Tribo Notes

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4.1. Introduction: Wear is defined as the gradual loss of material from the interacting surfaces during the relative motion under the normal load. Wear is classified as mild wear and severe wear. Mild wear is therefore generally associated with low loads where metallic interactions are somewhat inhibited and the wear debris consists of fine particles and is usually in the form of oxides. This does not imply that metallic contacts hav e never occur red at al l, si nce the result ing metallic debris would tend to become oxidized at the high local temperature at the interface. Nevertheless the nature of the surf ace as pe ri ty in te ra ct io n is re la ti ve ly ge nt le , resulting in characteristically mild wear and smoothing of the surfaces.
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    4.1. Introduction:

    Wear is defined as the gradual loss of material from

    the interacting surfaces during the relative motion under the

    normal load. Wear is classified as mild wear and severe

    wear. Mild wear is therefore generally associated with lowloads where metallic interactions are somewhat inhibited

    and the wear debris consists of fine particles and is usually

    in the form of oxides. This does not imply that metallic

    contacts have never occurred at all, since the resulting

    metallic debris would tend to become oxidized at the high

    local temperature at the interface. Nevertheless the nature

    of the surface asperity interaction is relatively gentle,

    resulting in characteristically mild wear and smoothing of

    the surfaces.

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    Fig. 4.1 The transition phenomena in wear

    At higher load a much coarser wear process occurs.

    The wear debris is of a much larger particle-size, the worn

    surfaces are much rougher and the increase in volume

    changes the wear rate by several orders of magnitude. This

    is the so-called severe wear regime. A starting fact about

    these two types of wear behavior is the very rapid transition

    from one mode to the other as the load is increased (fig.

    4.1). In this figure it should be noted that the wear rate

    suddenly changes by more than one hundred times. With

    some materials at even higher loads the increasing

    temperatures cause metallurgical changes in the materials

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    such as to increase their inherent hardness. These effects

    can then lead to a second transition from the severe wear

    back to the mild wear regime.

    4.2. Mechanisms of Wear:

    We now consider the detailed mechanisms by which

    material may be removed from the surface. The most

    common mechanisms are:(a) Adhesive wear, (d) Corrosive wear.

    (b) Abrasive wear, (e) Erosive wear

    (c) Fatigue wear

    In some situations more than one of these mechanisms

    may be operative at the same time, and this is one of the

    reasons for the complexity of wear studies.

    4.2.1. Adhesive Wear:

    When the two surfaces are having identical hardness

    then the contact between surfaces occurs at the tips of the

    asperities, which then deform under load. Tile nature of the

    adhesion between such asperity interactions is modified by

    surface films so that the metallic adhesion characterized in

    the simple friction theory is somewhat modified. But as

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    translation occurs these surface films are to some extent

    disrupted and adhesion will occur at a certain proportion of

    these contact, as can be appreciated in view of thedistribution of asperity heights discussed in chapter 2.

    From these considerations and our knowledge of the

    nature of the contact of rough surfaces we can now predict

    a wear equation, If one assumes that the wear particles are

    geometrically similar, the wear volume would be expectedto be proportional to the real areas of contact at which

    adhesion occurs, and also to the distance of sliding. Since

    the real area of contact for the plastic interaction of

    asperities is given by

    A = W / H

    The wear volume V is given by

    V A x L W x L

    H

    Where L is the distance of s\liding. Thus the adhesive wear

    law becomes WV = K W x L

    H

    Or in words the: laws of adhesive wear are:

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    (a) The volume of Wear is proportional to the distance

    of sliding. This relationship has been justified by

    experience for a wide range of conditions.(b) The volume of wear is proportional to the applied

    load. This has also been shown to be true in many tests for

    limited ranges of load, although as wear mechanisms

    change with increasing load some abrupt transitions have

    been observed; see fig. 4.1.(c) The volume of wear is inversely proportional to the

    hardness of the softer material. This has also been shown to

    be valid, particularly for pure metals.

    Recalling the physical nature of the wear process

    arising from adhesion we can give a physical meaning to

    the constant of proportionality K. often called the adhesive

    wear coefficient or the Archard constant. Surface films

    together with the asperity contact forms the adhesive

    contacts are only significant on adhesive wear. Since

    shearing due to sliding probably formed where the

    junctions are stronger than the underlying material, So that

    some material from the surfaces is torn away and

    eventually released by the continued sliding. So we can see

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    that K may be probability factor, that is, the factor which

    indicates the probability of wear particles being created by

    the adhesive effect between the populations of asperities onthe two rubbing surfaces.

