Static Friction Force Research Articles

New insight into the mechanism of static friction: A theoretical prediction of the effect of loading history on static friction force based on the static friction model proposed by Lorenz and Persson

This study provides a new insight into the field of static friction. Based on the static friction model developed by Lorenz and Persson, in which it is assumed that a slip distance characterizes the level of frictional shear stress acting on the contact interface, we pointed out that tangential loading history is an important factor for determining the value of static friction. The stop-restart motion increased the level of static friction force, while the stop-inversion motion reduced the static friction.

Experimental Investigation of the Correlation Between Adhesion and Friction Forces

In this study, the effect of adhesion on evolution of friction during the transition of the contact from pre-sliding into full sliding was investigated. In order to achieve the objectives, a micro optical friction (MOF) apparatus was developed to conduct dry sliding friction experiments and to allow for in situ visualization of the contact area for a sphere-on-flat configuration. MOF apparatus was used to measure friction under various load and speed combinations. The friction results exhibit the commonly observed behavior in friction (i.e., static friction is larger than dynamic friction). The results also demonstrated that the difference between static and dynamic friction forces increased with an increase in the applied normal load. We hypothesize and demonstrate that the difference between the measured maximum friction force commonly referred to as static friction force and the steady state or dynamic friction force divided by the dynamic coefficient of friction is the force of adhesion. The adhesion force results obtained from our experimental investigation corroborate well with the force of adhesion described by the DMT model. The reduction in friction force is attributed to the diminishing of adhesion force during full sliding of the contact.

Effects of Stress Distribution at the Contact Interface on Static Friction Force: Numerical Simulation and Model Experiment

This study develops a simplified model that can simulate the dynamics of a split contact interface at the transition from static to kinetic friction. The model has a contact interface formed by multiple contacting points connected to a rigid base via a spring. From a numerical analysis of this model, the effect of the stress distribution at the contact interface on the level of static friction force was investigated. Consequently, it was found that the existence of the stop-restart motion can act to increase the macroscopic (apparent) static friction force. Thus, the numerical analysis demonstrated that the macroscopic static friction coefficient could be changed without varying the local static friction coefficient. The type of tangential loading history, i.e., the existence of stop-restart motion, is an important factor for characterizing the level of the static friction force. In other words, this implies that we can adjust the level of the macroscopic static friction coefficient without changes to the local static friction. Furthermore, the above numerical prediction was confirmed by a model experiment focusing on the sliding contact interface of an object built from separated rubber blocks.

Effects of nanostructured, diamondlike, carbon coating and nitrocarburizing on the frictional properties and biocompatibility of orthodontic stainless steel wires.

To evaluate and compare the effects of nanostructured, diamondlike, carbon (DLC) coating and nitrocarburizing on the frictional properties and biocompatibility of orthodontic stainless steel archwires. Plasma-enhanced chemical vapor deposition technology was applied to coat DLC films onto the surface of austenitic stainless steel wires, and salt-bath nitrocarburizing technology was employed to achieve surface hardening of other wires. Surface and cross-sectional characteristics, microhardness, modulus of elasticity, friction resistance, corrosion resistance, and cell toxicity of the modified and control wires were analyzed. The surfaces of the DLC-coated and nitrocarburized wires were both smooth and even. Compared with the control, the DLC-coated wires were increased in surface hardness 1.46 times, decreased in elastic modulus, reduced in kinetic friction coefficient by 40.71%, and decreased in corrosion current density by two orders of magnitude. The nitrocarburized wire was increased in surface hardness 2.39 times, exhibited an unchanged elastic modulus, demonstrated a decrease in maximum static friction force of 22.2%, and rose in corrosion current density two orders of magnitude. Cytotoxicity tests revealed no significant toxicity associated with the modified wires. DLC coating and nitrocarburizing significantly improved the surface hardness of the wires, reduced friction, and exhibited good biocompatibility. The nanostructured DLC coating provided excellent corrosion resistance and good elasticity, and while the nitrocarburizing technique substantially improved frictional properties, it reduced the corrosion resistance of the stainless steel wires to a lesser extent.

