As shown in Fig. 1.1 carbon graphite seal is employed to avoid leakage of steam from rotary joints of paper industry. Failure of this component occurs due to adhesive wear. Adhesive wear causes uneven surface that leads to reduction in mechanical contact area. For same imposed load, reduction in mechanical contacts, increases the level of stress and hence chances of failure.
Fig. 1.1: Carbon graphite seal |
| Example 2: Journal Bearings |
|
| The following figures(Fig. 1.3(a) and Fig. 1.3(b)) are examples of two journal bearing. Left hand side is photograph of centrally grooved engine journal bearing. It appears that bearing is worn out due to foreign particles. Right hand side is a photograph of an aluminum bearing subjected to heavy load, which causes shaft surface to run over bearing inner surface. In these examples of journal bearing, wear increases the clearance between shaft and bearing and leads to reduction in load support capacity of the bearing. Often such failures occur in absence of sufficient lubricant hydrodynamic film thickness due to relatively low speed. Learning tribology cultivates an understanding that at low speeds, the main purpose of oil is the lubrication and high viscosity oil will be preferred to low viscosity oil, while at high speeds the major purpose of oil is to act as a coolant and low viscosity lubricants are preferred to carry away frictional heat of operation. Here lubrication is a secondary consideration. |
|
Fig. 1.3(a): Abrasive wear and Fig. 1.3(b): Rubbing wear |
|
| Example 4: Magnetic Bearing |
|
| Magnetic bearings are known as non-contact levitation. In the figure given below(Fig. 1.4) a repulsive type permanent magnetic bearing is shown. Due to improper design and external noise factors, bearing failed within three hours of operation at relative speed of 115 rpm. |
|
Fig. 1.4: Wear scar due to edge loading
| Friction |
|
| Friction is the tangential resistance to motion. The occurrence of friction is a part of everyday life. It is needed so that we have control on our walking. On the other hand, in most of running machines friction is undesirable (energy loss, leading to wear of vital parts, deteriorating performance due to heat generation) and all sorts of attempts (i.e. using low friction materials, lubricating surfaces with oil or greases, changing design so that sliding can be reduced) have been made to reduce it. |
|
| Often coefficient of friction(μ) is considered a constant value for a pair of material. In addition, the value of μ is accounted much lesser than 1.0. In practice μ greater than 1.0, as shown in Table 2.1, has been observed. Generally coefficients of friction depend on parameters such as temperature, surface roughness and hardness. |
|
Table 2.1: Coefficient of friction for various metals sliding on themselves.
 |
|
| Fig. 2.1 indicates that under dry lubricant conditions, μ ranges between 0.1 to 1.0 for most of the materials. Very thin lubrication reduces coefficient by 10 times. |
|
Fig. 2.1: Coefficient of friction for various metals. |
|
| Generally, adhesion(Fig. 2.2) increases the friction. So, while selecting metal pairs, low adhesion metal pairs must be selected to reduce friction force. Similiar material pair must be avoided as similar materials have higher tendency of adhesion. |
|
Fig. 2.2: Adhesive Friction among various materials. |
|
| Static & Kinetic Frictions : |
|
| Before starting friction mechanisms, it is necessary to define static and kinetic friction. Let us consider a block on the surface getting pushed by a tangential force F. On application of 20 N load, block does not move. This second point on the graph(Fig. 2.3) shows that on application of 40 N, still block does not move. There is static force equilibrium between application force and friction force. On application of 50 N load, block just start sliding. At this point of load application friction force remains equal to 50 N, but friction resistance decreases subsequently to 40 N. In other words, static friction is higher than kinetic friction. Table 2.2 shows few published results of static/kinetic coefficient of friction. This table indicates that coefficient of friction is statistical parameter. It is difficult to obtain same value under various laboratory conditions. Further, there is a possibility of substantial decrease in kinetic friction relative to static friction. Stick-slip is a phenomenon where the instantaneous sliding speed of an object does not remain close to the average sliding speed. Stick-slip is a type of friction instability. |
|
Fig. 2.3: Difference between the static and kinetic friction may initiate ‘stick-slip’. |
|
Table 2.2: μ for wood-on-wood reported in various articles.
 |
|
| A friction is statistical parameter depends on a number of variable. There is a need to understand science of friction. |
|
| To understand the effect of material pair, role of lubrication, and environmental factors let us start with dry friction. The dry friction is also known as solid body friction and it means that there is no coherent liquid or gas lubricant film between the two solid body surfaces. Four theories given by Leonardo da Vinci, Amonton, Coulomb and Tomlison for dry lubrication are explained in following paragraph. |
|
Fig. 2.4: Amonton`s work. |
|
Leonardo da vinci(Earliest experimenter, 1452-1519) :
As per Leonardo, “Friction made by same weight will be of equal resistance at the beginning of movement, although contact may be of different breadths or length”.
“Friction produces the double the amount of effort if weight be doubled”. In other words, F α W. |
|
| G.Amontons, 1699 : The friction force is independent of the nominal area (F ≠ A) of contact between two solid surfaces. The friction force is directly proportional F α N to the normal component of the load. He considered three cases(Fig. 2.4) and showed that friction force will vary as per the angle of application of load. As per Amontons μ = 0.3 for most of materials. |
|
C.A.Coulomb 1781 (1736-1806) :
• Clearly distinguished between static & kinetic frictions. Friction due to interlocking of rough surfaces.
• Contact at discrete points μstatic ≥ μkinetic.
• f ≠ func(A).
• f ≠ func(v). |
|
Fig. 2.5: Coulomb friction model. |
|
| As per coulomb friction force is independent of sliding speed. But this law applies only approximately to dry surfaces for a reasonable low range of sliding speeds, which depends on heat dissipation capabilities of tribo-pairs. |
|
TOMLINSON’s Theory of Molecular attraction, 1929 :
Tomlison based on experimental study provided relation between friction coefficient & elastic properties of material involved. |
|
 |
|
Fig. 2.6: Examples on Tomlison formula. |
|
As per Tomlison due to molecular attraction between metal, cold weld junctions are formed. Generally load on bearing surface is carried on just a few points. These are subjected to heavy unit pressure, and so probably weld together. Adhesion force developed at real area of contact.
