Friction Force Model Research Articles

Mechanical modeling of friction phenomena in social systems based on friction force

Friction is not an inherent attribute in natural science. Indeed, there are various friction phenomena present in social systems. In this study, the researchers developed the general concept of social friction and distinguished the two-dimensional structure of explicit-implicit social friction phenomena. Specifically, explicit friction includes institutional friction, economic friction, behavioral friction, and migration friction. Implicit friction includes cultural friction, cognitive friction, interpersonal friction, technological friction, and information friction. Physical theories such as friction force, classical mechanics, and functional principles have been introduced to construct a social friction force model. This paper describes the emergence and evolution of social friction phenomena from the mechanics perspective and clarifies the various characteristics of social friction force in different areas. This study also provides a new theoretical perspective for examining social friction phenomena and adds innovative content to intersection studies in physics and the social sciences.

Two-phase data science framework for compensation of the friction force in CNC machines

ABSTRACT This study proposes a two-phase data science framework for the friction force and parameter estimation of the hysteresis effect segment in the servo-control systems of precision machines. The first phase uses an exponential-based friction force model to identify the model parameters by an autoregressive model and Z-transform. The second phase uses symbolic regression for the residual analysis to enhance the friction force estimation. An empirical study of three types of CNC machines under different working conditions is conducted to validate the two-phase data science framework and identify the change of the machining displacement considered to be a critical factor affecting friction force. The exponential-based model successfully eliminates the circular spike error caused by the friction force in the tapping center machine. The results indicate that the proposed two-phase framework improves mean absolute error by 5.6% on average in the tapping center, 6.5% in the milling machine and 7.6% in the turning and milling center, respectively.

Micro-Grinding Parameter Control of Hard and Brittle Materials Based on Kinematic Analysis of Material Removal

This article explores the intricacies of micro-grinding parameter control for hard and brittle materials, with a specific focus on Zirconia ceramics (ZrO2) and Optical Glass (BK7). Given the increasing demand and application of these materials in various high-precision industries, this study aims to provide a comprehensive kinematic analysis of material removal during the micro-grinding process. According to the grinding parameters selected to be analyzed in this study, the ac-max values are between (9.55 nm ~ 67.58 nm). Theoretical modeling of the grinding force considering the brittle and ductile removal phase, frictional effects, the possibility of grit to cut materials, and grinding conditions is very important in order to control and optimize the surface grinding process. This research introduces novel models for predicting and optimizing micro-grinding forces effectively. The primary objective is to establish a micro-grinding force model that facilitates the easy manipulation of micro-grinding parameters, thereby optimizing the machining process for these challenging materials. Through experimental investigations conducted on Zirconia ceramics, the paper evaluates a mathematical model of the grinding force, highlighting its significance in predicting and controlling the forces involved in micro-grinding. The suggested model underwent thorough testing to assess its validity, revealing an accuracy with average variances of 6.616% for the normal force and 5.752% for the tangential force. Additionally, the study delves into the coefficient of friction within the grinding process, suggesting a novel frictional force model. This model is assessed through a series of experiments on Optical Glass BK7, aiming to accurately characterize the frictional forces at play during grinding. The empirical results obtained from both sets of experiments—on Zirconia ceramics and Optical Glass BK7—substantiate the efficacy of the proposed models. These findings confirm the models’ capability to accurately describe the force dynamics in the micro-grinding of hard and brittle materials. The research not only contributes to the theoretical understanding of micro-grinding processes but also offers practical insights for enhancing the efficiency and effectiveness of machining operations involving hard and brittle materials.