Experimental analysis of tribological behaviour of advanced composite spools used in commercial pneumatic spool valves

In this paper, we present the study of the tribological conditions inside a pneumatic valve. The main goal is to analyse the friction behaviour of new pneumatic valve spools made of advanced composite materials in detail by using the experimental approach. The spools are intended to be used without any lubricant in the valve, therefore experimental tests are carried out in dry working conditions. On the basis of the measured force curves the static and dynamic friction forces are determined as well as the friction forces depended on the spool velocity. Finally, the spool with the best friction characteristics, the minimal friction forces, is defined. Also, the machinability of the composite spools is considered.

Effect of passive self-ligating bracket placement on the posterior teeth on reduction of frictional force in sliding mechanics.

ObjectiveThe purpose of this study was to investigate the static (SFF) and kinetic frictional forces (KFF) in sliding mechanics of hybrid bracket systems that involve placing a conventional bracket (CB) or active self-ligating bracket (ASLB) on the maxillary anterior teeth (MXAT) and a passive SLB (PSLB) on the maxillary posterior teeth (MXPT).MethodsThe samples consisted of two thoroughbred types (group 1, anterior-CB + posterior-CB; group 2, anterior-ASLB + posterior-ASLB) and four hybrid types (group 3, anterior-CB + posterior-PSLB-type 1; group 4, anterior-CB + posterior-PSLB-type 2; group 5, anterior-ASLB + posterior-PSLB-type 1; group 6, anterior-ASLB + posterior-PSLB-type 2) (n = 13 per group). After maxillary dentition alignment and maxillary first premolars removal in the stereolithographically-made typodont system, a 0.019 × 0.025-inch stainless steel wire was drawn through the right quadrant of the maxillary arch at 0.5 mm/min for 5 min. The SFF and KFF were measured with a mechanical testing machine and statistical analyses were performed.ResultsFour different categories of SFF and KFF were observed among all groups (all p < 0.001). Group 1 demonstrated the highest SFF and KFF; groups 4 and 3 were second and third highest, respectively. The fourth category included groups 2, 5, and 6. Placing PSLBs on the MXPT resulted in significant SFF and KFF reductions in cases with CBs on the MXAT, but not in cases with ASLBs on the MXAT.ConclusionsThese data might aid in the development of a hybrid bracket system that enables low-friction sliding of an archwire through the MXPT.

Frictional property comparisons of conventional and self-ligating lingual brackets according to tooth displacement during initial leveling and alignment: an in vitro mechanical study.

ObjectiveWe evaluated the effects of tooth displacement on frictional force when conventional ligating lingual brackets (CL-LBs), CL-LBs with a narrow bracket width, and self-ligating lingual brackets (SL-LBs) were used with initial leveling and alignment wires.MethodsCL-LBs (7th Generation), CL-LBs with a narrow bracket width (STb), and SL-LBs (In-Ovation L) were tested under three tooth displacement conditions: no displacement (control); a 2-mm palatal displacement (PD) of the maxillary right lateral incisor (MXLI); and a 2-mm gingival displacement (GD) of the maxillary right canine (MXC) (nine groups, n = 7 per group). A stereolithographic typodont system and artificial saliva were used. Static and kinetic frictional forces (SFF and KFF, respectively) were measured while drawing a 0.013-inch copper-nickel-titanium archwire through brackets at 0.5 mm/min for 5 minutes at 36.5℃.ResultsThe In-Ovation L exhibited lower SFF under control conditions and lower KFF under all displacement conditions than the 7th Generation and STb (all p < 0.001). No significant difference in SFF existed between the In-Ovation L and STb for a 2-mm GD of the MXC and 2-mm PD of the MXLI. A 2-mm GD of the MXC produced higher SFF and KFF than a 2-mm PD of the MXLI in all brackets (all p < 0.001).ConclusionsCL-LBs with narrow bracket widths exhibited higher KFF than SL-LBs under tooth displacement conditions. CL-LBs and ligation methods should be developed to produce SFF and KFF as low as those in SL-LBs during the initial and leveling stage.

Friction between Archwire of Different Sizes, Cross Section, Alloy and Brackets Ligated with Different Brands of Low Friction Elastic Ligatures- An Invitro Study.