Fig. 2.6 provides illustration related to Tomlison`s friction formula. This figure indicates f = 0.6558 for clean steel and aluminium, f = 0.742 for aluminium and titanium, and f = 0.5039 for clean steel and titanium. |
|
| Scientific Explanation of Dry Friction : |
|
| There are two main friction sources: Adhesion and Deformation. Force needed to plough asperities of harder surface through softer. In lubricated tribo-pair case, friction due to adhesion will be negligible, while for smoother surfaces under light load conditions deformation component of friction will be negligible. |
|
| Fig. 2.7 demonstrates the adhesion (cold weld) between two surfaces. Some force, Fa, is required to tear the cold junction. Fig. 2.8 demonstrates the deformation process. It shows a conical asperity approaching to a softer surface. To move upper surface relative to lower surface some force is required. |
|
• Two friction sources : Deformation and Adhesion.
• Resulting friction force (F) is sum of two contributing (Fa & Fd) terms.
• Lubricated tribo-pair case -- negligible adhesion.
• Smoother surfaces under light load conditions – Negligible deformation. |
|
Fig. 2.7: Adhesion |
|
Fig. 2.8: Abrasion(Deformation)[1]
| Adhesion and Ploughing in Friction |
|
| This theory is based on the fact that all surfaces are made of atoms. All atoms attract order one another by attractive force. For examples, if we press steel piece over indium piece (as shown in Fig. 2.9) they will bind across the region of contact. This process is sometimes called "cold welding," since the surfaces stick together strongly without the application of heat. It requires some force to separate the two surfaces. If we now apply a sideways force to one of surfaces the junctions formed at the regions of real contact will have to be sheared if sliding is to take place. The force to do this is the frictional force. Fig. 2.10 shows carbon graphite material adhered to stainless steel shaft. |
|
Fig. 2.9: Cold welding in steel and indium |
|
Fig. 2.10: Carbon graphite and stainless steel. |
|
| Theory of ADHESIVE Friction : |
|
| Bowden and Tabor developed theory of adhesive friction. As per this theory on application of W, initial contact at some of higher asperity tips occurs. Due to high stress those asperities suffer plastic deformation, which permits strong adhesive bonds among asperities. Such cold formed junctions are responsible for the adhesive friction. The real area of contact, A can be estimated by applied load W and hardness of the soft material, H. If s is shear stress of softer material, then force Fa required to break these bonds can be estimated by Equation Fa = As. The coefficient of friction due to adhesive friction is given by ratio of friction force to applied load W. Fig. 2.11 shows the formulation and breakage of cold junctions. |
|
• Two surfaces are pressed together under load W.
• Material deforms until area of contact (A) is sufficient to support load W, A = W/H.
• To move the surface sideway, it must overcome shear strength of junctions with force Fa.
• μ = Fa ⁄ W = s ⁄ H.
In other words shear strength(s) and hardness(H) of soft material decides the value of μ. This means whatever properties of the other harder pairing material, μ would not change. |
|
Fig. 2.11: Adhesion theory. |
|
For most of untreated materials H = 3 σy & s = σy/1.7321. Expected value of μ = 0.2, as μ = s ⁄ H. But for most of the material pair(shown in Fig. 2.12) μ is greater than 0.2. There is a huge difference between measured values of friction coefficient and estimated by theory of adhesion.
Theory is unable to estimate different μ for steel on indium and steel on lead alloy. Theory related to deformation needs to be explored. |
|
Fig. 2.12: Friction coefficients for various material pairs. |
|
| FRICTION due to DEFORMATION : |
|
| This theory is based on the fact that contact between tribo-pairs only occurs at discrete points, where the asperities on one surface touch the other. The slope of asperities governs the friction force. Sharp edges cause more friction compared to rounded edges. Expression for coefficient of friction can be derived based on the ploughing effect. Ploughing occurs when two bodies in contact have different hardness. The asperities on the harder surface may penetrate into the softer surface and produce grooves on it, if there is relative motion. |
|
Fig. 2.13: Deformation theory[1]. |
|
| Contact between tribo-pairs only occurs at discrete points. Assume n conical asperities of hard metal in contact with flat soft metal, vertically project area of contact. |
|
 |
|
| μd = (F/W), substituting the equations of F and W, we get μd = (2/π)cot θ : This relation shows important of cone angle, θ. Table 2.3 lists the μd for various θ values. |
|
| In practice slopes of real surfaces are lesser than 100 (i.e. θ > 800), therefore μd = 0.1. If we add this value(μd = 0.1), total μ, should not exceed 0.3. Total μ, representing contribution for both ploughing and adhesion terms. | Table 2.3
 |
|
|
| Ploughing By Spherical Asperity : |
|
| If we consider asperities on solid surfaces are spherical, vertical projected area of contact : |
|
Fig. 2.14: Spherical asperity. |
|
 |
|
| Generally h << R, therefore μd Ξ 0.1. This means total μ, should not exceed 0.3. |
|
| Summary of theories related to adhesion and ploughing effects. |
|
|  | 
Fig. 2.15: Summary of adhesion and ploughing. |
|
|
Three frictional theories were discussed :
• In first expression it is shown that friction depends on the lowest shear strength of the contact tribo-pair. Reducing shear strength and increasing the hardness reduces the coefficient of friction.
• Second expression shows the dependence of coefficient of friction on the angle of conical asperity.
• Third expression indicates lesser sensitivity of coefficient of friction compared to that of conical asperity.
None of these expression provides reliable estimation of coefficient of friction which we observe during laboratory tests. Bowden and tabor improved that theory of adhesion and incorporated the limiting shear stress concept.
| Junction Growth |
|
| Bowden and Tabor were motivated to think that contact area(shown in Fig. 2.16) might become much enlarged under the additional shear force and they proposed junction growth theory. They considered two rough surfaces subjected to normal load W and friction force at the interface. To explain their hypothesis they considered two dimensional stress system(Eq.(2.1)). If W force is in y-direction and force in x-direction is zero, then principle stresses can be expressed by Eq.(2.2) and Eq.(2.3). |
|
 ....Eq.(2.1) |
|
Fig. 2.16: Two contacting surfaces. |
|
 ....Eq.(2.2) |
|
| Where σ1 is first principal stress, and δ is elemental area. |
|
 ....Eq.(2.3) |
|
Substracting Eq.(2.3) from Eq.(2.2)
Where σ2 is second principal stress. |
|
 ....Eq.(2.4) |
|
If yield strength of material is σy = σ1 - σ2
and shear strength and τy = 0.5τy. On substituting and rearranging. |
|
 ....Eq.(2.5) |
|
| In Eq.(2.5) τy and W remain constant and this indicates that area of contact will increase with increasing friction force, till force reaches its limiting value. We can state that on application of additional incremental tangential force, there will be further plastic flow at constant shear stress, resulting in an incremental contact area of A. Bowden and Tabor called this increase the junction growth. Assume τi is shear stress of fractured interface. |
|
 |
|
 ...Eq.(2.6) |
|
| Using Eq.(2.6) coefficient of friction can be calculated from ratio τi / τy, as given in Table 2.4. |
|
Table 2.4
 |
|
| The above analysis applies only to clean surfaces. Understanding this mechanism motivates to apply thin film of low shear strength materials to the surfaces. Therefore in order to reduce maintenance cost and increase bearing life, interface shear strength of contacting surfaces need to be as low as possible. |
|
| How to reduce Junction Growth ? |
|
Two methods to reduce junction growth are contaminations (reducing adhesion) and lubrication.
