equilibrium, chemical

Condition in the course of a reversible chemical reaction in which no net change in the amounts of reactants and products occurs: Products are reverting to reactants at the same rate as reactants are forming products. For practical purposes, the reaction under those conditions is completed. Expressed in terms of the law of mass action, the reaction rate to form products is equal to the reaction rate to re-form reactants. The ratio of the reaction rate constants (i.e., of the amounts of reactants and products, each raised to the proper power), defines the equilibrium constant. Changing the conditions of temperature or pressure changes the reaction's equilibrium; a high temperature or pressure may be used to “push” a reaction that at ordinary conditions makes little product. See also H.-L. Le Châtelier.

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Condition in which the net force acting on a particle is zero. A body in equilibrium experiences no acceleration and, unless disturbed by an outside force, will remain in equilibrium indefinitely. A stable equilibrium is one in which small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body to equilibrium. An unstable equilibrium is one in which the least departures produce forces tending to increase the displacement. A brick lying on the floor is in stable equilibrium, while a ball bearing balanced on a knife-edge is in unstable equilibrium.

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Branch of engineering concerned with the design, manufacture, installation, and operation of engines, machines, and manufacturing processes. Mechanical engineering involves application of the principles of dynamics, control, thermodynamics and heat transfer, fluid mechanics, strength of materials, materials science, electronics, and mathematics. It is concerned with machine tools, motor vehicles, textile machinery, packaging machines, printing machinery, metalworking machines, welding, air conditioning, refrigerators, agricultural machinery, and many other machines and processes essential to an industrial economy.

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Sum of a system's kinetic energy (KE) and potential energy (PE). Mechanical energy is constant in a system that experiences no dissipative forces such as friction or air resistance. For example, a swinging pendulum that experiences only gravitation has greatest KE and least PE at the lowest point on the path of its swing, where its speed is greatest and its height least. It has least KE and greatest PE at the extremities of its swing, where its speed is zero and its height is greatest. As it moves, energy is continuously passing back and forth between the two forms. Neglecting friction and air resistance, the pendulum's mechanical energy is constant.

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or mechanical efficiency

In mechanics, the measure of the effectiveness with which a system performs. It is stated as the ratio of a system's work output to its work input. The efficiency of a real system is always less than 1 because of friction between moving parts. A machine with an efficiency of 0.8 returns 80percnt of the work input as work output; the remaining 20percnt is used to overcome friction. In a theoretically frictionless, or ideal, machine, the work input and work output are equal, and the efficiency would be 1, or 100percnt.

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Force-amplifying effectiveness of a simple machine (lever, wedge, wheel and axle, pulley, or screw). The theoretical mechanical advantage of a system is the ratio of the force that performs the useful work to the force applied, assuming there is no friction in the system. In practice, the actual mechanical advantage will be less than the theoretical value by an amount determined by the amount of friction.

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A bearing is a device to permit constrained relative motion between two parts, typically rotation or linear movement. Bearings may be classified broadly according to the motions they allow and according to their principle of operation as well as by the directions of applied loads they can handle.

Bearing friction

Low friction bearings are often important for efficiency, to reduce wear and to facilitate high speeds. Essentially, a bearing can reduce friction by virtue of its shape, by its material, or by introducing and containing a fluid between surfaces.

  • By shape, gains advantage usually by using spheres or rollers.
  • By material, exploits the nature of the bearing material used. (An example would be using plastics that have low surface friction.)
  • By fluid, exploits the low viscosity of a layer of fluid, such as a lubricant or as a pressurized medium to keep the two solid parts from touching.
  • By fields, exploits electromagnetic fields, such as magnetic fields, to keep solid parts from touching.

Combinations of these can even be employed within the same bearing. An example of this is where the cage is made of plastic, and it separates the rollers/balls, which reduce friction by their shape and finish.

Principles of operation

There are at least six common principles of operation:


Common motions permitted by bearings are:

  • Axial rotation e.g. shaft rotation
  • Linear motion e.g. drawer
  • spherical rotation e.g. ball and socket joint
  • hinge motion e.g. door


Bearings vary greatly over the size and directions of forces that they can support.

Forces can be predominately radial, axial (thrust bearings) or moments perpendicular to the main axis.


Bearings vary typically involving some degree of relative movement between surfaces, and different types have limits as to the maximum relative surface speeds they can handle, and this can be specified as a speed in ft/s or m/s.

For rotational bearings generally performance is defined in terms of the product 'DN' where D is the diameter (often in mm) of the bearing and N is the rotation rate in revolutions per minute.

Generally in terms of relative speed of the moving parts there is considerable overlap between capabilities, but plain bearings can generally handle the lowest speeds while rolling element bearings are faster, followed by fluid bearings and finally magnetic bearings which have no known upper speed limit.


Fluid and magnetic bearings can potentially give indefinite life.

Rolling element bearing life is statistical, but is determined by load, temperature, maintenance, vibration, lubrication and other factors.

