Tribology is the science and engineering of understanding friction, lubrication and wear phenomena for interacting surfaces in relative motion. It is highly interdisciplinary, drawing on many academic fields, including physics, chemistry, materials science, mathematics, biology and engineering. The fundamental objects of study in tribology are tribosystems, which are physical systems of contacting surfaces. Subfields of tribology include biotribology, nanotribology and space tribology. It is also related to other areas such as the coupling of corrosion and tribology in tribocorrosion and the contact mechanics of how surfaces in contact deform. Approximately 20% of the world's energy (2012) is consumed by friction and wear in the transportation, manufacturing, power generation, and residential sectors.
Etymology The word tribology derives from the Greek root τριβ- of the verb τρίβω, tribo, "I rub" in classic Greek, and the suffix -logy from -λογία, -logia "study of", "knowledge of". Peter Jost coined the word in 1966, in the eponymous report which highlighted the cost of friction, wear and corrosion to the UK economy.
History
Early history Despite the relatively recent naming of the field of tribology, quantitative studies of friction can be traced as far back as 1493, when Leonardo da Vinci first noted the two fundamental 'laws' of friction. According to Leonardo, frictional resistance was the same for two different objects of the same weight but making contact over different widths and lengths. He also observed that the force needed to overcome friction doubles as weight doubles. However, Leonardo's findings remained unpublished in his notebooks. The two fundamental 'laws' of friction were first published (in 1699) by Guillaume Amontons, with whose name they are now usually associated. They state that:
the force of friction acting between two sliding surfaces is proportional to the load pressing the surfaces together the force of friction is independent of the apparent area of contact between the two surfaces. Although not universally applicable, these simple statements hold for a surprisingly wide range of systems. These laws were further developed by Charles-Augustin de Coulomb (in 1785), who noticed that static friction force may depend on the contact time and sliding (kinetic) friction may depend on sliding velocity, normal force and contact area. In 1798, Charles Hatchett and Henry Cavendish carried out the first reliable test on frictional wear. In a study commissioned by the Privy Council of the UK, they used a simple reciprocating machine to evaluate the wear rate of gold coins. They found that coins with grit between them wore at a faster rate compared to self-mated coins. In 1860, Theodor Reye proposed Reye's hypothesis. In 1953, John Frederick Archard developed the Archard equation which describes sliding wear and is based on the theory of asperity contact. Other pioneers of tribology research are Australian physicist Frank Philip Bowden and British physicist David Tabor, both of the Cavendish Laboratory at Cambridge University. Together they wrote the seminal textbook The Friction and Lubrication of Solids (Part I originally published in 1950 and Part II in 1964). Michael J. Neale was another leader in the field during the mid-to-late 1900s. He specialized in solving problems in machine design by applying his knowledge of tribology. Neale was respected as an educator with a gift for integrating theoretical work with his own practical experience to produce easy-to-understand design guides. The Tribology Handbook, which he first edited in 1973 and updated in 1995, is still used around the world and forms the basis of numerous training courses for engineering designers. Duncan Dowson surveyed the history of tribology in his 1997 book History of Tribology (2nd edition). This covers developments from prehistory, through early civilizations (Mesopotamia, ancient Egypt) and highlights the key developments up to the end of the twentieth century.
Jost report The term tribology became widely used following The Jost Report published in 1966. The report highlighted the huge cost of friction, wear and corrosion to the UK economy (1.1–1.4% of GDP). As a result, the UK government established several national centres to address tribological problems. Since then the term has diffused into the international community, with many specialists now identifying as "tribologists".
