Coulomb Friction Model Research Articles

Experimental, analytical and numerical assessment of the bond-slip behaviour in concrete-filled-FRP tubes

The interfacial bond between the fiber-reinforced polymers tube (FRP-T) and its concrete core (CC) is necessary to transfer the loads from the FRP-T to the CC. In this study authors present an experimental investigation of the interfacial bond strength between the circular pultruded FRP-Ts (with or without sand-coating) and a CC. It also aims to evaluate the use of sand-coating as a bond enhancer to improve the interfacial bond strength of the concrete filled FRP tube members. Twelve (12) full-scale circular CFFT specimens with 200 mm length and 12,7 mm wall thickness were tested, with two different diameters (305 mm and 406 mm) and two different inner surface texture (sand-coated or not). The driving force and the slippage between the FRP-T and its CC were captured to plot the interfacial bond-slip relationships for each specimen. The experimental results showed that the measured interfacial bond stress between the pultruded FRP-T and its CC (without sand-coating) was varying from 0.022 MPa to 0.028 MPa then could therefore be neglected. Meanwhile, the interfacial bond strength of the same tube with sand-coating was varying from 0.43 MPa to 1.00 MPa. Consequently, sand-coating as a bond enhancer was proven to significantly improve the interfacial bond strength of the pultruded FRP-T. This paper also presents results from an analytical model and a F.E. simulation model of the interfacial bond-slip behaviour for CFFT members. Coulomb stick-slip friction model is used to characterise the interfacial connection behaviour between the FRP-T and its CC. Experimental, analytical and numerical results are consistent.

A first-order lumped parameters model of electrohydraulic actuators for low-inertia rotating systems with dry friction

In aerospace engineering, there are several control systems affected by dry friction, which are characterized by low inertia and high working frequencies. For these systems, it is possible to use a downgraded, first-order dynamic model to represent their behaviour properly without run into numerical problems that would be harmful for the solution itself and would require high computational power to be solved, which means more weight, costs, and complexity. Yet, the effect of dry friction is still possible to be accounted for accurately using a new algorithm based on the Coulomb friction model applied to the downgraded, first-order dynamic model. In this paper, the degraded first-order model is applied to an electrohydraulic servomechanism with its PID control unit, hydraulic motor, electrohydraulic servo-valve, and applied load. These components represent a classic airplane actuator system. The downgraded model will be compared to the second-order one focusing on the pros and cons of the reduction process with a focus on the effect of dry friction for reversible and irreversible actuators.

Modelling in-plane dynamic response of a fastening system for horizontal concrete facade panels in RC precast buildings

The paper presents experimental and analytical studies of the dynamic in-plane response of typical fastening systems for horizontal cladding panels in RC precast industrial buildings in Central Europe. The system consists of two main parts: a pair of top bolted connections, which provide the horizontal stability of the panel, and a pair of bottom cantilever connections, which support the weight of the panel. A typical response mechanism of the fastening system consists of three distinct stages: sliding with limited friction, contact with the panel causing an increase in the connection stiffness, and failure. It has been found that the capacity of the complete system is limited by the displacement capacity of the top connections, which are the most critical components. Therefore, it is better to express the capacity of the entire system in terms of displacements.Appropriate numerical models for the complete fastening system have been proposed and validated by the results of the presented experiments. The top and bottom connections were analysed separately and showed physically different response behaviours. The typical Coulomb friction model was used to describe the friction in the top connection, whereas the viscous friction model better simulated variable friction in the bottom connection. The contacts that occur when the gap for sliding of panels closes were simulated by an abrupt increase of the stiffness of the connection.

Frictional behavior during cold ring compression process of aluminum alloy 5052

The friction is the considerable boundary condition in bulk metal forming. In this paper, the ring compression test was used to evaluate the friction coefficient and factor in Coulomb friction model and Tresca friction model for the plastic deformation of aluminum alloy AA5052. The micro-macro analysis method combining surface morphology and micro-texture was used to explore the friction behaviors in AA5052 cold forming process. In general, the magnitude (μ or m) of friction changes before and after a deformation threshold during ring compression. The maximum change rate of the magnitude (μ or m) before and after the deformation threshold is close to 18.5% under the present experimental conditions, and the change rate decreases with increasing loading speed. The lubrication using MoS2 is better than that using oil at lower speeds (0.15 mm/s, 1.5 mm/s), but the lubrications for MoS2 and oil are similar at higher speeds (15 mm/s). The surface roughness, three-dimensional topography, and surface texture of compressed ring have a sudden change around the deformation threshold, which deviate from the previous evolution trend. The increased friction after deformation threshold also promotes the formation of sufficient shear strain layer in the subsurface plane of the compressed ring, and then it hinders the formation of the typical deformation textures with β-oriented line and promotes the appearance of shear textures such as 001110, 111uvw and hkl110 textures.

