Friction Model Research Articles

Novel Approach to Analyzing Friction Losses by Modeling the Microflow of Lubricating Oil between the Piston Rings and Cylinder in Internal Combustion Engines

This work focuses on the evolution of lubrication wedge shaping in internal combustion piston engines, taking into account liquid microflows on curved surfaces and coating microgeometries. It introduces a new approach to the analysis of friction losses by simulating the microflow of lubricating oil between the surfaces of piston rings cooperating with the cylinder surface. The models used take into account three types of microgeometry and material expansion. Key results indicate that microirregularities with a stereometry of 0.1–0.2 µm significantly influence the distribution of oil film thickness in the phase of maximum working pressure, which is critical for the functioning of the seal ring. The innovation of the work consists of demonstrating that, despite small changes in the friction force and power in the piston rings, changes in the minimum values of the oil film thickness are significant. The work highlights the failure to take into account microgeometry parameters in friction models, which leads to significant errors in the simulation results, especially in terms of oil film continuity and the contribution of mixed friction. The simulations also indicate that advanced geometric models with high mesh resolution are necessary only for the assessment of changes in oil film thickness during the highest pressure increase in the combustion chamber and taking into account various mixed friction conditions. The results suggest significant progress in engine design and performance, confirming the importance of advanced fluid and mixed friction models in piston engine lubrication research.

Nonlinear dynamics of a dual-rotor system with active elastic support/dry friction dampers based on complex nonlinear modes

In this study, the nonlinear dynamics of a dual-rotor system with active elastic support/dry friction dampers (ESDFDs) are investigated based on complex nonlinear modes (CNMs). The finite element method (FEM) combined with a full-3D friction model is introduced to construct the governing equation for the system. Additionally, the Craig–Bampton technique is applied to downscale the finite element model of the system. Based on the reduced order model (ROM), the nonlinear modal damping ratio of the target mode is employed to measure the dry friction damping performance of active ESDFD. The effects of the active ESDFD position, normal force, and tangential contact stiffness on the nonlinear modal damping ratio and modal frequency are analysed. Moreover, the softening characteristics of the active ESDFD are revealed, and the critical speed intervals of the active ESDFD/dual-rotor system are determined. Furthermore, by using the harmonic balance–alternating frequency/time domain (HB–AFT) method, the steady-state response of the system under unbalanced excitation is calculated. The accuracy and effectiveness of nonlinear modal analysis are validated based on the relationships between nonlinear modes and steady-state unbalanced responses. Conversely, the vibration mitigation effects of active ESDFD are determined by the unbalanced response amplitude. Additionally, the controllable region and optimal normal force for effective vibration control in the target mode are defined. Depending on the controllable region, a control strategy for turning on/off the optimal normal force is developed. The findings demonstrate that the developed control strategy enables the active ESDFD to significantly reduce the response amplitude of the dual-rotor system across various excitation levels, showing substantial potential for engineering applications.

A Novel Friction Compensation Method for Machine Tool Drive Systems in Insufficient Lubrication.

Friction is the dominant factor restricting tracking accuracy and machining surface quality in mechanical systems such as machine tool feed-drive. Hence, friction modeling and compensation is an important method in accurate tracking control of CNC machine tools used for welding, 3D printing, and milling, etc. Many static and dynamic friction models have been proposed to compensate for frictional effects to reduce the tracking error in the desired trajectory and to improve the surface quality. However, most of them focus on the friction characteristics of the pre-sliding zone and low-speed sliding regions. These models do not fully describe friction in the case of insufficient lubrication or high acceleration and deceleration in machine tool systems. This paper presents a new nonlinear friction model that includes the typical Coulomb-Viscous friction, a nonlinear periodic harmonic friction term for describing the lead screw property in insufficient lubrication, and a functional component of acceleration for describing the friction lag caused by the acceleration and deceleration of the system. Experiments were conducted to compare the friction compensation performance between the proposed and the conventional friction models. Experimental results indicate that the root mean square and maximum absolute tracking error can be significantly reduced after applying the proposed friction model.