Significance Despite considerable research since the Jost Report, the global impact of friction and wear on energy consumption, economic expenditure, and carbon dioxide emissions are still considerable. In 2017, Kenneth Holmberg and Ali Erdemir attempted to quantify their impact worldwide. They considered the four main energy consuming sectors: transport, manufacturing, power generation, and residential. The following were concluded:
In total, ~23% of the world's energy consumption originates from tribological contacts. Of that, 20% is to overcome friction and 3% to remanufacture worn parts and spare equipment due to wear and wear-related. By friction reduction and wear protection, energy losses in machinery could lower total energy consumption. The largest short term energy savings are envisioned in transport (25%) and in power generation (20%) while the potential savings in the manufacturing and residential sectors are estimated to be ~10%. In the longer term, savings would be 55%, 40%, 25%, and 20%, respectively. Implementing advanced tribological technologies can also reduce global carbon dioxide emissions by as much as 1460 million tons of carbon dioxide equivalent (MtCO2) and result in 450000 million euros cost savings in the short term. In the long term, the reduction could be as large as 3140 MtCO2 and the cost savings 970000 million euros. Classical tribology covering such applications as ball bearings, gear drives, clutches, brakes, etc. was developed in the context of mechanical engineering. It also embrace micro- and nanotechnology as well as aspects of biology and medicine.
Fundamental concepts
Tribosystem
The concept of tribosystems is used to provide a detailed assessment of relevant inputs, outputs and losses to tribological systems. Knowledge of these parameters allows tribologists to devise test procedures for tribological systems.
Tribofilm
Tribofilms are thin films that form on tribologically stressed surfaces. They play an important role in reducing friction and wear in tribological systems.
Stribeck curve
The Stribeck curve shows how friction in fluid-lubricated contacts is a non-linear function of lubricant viscosity, entrainment velocity and contact load.
Physics
Friction
The word friction comes from the Latin "frictionem", which means rubbing. This term is used to describe all those dissipative phenomena, capable of producing heat and of opposing the relative motion between two surfaces. There are two main types of friction:
Static friction Occurs between surfaces in a fixed state, or relatively stationary. Dynamic friction Occurs between surfaces in relative motion. The study of friction phenomena is a predominantly empirical study and does not allow to reach precise results, but only to useful approximate conclusions. This inability to obtain a definite result is due to the extreme complexity of the phenomenon. If it is studied more closely it presents new elements, which, in turn, make the global description even more complex.
Laws of friction All the theories and studies on friction can be simplified into three main laws, which are valid in most cases:
First law of Amontons The frictional force is directly proportional to the normal load. Second law of Amontons Friction is independent of the apparent area of contact. Third law of Coulomb Dynamic friction is independent of the relative sliding speed. Coulomb later found deviations from Amontons' laws in some cases. In systems with significant nonuniform stress fields, Amontons' laws are not satisfied macroscopically because local slip occurs before the entire system slides.
Static friction Consider a block of a certain mass m {\displaystyle m} , placed in a quiet position on a horizontal plane. To move the block, an external force F → out {\displaystyle {\vec {F}}_{\text{out}}} must be applied, in this way we observe a certain resistance to the motion given by a force equal to and opposite to the applied force, which is precisely the static frictional force F → sf {\displaystyle {\vec {F}}_{\text{sf}}} . By continuously increasing the applied force, we obtain a value such that the block starts instantly to move. At this point, also taking into account the first two friction laws stated above, it is possible to define the static friction force as a force equal in modulus to the minimum force required to cause the motion of the block, and the coefficient of static friction μ {\displaystyle \mu } as the ratio of the static friction force F → sf {\displaystyle {\vec {F}}_{\text{sf}}} . and the normal force at block N → {\displaystyle {\vec {N}}} , obtaining | F → sf | ≤ μ | N → | . {\displaystyle {\left|{\vec {F}}_{\text{sf}}\right|}\leq \mu {\left|{\vec {N}}\right|}.}