    Fig. 42 Surface contact of an identical

    hemispherical asperity

    Theory of Adhesive Wear:

    Consider two surfaces of an identical material having

    the same hardness. Assume that the asperities on both the

    surfaces are identical. In nature of such surfaces are in

    contact then the deformed area of the asperities is a circular

    area of radius 'a' under the application of load W.

    Consider anyone asperity in contact when the asperity

    is in relative motion the function of asperity will be shear

    from the weaker bond of the asperity. Let the load carried

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    by anyone asperity is W1 = W/n where n is the total

    numbers of asperities in contact.

    Let the particle separate out from such asperity is of ahemispherical in shape having a radius, a

    The volume of material in dist. is vol. of sphere V/2 =

    2/3 r3.

    V1 = (4/3 a3) / 2 ( = 2a)X X

    V1 = 1 = 1/3 a2 = 1/3 A1

    X 3

    Since a2 is the area of contact, where is proportional to the

    ratio W1/H.

    Where H = hardness of material.

    A1 W1

    But A = A1 + A2 + + An

    W = W1 + W2 + + Wn

    & also

    A1 = A2 = A1 = = An for similar shape of

    asperity

    W1 = W2 = W1 = = Wn

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    A = n A1

    W = n W1

    A1 = A / n W1 = W / n

    A W

    The total volume of wear from the surface, if all the

    asperities are effective in removing the material then.

    V = n V1

    V1 = 1 A1 = 1 W1

    X 3 3 H

    Therefore volume of wear for displacement is

    V1 = 1 W1X3 H

    V = n V1

    = n . 1 W1X But nW1 = WT = W

    3 H

    V = W X

    3 H

    If wear constant Kadh can be introduced for considering

    the actual numbers of the asperity in contact.

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    V= Kadh. W / 3H.

    Kadh = 1, When all asperities in contact are effective in

    wear= 0.1, When out of 1000 asperities 100 asperities

    are effective in wear

    = 0.01, When out of 1000 asperities 10 asperities

    are effective in wear.

    Also,= u . t

    = DN /60 . t

    4.2.2. Abrasive Wear:

    This type of wear arises from the cuttion acting of

    hard surface rubbing on softer materials, as for example,

    when hard surface asperities act rather like cutting tools

    and remove material from softer materials. Another

    example arises when loose debris of any kind is trapped

    between sliding surfaces. Such debris may be extraneous,

    such as sand particles, or may be the actual wear particles

    created by the primary wear process.

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    One method of reducing the first type of abrasive wear

    is to ensure high quality of surface finish of the mating

    surfaces particularly the hard surface. With modern production methods this type of wear is no longer as

    serious problem. The second type of abrasive wear is more

    difficult to eliminate. Suitable sealing and filtration can

    reduce correct design of the contact geometry. It is often

    desirable to provide grooves or other such recesses on thesurfaces of bearings, which allow the debris to escape

    from the contact geometry.

    Fig. 4.3 Wear due to a single conical asperity

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    Fig. 4.4 Abrasive wear due to Which Olly

    Consider two dissimilar surface materials in contactand is in relative motion. Assume that the hard surface

    asperities remove the material from relatively soft material

    surface.

    Let the hard surface asperities are of conical in shape

    having radius a at the contact and height h at the

    penetration in soft material. The asperity angle is ,

    consider anyone such asperity for analysis the volume of

    material to be removed from soft material in distance x is

    V = The projected area of conical asperity in the

    direction of motion x distance x.

    = x 2a x h x X but h = a. tan

    V = a . a tan . x

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    = a2 tan . x

    For plastic deformation of material

    W A ( area of contact)

    = A . H

    i.e. W = A . H = A . H/3

    The area of contact in the direction of a normal load is A =

    a2 / 2

    W = a2 / 2 . H

    a2 = 2W / H

    Substituting value of a2 in equation of volume

    V = a2 tan . X

    Vabr = 2W tan . X

    H

    Here Kabr = X tan = 6 tan

    Vabr = Kabr. W.XH

    Where Vadh = 1/3 W.X . KadhH

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    Vw = Vadh + Vabr = Kadh W.X + Kabr+ W.X

    3 H H

    V = Kw. W.X

    H

    Where Kw = Kabr + Kadh /3

    In all practical cases the wear occurs due to the

    abrasive and adhesive wear. Therefore the general equation

    of wear can be given as

    Vw = Kw. W.XH

    4.2.3. Fatigue Wear:

    It is well known that if materials are loaded and

    unloaded cyclically they exhibit fatigue failure. This type

    of failure can occur after large number of loading cycles,

    even though the load is less than that which we could

    normally expect to produce failure in a single load

    application. It is usual to express such behavior bay

    logarithmic graph of stress S against the number N of

    cycles to failure (the S/N curve, as it is usually called) such

    as fig. 4.5. Here we see that the lower the applied cyclical

    stress have the longer the life of the material.