Application of Dissipative Contact Force Model for Contact–Impact Analysis in Deep Groove Ball Bearing

This work proposes a new dynamic model for evaluating the nonlinear characteristics of deep groove ball bearing considering the contact–impact characteristics. With clearance taken into account, the elements of the deep groove ball bearing are modeled as the contact bodies. The normal force in the contact bodies is established by the dissipative contact force model, which includes elastic deformation and energy loss. Based on the modified Coulomb friction model, the tangential force can be established. The dynamic analysis model of deep groove ball bearing with contact–impact characteristics is obtained. Moreover, the experimental platform is established and the dynamic performance experiment is conducted. Finally, the influence of structure features on the dynamic behavior of deep groove ball bearing is discussed in detail. The simulation results could represent that clearance plays an important element in evaluating accurately the dynamic behavior of deep groove ball bearing, which would cause strong nonlinear mechanical systems.

Observer-based adaptive fuzzy control of stabilized platform in rotary steerable system with input saturation and output constraint

This paper explores the control strategy for toolface tracking in the stabilized platform of a rotary steerable system, considering both input saturation and output constraint. To mitigate the impact of unknown friction torque and modeling error on the stabilized platform, we propose an adaptive fuzzy backstepping control approach. A fuzzy state observer is specifically devised to handle the uncertain state arising from unknown friction torque and modeling errors. Introducing an auxiliary system effectively compensates for input saturation, and the resolution of the output error constraint is achieved through the construction of a barrier Lyapunov function. Furthermore, employing the Lyapunov method establishes that all signals in the entire closed-loop control system are semi-globally uniformly ultimately bounded. Simulation results confirm the efficacy of the proposed control methodology.

Friction and Wear Mechanisms of Ti3SiC2/Cu Composites under the Synergistic Effect of Velocity–Load Field at 800 °C

Ti3SiC2/Cu composites were prepared using spark plasma sintering technology, and the effect of the velocity–load bivariate on the tribological behaviors of the Ti3SiC2/Cu-45# steel tribo-pair at 800 °C was investigated. The physical change and frictional chemical reaction during the friction process were analyzed based on the morphology characterization and frictional interface phases. The related friction and wear mechanism model was established. The results showed that the influence of velocity and load on the tribological performance of the Ti3SiC2/Cu-45# steel tribo-pair was not monotonically linear. When both the velocity and load were large, the coordinated effect of the two led to a low friction coefficient (0.52). At 800 °C, the velocity mainly affected the exfoliation and re-formation of the oxide film on the wear surface of the Ti3SiC2/Cu-45# steel tribo-pair, while the load affected the extrusion and fragmentation of the oxide film on the wear surface of the tribo-pair. In the friction process, frictional oxidation was the main influencing factor for the formation of the oxide film. When the velocity and load were small, the main frictional oxide consisted of SiO2−x and a small amount of CuO. When the velocity reached 1 m/s and the load reached 3 N, the oxide film was partially broken down and flaked off, and the matrix of the Ti3SiC2/Cu composite was exposed and oxidized, at which time the oxide film was composed of SiO2−x, TiO2, CuO, and Fe2O3. Under the synergistic effect of the velocity–load–temperature field, the friction and wear mechanism of the Ti3SiC2/Cu-45# steel tribo-pair changed from abrasive wear to frictional oxidation wear with the increase in velocity and load.

Finite element method based modeling of cutting forces and cutting temperature in micro-milling LF21

The demands for aluminum alloy LF21 micro precision parts are increasing in the fields of aerospace, high-tech electronic products, and the other fields. Micro-milling is an effective technology for machining small LF21 precision parts. Cutting forces and temperature are crucial factors in micro-milling process, directly affect tool vibration, tool wear, and surface quality of the workpiece, and even result in large deformation of the tool and workpiece. Direct measurement of cutting forces during micro-milling requires high-precision and expensive instruments. Moreover, due to the small cutting area in micro-milling, it is challenging to achieve accurate measurements of cutting area temperature. Therefore, accurate prediction of cutting forces and temperature in micro-milling is urgent and challenging. Nowadays, there are few studies on prediction of cutting forces in micro-milling LF21. The study on prediction of temperature in micro-milling LF21 is still blank. To solve the above problems, this paper proposes a finite element method based on modeling for prediction of cutting forces and temperature in micro-milling LF21. ABAQUS software is adopted. First, the geometry models of the micro-milling tool and workpiece are established. Then, the assembly and mesh division of the established models are completed. Johnson-Cook constitutive model and Johnson-Cook damage criteria are used to describe the material constitutive relationship and chip separation criteria, respectively. The suitable tool-workpiece friction models are determined. Finally, the simulation of the micro-milling LF21 process is achieved. Experiments of micro-milling LF21 are conducted and the cutting forces are measured using the dynamometer. The validity of the built process simulation model and the correctness of the cutting force prediction results are verified by the comparison of experiment and simulation cutting forces. Then, the prediction of temperature is achieved based on the verified process simulation model of micro-milling LF21.

