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    The Greeks, including Aristotle , Vitruvius , and Pliny the Elder , were interested in the cause and mitigation of friction. The classic laws of sliding friction were discovered by Leonardo da Vinci in , a pioneer in tribology , but the laws documented in his notebooks, were not published and remained unknown.

    Amontons presented the nature of friction in terms of surface irregularities and the force required to raise the weight pressing the surfaces together.

    The understanding of friction was further developed by Charles-Augustin de Coulomb The distinction between static and dynamic friction is made in Coulomb's friction law see below , although this distinction was already drawn by Johann Andreas von Segner in John Leslie — noted a weakness in the views of Amontons and Coulomb: If friction arises from a weight being drawn up the inclined plane of successive asperities , why then isn't it balanced through descending the opposite slope?

    Leslie was equally skeptical about the role of adhesion proposed by Desaguliers, which should on the whole have the same tendency to accelerate as to retard the motion.

    Arthur Jules Morin developed the concept of sliding versus rolling friction. Osborne Reynolds derived the equation of viscous flow. This completed the classic empirical model of friction static, kinetic, and fluid commonly used today in engineering.

    Ewing investigated the continuity between static and kinetic friction. The focus of research during the 20th century has been to understand the physical mechanisms behind friction.

    Frank Philip Bowden and David Tabor showed that, at a microscopic level , the actual area of contact between surfaces is a very small fraction of the apparent area.

    The development of the atomic force microscope ca. These two discoveries explain Amonton's first law below ; the macroscopic proportionality between normal force and static frictional force between dry surfaces.

    The elementary property of sliding kinetic friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws:.

    Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are 'static friction' " stiction " between non-moving surfaces, and kinetic friction sometimes called sliding friction or dynamic friction between moving surfaces.

    Coulomb friction, named after Charles-Augustin de Coulomb , is an approximate model used to calculate the force of dry friction. It is governed by the model:.

    Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion.

    In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence.

    This maximum force is known as traction. The force of friction is always exerted in a direction that opposes movement for kinetic friction or potential movement for static friction between the two surfaces.

    For example, a curling stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement.

    Note that it is not the direction of movement of the vehicle they oppose, it is the direction of potential sliding between tire and road.

    The normal force is defined as the net force compressing two parallel surfaces together, and its direction is perpendicular to the surfaces.

    In this case, the magnitude of the friction force is the product of the mass of the object, the acceleration due to gravity, and the coefficient of friction.

    However, the coefficient of friction is not a function of mass or volume; it depends only on the material.

    For instance, a large aluminum block has the same coefficient of friction as a small aluminum block. However, the magnitude of the friction force itself depends on the normal force, and hence on the mass of the block.

    If the object is on a tilted surface such as an inclined plane, the normal force is less, because less of the force of gravity is perpendicular to the face of the plane.

    Therefore, the normal force, and ultimately the frictional force, is determined using vector analysis, usually via a free body diagram.

    Depending on the situation, the calculation of the normal force may include forces other than gravity. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction.

    Coefficients of friction range from near zero to greater than one. It is an axiom of the nature of friction between metal surfaces that it is greater between two surfaces of similar metals than between two surfaces of different metals— hence, brass will have a higher coefficient of friction when moved against brass, but less if moved against steel or aluminum.

    This is usually larger than its kinetic counterpart. The coefficient of static friction exhibited by a pair of contacting surfaces depends upon the combined effects of material deformation characteristics and surface roughness , both of which have their origins in the chemical bonding between atoms in each of the bulk materials and between the material surfaces and any adsorbed material.

    The fractality of surfaces, a parameter describing the scaling behavior of surface asperities, is known to play an important role in determining the magnitude of the static friction.

    Arthur Morin introduced the term and demonstrated the utility of the coefficient of friction. Both static and kinetic coefficients of friction depend on the pair of surfaces in contact; for a given pair of surfaces, the coefficient of static friction is usually larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon.

    Most dry materials in combination have friction coefficient values between 0. Values outside this range are rarer, but teflon , for example, can have a coefficient as low as 0.

    A value of zero would mean no friction at all, an elusive property. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2.

    For example, silicone rubber or acrylic rubber -coated surfaces have a coefficient of friction that can be substantially larger than 1.

    While it is often stated that the COF is a "material property," it is better categorized as a "system property.

    The latter speed, of course, does not determine the COF uniquely; if the pin diameter is increased so that the frictional heating is removed rapidly, the temperature drops, the pin remains solid and the COF rises to that of a 'low speed' test.

    Under certain conditions some materials have very low friction coefficients. An example is highly ordered pyrolytic graphite which can have a friction coefficient below 0.

    Static friction is friction between two or more solid objects that are not moving relative to each other.

    For example, static friction can prevent an object from sliding down a sloped surface. Static friction is considered to arise as the result of surface roughness features across multiple length-scales at solid surfaces.