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    Fig. 4.5 A typical S-N fatigue curve

    Fig. 4.5 shows a typical S-N fatigue curve. If we

    consider the interaction of asperities during the sliding of

    one surface over another we can see the possibility of

    fatigue mechanisms being broken off the asperities to

    produce wear debris. A simple experiment to illustrate this

    is to run one's finger a many times along the teeth of a

    comb. The teeth (asperities) are continuously being loaded

    and unloaded due to repeated traversals by ones finger and

    after many cycles they ultimately break due to fatigue.

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    4.2.4. Corrosive Wear:

    Any clean metal surface reacts with its environment to

    form contaminant films, and the rate of formation of suchmm is initially very rapid but decreases as the corrosive

    film thickens. In many instances, such as oxide (rust) films

    on steel, these surface films adhere only loosely to the

    surface. Rubbing therefore removes the films leaving

    exposed clean metal, which immediately reacts with itsenvironment to provide new surface films, which are again

    removed during ragging. So materials continuously bang

    removed from the surface, and wear is taking place. The

    chemistry of such reaction is beyond the scope of this book,

    but fortunately is not needed for the understanding of the

    basic mechanism.

    A further effect of corrosive environments is to

    enhance the abrasive action of wear debris. Most metal

    oxides are harder than the metal itself sot that if metal

    debris is created, this becomes oxidized and gives a rate of

    abrasion greater than that which would otherwise occur. A

    good example of this occurs with relatively soft aluminum,

    where the oxidized wear debris is very hard abrasive.

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    Indeed aluminum oxide is often used as the cutting agent in

    girding wheels and the like.

    Corrosive effects are not entirely deleterious. In thechapter on friction it has already been shown that the

    presence of oxide films in preventing metal-to-metal

    contact greatly reduces the coefficient of friction. In other

    applications surface films are deliberately produced to

    avoid metallic contact. The so-called E.P. (extremepressure) additives to lubricating oil produce surface films

    such as chlorides and sulphides and provide protective

    surface layers. In a sense these could be more properly be

    called extreme temperature films rather than extreme

    pressure films. Their main characteristic is that chemical

    stability at the high temperatures of the high pressure

    contacts in such situations as hypoid gears as used in motor

    car back axles.

    4.2.5. Erossive Wear:

    Erossive wear is mainly because of the erossion which

    is a combined effect of mechanical stresses under the

    ambient condition for example the wear on the bearing

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    surface of a concrete mixture operated in an open

    atmosphere.

    4.2.6. Fretting:

    This is not really a separate mechanism of wear but it

    is treated separately because it arises in rather special

    circumstances. It shows one particular wear process may be

    a complicated combination of several mechanisms of wear,and also demonstrates the deleterious effects of any wear

    debris which may become trapped in the contact system.

    Fretting effects are associated with the contact of surfaces

    in which the sliding motion is an oscillation of relatively

    small amplitude, often only a few micrometers. Since

    vibrations occur in virtually all machines we find fretting

    occurring between surfaces in contact such as bolted

    components, splines and components located by friction

    rise to small amplitude oscillatory displacements between

    the surfaces in contact.

    4.3. Tribological Properfies of Plastics:

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    In recent years there has been a significant growth in

    the use of plastics to replace metals in many bearing

    applications. In general the friction and wear of plastics canbe explained by the adhesion theories already discussed.

    The friction coefficients of plastics are not particularly low,

    but their main advantage is that they wear at reasonably

    low and predictable rates. One notable exception to this

    behavior is PTFE (polytetrafluoroethylene) whose frictioncoefficient may be very low, about 0.05. This very low

    friction value seems to be associated with the very low

    adhesion of this material, because of this it is used in non-

    stick kitchenware. It is also reasonably hard due to the

    mechanical interlocking of its molecules. So it is

    extensively used in bearings, where the loads and speeds

    are moddest, sine its is almost self-lubricating and is highly

    reliable.

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    Fig. 4.6.The change in dimension due to wear.

    A useful design parameter for all trips of plastics used

    in bearings is the pv factor (which is the product of thenominal contact pressure and the sliding speed.).