Contamination : A few molecules thick oxide layer (encountered with metals in air) on the surface(as shown in Fig. 2.17) can reduce the friction (i.e. μ = 0.1 to 0.3). |
|
Fig. 2.17: Surface contamination |
|
| The surface film prevents the surfaces from sticking together strongly and allows only a small amount of junction growth to occur. The formation and breakage of contamination layer is a dynamic process; therefore, there is possibilities of variation in μ. |
|
• Weak(ductile) metal, weak oxide : Film easily broken, rapid junction growth, and high μ Examplesa: indium, gold.
• Weak metal, strong oxide : Transition from low to high μ as load increases(as shown in Fig. 2.18) e.g. Copper, Iron.
• Strong metal, strong oxide : Low μ at all loads. Examples: steel, chromium. |
|
Fig. 2.18: Variation in μ with load. |
|
| Note : Both junction growth and ploughing (two/three) effects play role, and either of these may dominate friction behavior. |
|
| Lubrication to reduce Junction Growth : |
|
1. To reduce junction growth minimum value of ratio τi/τy(Eq. 2.1) must be selected.
2. Lubricant: Presence of liquid lubricant reduces chances of junction growth. One way is to choose liquid lubricant which has a low value of τ.
3. Use of suitable contacting materials : Using less reactive material (but high hardness) materials, which result in low shear strength of interface.
4. Never use same metal or closely similar metals in tribo-pair : (μCopper on copper = 1.0, μAluminum - lowcarbonsteel = 0.8, μSilver - lowcarbonsteel = 0.3).
5. Ductility : Use materials of limited ductility. These materials after a small amount of junction growth will fracture rather than flow further. |
|
| Sliding Dry Friction with Time : |
|
Sliding in dry contact starts with running-in period :
• High rate of ploughing of softer surface by asperities :
- Relatively low adhesion.
• Rupture/breakage of asperities polish surface :
- Reduce ploughing coefficient but increase coefficient of adhesion.
- On removal of contaminating layers, adhesion coefficient increases. |
|
Fig. 2.19: Sliding friction vs time. |
|
| Coefficient of friction varies with sliding time. Essentially, a dry contact starts with a running in period(as shown by 'Line 1' in Fig. 2.19). Initially, the friction force is largely a result of ploughing of the surface by asperities. Adhesion does not play much significant role due to surface contamination. Asperity deformation takes place and affects the static coefficient of friction and surface is easily polished. This is the main reason of reduction in friction coefficient, as shown in Fig. 2.19 by 'Line 1'. Consequently the coefficient of friction in the initial stage is largely independent of the material combination. But if polishing wear process is able to remove the contaminating layers, elements of bare surface will appear, resulting in increase in the coefficient of friction due to increased adhesion as shown by 'Line 2'. In addition the coefficient of friction increases due to rapid increase in the number of wear particles entrapped between the sliding surfaces as a consequence of higher wear rates as shown by 'Line 3', 'Line 4', 'Line 5' and 'Line 6' in Fig. 2.19. The deformation of asperities continues and the adhesion effect increases due to larger clean interfacial areas. Some of the wear particles are trapped between the surfaces, causes ploughing. A steady state friction conditions arrives depending on the worn out surfaces. |
|
| Laws of Rolling Friction |
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| Coefficient of friction due to rolling (μr) is generally smaller than that caused by sliding action. Therefore wherever possible rolling friction compared to sliding friction is desired. μr is defined as the force required to maintain steady rolling, divided by the load carried by the roller. Rolling friction coefficients often depend on hardness of contacting solids. On increasing hardness, elastic deformation under load decreases. Therefore, hysteresis loss and so the value of μr decreases. For hard smooth steel rollers, the coefficient of rolling friction ranges between 0.01 and 0.001. A roller or sphere made of soft material(as shown in Fig. 2.20) when rolled over other soft surface, generates a higher level of rolling friction. |
|
| Sources of Rolling Friction : |
|
It is important to know the source of rolling friction, so that proper actions may be implemented to control the rolling friction. Let us consider a hard steel ball which rolls over a softer rubber such as shown in Fig. 2.20. As it rolls along, the ball displaces rubber elasto-plastically around and ahead of it. The force required to display rubber is almost equal to the observed rolling friction. Thus, the rolling friction is essentially a measure of the force required to deform other material. With a very bouncy rubber rolling friction will be lesser compared to a very soggy rubber.
The main contributions to friction in rolling contacts are :
1. Micro-slip effect within the contact area.
2. Elastic hysteresis of the contacting materials.
3. Plastic deformation of the materials, and
4. Adhesion effects in the contact. |
|
| It is important to note that lubricant cannot reduce deformation of surface; therefore, lubricants have very little effect(except reduction in adhesion effects) on the rolling friction. |
|
Fig. 2.20: Rolling friction in rubber. |
|
| Examples of Rolling Friction : |
|
• Ball bearings :
Rolling are made of high strength (induced stresses are lesser than elastic compressive strength) materials having hystereis losses lesser than one percent. Due to such materials(μ = 0.001).
