dynamics model of multi-tooth meshing

The prediction of load-dependent losses of gear pairs is a topic of constant concern, which depends largely on the modelling of friction coefficient in tooth meshing. Although the current load-sharing based models can handle the friction coefficient in mixed elastohydrodynamic lubrication regimes, dynamics behaviour of each tooth pair or the time variation of direction of normal contact load is not taken into consideration. This study proposes a new method for modelling efficiency of spur gear pairs in transient operating conditions by coupling the multi-tooth meshing model with the friction coefficient model. The friction coefficient is modelled through load-sharing function, and the gear dynamics model is established with regard to alternate meshing of single-double tooth pair and time variation of direction of normal load and mesh stiffness. The model is validated by comparing the calculated results of friction coefficients and load-dependent losses with experimental data in published literatures, showing good agreement. At the end, the efficiency model is applied to two types of gear pairs to investigate the influence of tooth shapes and operating parameters on the load-dependent losses of gear pairs.

A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears

As a critical component of the joint gearbox, spur gear pairs play a crucial role in energy conversion, limiting the performance of a collaborative robot. Accurately assessing their instantaneous efficiency and torque fluctuation is essential for developing high-precision robot joint control models. This study proposes a computational model to predict the instantaneous efficiency and torque fluctuation of spur gears under typical operating conditions. The model incorporates a torque balance model, a load distribution model, and a friction model to reflect the relationship between gear meshing position and efficiency. The instantaneous efficiency and torque fluctuation of gear pairs were compared with the Coulomb friction model with an average friction coefficient and the elastohydrodynamic lubrication model with a time-varying friction coefficient. The effect of gear contact ratio on efficiency is analysed, while the instantaneous efficiency and torque fluctuation of gears are studied under varying operating conditions. The results indicate a maximum efficiency difference of 1.86 % between the two friction coefficient models. Under specific operating conditions, the instantaneous efficiency variation of the gear pair can reach 3.34 %, and the torque fluctuation can reach 5.19 Nm. Finally, this study demonstrates the effectiveness and accuracy of the proposed method through comparative analysis.

Blasius–Rayleigh–Stokes nanofluid dusty flow influenced by Cattaneo–Christov double diffusion and melting heat transfer — application of response surface methodology

This paper focuses on the study of Blasius–Rayleigh–Stokes nanofluid dusty flow with generalized Fourier and Fick laws under the influence of a transitive magnetic field. The Blasius–Rayleigh–Stokes nanofluid dusty flow has significant applications in various fields, including the design of heat exchangers, microfluidic devices and industrial processes involving the transportation of suspended particles in fluids. This paper considers the impact of melting heat transfer at the surface boundary. By employing relevant transformations, the mathematical model is transformed into a system of self-similar equations. The solution to this set of highly nonlinear equations is obtained using the bvp4c numerical method in combination with the response surface methodology (RSM) statistical approach. The results are presented through graphical illustrations and numerically calculated tabulated values. It is observed that the fitted model for the skin friction coefficient [Formula: see text] optimal. Moreover, the model parameters [Formula: see text], Q, [Formula: see text], M and L are linearly and quadratically significant in explaining the variation presented for skin friction coefficient [Formula: see text]. This indicates the response skin friction coefficient [Formula: see text] is minimized to 0.005 at [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] and is maximized to 1.387 at [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

Study on Resistance Loss of Fly Ash Slurry Multistage High‐Pressure Grouting Pipeline Based on Fluent

In order to understand the resistance loss along the way during multistage high‐pressure slurry transportation, the flow state of fly ash slurry in the pipeline was simulated by Fluent software in this paper, and the effects of pipe diameter D, pipe transportation flow rate Q, and fly ash mass concentration Cw on the resistance loss along the pipeline were studied. The fly ash slurry is a non‐Newtonian Bingham fluid that moves in a turbulent state in a pipeline. When simulating the flow of fly ash slurry using Fluent software, the mesh type is a mixed mesh of hexahedron and wedge shapes, and the viscous model is selected as realizable k‐ε Turbulence Model, with Enhanced‐Wall Function (EWF) selected as the wall function, combined with a four‐layer boundary layer mesh, which can more accurately capture the details of velocity changes at the wall, thereby improving the accuracy of the model. The inlet of the model is the velocity inlet, and the outlet is the pressure outlet. The coupled algorithm is chosen as the solution method. Under these conditions, the model converges quickly and the calculation accuracy is high. The results show that the resistance loss along the pipeline decreases as a power function with the increase of pipeline diameter, and there is a polynomial relationship between the pipeline flow and the resistance loss along the pipeline, while the mass concentration of fly ash slurry changes linearly with the resistance loss along the pipeline. In addition, three friction coefficient models, namely Blasius formula, Colebrook–White equation, and Wilson–Thomas model, were selected according to the flow characteristics of fly ash slurry. Based on the Blasius formula with the smallest relative calculation error, the Blasius formula was modified by multiple linear regression analysis to improve the accuracy of the frictional resistance coefficient model and to provide help for the design and use of separate layer grouting conveying system.