Friction in orthodontic treatment does exist and is thought to reduce the efficiency of orthodontic appliances during sliding mechanics. During sliding mechanics, a friction force is produced at the bracket archwire-ligature unit which tends to counteract the applied force and in turn resists the desired movement. The aim of this invitro study was to determine the friction between archwire of different sizes, cross section, alloy and brackets ligated with different brands of low friction elastic ligatures. An 0.022-in slot, 10 stainless steel brackets and various orthodontic archwires which were ligated with low-friction ligatures and subjected to evaluate frictional resistance i.e. static friction and dynamic friction. The archwires of 0.014″ and 0.016″ nickel titanium (NiTi), 0.016 × 0.022″ stainless steel (SS), 0.017 × 0.025″ NiTi, 0.017 × 0.025″ SS, 0.017 × 0.025″ titanium molybdenum alloy (TMA), 0.019 × 0.025″ SS were used. Each bracket/archwire combination was evaluated 10 times at room temperature of 27 ± 2°C. The study groups included Group I of conventional round shape module with reduced friction coating i.e. super slick and synergy and Group II contained figure of "8" shape module i.e. Octavia ties and Slide ligature. The mean static friction force and dynamic friction force for all 7 types of wires was lower in Group II (C, D) combined compared to Group I (A, B) and the difference was statistically very highly significant (p<0.001). Super slick and synergy can be used in the initial and final phase of treatment when full engagement of archwire in the bracket slot is necessary for proper tip and torque expression. Slide and Octavia ties modules can be used in the premolar brackets during en mass retraction when using friction mechanics.

Non-prehensile manipulation planning of a three-rigid-link object using two cooperative robot arms

This work presents the dynamic modelling, the static analysis, and a proposed control algorithm for non-prehensile manipulation of a three rigid link object manipulated by two cooperative robot arms in a plane. The system is configured so that one arm is in contact with two links, while the other arm is in contact with the third link. The purpose of the static analysis is to obtain the interaction forces as well as their locations required to hold the object for a specified configuration. The dynamic model of the system is introduced, and the static analysis, considering both the frictionless and frictional contact cases, is deduced. The effect of changing the direction of the static frictional forces at the multi contact points on the static problem is introduced. A PD controller with feed forward acceleration is proposed to perform the manipulation task. Simulation results show the validity of the proposed control scheme.

Comparison of Theoretical and Measured Forces on Magnetically Propelled Microrobots in a Vascular Phantom

Microrobots can travel in blood flow to targets that are currently difficult to reach. Stationary control is a prerequisite and requires the prediction of major influencing forces. During experiments, a magnetic cylindrical microrobot was moved in a tube filled with water or a glucose mixture (blood analog), controlled by an external electromagnetic field. The experimental results showed that the magnetic field gradient needed to be increased at the highest rate for smaller microrobots in the glucose mixture. At low fluid flow velocities, a magnetic gradient field of approximately 130–200 mT/m was required to overcome the static friction force, which was significantly higher than the drag force.

The Effects of In-Office Reconditioning on the Slot Dimensions and Static Frictional Resistance of Stainless Steel Brackets.

Orthodontists are commonly faced with the decision of what to do with loose brackets, and with inaccurately located brackets that need repositioning during treatment. One solution is to recycle the brackets. The potential effects of reconditioning a bracket are dependent upon many factors which may result in physical changes like alteration in slot tolerance, which may influence sliding mechanics by affecting frictional resistance. To study and compare the dimensional changes in the bracket slot width and depth in reconditioned brackets from unused brackets under scanning electronic microscope and to study and compare any consequent effects on the static frictional resistance of stainless steel brackets after reconditioning and in unused brackets. Dentarum manufactured 90 stainless steel central incisors edgewise brackets of size 0.22 X 0.030″ inch and 0° tip and 0°angulation were taken. 60 samples for measuring frictional resistance and 30 samples for measuring slot dimensions. Ortho organizers manufactured stainless steel arch wires 0.019 X 0.025″ straight lengths 60 in number were considered for measuring static frictional resistance. The mean slot width and depth of new brackets were 0.0251″ and 0.0471″, which exceeded the manufacturers reported nominal size of 0.022″ X 0.030″, by 0.003″ and 0.017″. The reconditioned brackets demonstrated a further increase in mean slot width and depth to 0.028″ and 0.0518″ that is by 0.0035″ and 0.0047″ which is statistically significant (p=0.001, 0.002). The mean static frictional forces of the reconditioned brackets was nearly similar to that of new brackets that is 0.3167N for reconditioned brackets and 0.2613 N for new brackets. Although the reconditioning process results in physical changes to bracket structure this does not appear to result in significant effect on ex-vivo static frictional resistance.