In practice, the balls must be surrounded by cage to separate them and prevent the rubbing on one another. But sliding between the cage and balls occurs, and this sliding friction is often far greater than the rolling friction. Lubricants are used to reduce the sliding friction between balls and cage and to prevent corrosion of the metal parts. |
|
• Automobile Tires :
In free rolling, the tire is deformed as it meets the road surface and recovers as it leaves. If there is negligible slip between tire and road the energy loss is not large and μ = 0.01 to 0.03. However, If the tire is made of a rubber with a higher hysteresis loss (or filled with lesser air-pressure), the rolling friction is larger and there is a larger power loss. High hysteresis loss by tire, increases controllability (better gripping of the road during accelerating, decelerating or cornering) and comfort (acts as shock absorber in passing over rough road). Therefore, automobile tire material provides trade off between "rolling friction", "Controllability" and "Comfort".
| Friction Instability |
|
| Friction instability generally occurs due to large difference in the value of static and kinetic coefficient of friction. Ideally lubricated condition having coefficient of friction equal to 0.00025 shall be preferred, but there is a possibility of variation in static and kinetic coefficient of frictions. If we assume that static coefficient of friction under lubricated conditions is equal to 0.01 and kinetic coefficient of friction is equal to 0.00025, then this lubricated contact may not be preferred. |
|
| Friction Induced Vibrations (Instability) : |
|
Difference between static and kinetic friction coefficients, initiates a “stick-slip” process. Instantaneous sliding speed of an object does not remain close to the average sliding speed and friction torque coefficient decreases as velocity increases as shown in Fig. 2.21. With respect to Fig. 2.21 (Torque = coefficient of friction * normal load * torque arm).
Since normal load and torque arm remains constant, hence Fig. 2.21 shows the variation of coefficient of friction with speed. |
|
Fig. 2.21: Friction performance of MR brake. |
|
Possible reasons for stick-slip phenomenon :
• Interlocking of asperities during stick phenomenon but separation during sliding.
• Adhesion during stick action and breakage of weld joint during sliding.
• Electrostatic charge during stick event.
To avoid this phenomenon either :-
• Increase operating speed or
• Reduce the difference between μs and μk. |
|
Due to difference in static and dynamic friction forces (as shown in Fig. 2.22), unbalance force (static–dynamic friction force) cause a sudden acceleration. The velocity of M increases until the drive force falls to dynamic friction force. Eventually M comes to rest as shown in Fig. 2.23.
• Overall stick-slip behavior of systems depends on stiffness, inertia, damping and magnitude of unbalanced force. |
|
Fig. 2.22: Stick slip. |
|
Fig. 2.23: Variation of vibration parameters. |
|
Friction can be modeled in two ways :
(a) Stiction case : Instantaneous reduction in friction force as shown in Fig. 2.24. A hypothetical case.
(b) Negative and gradient case : Gradual reduction in friction force as shown in Fig. 2.25 is a practical case. Often this friction model is used to find possibility of friction instability. |
|
Fig. 2.24: Stiction case[1]. | 
Fig. 2.25: Negative and gradient case[1]. |
|
|
| Damped vibration[1] : |
|
To understand friction instability let us consider system shown in Fig. 2.22.
A mathematical model of system is given in Eq.(2.7) |
 ....Eq.(2.7) |
|
| Introducing damping factor. |
 |
|
 ....Eq.(2.8) |
|
| There are three possible situations, which we can derive from Eq.(2.8) |
|
 ....Eq.(2.9) |
|
 ....Eq.(2.10) |
|
 Eq.(2.11) |
|
| All three cases(underdamped, overdamped and critical damped) reduce vibration amplitude with time as shown in Fig. 2.26. But there is a possibility of negative damping (ζ < 0) |
|
Fig. 2.26: Positive damping. |
|
Fig. 2.27: Negative damping. |
|
| Negative damping causes instability. If this happens due to friction, then we term it as “Friction Instability”. |
|
| Forced damped vibrations[1] : |
|
 ....Eq.(2.12) |
|
| In the present case external force, F(t) is friction force. |
|
 ....Eq.(2.13) |
|
| Let us assume friction force is represented as |
|
 ....Eq.(2.14) |
|
| Substituting Eq.(2.14) in Eq.(2.13), |
 ....Eq.(2.15) |
 |
 ....Eq.(2.16) |
|
| If system damping, C is low and λ is large then overall negative damping results, and motion may become instable. |
|
Fig. 2.28: Friction instability. |
|
To avoid friction instability :
• Increase, the system damping(C).
• Lubricate or otherwise form a surface film to ensure positive friction versus velocity relationship(reduce gap between static and kinetic coefficient of friction). |
|
|
| References : |
|
1. J Halling, Principles of Tribology, The Macmillan Press Ltd, London, 1975.
Introduction of Wear
|
|
Undesirable removal of material from operating solid surface is known as wear. There are two definitions :
(1) Zero wear : Removal of material which causes polishing of material surfaces may be known as "Zero wear". It may increase performance. It is for betterment, so it is not undesirable. |
|
| Zero wear is basically a polishing process in which the asperities of the contacting surfaces are gradually worn off until a very fine, smooth surface develops. Generally, “polishing-in” wear is desirable for better life of tribo-pair. Fig. 3.1(a) shows polished surface of helical gear which occurs due to slow loss of metal at a rate that will have a little affect on the satisfactory performance within the life of the gears. |
|
Fig. 3.1(a): Zero wear of helical gear. |
|
| (2) Measurable wear : Removal of material from surface that increases vibration; noise or surface roughness may be treated an "Measureable wear". Often we measure wear in volume/mass reduction. Undesirable removal of material occurs in measurable wear. |
|
| Measurable wear refers to a loss of material which must be counted to estimate the life of tribo-pair. The extent of measurable weardepends on the lubrication regime, the nature of the load, the surface hardness and roughness, and on the contaminants in the lubricating oil. A typical example of measurable wear in helical gear is shown in Fig. 3.1(b) which is typically known as pitting wear. |
|
Fig. 3.1(b): Measurable wear of helical gear. |
|
Pitting is a surface fatigue failure which occurs due to repeated loading of tooth surface and the contact stress exceeding the surface fatigue strength of the material. Material in the fatigue region gets removed and a pit is formed. The pit itself will cause stress concentration and soon the pitting spreads to adjacent region till the whole surface is covered with pits. Subsequently, higher impact load resulting from pitting may cause fracture of already weakened tooth. Sometimes impurities in materials provide nucleus for crack generation as shown in Fig. 3.1(c). Fig. 3.1(d) shows merger of generated cracks, which finally detaches from the surface as shown in Fig. 3.1(e). Such formation of pits (removal of material) comes undermeasurable wear. |
|
Fig. 3.1: Formation of pit. |
|
| Many time the change in surface profile alters the optimum value of clearance and reduces load capacity of machine components. Let us consider Fig. 3.2 of worn out rollers. Sliding to rolling ratio for these worn out rollers increase with wear rate and usage of rolling element bearing loses its purpose. |
|
Fig. 3.2: Worn out rollers. |
|
| This Fig. 3.3 shows variation in bearing clearance due to abrasion of the bearing surface. With increase in bearing clearance load capacity of bearing decreases as shown in Fig. 3.4. X-axis of Fig. 3.4 represents radial clearance which is given by 0.1% of radius multiplied with the factor depicting increase in clearance due to wear. |
|
Fig. 3.3: Abrasion marks on bearing bore. | 
Fig. 3.4: Effect of clearence on load. |
|
|
Removal of material from operating solid surfaces by solid particles depends upon Load, Velocity, Environment, and Materials. Removal of material from operating solid surface by Fluid (liquid/gas) depends upon Velocity, pressure, Environment and material.