Dynamics Modeling and Parameter Identification for a Coupled-Drive Dual-Arm Nursing Robot

A dual-arm nursing robot can gently lift patients and transfer them between a bed and a wheelchair. With its lightweight design, high load-bearing capacity, and smooth surface, the coupled-drive joint is particularly well suited for these robots. However, the coupled nature of the joint disrupts the direct linear relationship between the input and output torques, posing challenges for dynamic modeling and practical applications. This study investigated the transmission mechanism of this joint and employed the Lagrangian method to construct a dynamic model of its internal dynamics. Building on this foundation, the Newton-Euler method was used to develop a dynamic model for the entire robotic arm. A continuously differentiable friction model was incorporated to reduce the vibrations caused by speed transitions to zero. An experimental method was designed to compensate for gravity, inertia, and modeling errors to identify the parameters of the friction model. This method establishes a mapping relationship between the friction force and motor current. In addition, a Fourier series-based excitation trajectory was developed to facilitate the identification of the dynamic model parameters of the robotic arm. Trajectory tracking experiments were conducted during the experimental validation phase, demonstrating the high accuracy of the dynamic model and the parameter identification method for the robotic arm. This study presents a dynamic modeling and parameter identification method for coupled-drive joint robotic arms, thereby establishing a foundation for motion control in humanoid nursing robots.

Transient Friction Analysis of Pressure Waves Propagating in Power-Law Non-Newtonian Fluids

Modulated pressure waves propagating in the drilling fluids inside the drill string are a reliable real-time communication technology that transmit data from downhole to the surface during oil and gas drilling. In the analysis of pressure waves’ propagation characteristics, the modeling of transient friction in non-Newtonian fluids remains a great challenge. This paper establishes a numerical model for transient pipe flow of power-law non-Newtonian fluids by using the weighted residual collocation method. Then, the Newton–Raphson method is applied to solve the nonlinear equations. The numerical method is validated by using the theoretical solution of Newtonian fluids and is proven to converge reliably with larger time steps. Finally, the influencing factors of the wall shear stress are analyzed using this numerical method. For shear-thinning fluids, the friction loss of periodic flow decreases with the increase in flow rate, which is opposite to the variation law of friction with the flow rate for stable pipe flow. Keeping the amplitude of pressure pulsation unchanged, an increase in frequency leads to a decrease in velocity fluctuations; therefore, the friction loss decreases with the increase in frequency.

Trajectory design based on frictional resistance of deflector in a hydraulic radial drilling system

The trajectory design is a key factor affecting the frictional resistance of the deflector, which is crucial for the drilling ability of the hydraulic radial drilling system. In this research, the trajectory design model and geometric constraints model of a deflector are established by analyzing the geometric relationship of the deflector and considering the geometric constraints of the casing. According to the actual contact form between the high-pressure hose and the deflector, the theoretical model of frictional resistance is built based on segmental rigidization and micro-element methods. The theoretical model is verified by the deflector friction experiment. The results demonstrate a good agreement between the experimental results of friction resistance of different sizes of high-pressure hoses and the theoretical results, with an error of less than 7%. The influence of critical parameters of deflector trajectory on the friction resistance is studied by coupling the geometric constraints model and the frictional resistance theoretical model of the deflector. The findings show that the deflector’s frictional resistance increases with the inclination angle β of the inclined-straight section and decreases with the increase in the radius R of the bending segment, the inclination angle ω of the straightening segment, and the channel radius of r deflector. A new trajectory parameters of the deflector are presented by taking a five-inch casing as an example, they are β = 9°, R = 92 mm, ω = 108°, r = 17 mm. The research results provide a theoretical rationale for designing a low-frictional resistance deflector.