Coulomb friction with rolling resistance as a cone complementarity problem

Coulomb friction model with unilateral contact is a basic, but reliable, model to represent the resistance to sliding between solid bodies. It is nowadays well-known that this model can be formulated as a second–order cone complementarity problem, or equivalently, as a variational inequality. In this article, the Coulomb friction model is enriched to take into account the resistance to rolling, also known as rolling friction. Introducing the rolling friction cone, an extended Coulomb's cone, and its dual, a formulation of the Coulomb friction with rolling resistance as a cone complementarity problem is shown to be equivalent to the standard formulation of the Coulomb friction with rolling resistance. Based on this complementarity formulation, the maximum dissipation principle and the bi-potential function are derived. Several iterative numerical methods based on projected fixed point iterations for variational inequalities and block-splitting techniques are given. The efficiency of these methods strongly relies on the computation of the projection onto the rolling friction cone. In this article, an original closed-form formula for the projection on the rolling friction cone is derived. The abilities of the model and the numerical methods are illustrated on the examples of a single sphere sliding and rolling on a plane, and of the evolution of spheres piles under gravity.

Accurate Energetic Constraints for Passive Grasp Stability Analysis

Passive reaction effects in grasp stability analysis occur when the contact forces and joint torques applied by a grasp change in response to external disturbances applied to the grasped object. For example, nonbackdrivable actuators (e.g. highly geared servos) will passively resist external disturbances without an actively applied command; for numerous robot hands using such motors, these effects can be highly beneficial as they increase grasp resistance without requiring active control. We introduce a grasp stability analysis method that can model these effects, and, for a given grasp, distinguish between disturbances that will be passively resisted and those that will not. We find that, in order to achieve this, the grasp model must include accurate energetic constraints. One way to achieve this is to consider the Maximum Dissipation Principle (MDP), a part of the Coulomb friction model that is rarely used in grasp stability analysis. However, the MDP constraints are non-convex, and difficult to solve efficiently. We thus introduce a convex relaxation method, along with an algorithm that successively refines this relaxation locally in order to obtain solutions to arbitrary accuracy efficiently. Our resulting algorithm can determine if a grasp is passively stable, solve for equilibrium contact forces and compute optimal actuator commands for stability. Its implementation is publicly available as part of the open-source GraspIt! simulator.

Performance estimation of resonance-enhanced dual-buoy wave energy converter using coupled time-domain simulation

This paper presents the modeling methodology and performance evaluation of the resonance-enhanced dual-buoy WEC (Wave Energy Converter) by HEM (hydrodynamic & electro-magnetic) fully-coupled-dynamics time-domain-simulation program. The numerical results are systematically compared with the authors’ 1/6-scale experiment. With a direct-drive linear generator, the WEC consists of dual floating cylinders and a moon-pool between the cylinders, which can utilize three resonance phenomena from moon-pool dynamics as well as heave motions of inner and outer buoys. The contact and friction between the two buoys observed in the experiment are also properly modeled in the time-domain simulation by the Coulomb-friction model. Moon-pool resonance peaks significantly exaggerated in linear potential theory are empirically adjusted through comparisons with measured values. A systematic comparative study between the simulations and experiments with and without PTO (power-take-off) is conducted, and the relative heave displacements/velocities and power outputs are well matched. Then, parametric studies are carried out with the simulation program to determine optimum generator parameters. The performance with various wave conditions is also assessed.

STABILITY ANALYSIS OF REUSABLE LAUNCH VEHICLE LANDING STRUCTURE$^{\bf 1)}$

Many countries carried out the research on vertical take-off and vertical landing reusable launch vehicle (RLV) in recent years. The touchdown stability of the RLV when landing vertically on the platform is a key issue for the RLV reuse. Since the structural scheme of the RLV has not been completed in the initial stage of design, and there are no detailed dynamic models for touchdown stability analysis, it is difficult to carry out the dynamic simulation of landing process, therefore the research on estimation method of landing stability is needed. Based on the generalized impact law, this paper analyzes the multiple impacts between the RLV and the landing platform in a two-dimensional landing mode, and the tangential restitution coefficients is given by Coulomb friction model at the impulse level. Firstly, the admissible domain of restitution coefficients in the general motion mode is given through the energetic constraint and unilateral constraints, and the admissible domain of restitution coefficients in two typical motion modes is given as well. Secondly, considering the role of buffer in the landing leg, the collision between the RLV and the platform is approximated as a completely inelastic collision, and accordingly the kinematic restitution coefficients is obtained. Therefore, combined with the kinematic analysis and energy method, a touchdown stability criterion is proposed, which discriminates whether an RLV will fall or not after impacts the platform. In the end, taking an RLV landing prototype as an example, the effects of some key parameters on touchdown stability are analyzed, including the touchdown velocity, the span of supporting leg and the friction coefficient between supporting leg and platform. The results show that the touchdown stability criterion proposed in this paper, is more accurate than the energy method, and the coupling relationship between touchdown velocity, angular velocity and friction coefficient can be considered.