    These features, known as asperities are present down to nano-scale dimensions and result in true solid to solid contact existing only at a limited number of points accounting for only a fraction of the apparent or nominal contact area.

    The static friction force must be overcome by an applied force before an object can move. The instant sliding occurs, static friction is no longer applicable—the friction between the two surfaces is then called kinetic friction.

    However, an apparent static friction can be observed even in the case when the true static friction is zero. An example of static friction is the force that prevents a car wheel from slipping as it rolls on the ground.

    Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground, so it is static rather than kinetic friction.

    The maximum value of static friction, when motion is impending, is sometimes referred to as limiting friction , [39] although this term is not used universally.

    Kinetic friction , also known as dynamic friction or sliding friction , occurs when two objects are moving relative to each other and rub together like a sled on the ground.

    New models are beginning to show how kinetic friction can be greater than static friction. The origin of kinetic friction at nanoscale can be explained by thermodynamics.

    N2 - The aim of this paper is to fit the friction compensation problem in the field of modern polytopic and Linear Matrix Inequality LMI based control design methodologies.

    AB - The aim of this paper is to fit the friction compensation problem in the field of modern polytopic and Linear Matrix Inequality LMI based control design methodologies.

    Overview Fingerprint. Abstract The aim of this paper is to fit the friction compensation problem in the field of modern polytopic and Linear Matrix Inequality LMI based control design methodologies.

    Friction is the force which opposes resists motion of the body. The peak and valleys on the surfaces of bodies may be due to a random arrangement of coarse particles, for example the surface of a grinding stones.

    The Advantages and Disadvantages of Friction in Daily Life. Realize the advantages and disadvantages of friction in daily life.

    Advantages of Friction. Thefriction force has several advantages which includes the following:. It helps in walking process.

    Disadvantages of friction. Frictional force has several dis-advantages which include the following:.

    Cause machinery to heat up and can cause wear and tear. Methods of Reducing Friction. Describe methods of reducing friction. The methods of reducing friction between surfaces include the following:.

    Polishing: Polishing the surface reduces the roughness and hence reduces friction. It is a simple cylinder on which a body to be pulled RESTS. These arerollers that are fixed to a moving body, held in place by cylinders or axles which are threaded in their centers.

    Types of Friction. Identify types of friction. There are three main types of friction in daily life which include the following:.

    Static friction: an opposing force between two solid objects at rest. Limiting Friction. Determine limiting friction. Limiting friction is the maximum frictional force existing between two bodies in contact.

    Example 1. Friction loss under conditions of laminar flow follow the Hagen—Poiseuille equation , which is an exact solution to the Navier-Stokes equations.

    In many practical engineering applications, the fluid flow is more rapid, therefore turbulent rather than laminar. Under turbulent flow, the friction loss is found to be roughly proportional to the square of the flow velocity and inversely proportional to the pipe diameter, that is, the friction loss follows the phenomenological Darcy—Weisbach equation in which the hydraulic slope S can be expressed [10].

    Furthermore, it varies as well with the flow velocity V and on the physical properties of the fluid usually cast together into the Reynolds number Re.

    Thus, the friction loss is not precisely proportional to the flow velocity squared, nor to the inverse of the pipe diameter: the friction factor takes account of the remaining dependency on these parameters.

    With these quantities as inputs, the friction factor f D can be expressed in closed form in the Colebrook—White equation or other fitting function , and the flow volume Q and flow velocity V can be calculated therefrom.

    Friction loss takes place as a gas, say air, flows through duct work. For specific choices of duct material, and assuming air at standard temperature and pressure STP , standard charts can be used to calculate the expected friction loss.

    The three values chosen for friction loss correspond to, in US units inch water column per feet, 0. Note that, in approximation, for a given value of flow volume, a step up in duct size say from mm to mm will reduce the friction loss by a factor of 3.

    Because both friction and load are measured in units of force such as pounds or newtons , the coefficient of friction is dimensionless. The value of the coefficient of friction for a case of one or more bricks sliding on a clean wooden table is about 0.

    The frictional force itself is directed oppositely to the motion of the object. Because the friction thus far described arises between surfaces in relative motion, it is called kinetic friction.

    Static friction , in contrast, acts between surfaces at rest with respect to each other. The value of static friction varies between zero and the smallest force needed to start motion.

    This smallest force required to start motion, or to overcome static friction, is always greater than the force required to continue the motion, or to overcome kinetic friction.

    Rolling friction occurs when a wheel, ball, or cylinder rolls freely over a surface, as in ball and roller bearings.

    The main source of friction in rolling appears to be dissipation of energy involved in deformation of the objects. If a hard ball is rolling on a level surface, the ball is somewhat flattened and the level surface somewhat indented in the regions in contact.

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