Design of Adaptive Finite-Time Backstepping Control for Shield Tunneling Systems with Constraints

This paper focuses on the finite-time tracking control problem of shield tunneling systems in the presence of constraints on the states and control input. By modeling the system based on the LuGre friction model, an effective method of tracking control in finite time is designed to overcome these actual constraints at the same time. First, the constraint on the system state is transformed into a symmetric constraint on the tracking error, and the constraint on control input is handled by designing an auxiliary differential equation. Then, radial basis function (RBF) neural networks are introduced to approximate the uncertainties. Next, using an adaptive finite-time backstepping method and choosing a logarithmic barrier Lyapunov function (BLF), a finite-time controller is designed to realize the finite-time stability of the closed-loop system. Finally, a simulation example is given to verify the correctness and validity of the theoretical results.

Modelling of Static and Dynamic Elastomer Friction in Dry Conditions

Understanding the tribological behavior of elastomers in dry conditions is essential for sealing applications, as dry contact may occur even in lubricated conditions due to local dewetting. In recent decades, Persson and co-authors have developed a comprehensive theory for rubber contact mechanics and dry friction. In this work, their model is implemented and extended, particularly by including static friction based on the bond population model by Juvekar and coworkers. Validation experiments are performed using a tribometer over a wide range of materials, temperatures and speeds. It is shown that the friction model presented in this work can predict the static and dynamic dry friction of various commercial rubber materials with different base polymers (FKM, EPDM and NBR) with an average accuracy of 10%. The model is then used to study the relevance of different elastomer friction contributions under various operating conditions and for different roughness of the counter surface. The present model will help in the development of novel optimized sealing solutions and provide a foundation for future modeling of lubricated elastomer friction.

Computational framework for predicting friction law under mixed-boundary lubrication, and its application to sheet metal forming process

The role of friction in the forming of automotive parts composed of ultra-high-strength lightweight metals has become increasingly important as industry attempts to overcome inferior formability and springback against enhanced strength. At the tool-design stage, finite-element simulations should use more accurate and efficient friction models that account for complex friction behavior between the metal and tool surfaces. Complex friction behavior is commonly dependent on contact pressure, sliding velocity, microscale surface effects (or roughness), and lubrication, among other factors. This study presents a microscale, asperity-based friction model of mixed-boundary lubrication. The developed hydrodynamic friction model is based on the load-sharing concept, which considers the lubrication area and metal-to-metal contact separately. Lubricant film thickness is calculated to couple the existing boundary lubrication model, and film lubrication behavior is formulated using finite-element programming of the Reynolds equation to obtain the hydrodynamic pressure. The proposed computational framework is validated by simulating an in-line incremental die-forming process. The result shows that the predicted friction law with multi-scale, mixed-boundary lubrication can be efficiently applied to realistic sheet-metal-forming simulations with reasonable accuracy by accounting for complex frictional behavior.

Friction between a single platelet and fibrinogen

Friction has been considered to mediate physiological activities of cells, however, the biological friction between a single cell and its ligand-bound surface has not been thoroughly explored. Herein, we established a friction model for single cells based on an atomic force microscopy (AFM) combined with an inverted fluorescence microscopy (IFM) to study the friction between a highly sensitive platelet and fibrinogen-coated surface. The study revealed that the friction between the platelet and fibrinogen-coated tip is mainly influenced by specific ligand–receptor interaction. Further, we modeled the biological friction, which consists of specific interaction, non-specific interaction, and mechanical effect. Besides, the results suggested that the velocity can also affect specific ligand–receptor interactions, resulting in the friction change and platelet adhesion to fibrinogen surfaces. The study built a friction model between a single cell and its ligand-bound surface and provided a potential method to study the biological friction by the combination of AFM and IFM.

A semi-conservative depth-averaged material point method for fast flow-like landslides and mudflows

We present a two-dimensional semi-conservative variant of the depth-averaged material point method (DAMPM) for modeling flow-like landslides. The mathematical model is given by the shallow water equations, derived from the depth-integration of the Navier–Stokes equations with the inclusion of an appropriate bed friction model and material rheology, namely Voellmy and the depth-integrated Bingham viscoplastic stress model, respectively. After assessing the accuracy and performance of the proposed numerical method by means of several idealized benchmarks, we test its behavior in a realistic scenario.