Dynamics Analysis of Spatial Landing-Gear Mechanism with Hinge Clearance and Axis Deviation

The hinge clearance and rotation axis deviation of aircraft landing-gear retraction mechanism are unavoidable due to factors, such as manufacture, assembly, wear, and wing deformation. Such negative factors affect the dynamic response of the mechanism itself, which is more serious for spatial mechanisms. To study this effect, both numerical and experimental investigations on a spatial landing-gear mechanism are carried out in this study. To build the numerical model, the nonlinear contact force model and modified Coulomb friction model are adopted in the hinge clearance of the landing-gear mechanism. Considering the flexibility effect, some key moving parts, such as sidestay links, are flexibly processed to deal with the axis deviation problems. Based on the proposed model, the influences of clearance size and axis deviation value on the dynamic behaviors of spatial landing-gear mechanism are studied. Both the test and simulation results indicate that the clearance and axis deviation have little effect on the actuation response of the retraction mechanism if they are within reasonable ranges. Nevertheless, the axis deviation is greatly influential to the load on structure and the friction in hinge, whereas the clearance mitigates the adverse effects on the motion of mechanism caused by the axis deviation to some extent.

Dynamics and Control of a Flexible-Link Flexible-Joint Space Robot with Joint Friction

Multi-DOF flexible space robots play a significant role in the on-orbit service. The flexibility of the robots is mainly caused by the flexible links and some flexible drive elements in joints. The vibration generated by the component flexibility can affect the accuracy of control. In this paper, the dynamics and control issues of flexible-link flexible-joint (FLFJ) space robots considering joint friction are studied. Firstly, the Spong’s model is employed to depict flexible joints, and the Coulomb friction model is adopted to describe joint friction. Then based on the single direction recursive construction method and velocity variation principle, dynamic equations of the system are derived. Secondly, a trajectory of joint motion is given and a trajectory tracking controller with friction compensation is designed with the computed torque method. Finally, several numerical simulations are carried out to verify the accuracy of the dynamic model and illustrate the effect of joint friction and joint flexibility on the dynamic characteristics of space robots. Besides, simulation results suggest that the controller designed in this paper could effectively achieve the trajectory tracking control for the 6-DOF FLFJ space robot with joint friction.

Dynamic performance of planar mechanism with joint clearance considering stochastic parameters

Due to the influence of working temperature and pressure, collision restitution coefficient, Poisson’s ratio, friction coefficient and other material parameters could range in different intervals. However, the uncertainties and variability of material parameters is usually ignored in most researches. Along with vibration and wear, joint clearance is inevitable and widely exists in mechanical devices, which also should be taken into consideration. In this paper, the kinematic and dynamic equations are developed based on continuous Lankarani-Nikravesh contact model and the modified Coulomb friction model using a typical crank-slider mechanism as the research object. The influence of stochastic parameters (obeying normal distribution) on the dynamic characteristics of crank-slider mechanism is studied. In addition, dynamic analysis of the crank-slider mechanism with cylindrical joint clearance of different sizes is carried out in MATLAB environment. Results show that parameter random uncertainty should also be involved in dynamic models.

CFD Assisted Steady-State Modelling of Restrictive Counterbalance Valves

The counterbalance valve is an important component in many hydraulic applications and its behaviour hugely impacts system stability and performance. Despite that, CBVs are rarely modelled accurately due to the effort required to obtain basic model parameters and the complexity involved in identifying expressions for flow forces and friction. This paper presents a CFD assisted approach to steady-state modelling of CBVs. It is applied to a 3-port restrictive commercially available counterbalance valve. The model obtained is based on detailed measurements of the valve geometry, a single data set and CFD modelling and includes flow forces and friction. The CFD assisted model is compared to experimental data at three temperatures and two versions of more classical steady-state model based on the orifice equation, uniform pressure distribution and experimental results. The results support the CFD assisted approach as a way to increase modelling accuracy. The load pressure corrected coulomb friction model used manages to capture the changes to hysteresis with temperature but not the changes with pilot pressure.