ON THE THEORY OF FRICTION SYSTEMS WITH HEREDITARY TYPE FRICTION

The work is devoted to the study of the nonlinear dynamics of frictional vibration systems, which take into account, when developing mathematical models of vibration systems, an essentially nonlinear function that describes the work of friction forces with memory. The problem considered in the work combines two well-known Painleve? problems and the problem of studying the friction forces of hereditary friction. In both cases, we are talking about the idealization of real elastic bodies and flexible bonds with ideal absolutely hard and rigid ones. Using the well-known experimentally proven hypothesis of A.Yu. Ishlinsky and I.V. Kragelsky about the hereditary dependence of the coefficient of friction of relative rest at low speeds of movement of bodies, the dynamic system under study is transformed from autonomous to non-autonomous, in which new types of movements that have not previously been observed in the study of vibration systems appear. In particular, taking into account the Painleve? paradox entails the previously unexpected possibility of the occurrence of instability and self-oscillations, and taking into account the heredity of the friction coefficient leads to the appearance of chaotic movements of bodies. A numerical and analytical method has been developed for studying the behavior of the dynamic characteristics of friction vibration systems depending on the chosen model of the relative static friction coefficient. Based on the main parameters, the new bifurcation diagrams presented in this work demonstrate the presence of arbitrarily complex periodic regimes of body motion, including chaotic ones. It has been established that the transition to chaotic modes of motion occurs according to the well-known period doubling scenario. Analytical relations are given for point mappings of Poincare? surfaces, which made it possible to obtain succession functions illustrating arbitrarily complex modes of body motion, including chaotic ones. It is noted that such body movements were not found during the study of such vibration systems.

Effect of different friction coefficient models on numerical simulation of inertia friction welding of 2219 Al alloy to 304 stainless steel

In inertia friction welding (IFW) of Al alloy to steel, the friction coefficient of interface influences the friction heat production and determines the accuracy of the numerical simulation of welding process. A fully coupled three-dimensional model was established to simulate the IFW process of 2219 Al alloy to 304 stainless steel. By taking different simplifications in the influencing factors (i.e., temperature, sliding velocity, and pressure) of friction coefficient, three types of friction coefficient models were established and utilized in the simulation of IFW process. The strain compensated Arrhenius and Johnson-Cook models were employed to describe the deformation behavior of Al alloy and steel, respectively. Both Al alloy and steel were assumed to be the elastic-plastic body, and the friction stress was calculated by the Coulomb friction model. The friction interface temperature, angular velocity attenuation, axial shortening distance, and joint appearance were measured to verify and compare the accuracy of the established models. The temperature and stress evolutions during the IFW process were also analyzed. With the smallest error in validation, the friction coefficient model, which was a function of temperature, sliding rate, and pressure, showed the best accuracy in describing the friction behavior. By considering the effect of pressure, a more accurate shear stress at the center region of the interface was calculated with a lower value. It means that the friction resistance at the region was lower, promoting the flow of internal Al alloy and the formation of curly-shape flash.

Evaluation of the tribological behavior of a brake disc-pad friction pair using a fuzzy inference model based on an adaptive network (ANFIS)

The purpose of this research is to forecast the tribological behavior of the materials used in the field of braking systems using an Artificial Neural Network (ANN) based on the experimental data obtained by measuring the friction between the friction linings and the brake disc of a bicycle in the translational movement. The data analysis results from this research show that the estimates and forecasts with the proposed model (ANFIS) of the dynamic friction coefficient (COF) between the pads and the disc in translational motion using the ANN have been confirmed to be powerful and useful. The experimentally determined average value of the dynamic COF was 0.2003 with a standard deviation of 0.0233 in the range of values of 0.1244-0.3013.