As wear increases power losses increases, oil consumption increases, rate of component replacement also inreases. Ultimately, it reduces efficiency of the system. Therefore, as far as possible wear should be minimized. |
|
| Wear Mechanisms : |
|
Wear can be classified based on the ways that the frictional junctions are broken, that is, elastic displacement, plastic displacement, cutting, destruction of surface films and destruction of bulk material. There are many types of wear mechanisms, but we shall discuss about common wear mechanisms, which are:
• Abrasive Wear : polishing, scouring, scratching, grinding, gouging.
• Adhesive Wear : galling, scuffing, scoring.
• Cavitation (interaction with fluid).
• Corrosive Wear (Chemical nature).
• Erosive Wear.
• Fatigue : delamination.
• Fretting Wear.
| Adhesive Wear |
|
| Adhesive wear is very common in metals. It is heavily dependent on the mutual affinity between the materials. Let us take example of steel and indium [Fig. 3.5(a)]. When steel pin under load is pushed [Fig. 3.5(b)] in indium block, and subsequently retracted [Fig. 3.5(c)], a thin layer of indium transferred on the steel pin. Similar behavior is observed by pushing brass metal in indium metal. This behavior demonstrates the loss of indium material, which occurs due to high value of adhesive force between steel and indium. If steel pin is subjected to normal load as well as tangential load [Fig. 3.5(d)] then severe wear of indium material occurs. By introducing a thin layer of lubricant at the interface of indium and metal, the severe wear can be reduced to mild wear. Shear strength of lubricant layer is much smaller than shear strength of indium metal, therefore weak interface between steel and indium occurs which can be sheared easily and wear rate reduces to mild value. |
|
Fig. 3.5: Adhesive wear. |
|
| All theories which predict wear rates start from the concept of true area of contact. It is usually assumed that the true area of contact between two real metal surfaces is determined by the plastic deformation of their highest asperities. Severity of adhesive wear is based on the area of contact which is given by A = W/H. Here, W is load applied to press one surface over other surface and H is hardness of soft material. This expression provides appropriate results if whole load is supported due to plastic deformation of the surface. However, for elasto-plastic deformation, the expression needs to be slightly modified. (A = (W/H)n where (2/3 < n < 1). Here assumption is that higher asperities could be deformed plastically, while the lower contacting asperities are subject to within elastic limits. In addition, the adhesive wear will depend on the shear strength of friction junctions. This means total true area of contact consists of plastic and elastic asperity contacts and shear strength of the contacting asperities vary in shear strength and thus influence the rate of adhesive wear. If the junction is weaker than the material on either side of it, shearing occurs at the interface itself Fig. 3.6(a). There will be little surface damage and little wear. This situation occurs if sliding occurs within the surface oxide layer. If the junction is stronger than one of the metals, shearing will not occur at the interface but at a little distance within the softer metal [Fig. 3.6(b) and Fig. 3.6(c)]. This may lead to an enormous increase in wear rate. |
|
Fig. 3.6: Location of shear plane. |
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| Scoring wear, a severe form of adhesive wear, occurs due to tearing out of small particles that weld together as a result of overheating (due to high contact pressure and/or high sliding velocity) of the tooth mesh zone, permitting metal to metal contact shown in Fig. 3.6(d). After welding, sliding forces tear the metal from the surface producing a minute cavity in one surface and a projection on the other. The wear initiates microscopically, however, it progresses rapidly. Scoring is sometimes referred to as galling, seizing or scuffing. |
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Fig. 3.6(d): Scoring. |
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Fig. 3.7(a): Contaminant layers on metal surface. |
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Fig. 3.7(b): Surface asperities on metal surface. |
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Fig. 3.7(c): Interaction between contaminant layers and surface asperities on metal surface. |
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| Steps leading to Adhesive Wear : |
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It is well known that macroscopically smooth surfaces are rough on micro scale as shown in Fig. 3.7(a) and Fig. 3.7(b). When two such surfaces are brought together as shown in Fig. 3.7(c), contact is made at relatively few isolated asperities. As a normal load is applied, the local pressure at the asperities becomes extremely high. In the absence of surface films the surfaces would adhere but a small amount of contaminant prevents adhesion under purely normal loading. However, relative tangential motion at the interface disperses the contaminant films at the points of contact, and welding of the junctions can take place. Continued sliding causes the junctions to be sheared and new junctions to be formed. The amount of wear depends on the position at which the junction is sheared as shown in Fig. 3.6(a) to (c). If shearing occurs at the interface then wear is negligible. If shear takes place away from the interface then metal is transferred from one surface to the other. With further rubbing, some of the transferred material is detached to form loose wear particles. We can summarize these steps as :
• Deformation of contacting asperities Fig. 3.8(a).
• Removal (abrasion) of protective oxide surface film.
• Formation of adhesive junctions Fig. 3.8(b).
• Failure of junction by pulling out large lumps and transfer of materials Fig. 3.8(c). |
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Fig. 3.8: Steps leading to adhesive wear. |
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Fig. 3.9: Wear transition[1]. |
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| Laws of Adhesive Wear : |
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• Wear Volume proportional to sliding distance of travel (L)
- True for wide range of conditions except where back transfer occurs.
• Wear Volume proportional to the load (W)
- Dramatic increase beyond critical load as shown in Fig. 3.9.
• Wear volume inversely proportional to hardness(H) of softer material
Using these laws, wear volume is given by V = K1WL/3H. This equation is known as Archard’s Wear Equation.