For plain bearings some materials give much longer life than others. Some of the John Harrison clocks still operate after hundreds of years because of the lignum vitae wood employed in their construction, whereas his metal clocks are seldom run due to potential wear.


Many bearings require periodic maintenance to prevent premature failure, although some such as fluid or magnetic bearings may require little maintenance.

Most bearings in high cycle operations need periodic lubrication and cleaning, and may require adjustment to minimise the effects of wear.

History and development

An early type of linear bearing was an arrangement of tree trunks laid down under sleds. This technology may date as far back as the construction of the Pyramids of Giza, though there is no definitive evidence. Modern linear bearings use a similar principle, sometimes with balls in place of rollers.

The first plain and rolling-element bearings were wood, but ceramic, sapphire or glass can be used, and steel, bronze, other metals, and plastic (e.g., nylon, polyoxymethylene, teflon, and UHMWPE) are all common today. Indeed, stone was even used in various forms. Think of the "jeweled pocket watch", which incorporated stones to reduce frictional loads, and allow a smoother running watch. Of course, with older, mechanical timepieces, the smoother the operating properties, then the higher the accuracy and value. Wooden bearings can still be seen today in old water mills where the water has implications for cooling and lubrication.

Rotary bearings are required for many applications, from heavy-duty use in vehicle axles and machine shafts, to precision clock parts. The simplest rotary bearing is the sleeve bearing, which is just a cylinder inserted between the wheel and its axle. This was followed by the roller bearing, in which the sleeve was replaced by a number of cylindrical rollers. Each roller behaves as an individual wheel. The first practical caged-roller bearing was invented in the mid-1740s by horologist John Harrison for his H3 marine timekeeper. This used the bearing for a very limited oscillating motion but Harrison also used a similar bearing in a truly rotary application in a contemporaneous regulator clock.

An early example of a wooden ball bearing (see rolling-element bearing), supporting a rotating table, was retrieved from the remains of the Roman Nemi ships in Lake Nemi, Italy. The wrecks were dated to 40 AD. Leonardo da Vinci is said to have described a type of ball bearing around the year 1500. One of the issues with ball bearings is that they can rub against each other, causing additional friction, but this can be prevented by enclosing the balls in a cage. The captured, or caged, ball bearing was originally described by Galileo in the 1600s. The mounting of bearings into a set was not accomplished for many years after that. The first patent for a ball race was by Philip Vaughan of Carmarthen in 1794.

Friedrich Fischer's idea from the year 1883 for milling and grinding balls of equal size and exact roundness by means of a suitable production machine formed the foundation for creation of an independent bearing industry.

A patent, reportedly the first, was awarded to Jules Suriray, a Parisian bicycle mechanic, on 3rd August 1869. The bearings were then fitted to the winning bicycle ridden by James Moore in the world's first bicycle road race, Paris-Rouen, in November 1869.

The modern, self-aligning design of ball bearing is attributed to Sven Wingquist of the SKF ball-bearing manufacturer in 1907.

Henry Timken, a 19th century visionary and innovator in carriage manufacturing, patented the tapered roller bearing, in 1898. The following year, he formed a company to produce his innovation. Through a century, the company grew to make bearings of all types, specialty steel and an array of related products and services.

The Timken Company (Sale $4,973.4M, 2006), The SKF company($6,195.1M, 2005), the Schaeffler Group (Private), the NSK company($5,344.5M, 2006), and the NTN Bearing company($3,697.8M, 2006) are now the largest bearing manufacturers in the world.


There are many number of different types of bearings.

Type Description Stiffness Speed Life Notes
Plain bearing Rubbing surfaces, with lubricant Good, provided wear is low, but some slack is normally present Low to moderate (often requires cooling) Moderate (depends on lubrication) The simplest type of bearing, widely used, relatively high friction
Rolling element bearing Ball or rollers are used to prevent or minimise rubbing Good, but some slack is usually present Moderate to high (often requires cooling) Moderate (depends on lubrication, often requires maintenance) Used for higher loads than plain bearings with lower friction
Jewel bearing Off-center bearing rolls in seating Low due to flexing Low Adequate (requires maintenance) Mainly used in low-load, high precision work such as clocks
Fluid bearing Fluid is forced between two faces and held in by edge seal Very high Very high (speed usually limited by seals) Virtually infinite in some applications, may wear at startup/shutdown in some cases Can fail quickly due to grit or dust or other contaminants. Maintenance free in continuous use.
Magnetic bearings Faces of bearing are kept separate by magnets (electromagnets or eddy currents) Low Infinite Indefinite Often needs considerable power. Maintenance free.
Flexure bearing Material flexes to give and constrain movement Low Very high Very high or low depending on materials and strain in application Limited range of movement, no backlash, extremely smooth motion
Stiffness is the amount that the gap varies when the load on the bearing changes, it is distinct from the friction of the bearing.

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