Cutting force reduction mechanism in ultrasonic cutting of aramid honeycomb

Aramid honeycomb has extensive applications in the aerospace and rail transportation industries. Ultrasonic cutting (UC) with the straight blade (SB) is an advanced technology used for the profile machining of honeycomb materials. Cutting force is an important factor affecting machining quality, and its accurate modelling is particularly important. However, SB is a flake tool, and chips of honeycomb are removed in block or strip forms during cutting, and its structure and material removal method are obviously different from conventional machining. Existing simplified cutting force models based on kinematic analyses and experiments are incapable of describing the cutting process. In this paper, a geometrical kinematics analysis of SB is conducted. Further, the modelling of tool-workpiece contact rate (TWCR) for UC with SB is established, which is utilized to analyze the tool-material contact state. Based on the principle of conservation of energy, the fracture force at the blade edge is analyzed. Based on the analysis of instantaneous friction force, the friction force model on blade surfaces is established. Multiple-cutting experiments are conducted to separate fracture force and friction force. The influence of machining parameters (ultrasonic amplitude, lead angle, cutting speed) on TWCR, cutting force, fracture force, and friction force have been theoretically and experimentally studied, and the reduction mechanism of the cutting force is revealed. Furthermore, the machining quality under different machining parameters is observed and the relationship with cutting force is analyzed. The paper not only provides theoretical guidance for the study of the UC mechanism but also helps to guide the UC process of aramid honeycomb.

Initiation of motion for an isolated finite size particle in a rotating tank flow

The initiation of motion of an isolated finite size particle within a rotating fluid in a tank is investigated experimentally. The study leverages on the absence of slip velocity to explore the impact rotation has on the initiation of the motion of a particle. Results show that the motion, when it occurs, is purely radial. It is initiated when the centrifugal force acting on the particle overcomes the friction force exerted on it by the tank bottom. A model of friction force that reproduces the experimental data quite well is proposed. It is based on the classical Coulomb’s friction law and pressure considerations. Denoting rc as the radial position of a particle when its motion starts, the critical radius r∗c=rc/d essentially depends on the density ratio γ, the Froude number Frω=ω2d/g but also the ratio of the tank radius to the particle size: α=R/d . Frω is based on the particle diameter d, the shear velocity ΔU=ωd with ω the rotation rate and g the acceleration due to gravity. The agreement of the model with the experimental data is obtained for the same friction coefficient λ = 0.019 whatever the particles. The value is not far from the value 0.05 generally expected for lubricated smooth plastic/plastic friction coefficients. The model also shows that for a given tank radius a critical rotation speed exists below which, no initiation of motion can be expected.

Modeling and Control of a Snake Robot using SimMechanics

Snake robots are biological inspired robots designed to locomote in an unwanted environment. The mechanism comprises of serially connected links through rotational joints capable of rotating its body in one or more plans. In this paper, snake robot model is proposed. The proposed model consists of a 10-links physically connected through joints. The aim of this work is to propel a snake robot consisting of 10-link through the n-1 rotary joint on the serpentine aisle. Structure of the entire mechanical model of a snake is created in Simmechanics, MATLAB library tool within Simulink environment. The mechanics for the motion of snake robot including dynamics, kinematics and friction force models are developed in order to find the nth link location in a 3D environment. In addition, we have also established the joint angle to activate the robot’s link on a serpenoid terrain. To control the entire movement comprising position, speed and torque at each joint of the snake robot, control system is altered. This system is further composed of 3 proportional controllers having a sensor to take measurement results from an actuator. The simulation studies showing performance of the system are conducted to determine the control parameters of the system measured through joint sensor via scope, graph and display units. From simulation results it is shown that the snake robot followed the serpentine wave motion.

A ship evacuation model considering the interaction between pedestrians based on cellular automata

This paper proposes the CAIE (cellular automata with interaction effect) model to evaluate ship passenger evacuation capability. The CAIE model simulates the interaction between passengers by establishing the friction and repulsive force model between passengers, derives the formula of the desired velocity's effect on the movement ability, reflects the influence of a high-density environment on the movement velocity of personnel, and defines push-crossing behavior rules to simulate opposite-flow movement. The proposed CAIE model is verified by passenger evacuation simulation experiments in single-exit cabins under the condition of opposite passenger traffic. The results demonstrate that the CAIE model has similar passenger movement rules as the social force model in terms of the arching and faster-is-slower phenomena. The results also show that the CAIE model meets the test requirements for the MSC.1/Circ.1533 communication of the advanced evacuation simulation model. Finally, the evacuation simulation analysis is performed on a small polar cruise ship using the CAIE model, Pathfinder software, and Maritime Exodus software. The comparison results indicate that the simulation results of the three models and their distributions of evacuation time are consistent. Therefore, the proposed CAIE model can be used to evaluate the evacuation ability of ships.