Superlubric-pinned transition in sliding incommensurate colloidal monolayers

Two-dimensional (2D) crystalline colloidal monolayers sliding over a laser-induced optical lattice providing the periodic ``corrugation'' potential recently emerged as a new tool for the study of friction between ideal crystal surfaces. Here, we focus in particular on static friction, the minimal sliding force necessary to depin one lattice from the other. If the colloid and the optical lattices are mutually commensurate, the colloid sliding is always pinned by static friction; however, when they are incommensurate, the presence or absence of pinning can be expected to depend upon the system parameters, like in one-dimensional (1D) systems. If a 2D analogy to the mathematically established Aubry transition of one-dimensional systems were to hold, an increasing periodic corrugation strength ${U}_{0}$ should turn an initially free-sliding, superlubric colloid into a pinned state, where the static friction force goes from zero to finite through a well-defined dynamical phase transition. We address this problem by the simulated sliding of a realistic model 2D colloidal lattice, confirming the existence of a clear and sharp superlubric-pinned transition for increasing corrugation strength. Unlike the 1D Aubry transition, which is continuous, the 2D transition exhibits a definite first-order character, with a jump of static friction. With no change of symmetry, the transition entails a structural character, with a sudden increase of the colloid-colloid interaction energy, accompanied by a compensating downward jump of the colloid-corrugation energy. The transition value for the corrugation amplitude ${U}_{0}$ depends upon the misalignment angle $\ensuremath{\theta}$ between the optical and the colloidal lattices, superlubricity surviving until larger corrugations for angles away from the energetically favored orientation, which is itself generally slightly misaligned, as shown in recent work. The observability of the superlubric-pinned colloid transition is proposed and discussed.

Dependence of static friction force on stiffness and lubricant structure in a confined chain

We use a chain of harmonically interacting atoms confined between two sinusoidal substrate potentials in which the top substrate is driven by the driving force. This system is closely related to physical situations with confined lubricant films. The dependence of the static friction force on the system parameters such as the equilibrium spacing and the strength is presented. It is found that the better lubricant films are materials with larger interatomic interaction strength, and the lubricant structure is in the certain region.

Numerical modeling of particle embedment during solid particle erosion of ductile materials

Particle embedment may occur in erosion testing, abrasive jet machining, blast cleaning and other industrial processes in which high speed impact of particles on relatively ductile targets occurs. It may strongly affect erosion rates, and lead to undesirable changes in surface roughness. Three-dimensional smoothed particle hydrodynamics (SPH) simulations were used to simulate particle embedment when 219.2µm and 362.9µm angular silicon carbide particles impacted a strain and strain rate hardening 6061-T6 aluminum alloy target under various process conditions. The models were assessed by comparison with measured embedment. Analysis of the results showed the following: (i) once the value of the effective friction coefficient between the substrate and the abrasive was determined by comparing predicted and measured embedment at one set of process conditions (particle velocity, size, angle of attack), the same friction coefficient could be used in models of all other combinations of process conditions to correctly predict embedment. (ii) Consistent with a previous simplified rigid-plastic analysis of idealized rhomboid particles impacting a polymer target, the static frictional force occurring after the maximum depth has been reached, the particle orientation and the impact angle all strongly affected embedment. Unlike the previous simplified model, the present model considered local strain rate and strain hardening, making it applicable for ductile metal targets. (iii) Consistent with some, but not all, reports in the literature, embedment at a given velocity increased with particle size. (iv) For a given particle size, embedment increased with incident velocity. (v) A critical minimum velocity below which embedment would not occur was predicted. The trends were discussed in terms of embedment mechanisms and particle impact kinematics. Overall, the work demonstrates that SPH methods can be used to provide insight into complex solid particle erosion phenomena.

Motion Driven by Strain Gradient Fields.

A new driving mechanism for direction-controlled motion of nano-scale objects is proposed, based on a model of stretching a graphene strip linked to a rigid base with linear springs of identical stiffness. We find that the potential energy difference induced by the strain gradient field in the graphene strip substrate can generate sufficient force to overcome the static and kinetic friction forces between the nano-flake and the strip substrate, resulting in the nanoscale flake motion in the direction of gradient reduction. The dynamics of the nano-flake can be manipulated by tuning the stiffness of linear springs, stretching velocity and the flake size. This fundamental law of directional motion induced by strain gradient could be very useful for promising designs of nanoscale manipulation, transportation and smart surfaces.