The value of k1 depends on elastic plastic contacts, shearing of those contacts, effect of environment, mode of lubrication, etc. This expression of wear volume is a simple expression, as it does not require to estimate constant n(A = (W/H)n), individual shear strength of elastic and plastic junctions, effect of lubricant thickness, roughness, etc. |
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| Archard assumed that the contact between tribo-pair involve formation and breakage of junctions. In other words, contacts occurs only at asperities. The real area of contact of contacting surfaces, as distinguished from the apparent or geometric area of contact, is the instantaneous sum of the areas of all junctions. The Archard model is demonstrated in Fig. 3.10, where cross section of asperities after plastic deformation is assumed to be circular. First sketch demonstrates the approach of junction forming asperities. Area of contact increases with sliding distance and subsequently decreases. But this process is continuous and happens among number of asperities. On average, it is assumed that n asperities will be in contact at any frame of time. |
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| Understanding of wear constant k1 : |
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k1 is a dimensionless constant expresses the probability of removing a wear particle. Factor k1 (often referred as index of severity) represents the fraction of the friction junctions producing wear.
• k1 = 1. Every junction involved in the friction process produces a wear fragment.
• k1 = 0.1. One tenth of the friction junctions produce wear fragments. For clean gold surfaces k1 is between 0.1 and 1. For clean-copper surfaces k1 is between 0.1 and 0.01. Clean gold surfaces wear about ten times more rapidly than clean copper surfaces.
• k1 = 10-7 means that of the junctions responsible for friction only one in ten million produces a wear fragment. |
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| Relation between Coefficient of Friction and Wear Constant : |
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Table 3.1: Data related to friction coefficient and wear rate.
 |
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Table 3.1 shows some relation between coefficient of friction and wear rate. To establish relation between µ and k1, Rowe proposed modified adhesion theory. In Eq.(3.1) km is constant and β is fractional surface film defect. This means β fraction of contact area is under dry lubrication, while one minus β contact area is under lubricated condition. Here lubricated condition means shear strength of interface lower than shear strength of bulk material.
ν = km √(1+μ2) β(W/H)...Eq.(3.1)
ν = wear volume per unit sliding distance.
v = K1W/3H ...Eq.(3.2)
It is interesting to compare Rowe`s equation(3.1) with Archard`s equation(3.2). There are three constants in equation(3.1) while only one constant in equation(3.2). |
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Equation(3.3) provides a modified form of wear constant k1. In this equation, 'h' represents the thickness of asperity while 'l' represents the length of asperity. P is the probability of wear particle formation. For spherical asperity, l = 2*h which means k1 is equal to probability of wear particle formation. But if h is greater than radius of sphere then k1 will be greater than P. Similar if h is lesser than sphere radius than k1 will be lesser than P. This relation has its merits but difficulties lies in determining h, l and P.
K1 = 2(h/l)P....Eq.(3.3)
In literature there are many wear equations[2], but the most popular equation is Archard`s equation(3.2). |
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| Some Guidelines based on Adhesive Wear : |
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For longer service life or reliability of devices/machines, designers always aim for mild wear regime. It means wear particle coming out from the surfaces need to be much smaller in size. For getting this conditions dissimilar metals are usually chosen to run together as they do not weld together easily. If the metals are already at their maximum hardness, as in rolling bearing steel, no further work hardening is possible, so identical metals can be used for both elements.
If severe wear behavior cannot be avoided, such as in ore processing or earth moving equipments, routine maintenance is essential. For example, outer ring of rolling element bearings, if subjected to severe wear, then it can be rotated by few degrees to avoid wear of same localized surface. Many plastics undergo a transition from mild to severe wear as a function of sliding speed (that increases temp.) or combination of sliding and contact pressure. For better life of those plastics, load & speed conditions must be closely controlled. |
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Fig. 3.11: Pin on disk arrangement. |
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| Example : To find the best material for a dry journal bearing few tests were conducted on pin on disk machines(Fig. 3.11). Disk material remained AISI 1040 steel. While pin materials were: A (225), B(30), C(50), D (70), and E (100). Numbers in bracket for materials A,B,.....E are surface hardness BHN. Find the best material for following experimental results. The wear on the pin can be measured with a toolmaker’s microscope by measuring the size of wear scar. |
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Table 3.2: Experimental data.
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As per Table 3.2, wear scar(d) is maximum for test 7(20.83 mm) and minimum for test 2(8.81 mm).
To find the best material following equation can be used.
Wear volume, V = k1 W L/3H = πd4/64R
where sliding distance, L = test duration * sliding speed. |
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 | Table 3.3
 |
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| Wear constant(K12345) for various tests has been listed in Table 3.3. The result of tests 4 & 5 are favorable therefore material B may be treated as best material. The values corresponding to material A in the table represent the transition behavior of metal(A) from mild wear to severe wear. |
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| Mild Wear : |
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In mild adhesive wear, small wear fragments (0.01 to 1 μ m) mostly of metal oxides are generated.
This kind of wear occurs at flow contact pressure (below transition limit) and sliding velocity. Formation of black powdered oxide is typical example of mild wear.
At higher velocities more oxidation replenishes losses due to break-away of oxide fragment as wear debris, therefore at higher velocities mild wear is possible.
In some cases at higher loads, a hard surface layer (most likely martensite) is formed on carbon-steel surfaces because of high flash temperatures, followed by rapid quenching as heat is conducted into underlying bulk, and mild wear in such situation is possible. In short if oxide or contamination layers remain throughout operating time, wear will be in mild regime. |
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Fig. 3.12: Mild wear. |
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| Severe Adhesive Wear : If load increases, the oxide film cracks off, exposing fresh metal which welds and wear rate may increase several hundred fold. Typical debris size range 20 to 200 μm metallic particles. |
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Fig. 3.13: Debris in severe wear. |
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| Seizure : |
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Seizure means “to bind” or “fasten together”. It is a result of mutual plastic deformation of materials and it is an extreme form of adhesive wear. Let us take example of inner ring and rollers of roller bearing, shown in Fig. 3.14. In ordinary cases after seizure, components do not get separated on their own. Manual force is required to separate the parts. In other words, after seizure tribo-pair loses its utility and cannot be used without proper reconditioning. The figure clearly demonstrate the grooves made at inner ring and loss of material from roller surfaces. The relative sliding motion between two contacting solids generally results in a loss of mechanical energy due to friction. The power dissipation associated with friction results in an increase in temperature of the sliding bodies. Causes for seizure are :
(1). Poor heat dissipation. It is related to material properties such thermal conductivity.
(2). Poor lubrication system or improper lubricant also cause seizure.
(3). Smaller clearances. It is related to improper design.
(4). Installation errors. It is related to maintenance.