Dynamic analysis for mechanical system with clearance joint considering dependent interval parameters

Uncertainties caused by measuring errors or incomplete knowledge affect the dynamic response and functional reliability of the mechanical system, particularly for the mechanisms with clearance joints. Considering that dependency between the interval parameters in the uncertain quantification of mechanical systems with clearance joints is prone to be ignored, in this article, a dynamic analysis procedure considering the correlation between interval parameters is presented. Firstly, the continuous contact force model and modified friction force model are embedded into the deterministic dynamic governing equations of the mechanical system with clearance joints derived by the Lagrangian method. To characterize the correlation between interval uncertainties, the convex ellipsoid model is employed, and a Chebyshev-based convex scanning method is developed to obtain the bounds of dynamic response. Finally, a robot manipulator with clearance joint considering dependent uncertainties is illustrated as an example to investigate the clearance effect and correlations between uncertainties on the dynamic behavior. In the numerical simulation, the geometrical parameters of the manipulator arm are regarded as dependent interval parameters. The results show that the dependence between interval uncertainties induces relatively conservative bounds and should be considered carefully in the case of a large clearance size existing in the mechanical system.

A combined experimental and analytical method to determine the EHL friction force distribution between rollers and outer raceway in a cylindrical roller bearing

Friction force is a crucial factor causing power loss and fatigue spalling of rolling element bearings. A combined experimental and analytical method is proposed to quantitatively determine the elastohydrodynamic lubrication (EHL) friction force distribution between rollers and outer raceway in a cylindrical roller bearing (CRB). An experimental system with the instrumented bearing and housing was developed for measuring radial load distribution and friction torque of bearings. A simplified model of friction force expressed by dimensionless speed, load, and material parameters was given. An inequality constrained optimization problem was established and solved by using an experimental data-driven learning algorithm for determining the uncertain parameters in the model. The effect of speed, load, and lubricant property on friction force and friction coefficient was discussed.

Improved friction model applied to plane sliding connections by a large deformation FEM formulation

Friction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect.

Dynamics Analysis and Chaos Identification of Compound Pendulum Jaw Crusher with Joint Clearance

A dynamic model of the working mechanism of a compound pendulum jaw crusher with clearance is established by the Lagrange multiplier method (LMD) based on the L-N contact force model and modified Coulomb friction force model. The correctness of the dynamic model is verified by MATLAB and Adams comparison simulation, and the best selection range of driving speed and clearance size is determined according to the laminating crushing theory (LCT). The effects of driving speed and clearance size on the shock and chaos phenomenon in the clearance mechanism are analyzed, as well as the vibration force applied to the foundation. The results show that, under the premise of meeting the requirements of crusher production capacity, increasing the driving speed and reducing the clearance size can weaken the shock and chaos phenomenon during the operation of the mechanism, improve the dynamic performance and enhance the operation stability, and the service life of foundation is prolonged with the stability of vibration force. Furthermore, the optimal combination of driving speed and clearance size is determined, which provides a theoretical basis for the optimization of the vibration force of the jaw crusher.

Friction torque analysis of planetary roller screw based on the creepage theory

The creepage characteristics of the contact interface are analyzed based on rolling contact theory in this paper. Moreover, creepage parameters such as creepage rate, spinning rate, and Heathcote slip were obtained. The Kalker creepage theory model is employed to determine the friction force within the thread contact interface. The planetary roller screw (PRS) friction force and dynamics model was established based on the Lagrange method. The PRS friction force model is then experimentally validated. Finally, the influence of working conditions and creepage parameters on the friction torque, transmission efficiency, and relative contact interface sliding velocity are analyzed. The results show that the friction coefficient and creepage parameters have significant effect on the friction torque of the PRS.

Adaptive variable impedance position/force tracking control of fracture reduction robot.

The operation object of robot-assisted fracture reduction surgery is the musculoskeletal tissue with rigid-compliance coupling characteristics. It is necessary to improve the interactive compliance and safety between the reduction robot and the musculoskeletal tissue. An adaptive variable impedance position/force tracking control strategy based on friction compensation is proposed. The stiffness of the reduction robot can be adaptively adjusted according to the contact force between the end-effector and the environment. The Stribeck friction force model of the branch chain electric cylinder is derived to improve the motion control performance. The fracture reduction experiment is completed. The experimental results show that the adaptive variable impedance position/force control strategy can realize position and force tracking in fracture reduction. A safety control strategy is proposed and applied to robot-assisted fracture reduction surgery, which improves the coordination and compliance of the human-robot interaction between the reduction robot and the patient.