Ultracompact Planar Positioner Driven by Unbalanced Frictional Forces

This paper proposes a new ultracompact planar positioner driven by unbalanced frictional forces. The prototype of the designed positioner is 17 mm × 17 mm × 9 mm in size, and is simply constructed using lead zirconate titanate piezoelectric elements, neodymium magnetic feet, and junction pieces. Alternating static and kinetic frictional forces are utilized to control the motion of the positioner. The working principle is illustrated, and the performance of the positioner is evaluated under atmospheric and vacuum conditions. Under atmospheric conditions, the positioner had a minimum step size of approximately 17 nm at 55 V, a maximum step size of approximately 1.6 μm, and a moving speed of approximately 4 μm/s at 138 V. However, the step size significantly decreased in vacuum. The step size can be controlled by adjusting the frictional forces on the magnetic feet. In addition, the positioner showed instability caused by the wear of the stainless plate. This problem was resolved by using a borosilicate glass that was fixed on the stainless plate, and the position accuracy was obviously improved.

Kinetic and static friction between alumina nanowires and a Si substrate characterized using a bending manipulation method

Abstract

Effect of Surface Grooves on the Static Friction of an Elastic Slider

Numerous studies have proved the usefulness of surface patterning for the modification of tribological performances of sliding contacts. Here we investigate the effects of patterning on the tribological properties of a slider over a solid substrate. We show that, depending on the numerical density of surface grooves, the tribological properties can change significantly. A low density of surface patterning leads to a decrease of static friction force, while a higher density weakens this effect. The decrease is related to a non-uniform distribution of surface stress induced by patterning. We believe these findings and approach to be relevant for technological applications and related optimal design.

A simple criterion for determining the static friction force between nanowires and flat substrates using the most-bent-state method

A simple criterion was developed to assess the appropriateness of the currently available models that estimate the static friction force between nanowires and substrates using the ‘most-bent-state’ method. Our experimental testing of the static friction force between Al2O3 nanowires and Si substrate verified our theoretical analysis, as well as the establishment of the criterion. It was found that the models are valid only for the bent nanowires with the ratio of wire length over the minimum curvature radius no greater than 1. For the cases with greater than 1, the static friction force was overestimated as it neglected the effect of its tangential component.

Steady and transient sliding under rate-and-state friction

The physics of dry friction is often modelled by assuming that static and kinetic frictional forces can be represented by a pair of coefficients usually referred to as μs and μk, respectively. In this paper we re-examine this discontinuous dichotomy and relate it quantitatively to the more general, and smooth, framework of rate-and-state friction. This is important because it enables us to link the ideas behind the widely used static and dynamic coefficients to the more complex concepts that lie behind the rate-and-state framework. Further, we introduce a generic framework for rate-and-state friction that unifies different approaches found in the literature.We consider specific dynamical models for the motion of a rigid block sliding on an inclined surface. In the Coulomb model with constant dynamic friction coefficient, sliding at constant velocity is not possible. In the rate-and-state formalism steady sliding states exist, and analysing their existence and stability enables us to show that the static friction coefficient μs should be interpreted as the local maximum at very small slip rates of the steady state rate-and-state friction law.Next, we revisit the often-cited experiments of Rabinowicz(J. Appl. Phys., 22:1373–1379, 1951). Rabinowiczfurther developed the idea of static and kinetic friction by proposing that the friction coefficient maintains its higher and static value μs over a persistence length before dropping to the value μk. We show that there is a natural identification of the persistence length with the distance that the block slips as measured along the stable manifold of the saddle point equilibrium in the phase space of the rate-and-state dynamics. This enables us explicitly to define μs in terms of the rate-and-state variables and hence link Rabinowicz's ideas to rate-and-state friction laws.This stable manifold naturally separates two basins of attraction in the phase space: initial conditions in the first one lead to the block eventually stopping, while in the second basin of attraction the sliding motion continues indefinitely. We show that a second definition of μs is possible, compatible with the first one, as the weighted average of the rate-and-state friction coefficient over the time the block is in motion.