Vibration analysis of a flexible gearbox system considering a local fault in the outer ring of the supported ball bearing

Ball bearings are key components in the gear transmission system. Supported ball bearings have great influences on the vibrations of the gear transmission system, especially the presence of the local faults. Although some reported works formulated the local fault in the supported bearings of the gear transmission system, the box and shaft were considered as rigid bodies. To overcome this problem, a rigid-flexible coupling dynamic model for a flexible gearbox with the supported ball bearings is developed, which cannot be described by the previous multibody models. The local fault in the supported bearing is described by a time-varying impact force model with a half-sine profile. The bearing clearance, flexible shaft, and box are considered in the rigid-flexible coupling dynamic model. The flexible shaft and box are formulated by a finite element method. The damping and contact stiffness in the bearings and gears are obtained by the previous methods in the listed works. The frictions between the mating components are formulated by the Coulomb friction model. An experimental study is applied to validate the rigid-flexible coupling dynamic model. The effects of the faults on the vibration transmission characteristics are investigated. The results provide that the local fault in the supported bearings will greatly affect the vibrations of the gearbox system. Moreover, it depicts that the vibration collection point for the defective bearings should be located at the same side to obtain better singles. This work can provide a more reasonable method for understanding the vibration transmission characteristics of the gearbox system with the local faults in the supported bearings than the reported multibody models.

Experimental measurement on friction performance of PDC bearings for oil drilling under different working conditions

Abstract As a kind of superhard material, the polycrystalline diamond compact (PDC) has been extensively used in engineering with its high strength and high wear resistance. Meanwhile, PDC has been increasingly used in bearing design to improve bearing capacity and service life. However, as a bearing material, its friction coefficient under different working conditions is not clear although it is a very important parameter. In this paper, the authors proposed a theoretical model of friction measurement and design a set of measurement rig to investigate the friction characteristics of the PDC bearing. The measurement equipment is developed based on the Coulomb friction model, with the three measurement environments taken into consideration: dry, water and drilling mud. A pair of thrust ball bearing was used in the measurement equipment to equilibrium axial load. But the friction coefficient of thrust ball bearing is proved far less than that of the PDC bearing in the experiment. The frictional coefficient of PDC bearings can be stabilized at about 0.12 under dry friction or water lubrication conditions and increase to 0.2 when tested under drilling fluid environment. Measuring the friction coefficient of PDC bearing -especially under drilling fluid environment can not only provide support for the design of the downhole tool where the bearing friction coefficient obviously affects the feasibility and agility of the tool but also help people to deepen the understanding of PDC materials.

Dynamic Responses of Planar Multilink Mechanism considering Mixed Clearances

Translational and revolute joints are the main kinds of joints in planar multilink mechanisms. Translational and revolute clearance joints have great influence on dynamical responses of planar mechanisms. Most research studies mainly focused upon revolute clearance of planar mechanisms based upon the modified Coulomb friction model, some studies investigated clearance of the pin-slot joint, and few studies researched mixed clearances (considering both translational clearance and revolute clearance) based on the LuGre friction model. Dynamic response of the 2-DOF nine-bar mechanism considering mixed clearances based on the LuGre model is investigated in this work. The dynamic model with mixed clearances is built by the Lagrange multipliers. Dynamic responses including motion output of the slider, driving torques, contact forces, shaft center trajectories at revolute clearance pairs, and slider trajectory inside the guide are analyzed, respectively. Influences of different friction models on dynamic responses are studied, such as LuGre and modified Coulomb’s friction models. Effects of different clearance values and different driving speeds on dynamic responses with mixed clearances are both analyzed. Virtual prototype model considering mixed clearances is carried out through ADAMS to verify correctness.

Dynamic characteristics of a shrouded blade with impact and friction

A simplified computational model of a twisted shrouded blade with impact and friction is established. In this model, the shrouded blade is simulated by a flexible Timoshenko beam with a tip-mass, and the effects of centrifugal stiffening, spin softening, and Coriolis force are considered. Impact force is simulated using a linear spring model, and friction force is generated by a tangential spring model under sticking state and a Coulomb friction model under sliding state. The proposed model is validated by a finite element model. Then, the effects of initial gap and normal preload, coefficient of friction, and contact stiffness ratio (the ratio of tangential contact stiffness to normal contact stiffness) on system vibration responses are analyzed. Results show that resonant peaks become inconspicuous and impact plays a dominant role when initial gaps are large between adjacent shrouds. By contrast, in small initial gaps or initial normal preloads condition, resonant speed increases sharply, and the optimal initial normal preloads that can minimize resonant amplitude becomes apparent. Coefficient of friction affects the optimal initial normal preload, but it does not affect vibration responses when the contact between shrouds is under full stick. System resonant amplitude decreases with the increase of contact stiffness ratio, but the optimal initial normal preload is unaffected.