Dynamic Friction-Slip Model Based on Contact Theory

In ultra-precision positioning equipment, the positioning accuracy is affected by the friction characteristics, especially the pre-slip stage. At present, the research on friction mainly includes contact theory and the dynamic friction process. There is no time variable in contact theory models, so they only apply to the stage of static contact, while the establishment of a friction dynamics model depends on parameter identification and cannot reflect the influence of a rough morphology and load. Therefore, neither theory can elucidate the ultra-precise slip mechanism. In this paper, maximum static friction force, tangential stiffness, and tangential damping models of contact surfaces were deduced through fractal contact theory. By substituting the contact parameters into the modified LuGre model, a dynamic slip model of the mask was established. Finally, the above model was verified by a reticle dynamic slip measurement system. The experimental results showed that in the pre-slip stage of the reticle, with an increase in the normal external load, the slippage of the reticle decreased. The theoretical value calculated by the model was basically consistent with the experimental value, and the slippage of the reticle mainly originated from the tangential deformation and relative sliding of the contact surface. With the increase in the normal external load, the proportion of the tangential deformation in the sliding of the entire contact surface was larger. For the change in slippage during different motion stages, the theoretical value was close to the experimental value after eliminating system errors such as vibration and fiber bending, which proved the correctness of the model in this paper.

Droplet and bubble wetting behaviors: The roles of surface wettability and roughness

Droplet and bubble wettability are important parameters for characterizing the wetting propensity of solid surface. Recent studies have shown significant differences between the wetting behaviors of droplet and bubble, specifically apparent contact angle (ACA) and contact angle hysteresis (CAH). However, very few studies have systematically investigated and examined the differences. Additionally, there is a lack of comprehensive knowledge and experimental observations about the effects of surface roughness on the droplet and bubble wetting behaviors under different wetting states. These knowledge gaps restrict our understanding of the wetting dynamic process. In this study, by varying surface roughness and modifying wettability with silane coupling agent KH-550, we evaluated droplet and bubble CAHs from strong hydrophilicity to hydrophobicity using a novel gas-driven method and the moving needle method, and analyzed the measurements using the friction force model. Young contact angle (YCA) was calculated to characterize the intrinsic wettability of three-phase system and experimental observations were interpreted in detail. The results show that the impact of roughness on droplet CAH varies in different wetting states caused by coupled effect between solid-liquid affinity and rough microstructure. A critical YCA for effective spreading is observed in bubble wetting behaviors for the first time, above which bubble ACA and CAH abruptly change. The increase of roughness reduces bubble ACA and CAH. With a critical Young contact angle as the turning point, the difference between droplet and bubble wetting behaviors as well as the effect of roughness vary. Additionally, after bubble fully spreads, its advancing angles are equal to droplet ACAs, and its ACAs are equal to droplet receding angles on relatively smooth surface. These intriguing findings are supplementary to current knowledge about droplet and bubble wetting behaviors.

Study on Wear Characteristics of Revolute Clearance Joints in Mechanical Systems.

The existence of clearance causes contact-impact forces in joints, which lead to surface wear and incessant material loss of the joint surface during the motion of mechanisms. In this work, the wear characteristics of dry revolute clearance joints in planar mechanisms are studied using a computational methodology. The normal contact force model and the tangential friction force model are established to describe the contact-impact in clearance joints. Then, the dynamic wear model based on the Archard’s wear model is established to predict the wear characteristics of clearance joints in mechanisms. The dynamic wear depths of clearance joints are obtained in two steps. The first step is the dynamics analysis of mechanisms to obtain the contact and sliding characteristics between the bearing and journal in the clearance joint. The second step is the dynamic wear depth analysis of clearance joints based on dynamic Archard’s wear model. Finally, a planar slider-crank mechanism with two revolute clearance joints between the connecting rod and its adjacent links is used as the implement example. Different case studies are performed to investigate the wear characteristics of clearance joints in mechanical systems.