    Consider a block of this material sliding on a metal

    surface, fig. 4.6. The rate of energy dissipation against

    friction is Wv. It is reasonable to assume that the volume

    wear rate of the block. V = dV / dt, is proportional to this

    rate of energy dissipation, so

    V Wv.

    The block will therefore wear to a depth d such that

    the volume wear V is given by

    V= Ad.

    Hence its rate

    V= Ad.

    Where d is the rate of increase of d with time. Thus

    d = V Wv

    A AThis shows that the rate of change of dimension of the

    block is proportional to the product Pv. This is the rate of

    change of bearing clearance with time in any practical

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    application and as such as in more useful parameter than

    the actual volume of material removed.

    For any material the allowable value of the pv productmay be defined and fig. 2.7 shows a typical result of PTFE

    if the wear rate is to be a dimensional change of 25 mm in

    100 hours.

    Plastic bearings and particularly PTFE bearings must

    be operated within their approved pv ratings. These ratingsare associated with wear and are particularly subject of

    thermal effects due to the decomposition of the surface.

    Thus at their ambient temperatures the pv factor for such

    materials is considerably reduced. Such materials when

    used in practical bearing designs are often associated with a

    metallic matrix which provides additional strength and

    improves the thermal conductivity thus allowing the easier

    escape of the heat generated in rubbing. When plastics

    slide, problem can arise from the generation of electrostatic

    charges. In such 10 situations, designers must incorporate

    earth paths to minimize the build-up of charges.

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    Fig. 4.7 A typical 'pv' curve

    4.4. The Measurement of Wear:

    In most engineering machinery the rate of wear is

    relatively small, typically changes in dimensions of

    micrometers per year. Also wear takes place in real time

    and laboratory tests aye to devise conditions where the

    wear processes are considerably accelerated so that results

    are produced in days rather than years. In so far as such

    tests are artificially accelerated their results should viewed

    with some caution.

    4.4.1. High-Pressure Contact Tests:

    These tests produce accelerated results by applying

    loads over very small areas of contact. Various geometrical

    arrangements are used as shown in fig. 4.8. In each of these

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    tests specimen A is the material being worn away, the

    degree of wear being measured by either a change in

    dimensions or a loss of mass from the material., Many suchmachines also measure the frictional force at the contact.

    Fig. 4.8 Pin on Ring

    Fig. 4.9 Pin on Disc

    Such contact geometries can be studied either in the

    ordinary atmosphere or in a totally enclosed chamber where

    the atmosphere may be controlled, as to such properties as

    the gaseous environment, pressure, temperature and

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    humidity. A very common form of such apparatus is

    designed to carry out these tests at various reduced

    pressures. In a high vacuum the formation of oxide films isinhibited, so we obtain useful information on the friction

    and wear of the materials themselves. UHV apparatus is

    also useful for measuring the adhesion between surfaces in

    contact, and we have already seen that such information is

    very valuable to our understanding of friction.

    Fig. 4.10 A simple crossed cylinder wear machine

    More complex geometrical arrangements are shown in

    fig. 4.11. The Fig. 4.11 (a) shows the four-ball arrangement

    in which a rotating ball rubs against three stationary balls to

    produce wear scars whose size is an indication of the

    volume wear. This arrangement is extremely popular for

    industrial testing since the test specimens, the balls, are

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    readily available at low cost from ball bearing

    manufacturers. Fig. 4.11(b) shows the so-called disc

    machine which is very useful for the study of wear undercombinations of rolling and sliding. When the peripheral

    speed of both discs is the same one has pure rolling whilst a

    difference in speeds implies some additional sliding. This

    rather complex roll/ slide process often occurs in

    machinery, perhaps the best example being the contactbetween meshing gear teeth depicted in fig. 4.12. At the

    initial contact we have rolling and sliding between the teeth

    which becomes pure rolling at the pitch point B followed

    by rolling with sliding in the opposite sense during the arc

    of disengagement.

    Fig. 4.11 The four ball wear machine and disc on disc

    wear machine

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    A. Initial contact - rolling and sliding

    B. Pitch point contact-pure rolling

    C. Final contact-rolling and sliding

    Fig. 4.12 The progress of contact between gear teeth

    ( Solved Problems )

    EX.1. A pin on disc experiment the rate of vol. of wear

    observed was 0.1 mm3/min. Pin was placed at 30 mm

    radial distance from the centre of disc. The disc was

    rotated at 500 rpm. Load on pin is 20 N. Material of pin

    is brass, hardness is 120 N/mm2. Material of disc is steel,

    hardness 280 N/mm2. Determine the wear constant.