Mitigation Effect of Perforation Drilling on the Sliding Risk during Spudcan Installation Close to Footprints

Perforation drilling is a promising technique to mitigate the sliding risk of jack-up units installed around footprints. Based on the coupled Eulerian–Lagrangian (CEL) method, a 1/2 finite element model, including a rigid Lagrangian spudcan and a Eulerian soil part, was established, and the contact interface was modelled with the Coulomb friction model. Validated against an indoor perforation test, the model was adopted to investigate the mitigation mechanism and effects of the borehole diameter, number, depth, and the drilling range. The simulations reveal that the mitigation efficiency increases with the borehole diameter, number, and depth. However, it shows little improvement if the borehole depth increases beyond double footprint depth. The semi-drilling at the outer side of the footprint is a little more effective than the full-drilling at both the inner and outer sides of the footprint. The present work emphasizes the effects of perforation drilling parameters on the mitigation efficiency, which are of great significance to guide the engineering practice and guarantee the safe operation of the jack-up reinstallation close to existing footprints.

XFEM based node scheme for the frictional contact crack problem

In this paper, based on the nodal displacement of the crack surface element, a novel node-scheme method is proposed to model the frictional contact problem in the framework of extended finite element method (XFEM). The paper systematically illustrates the novel node-scheme including the fundamentals of the proposed method, the coupled Coulomb's friction model. The novelty of the proposed method is that the node-scheme method is first introduced into the XFEM, it can consider the stress redistribution in the local part of the crack surface, and it has the advantage of solving the locking phenomenon in the numerical simulation of the frictional contact problem. The numerical results show that the proposed method is accurate and applicable to efficiently solve the frictional contact crack problem.

Seismic Response of Building Structures with Sliding Non-structural Elements

Interaction between a structure under base excitation and heavy non-structural elements that it supports is significant in the seismic analysis and design of the structure. Heavy non-structural elements may slide/rock under base excitation, and this dynamic action affects the seismic behavior of the supporting structure. Hence, in this study, a numerical model was presented to describe the seismic behavior of a primary structure (PS) supporting non-structural elements referred to as secondary bodies (SBs). The governing equations of motion for PS and SBs were developed considering Coulomb's friction model. Seismic hazard levels corresponding to Indian seismic zone III (medium hazard level) and V (highest hazard level) were considered. A parameter called displacement ratio (DR) was defined to quantify the sliding effect of SBs on the displacement response of the PS. A parametric study has been conducted to understand the variation in the DR due to varied time period of the structure, live loads to structure mass ratios and coefficients of friction between PS and SBs. From the analysis of results, it was concluded that the DR varies significantly with the time period, mass ratios, and coefficient of friction values. It can also be found from the study that the energy dissipation due to sliding of SBs was more in the highest hazard level than medium hazard level. Finally, the conditions for which the full mass of sliding secondary bodies should be considered in the seismic design of the structure are also presented.

Robust Optimization of Planar Constrained Mechanical System with Varying Joint Clearance Size Based on Sensitivity Analysis

This paper is devoted to a general methodological study on sensitivity analysis and robust optimization for a planar crank-slider mechanism in presence of joint clearances and random parameters and investigate the effects of parameter uncertainty on optimization results when joint clearance sizes are constantly changing due to wear. The first-order sensitivity analysis based on the response surface proxy model is performed. Then, a multiobjective robust optimization algorithm based on sensitivity analysis is carried out to reduce the undesirable effects of joint clearances and random parameters. In the algorithm, a multiobjective robust optimization model derived from the mean and variance of the objective function is constructed. Here, the objective function is defined based on the consideration of reducing the contact force generated at all clearance joints. Additionally, in order to balance computational accuracy and efficiency in the multiobjective robust optimization process, high-precision Kriging agent models are established. The optimum values of design variables are determined by combining Monte Carlo sampling and multiobjective particle swarm optimization method. By combining the Baumgarte approach with Lankarani–Nikravesh contact force model and Coulomb friction model, the dynamic equations of the planar multibody system with clearance joints are established. The uniform probability distribution is applied for characterizing random parameters. Simulation results show that the influence of design variable variations on the objective function changes in relation to the joint clearance size, but their relative influence degree on the objective function will not vary with the size of joint clearances. Moreover, the optimal solution selected on the Pareto front will affect the average levels and peak fluctuations of the dynamic responses in multibody systems.