(5). The ability of the metals to seize or to join in solid state. |
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Fig. 3.14: Seizure of rolling elements. |
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| In others words, excessive loading & heating govern the Seizure phenomenon. To illustrate, all wear requires wear map as shown in the Fig. 3.15, are used. The two variables bearing pressure and sliding velocity, are under the control of the operator, and are easily measured. The field boundaries are lines along which two mechanisms give the same wear-rate. The contours show the total wear rate V; it is the sum of the contributions from all the mechanisms. The thickness of oxide layer is a function of three factors, the time required to rupture the oxide layer, time available to re-oxidize and rate of formation of the oxide layer. |
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Fig. 3.15: Wear-Mechanism Map[3].
| Abrasive Wear |
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| Abrasive wear, sometimes called cutting wear, occurs when hard particles slide and roll under pressure, across the tooth surface. Hard particle sources are: dirt in the housing, sand or scale from castings, metal wear particles, and particles introduced into housing when filling with lube oil. Scratching is a form of abrasive wear, characterized by short scratch-like lines in the direction of sliding. This type of damage is usually light and can be stopped by removing the contaminants that caused it. Fig. 3.16(a) shows abrasive wear of a hardened gear. |
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Fig. 3.16: Abrasive wear of gear. | 
Fig. 3.17: Two-Body abrasion |
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Abrasive wear is caused by the passage of relatively hard particles/asperities over a surface. Following are few well-known reasons of abrasive wear mechanisms :
- Micro-cutting : sharp particle or hard asperity cuts the softer surface. Cut material is removed as wear debris.
- Micro-fracture : generally occurs in brittle, e.g. ceramic material. Fracture of the worn surface occurs due to merging of a number of smaller cracks.
- Micro fatigue : When a ductile material is abraded by a blunt particle/asperity, the worn surface is repeatedly loaded and unloaded, and failure occurs due to fatigue.
- Removal of material grains : Happens in materials (i.e. ceramics) having relatively week grain boundaries. |
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Two other mechanisms, very similar to abrasive wear are :
- Erosive wear : Impact of particles against a solid surface is known as erosive wear.
- Cavitation wear : Localized impact of fluid against a surface during the collapse of bubbles is known as cavitation wear.
Basic modes of abrasive wear are classified as two body abrasion and three body abrasion. |
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| Two – Body Abrasion : |
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| This wear mechanism happens betweent two interacting asperities in physical contact, and one of it is harder than other. Normal load causes penetration of harder asperities into softer surface thus producing plastic deformations. To slide, the material is displaced/removed from the softer surface by combined action of microploughing & micro-cutting. |
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Fig. 3.18: Three-Body abrasion |
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| “Rabinowicz’s Quantitative Law for Two-Body Abrasive Wear : |
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Assume conical asperities indenting soft surface during traverse motion(as shown in Fig. 3.16) and all the material displaced by the cone is lost as wear debris. Here basic assumptions are :
• All asperities can be represented by equal dimensions cones.
• All the material displaced by the conical asperity in a single pass is removed as wear particles. |
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Load carried by nth asperity
wn = H(0.5 * πa2)
where H is the hardness.
• Volume swept by penetrated asperity. |
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| Total wear is sum of the wear caused by individual asperity. |
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 |
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| Three Body Abrasion : |
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Three body abrasion is material removed from softer surface by hard loose particles(Fig. 3.18), which are free to roll as well as slide over the surface, since they are not held rigidly. The hard particles may be generated locally by oxidation or wear from components of tribological system. Iron oxides wear debris produced during adhesive wear cause further damage due to abrasion. Due to rolling action, abrasive wear constant is lower compared to 2-Body abrasion. Generally K2B = 0.005 to 0.05; and K3B = 0.0005 to 0.005;
From above values of wear constants, one can conclude that wear rate is lesser in three body abrasion than two body abrasion. The reduction in 3-body abrasion occurs due to energy consumed in rolling motion of free hard particles. |
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| Abrasion by Magneto-Rheological Particles : |
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Fig. 3.19: M.R.Particles. |
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M.R.Fluids are known as smart fluids, which varied viscosity due to magnetic attraction among particles. If MR particles(Fig. 3.19) are spherical and relatively smaller in size compared to available clearance then abrasion by MR particles is negligible. But larger particle size and irregular shape of particles, may wear off contacting surfaces. Therefore a good design must use spherical/regular shape of MR particles having size much smaller than provided clearance.
| Corrosive Wear |
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• Chemical reaction + Mechanical action = Corrosive wear
The fundamental cause of Corrosive wear is a chemical reaction between the material and a corroding medium which can be either a chemical reagent, reactive lubricant or even air. Understanding the mechanisms of corrosive is important to reduce this kind of wear. Let us consider a jaw coupling used for connecting shaft and motor, as shown in Fig. 3.20. This coupling is corroded, due to moist environment and its outer dimensions have increased. If we rub this coupling with fingers, brown colour debris will get detached from the coupling surface. In other words, after chemical reactions, mechanical action is essential to initiate corrosive wear. |
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Fig. 3.20: Jaw coupling. |
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Stages of corrosive wear :
• Sliding surfaces chemically interact with environment (humid/industrial vapor/acid)
• A reaction product (like oxide, chlorides, copper sulphide)
• Wearing away of reaction product film.
The most corrosion films passivate (Fig. 3.21) or cease to grow beyond a certain thickness. This is favourable as corrosion process stops its own. But most corrosion films are brittle & porous, and mechanical sliding wears away the film. The formation and subsequent loss of sacrificial (Fig. 3.22) or short life-time corrosion films is the most common form of corrosive wear. |
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Fig. 3.21: Passivation of corrosion. Fig. 3.22: Continuous corrosion. |
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| Sliding surfaces may wear by chemically reacting with the partner surface or the environment, or both. The oxide layers resulting from reactions with the environment are typically 10 microns thick, and they may have a protective role unless the thickness tends to grow during the cyclic contact process. If the oxide layer grows, it becomes liable to break in brittle fracture, producing wear particles. Hard, broken-off oxide particles may then profoundly affect subsequent wear life as abrasive agents. If soft, ductile debris results, it may form a protective layer on the surface. |
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| Erosive wear |
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Erosive wear caused by the impact of particles (solid/liquid) against a solid surface. For example dust particles impacting on gas turbine blades and slurry impacting on pump impeller. Erosive wear rate(Ve) is function of :
1. Particles velocity (K.E.)
2. Impact angle and
3. Size of abrasive.
Ve = K.A(α).(particle_vel)n.(particle_size)3.
Relationship between wear rate and impact velocity is described by a power law. Here K is an empirical constant and n is a velocity exponent.
n = 2 to 2.5 for metals.
n = 2.5 to 3 for ceramics. |
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Angle of impact decides the magnitude of transfer. Angle between eroded surface & trajectory of particle immediately before impact can range from 00 to 900.