    Solution :

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    Data given:

    V = 0.1 mm3/min

    r = 30mmN = 500 rpm

    W = 20N

    Hp (pin) = 120 N/mm2

    Hd (disc) = 280 N/mm2

    V = Kw. W.2 rNt

    Hp

    V / t = Wear rate = 0.1 = Kw. 20 x 2 x x 30 x 500

    120

    Kw = 6.3662 x 10-6

    Ex.2. Determine the wear constant Kw by using a pin on

    disc wear measuring test ring. The testing data are as

    follows:

    (1) Pin diameter at the tip 3.0 mm.

    (2) The maximum diameter of the conical pin =

    10.0 mm

    (3) The cone height of the pin is = 9.0 mm.

    (4) Load on the pin = 50 N

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    (5) The disc diameter = 150 mm.

    (6) The pitch radius at pin contact = 60 mm.

    (7) r.p.m. of the disc. = 600.(8) The hardness of the pin = 20 N/mm2.

    If the experiment is conducted for 130 hours. The

    wear reading show the linear in unit of the wear

    volume. The final diameter of the pin was 8.0 mm. The

    material of the pin is brass and the material of the discis hardened steel. .

    If the above tested material is required to use in a

    machine for shaft and bearing. Determine the life of the

    bearing for a shaft rotating at 140 r.p.m. under a load of

    10N. The bearing diameter is 40mm. The maximum

    allowable radial wear is 1.0 mm. The length to diameter

    ratio of the bearing is 1.0.

    Solution:

    tan = (d2 d1)/2

    r= (10 3)/2 = 0.3888

    9

    = 21.25

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    Kw = 5 (dt3 d1

    3)H

    4 tan W.R.N.T

    t in sec:

    Time require = 130 hours

    = 130 x 60 x 60 secs.

    t = 468000 secs.

    Kw = 5 (83 33)20

    4 tan 2125 50 x 60 x 600 x 468000

    = 3.7013 x 10-8

    Ans = I

    Now N = 140 rpm

    Kw = 3.7013 x 10-8

    W = 10 N

    D = 40 mm

    L = 40 mm

    rw = 1.0 mm

    Life of the bearings t = (D) . rw. L . H

    Kw.W.DN/60

    = (40) x 1.0 x 40.20 x 603.7013 x 10-8 x 10 x x 40 x 140

    = 1.47428 x 108 sec. x 2

    = 40952.135 hours x 2

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    = 81904.3 hours.

    Ex.3. In an experiment of wear with the plastic bearing

    it is found that for the change in dimension of 0.1 mmunder the load of 1.5 N in a slender bearing. The

    velocity required is m/sec. For the same operating

    conditions, if the load and speed are doubled than what

    will be the change of dimensions?

    Data given:dt = 0.1 mm

    W = 1.5 N

    u = 1 m/sec.

    dd1 = W1 u ,

    dt1 A1

    &

    dd2 = W2 u2

    dt2 A2

    But

    A1 = A2

    W2 = 2 W1

    u2 = 2 W

    dt1 = dt2

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    dd2 = P2 u2dd1 P1 u1

    dd2 = 2.2

    0.1

    dd2 = 0.4 mm

    For the same operating conditions change of

    dimension is 0.4 mm if load & pressure both (velocity) are

    doubled.

    Ex.4. In a crossed cylinder wear measuring experiment

    the stationary specimen is brass in contact with a

    rotating cylinder made all of hardened cylinder having

    radius 50 mm and thickness 25 mm. is rotating at 500

    rpm. The rate of Wear was observed to be constant is

    found 2mm in 60 hours of a constant operation under a

    50 N load.

    Determine the wear const. if the hardness of brass

    is 120 N/mm2

    Solution:

    Data given:

    H = 120 N/mm2

    W = 50 N

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    R = 50 mm

    L = 25 mm

    N = 500 rpmt = 60 hours

    h = rw = 2 mm

    cos = R-h = 50.2 = 0.96

    R 50

    = 16.26

    Kw = R2 ( sin 2 / 2) L H

    W ( D N / 60) t

    t = 60 x 3600 secs.

    Kw = 502 [16.26 x /180 sin {(2 x 16.26 )/ 2}] 25 x

    120

    50 x [( x100 x 500)/ 60] x 60 x 3600

    = 3.977 x 10-6 Ans.