Dynamic friction Once the block has been put into motion, the block experiences a friction force with a lesser intensity than the static friction force F → sf {\displaystyle {\vec {F}}_{\text{sf}}} . The friction force during relative motion is known as the dynamic friction force F → df {\displaystyle {\vec {F}}_{\text{df}}} . In this case it is necessary to take into account not only the first two laws of Amontons, but also of the law of Coulomb, so as to be able to affirm that the relationship between dynamic friction force F → df {\displaystyle {\vec {F}}_{\text{df}}} , coefficient of dynamic friction k {\displaystyle k} and normal force N {\displaystyle N} is the following: | F → df | = k | N → | . {\displaystyle \left|{\vec {F}}_{\text{df}}\right|=k{\left|{\vec {N}}\right|}.}
Static and dynamic friction coefficients
At this point it is possible to summarize the main properties of the static friction coefficients μ {\displaystyle \mu } and the dynamic one k {\displaystyle k} . These coefficients are dimensionless quantities, given by the ratio between the intensity of the friction force F → f {\displaystyle {\vec {F}}_{f}} and the intensity of the applied load W → {\displaystyle {\vec {W}}} , depending on the type of surfaces that are involved in a mutual contact, and in any case, the condition is always valid such that: μ > k {\displaystyle \mu >k} . Usually, the value of both coefficients does not exceed the unit and can be considered constant only within certain ranges of forces and velocities, outside of which there are extreme conditions that modify these coefficients and variables. In systems with significant nonuniform stress fields, the macroscopic static friction coefficient depends on the external pressure, system size, or shape because local slip occurs before the system slides. The following table shows the values of the static and dynamic friction coefficients for common materials:
Rolling friction
In the case of bodies capable of rolling, there is a particular type of friction, in which the sliding phenomenon, typical of dynamic friction, does not occur, but there is also a force that opposes the motion, which also excludes the case of static friction. This type of friction is called rolling friction. Now we want to observe in detail what happens to a wheel that rolls on a horizontal plane. Initially the wheel is immobile and the forces acting on it are the weight force m g → {\displaystyle m{\vec {g}}} and the normal force N → {\displaystyle {\vec {N}}} given by the response to the weight of the floor. At this point the wheel is set in motion, causing a displacement at the point of application of the normal force which is now applied in front of the center of the wheel, at a distance b {\displaystyle b} , which is equal to the value of the rolling friction coefficient. The opposition to the motion is caused by the separation of the normal force and the weight force at the exact moment in which the rolling starts, so the value of the torque given by the rolling friction force is M → rf = b → × m g → {\displaystyle {{\vec {M}}_{\text{rf}}}={\vec {b}}\times m{\vec {g}}} What happens in detail at the microscopic level between the wheel and the supporting surface is described in Figure, where it is possible to observe what is the behavior of the reaction forces of the deformed plane acting on an immobile wheel. Rolling the wheel continuously causes imperceptible deformations of the plane and, once passed to a subsequent point, the plane returns to its initial state. In the compression phase the plane opposes the motion of the wheel, while in the decompression phase it provides a positive contribution to the motion. The force of rolling friction depends, therefore, on the small deformations suffered by the supporting surface and by the wheel itself, and can be expressed as | F → r | = b | N → | {\displaystyle \vert {\vec {F}}_{r}\vert =b\vert {\vec {N}}\vert } , where it is possible to express b {\displaystyle b} in relation to the sliding friction coefficient μ {\displaystyle \mu } as b = μ v r {\displaystyle b={\tfrac {\mu v}{r}}} , with r {\displaystyle r} being the wheel radius.