Modeling and analysis of nonlinear axial friction forces of tripod joints considering roughness characteristics of contact pairs

The nonlinear axial friction force (NAFF) induced by contact and friction between components of tripod joints constitutes an important dynamic characteristic of drive-shaft systems, which will lead to deterioration of the NVH (noise, vibration and harshness) performance of the vehicle. Based on the fractal theory, this paper proposes a novel modeling and analysis method for accurate estimation of NAFF considering micro contact and friction characteristics of contact pairs. An analytical model is developed for estimating the NAFF of tripod joints considering micro contact and friction characteristics of contact pairs. In the process of modeling, a modified distribution function is proposed to describe distributions of contact asperities between the curved surfaces to describe the contact and friction states between the rollers and the tracks inside tripod joints more accurately. The developed analytical model suggests that NAFF is related to the fractal parameters, the material parameters, the operating conditions and the distribution of asperities. The effectiveness of the analytical model is demonstrated by comparing the model-predicted NAFF with the measured data. Based on the developed model of NAFF, the influences of important input parameters on the magnitude of NAFF are qualitatively analyzed. Subsequently, Sobol' global sensitivity analysis method is used to further investigate the influences of important input parameters on the magnitude of NAFF. The results show that the proposed modeling and analysis method for estimating NAFF are essential to characterize relationships among NAFF and fractal parameters, material properties and distribution of asperities from a micro level, which could facilitate design optimization of the tripod joints.

Carbon brush wear calculation in marine environment based on temperature field analysis

In the marine environment, the working environment of the doubly fed wind generator carbon brush and slip-ring system is complicated, salt spray deposits and seawater erosion affect the temperature field and contact surface friction factor leading to carbon brush wear increase and shortened replacement cycle. The three-dimensional temperature field simulation model of the carbon brush and slip-ring system is established. The main factors affecting the carbon brush and slip-ring system temperature field are sliding velocity, load current, ambient temperature, contact surface condition and contact pressure applied to the brush. Wear capacity of carbon brushes is affected by contact surface temperature. An experimental platform combined with the salt spray test machine was built to carry out the contact current, contact pressure, salt spray concentration and experimental temperature experiment. The improved Coulomb-viscous friction force model was used for the wear prediction model. The sliding velocity, contact pressure, contact current, experimental temperature and salt spray concentration were introduced into the model. The experimental verification has shown that the prediction model can effectively predict the carbon brush wearing capacity under different conditions. This model can be applied to formulating the carbon brush wear amount and replacement cycle in the marine environment reducing operation and maintenance costs.

Identification of a Practical Digital Twin for Simulation of Machine Tools

A practical digital twin for machine tools is proposed in this study. The proposed digital twin is capable of time-domain simulation of machine tools and consists of a controller model, machining process model, and machine dynamic model. To predict the quality of the machined surface after the finishing processes, a precise dynamic model is required. The developed dynamic model consists of an interaction force model, vibration model, and friction force model. A linear auto regressive with exogenous inputs (ARX) model is adopted for the interaction and vibration models. Based on a systematic analysis of the disturbance forces of the machine tool, the friction characteristics are extracted to a displacement-dependent friction model and velocity-dependent friction model. A nonlinear Hammerstein model is adopted to identify the friction. Online identification systems based on the recursive least-squares (RLS) method are developed and tested for each model.

Modeling of Friction Forces for Linear Motion Ball Guides Considering Variation of the Friction Parameter with Operating Condition

Friction directly influences thermal deformation and transmission efficiency in a linear motion ball guide (LMBG). In existing friction force models for LMBGs, the friction parameter is usually empirically adopted as a constant, which leads to large error in model outputs when the friction parameter is sensitive to operating conditions, such as a light load or high velocity. In this study, a new model was built to calculate the contact load in LMBGs by considering elastic deformation of the carriage skirt, based on which we proposed a friction force model that considers variation of the friction parameter with operating condition. The friction force predicted by this model is in good agreement with experimental results, especially under operating conditions of light load and high velocity. To estimate the total friction force more conveniently and efficiently in practice, an equivalent friction coefficient for the tested LMBG, which combines sliding, viscous, and elastic hysteresis frictions, is proposed, and the modeled difference from the theoretical value falls within 10%.