- Low impact angle : cutting wear prevails, hardness resists wear.
- At large angle, fatigue wear prevails. Soft (ductile) material may be suitable. |
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Fig. 3.23: Impingement angle vs wear rate. |
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| If the speed is very low then stresses at impact are insufficient for plastic deformation to occur and wear proceeds by surface fatigue. When the speed is increased, it is possible for the eroded material to deform plastically on particle impact. In this regime, which is quite common for many engineering components, wear may occur by repetitive plastic deformation. If the eroding particles are blunt or spherical, thin plates of worn material form as a result of extreme plastic deformation. If the particles are sharp, cutting or brittle fragmentation prevail. Brittle materials on the other hand, wear by subsurface cracking. |
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| Example : Pneumatic Transportation : Steel pellets damage (wear out) elbow, larger speed, lower life. |
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Fig. 3.24: Pneumatic transportation. |
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| From tribological point of view, elbow must be reinforced with rubber inside the elbow to sustain the impact. |
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| Example : Engine particle (sand) separator |
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| Erosion by sand particles inside engine is a major problem. The design of helicopter engine must be modified to reduce the number of particles. |
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Fig. 3.25: Helicopter Engine. |
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| As per tribology, traveling distance of particles should be minimized. Based on this guideline modified design shown in Fig. 3.26 was proposed. |
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Fig. 3.26: Modified Engine. |
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| In new design, impacting angle is on higher side, and therefore material needs to selected accordingly. This improved design requires only 50% of the volume of the earlier design. In addition, scavenge pressure loss is reduced by 40%, which reduces wear rate. |
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| Fatigue Wear : |
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| Fatigue is attributed to multiple reversals(apply and release) of the contact stress, occurring due to cyclic loading such as in rolling bearings, gears, friction drives, cam and follower. Abrasive and Adhesive wear involve a large contribution from fatigue. Fig. 3.27 shows ‘surface fatigue’ failure of outer ring of roller bearing. At the start of bearing operation, the rolling bearings rely on smooth undamaged contacting surfaces for reliable functioning. A certain number of rolling contact cycles must elapse before surface defects are formed, and their formation is termed ‘contact fatigue’. Once the rolling surfaces of a bearing are pitted, its further use is prevented due to excessive vibration caused by pits passing through the rolling contact. |
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Fig. 3.27: Fatigue Wear. |
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Fig. 3.28: Fatigue wear during sliding. |
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| Fig. 3.28 illustrate the induced strains in top of the surface in the direction of sliding. Thickness “t” depends on the coefficient of friction. For high value of sliding of friction, material within 0.1 [mm] of the surface shifts in the direction of sliding due to deformation caused by the frictional force. Also, close to the surface the grain structure is orientated parallel to the wearing surface. Strains caused by shearing in sliding direction are present to some depth below the surface. The strain induced by sliding eventually breaks down the original grain structure at the surface to form dislocation cells. Materials vary greatly in their tendency to form dislocation cells. For example, aluminium, copper and iron have a high tendency to form dislocation cells. These dislocation cells are probable regions for void formation and crack nucleation. A primary crack originates at the surface at some weak point and propagates downward along weak planes such as slip planes or dislocation cell boundaries as shown in Fig. 3.29. When the developing crack reaches the surface, a wear particle is released. |
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Fig. 3.29: Mechanism of fatigue wear. |
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| In other words, pure materials (without any inclusions in it) may exhibit high service life. It was found that pure copper (99.96% purity) sliding against steel gives a wear rate ten times lower than any other material despite exhibiting the highest coefficient of friction of all the materials tested. On the other hand, a steel rich in carbide particles shows a low coefficient of friction and gives one of the highest wear rates. The wear rate was found to increase with inclusion density in the material, while friction was determined by adhesion factors so that complex impure materials exhibited the lowest friction coefficient. |
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| Fatigue Wear during Rolling : |
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During rolling, the local contact stresses are very high, which are concentrated over a small area and are repetitive. Such loading occurs in rolling bearings, gears, friction drives, cams and followers, etc. Steps leading to generation of wear particles are :
• Application of normal load that induce stresses at contact points.
• Growth of plastic deformation per cycle.
• Subsurface crack nucleation.
• Expansion of crack due to reversal of stress.
• Extension of crack to the surface due to traction force.
• Generation of wear particles. |
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| Cracking : |
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| Cracking is ultimate failure to split the component. In other words cracking results in complete failure of the component. Causes for cracking are excessive load with vibration, loose fit and excessive impact. To reduce cracking the correction of fits and vibration isolation are fool proof methods. |
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Fig. 3.30: Cracking.
| Fretting Wear |
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| Fretting Wear coined in 1927 by Tomlinson. It refers to small amplitude(1 to 300 μm), with high frequency oscillatory movement mainly originated by vibration. This generally occurs in mechanical assemblies (press fit parts, rivet / bolt joints, strands of wire ropes, rolling element bearings), in which relative sliding on micron level is allowed. It is very difficult to eliminate such movements and the result is fretting. Fretting wear and fretting fatigue are present in almost all machinery and are the cause of total failure of some otherwise robust components. |
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Fig. 3.32: Fretting wear. |
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| Fretting occurs wherever short amplitude reciprocating sliding between contacting surfaces(Fig. 3.32) is sustained for a large number of cycles. The centre(Fig. 3.32) of the contact may remain stationary while the edges reciprocate with an amplitude of the order of 1 micron to cause fretting damage. One of the characteristic features of fretting is that the produced wear debris is often retained within the contact due to small amplitude sliding. The accumulating wear debris gradually separates both surfaces(Fig. 3.33) and, in some cases, may contribute to the acceleration of the wear process by abrasion. The process of fretting wear can be further accelerated by temperature. Reciprocating movements as short as 0.1 micron in amplitude can cause failure of the component when the sliding is maintained for one million cycles or more. |
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Fig. 3.33: Process of Fretting wear. |
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| More details related to fretting wear is described by Waterhouse[1]. |
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| References : |
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1. Archard J F and Hirst W, The Wear of Metals under Unlubricated Conditions, Proc. R. Soc., London, A 236, 397-410, 1956.
2. Ludema K C, Friction, Wear, Lubrication: A textbook in Tribology, CRC Press, 2010.
3. Lim S C and Ashby M F, Wear Mechanism Maps, Acta Metall., Vol. 35 (1), 1-24, 1987.
4 NPTEL http://www.nptel.ac.in/courses/112102015/12 |
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