Factors Influencing Pavement Friction during Snowstorms

Operating an effective winter road maintenance program is a necessity for cities that face severe winter seasons. Snowstorms leave roads in a slippery surface condition that disrupts traffic flows and compromises drivers’ safety. Decision-makers use a variety of tools to control snow and ice on the roads, which include applying anti-icing chemicals before snowstorms, applying deicing substances on fresh snow, and clearing snow off the roads using snowplows. However, the influence of these tools on improving the overall road surface conditions has not been investigated. In this study, a location-specific and event-based framework was utilized to understand the impact of the different weather variables as well as maintenance operations on the variability of the pavement friction coefficients during snowstorms in urban environments. Using multilinear regression and ordinary least squares, friction coefficient models were calibrated. The final model was found to be a good fit for the data (R2 = 0.723). The model showed that the total precipitation during snowstorms, extremely low temperatures, and the potential for black ice formation worsen pavement friction significantly. On the other hand, plowing operations, the application of anti-icing chemicals before snowstorms, and frequent deicing operations all have a statistically significant impact on improving pavement friction. The model presented in this paper can be used to predict pavement friction on urban arterial and collector roads during snowstorms of different magnitudes, which could help the authorities in predicting the road surface conditions during forecasted snowstorms and deciding on the best course of action under these conditions.

Artificial neural network simulation and sensitivity analysis for optimal thermal transport of magnetic viscous fluid over shrinking wedge via RSM

PurposeThis study aims to model the important flow response quantities over a shrinking wedge with the help of response surface methodology (RSM) and an artificial neural network (ANN). An ANN simulation for optimal thermal transport of incompressible viscous fluid under the impact of the magnetic effect (MHD) over a shrinking wedge with sensitivity analysis and optimization with RSM has yet not been investigated. This effort is devoted to filling the gap in existing literature.Design/methodology/approachA statistical experimental design is a setup with RSM using a central composite design (CCD). This setup involves the combination of values of input parameters such as porosity, shrinking and magnetic effect. The responses of skin friction coefficient and Nusselt number are required against each parameter combination of the experimental design, which is computed by solving the simplified form of the governing equations using bvp4c (a built-in technique in MATLAB). An empirical model for Cfx and Nux using RSM and ANN adopting the Levenberg–Marquardt algorithm based on trained neural networks (LMA-TNN) is attained. The empirical model for skin friction coefficient and Nusselt number using RSM has 99.96% and 99.99% coefficients of determination, respectively.FindingsThe values of these matrices show the goodness of fit for these quantities. The authors compared the results obtained from bvp4c, RSM and ANN and found them all to be in good agreement. A sensitivity analysis is performed, which shows that Cfx as well as Nux are most affected by porosity. However, they are least affected by magnetic parameters.Originality/valueThis study aims to simulate ANN and sensitivity analysis for optimal thermal transport of magnetic viscous fluid over shrinking wedge.

Solid friction coefficient in a horizontal straight pipe of pneumatic conveying

Pressure drop prediction model has been well concerned in pneumatic conveying system design. The Barth’s additional pressure drop prediction model is one of the most widely accepted and applied models, in which the solid friction coefficient in horizontal straight pipe is particularly important. In this work, a regression model of solid friction coefficient was addressed on the basis of two dimensionless numbers (the inlet Froude number and the solid-gas loading ratio), which were conducted based on fly ash pneumatic conveying experiment data in a 16 m length pipeline. Then, the prediction accuracy of the regressed model was verified by the pressure drop of other pneumatic conveying pipeline system, 123 m and 139 m pipelines, respectively. The results show that solid friction coefficient gradually decreases with inlet Froude number, conversely, it increases with solid-gas loading ratio. And the regressed solid friction coefficient maintained relatively high accuracy in the prediction of pressure drop, for both fly ash pneumatic conveying pipelines of 16 m length and 123 m length. However, a different prediction accuracy appeared for the different loading ratio of 139 m length pipeline complete pneumatic conveying system. The pressure drop prediction accuracy sharply declines when solid-gas loading ratio is larger than 85.

Research on the Model for the Friction Coefficient of Resin-Based Friction Material and Its Experimental Verification

Resin-based friction materials have been widely used in the friction braking of automobiles and power machinery. Based on experiments for the variation law of friction and wear morphology, a new model for the friction coefficient of resin-based friction materials was proposed, which includes the effects of both the micro convex body on the surface of the friction material and the frictional film generated during the friction process. This quantitative model of friction coefficient materials was established for the modelling of shear strength, compressive strength, shear strength of the frictional film, contact load and wear morphology. The shear strength, compressive strength and wear morphology of the friction material were adjusted by changing the content of basalt fibers and flaky potassium magnesium titanate. Finally, the accuracy of this quantitative model of friction coefficient was verified through experiments on friction samples with different formulations and by changing the frictional contact load. The results show that the predicted friction coefficient of the model is in good agreement with the experimental friction coefficient, the difference between the upper and lower limits of the forecast is only 5.03% and 2.30%, respectively. Meanwhile, the influence of the ratio of shear strength to compressive strength on the friction coefficient is greater than the proportion of wear morphology. The proposed friction model provides a reference value for the study of new resin-based friction materials.