    Ex.5. A 30 mm long brass bearing is used to support a

    steel shaft having 50 mm diameter, and a steady radial

    load of 60 N. Shaft is rotating at 500 rpm. Shaft surface

    is having an average asperity angle 10. The hardness of

    the bearing material is 200 N/mm2. Determine the time

    required to exceed the radial wear 2 mm.

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    Solution:

    Data given:

    rw = 2 mmL = 30 mm

    D = 50 mm

    W = 60 N

    N = 500 rpm

    = 10.

    H = 200 N/mm2

    (Questions)

    1. Write short notes on the following:

    (i) Fatigue wear

    (ii) Pin on disc wear measurement.

    2. Explain cross cylinder wear machine.

    Define Wear. State the condition where wear proved

    to be boneficial.

    3. In pure abrasion wear, show that the wear quantity6 W.X

    V = 6 tan WX

    H

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    Where = average asperity angle.

    W = applied load.

    X = sliding distance.H = Hardness of material

    4. Explain four ball Wear machine.

    5. Classify the wear mechanisms. Explain the methods to

    eliminate the wear, of each mechanism.

    6. Define fatigue Wear.

    7. State the mechanisms of wear. Describe the methods to

    eliminate wear.

    8. Show that the change in dimension due to wear for the

    case of plastic - metal contact is proportional to the

    product of pressure and the relative velocity of the

    contact surfaces.

    9. Define abrasive wear.

    10. Define wear. Why do you consider that wear is

    beneficial in running in and planned obsolescence?

    11. Explain elimination of wear.

    12. Show that the volume of wear due to adhesion and

    abrasion is

    Vw = Kw W.x

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    H

    Where Kw = wear constant.

    13. A steel shaft runs within PTFE bearing at 10 m/sec.After 1000 operating hours the bearings were warn 2 mm

    radially. Find out the load on each bearing if the contact

    area of each bearing is 0.01 m2. The wear constant may

    be taken as 10-21 m2/N.

    Suggest the various possibilities to improve theperformance of such bearing.

    14. In a cross cylinder wear measuring experiment the

    stationary specimen is brass in contact with a rotating

    cylinder made out of hard steel; having radius 50 mm

    and thickness 40 mm is rotating at 960 rpm. The size of

    the stationary specimen is 100 mm length, 25 mm width

    and 25 mm height. The rate of wear was observed to be

    constant, 100 N load. Find out the wear constant Kw.

    If above tested material is required to use in a machine

    for shaft and bearing. Determine the life of the bearing

    for a shaft rotating at 250 rpm under load of 25 N. The

    maximum allowable radial wear is 0.5 mm and length of

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    the bearing is 75 mm. Take hardness of the brass = 120

    N/mm2.

    15. Show that the life of a sleeve bearing due to abrasivewear is

    L = b.l.H hrs.

    1800 kwWw

    Where b is the permissible radial wear of sleeve bearing

    l is the length of the sleeve bearing, m

    H is the hardness of sleeve bearing, N/m2.

    hw is the wear coefficient.

    W is the radial load, N

    is the angular velocity rad/sec.

    16. In an experiment on a pin-on-disc test rig the

    following observation were made:

    (i) Diameter of the pin and its material: 10 mm, Brass

    (ii) The pitch diameter of the disc and its material: 120

    mm Brass.

    (iii) The change in length of the cylindrical pin due towear in 150 hours: 5 mm

    (iv) The rotational speed of the disc is: 500 rpm.

    (v) The hardness of the pin is: 20 N/mm2

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    (vi) Load on pin is: 200 N.

    If the above tested material is to be used in a machine for

    shaft and bearing, determine the life of the brass bearingfor a steel shaft rotating at 150 rpm. under load of 50N.

    The permissible radial wear is 1.0 mm. The length/

    diameter ratio of the bearing is 1.0. The length of the

    bearing 50 mm.

    17. In a pin on disc experiment, the test piece pin was madeout of brass and disc was made out of stainless steel. The

    pin was located at 50 mm radial distance from the disc

    centre. The asperity angle on the disc surface was 3.

    The power required to rotate the disc at constant speed

    960 rpm was 500 watts. The testing data are as follows:

    Pin diameter at tip = 3.0 mm

    The maximum diameter of conical pin = 12.0 mm

    The cone height of pin = 12.0 mm.

    The hardness of pin material = 20 N/mm2

    The wear constant = 3.0 x 10-8.

    The wear reading shows the linear increment of the wear

    volume. Determine the time required for the experiment

    of wear if the final tip diameter of the pin is 10.0 mm.

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