Surfaces Going even deeper, it is possible to study not only the most external surface of the metal, but also the immediately more internal states, linked to the history of the metal, its composition and the manufacturing processes undergone by the latter. it is possible to divide the metal into four different layers:
Crystalline structure – basic structure of the metal, bulk interior form; Machined layer – layer which may also have inclusions of foreign material and which derives from the processing processes to which the metal has been subjected; Hardened layer – has a crystalline structure of greater hardness than the inner layers, thanks to the rapid cooling to which they are subjected in the working processes; Outer layer or oxide layer – layer that is created due to chemical interaction with the metal's environment and from the deposition of impurities. The layer of oxides and impurities (third body) has a fundamental tribological importance, in fact it usually contributes to reducing friction. Another fact of fundamental importance regarding oxides is that if you could clean and smooth the surface in order to obtain a pure "metal surface", what we would observe is the union of the two surfaces in contact. In fact, in the absence of thin layers of contaminants, the atoms of the metal in question, are not able to distinguish one body from another, thus going to form a single body if put in contact. Surface engineering techniques such as deposition of hard nitride coatings are widely used to improve tribological behaviour of mechanical components. Multicomponent coatings including Cr–V–N deposited by cathodic arc evaporation have demonstrated improved wear resistance and friction performance.
Origin of friction Contact between surfaces is made up of a large number of microscopic regions, in the literature called asperities or junctions of contact, where atom-to-atom contact takes place. The phenomenon of friction, and therefore of the dissipation of energy, is due precisely to the deformations that such regions undergo due to the load and relative movement. Plastic, elastic, or rupture deformations can be observed:
Plastic deformations – permanent deformations of the shape of the bumps; Elastic deformations – deformations in which the energy expended in the compression phase is almost entirely recovered in the decompression phase (elastic hysteresis); Break deformations – deformations that lead to the breaking of bumps and the creation of new contact areas. The energy that is dissipated during the phenomenon is transformed into heat, thus increasing the temperature of the surfaces in contact. The increase in temperature also depends on the relative speed and the roughness of the material, it can be so high as to even lead to the fusion of the materials involved. In friction phenomena, temperature is fundamental in many areas of application. For example, a rise in temperature may result in a sharp reduction of the friction coefficient, and consequently, the effectiveness of the brakes.
Cohesion theory The adhesion theory states that in the case of spherical asperities in contact with each other, subjected to a W → {\displaystyle {\vec {W}}} load, a deformation is observed, which, as the load increases, passes from an elastic to a plastic deformation. This phenomenon involves an enlargement of the real contact area A r {\displaystyle A_{\text{r}}} , which for this reason can be expressed as: A r = W → D , {\displaystyle A_{\text{r}}={{\vec {W}} \over D},} where D {\displaystyle D} is the hardness of the material definable as the applied load divided by the area of the contact surface. If at this point the two surfaces are sliding between them, a resistance to shear stress t {\displaystyle t} is observed, given by the presence of adhesive bonds, which were created precisely because of the plastic deformations, and therefore the frictional force will be given by F → a = A r t → {\displaystyle {\vec {F}}_{\text{a}}=A_{\text{r}}{\vec {t}}} At this point, since the coefficient of friction is the ratio between the intensity of the frictional force and that of the applied load, it is possible to state that μ = t D {\displaystyle \mu ={t \over D}} thus relating to the two material properties: shear strength t {\displaystyle t} and hardness. To obtain low value friction coefficients μ {\displaystyle \mu } it is possible to resort to materials which require less shear stress, but which are also very hard. In the case of lubricants, in fact, we use a substrate of material with low cutting stress t {\displaystyle t} , placed on a very hard material. The force acting between two solids in contact will not only have normal components, as implied so far, but will also have tangential components. This further complicates the description of the interactions between roughness, because due to this tangential component plastic