Validation of a three-dimensional two-phase code, CUPID, using a rod-bundle boiling test facility, SIRIUS-3D

In nuclear power plants, the occurrence of a three-dimensional mixing phenomenon in two-phase flow can help mitigate the peak cladding temperature of fuels in a core. Simulating this phenomenon necessitates subchannel-scale analysis. CUPID is a three-dimensional thermal hydraulic analysis code developed by KAERI. This paper presents the validation results of the code against rod bundle tests conducted using SIRIUS-3D, a 5 × 5 rod bundle test facility. One test utilized subchannel void sensors, while the other employed X-ray CT. To validate the SIRIUS-3D test data, subchannel-scale nodes were constructed for CUPID calculation. For improved convergence, the implicit friction calculation was conducted with a small CFL ratio. The drag coefficient interfacial friction model without the EVVD model yielded the best prediction. The void fraction was over-predicted at a low velocity of 0.1 m/s, which could be improved by reducing the interfacial friction.

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.

Dynamic Implications of Noncovalent Interactions in Amphiphilic Single-Chain Polymer Nanoparticles.

Single-chain polymer nanoparticles (SCNPs) combine the chemical diversity of synthetic polymers with the intricate structure of biopolymers, generating versatile biomimetic materials. The mobility of polymer chain segments at length scales similar to secondary structural elements in proteins is critical to SCNP structure and thus function. However, the influence of noncovalent interactions used to form SCNPs (e.g., hydrogen-bonding and biomimetic secondary-like structure) on these conformational dynamics is challenging to quantitatively assess. To isolate the effects of noncovalent interactions on SCNP structure and conformational dynamics, we synthesized a series of amphiphilic copolymers containing dimethylacrylamide and monomers capable of forming these different interactions: (1) di(phenylalanine) acrylamide that forms intramolecular β-sheet-like cross-links, (2) phenylalanine acrylamide that forms hydrogen-bonds but lacks a defined local structure, and (3) benzyl acrylamide that has the lowest propensity for hydrogen-bonding. Each SCNP formed folded structures comparable to those of intrinsically disordered proteins, as observed by size exclusion chromatography and small angle neutron scattering. The dynamics of these polymers, as characterized by a combination of dynamic light scattering and neutron spin echo spectroscopy, was well described using the Zimm with internal friction (ZIF) model, highlighting the role of each noncovalent interaction to additively restrict the internal relaxations of SCNPs. These results demonstrate the utility of local scale interactions to control SCNP polymer dynamics, guiding the design of functional biomimetic materials with refined binding sites and tunable kinetics.

Modelling of energy harvesting with bendable concrete and surface-mounted PVDF

Polyvinyl alcohol fiber reinforced engineered cementitious composite (ECC) using piezoelectric polymer film has attracted significant interest due to its energy harvesting potential. This work provides a theoretical model for evaluating the energy harvesting of bendable ECC using surface-mounted polyvinylidene fluoride (PVDF). In the mechanical part, concrete damage plasticity model based on the explicit dynamic analysis was utilized to simulate the dynamic flexural behavior of ECC beam under different dynamic loading rates. The mechanism of force transfer through the bond layer between the PVDF film and ECC specimen was simulated by a surface-surface sliding friction model wherein the PVDF film was simplified as shell element to reduce computational cost. Then, the electromechanical behavior of the piezoelectric film was simulated by a piezoelectric finite element model. A simplified model was also given for a quick calculation. The theoretical model was verified with the experimentally measured mechanical and electrical results from the literature. Finally, a parametric analysis of the effects of electromechanical parameters on the efficiency of energy harvesting was performed. The verified theoretical model can provide a useful tool for design and optimization of cementitious composite systems for energy harvesting application.

Stiction parameter identification for pneumatic valves with a simultaneous approach

In industrial processes, stiction in control valves is a common cause of degradation in control loop performance. It is important to identify and establish reliable stiction models to enhance control loop performance. This study focuses on constructing a precise model of the pneumatic control valve using the LuGre friction model. To improve the model, a smooth function based on probability density is introduced to alleviate the LuGre friction model. The maximum error resulting from this smoothing process is also analyzed. To estimate the valve stiction parameters, the direct transcription method is utilized to convert the problem from systems of ordinary differential equations into a nonlinear programming problem. The interior point method is then used to solve this problem. Furthermore, the estimability of the parameters is analyzed based on the reduced Hessian matrix before estimation. Numerical results demonstrate that the proposed approach in this study effectively estimates the stiction parameters of pneumatic control valves.