deformation comes with a lower load than when ignoring this component. A more realistic description then of the area of each single junction that is created is given by A i 2 = ( W → i D ) 2 + α ( F → i D ) 2 {\displaystyle {A_{\text{i}}}^{2}=\left({\frac {{\vec {W}}_{\text{i}}}{D}}\right)^{2}+\alpha \left({\frac {{\vec {F}}_{\text{i}}}{D}}\right)^{2}} with α {\displaystyle \alpha } constant and a "tangent" force F → i {\displaystyle {\vec {F}}_{\text{i}}} applied to the joint. To obtain even more realistic considerations, the phenomenon of the third body should also be considered, i.e., the presence of foreign materials, such as moisture, oxides or lubricants, between the two solids in contact. A coefficient c {\displaystyle c} is then introduced which is able to correlate the shear strength t {\displaystyle t} of the pure "material" and that of the third body t tb {\displaystyle t_{\text{tb}}}
t = c ⋅ t tb {\displaystyle t=c\cdot t_{\text{tb}}} with 0 < c < 1 {\displaystyle 0<c<1} . By studying the behavior at the limits it will be that for c = 0 {\displaystyle c=0} , t = 0 {\displaystyle t=0} and for c = 1 {\displaystyle c=1} it returns to the condition in which the surfaces are directly in contact and there is no presence of a third body. Keeping in mind what has just been said, it is possible to correct the friction coefficient formula as follows: μ = c [ α ( 1 − c 2 ) ] 1 / 2 {\displaystyle \mu ={\frac {c}{[\alpha (1-c^{2})]^{1/2}}}} In conclusion, the case of elastic bodies in interaction with each other is considered. Similarly to what we have just seen, it is possible to define an equation of the type A = K W → {\displaystyle A=K{\vec {W}}} where, in this case, K {\displaystyle K} depends on the elastic properties of the materials. Also for the elastic bodies the tangential force depends on the coefficient c {\displaystyle c} seen above, and it will be F → T = c A s {\displaystyle {\vec {F}}_{T}=cAs} and therefore a fairly exhaustive description of the friction coefficient can be obtained μ = c K s . {\displaystyle \mu =cKs.}
Friction measurements The simplest and most immediate method for evaluating the friction coefficient of two surfaces is the use of an inclined plane on which a block of material is made to slide. As can be seen in the figure, the normal force of the plane is given by m g cos θ {\displaystyle mg\cos \theta } , while the frictional force is equal to m g sin θ {\displaystyle mg\sin \theta } . This allows us to state that the coefficient of friction can be calculated very easily, by means of the tangent of the angle in which the block begins to slip. In fact we have μ = F a N = m g sin θ m g cos θ = sin θ cos θ = tan θ {\displaystyle \mu ={F_{\text{a}} \over N}={mg\sin \theta \over mg\cos \theta }={\sin \theta \over \cos \theta }=\tan \theta } Then from the inclined plane we moved on to more sophisticated systems, which allow us to consider all the possible environmental conditions in which the measurement is made, such as the cross-roller machine or the pin and disk machine. Today there are digital machines such as the "Friction Tester" which allows, by means of a software support, to insert all the desired variables. Another widely used process is the ring compression test. A flat ring of the material to be studied is plastically deformed by means of a press, if the deformation is an expansion in both the inner and the outer circle, then there will be low or zero friction coefficients. Otherwise for a deformation that expands only in the inner circle there will be increasing friction coefficients.
Lubrication
To reduce friction between surfaces and keep wear under control, materials called lubricants are used. Unlike what you might think, these are not just oils or fats, but any fluid material that is characterized by viscosity, such as air and water. Of course, some lubricants are more suitable than others, depending on the type of use they are intended for: air and water, for example, are readily available, but the former can only be used under limited load and speed conditions, while the second can contribute to the wear of materials. What we try to achieve by means of these materials is a perfect fluid lubrication, or a lubrication such that it is possible to avoid direct contact between the surfaces in question, inserting a lubricant film between them. To do this there are two possibilities, depending on the type of application, the costs to address and the level of "perfection" of the lubrication desired to be achieved, there is a choice between:
Fluidostatic lubrication (or hydrostatic in the case of mineral oils) – which consists in the insertion of lubricating material under pressure between the surfaces in contact; Fluid fluid lubrication (or hydrodynamics) – which consists in exploiting the relative motion between the surfaces to make the lubricating material penetrate.
Viscosity
The viscosity is the equivalent of friction in fluids, it describes the ability of fluids to resist the forces that cause a change in shape. Thanks to Newton's studies, a deeper understanding of the phenomenon has been achieved. He, in fact, introduced the concept of laminar flow: "a flow in which the velocity changes from layer to layer". It is possible to ideally divide a fluid between two surfaces ( S 1 {\displaystyle S_{1}} , S 2 {\displaystyle S_{2}} ) of area A {\displaystyle A} , in various layers. The layer in contact with the surface S 2 {\displaystyle S_{2}} , which moves with a velocity v {\displaystyle v} due to an applied force F {\displaystyle F} , will have the same velocity as v of the slab, while each immediately following layer will vary this velocity of a quantity d v {\displaystyle dv} , up to the layer in contact with the immobile surface S 1 {\displaystyle S_{1}} , which will have zero speed. From what has been said, it is possible to state that the force F {\displaystyle F} , necessary to cause a rolling motion in a fluid contained between two plates, is proportional to the area of the two surfaces and to the speed gradient: F ∝ A d v d y . {\displaystyle F\propto A{dv \over dy}.} At this point we can introduce a proportional constant μ {\displaystyle \mu } , which corresponds to the dynamic viscosity coefficient of the fluid, to obtain the following equation, known as Newton's law F = μ A d v d y {\displaystyle F=\mu A{dv \over dy}} The speed varies by the same amount d v {\displaystyle dv} of layer in layer and then the condition occurs so that d v / d y = v / L {\displaystyle dv/dy=v/L} , where L {\displaystyle L} is the distance between the surfaces S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} , and then we can simplify the equation by writing F = μ A v L . {\displaystyle F=\mu A{v \over L}.} The viscosity μ {\displaystyle \mu } is high in fluids that strongly oppose the motion, while it is contained for fluids that flow easily.
To determine what kind of flow is in the study, we observe its Reynolds number R e = ρ L v μ {\displaystyle Re={{\rho Lv} \over \mu }} This is a constant that depends on the fluid mass ρ {\displaystyle \rho } of the fluid, on its viscosity μ {\displaystyle \mu } and on the diameter L {\displaystyle L} of the tube in which the fluid flows. If the Reynolds number is relatively low then there is a laminar flow, whereas for R e ≃ 2000 {\displaystyle \mathrm {Re} \simeq 2000} the flow becomes turbulent. To conclude we want to underline that it is possible to divide the fluids into two types according to their viscosity:
Newtonian fluids, or fluids in which viscosity is a function of temperature and fluid pressure only and not of velocity gradient; Non-Newtonian fluids, or fluids in which viscosity also depends on the velocity gradient.
Viscosity as a function of temperature and pressure Temperature and pressure are two fundamental factors to evaluate when choosing a lubricant instead of another. Consider the effects of temperature initially. There are three main causes of temperature variation that can affect the behavior of the lubricant:
Weather conditions; Local thermal factors (like for car engines or refrigeration pumps); Energy dissipation due to rubbing between surfaces. In order to classify the various lubricants according to their viscosity behavior as a function of temperature, in 1929 the viscosity index (V.I.) was introduced by Dean and Davis. These assigned the best lubricant then available, namely the oil of Pennsylvania, the viscosity index 100, and at the worst, the American oil of the Gulf Coast, the value 0. To determine the value of the intermediate oil index, the following procedure is used: two reference oils are chosen so that the oil in question has the same viscosity at 100 °C, and the following equation is used to determine the viscosity index V . I . = L − O test L − H × 100 {\displaystyle V.I.={{L-O_{\text{test}}} \over {L-H}}\times 100} This process has some disadvantages:
For mixtures of oils the results are not exact; There is no information if you are outside the fixed temperature range; With the advancement of the technologies, oils with V.I. more than 100, which can not be described by the method above. In the case of oils with V.I. above 100 you can use a different relationship that allows you to get exact results V . I . = 10 N − 1 0.00715 + 100 {\displaystyle V.I.={{10^{N-1}} \over {0.00715}}+100}
N =