Engineering Tribology Episode 2 Part 5 ppt

The maximum contact temperature has therefore two components: the bulk temperature of the contacting solids and the maximum flash temperature rise, i.e.: where: T c is the maximum surfa

scar does not occur, i.e wear scar remains parallel to the worn surface The ‘tilt’ is also notobserved for very smooth surfaces The amount of wear that produces this ‘tilt’ is limited to adepth which is approximately equal to the original surface roughness At high levels ofsurface roughness, the EHL film sustains a reduction in minimum film thickness and ‘tilt’formation is obscured or prevented by rapid wear of the contact [70].

Cavity collapse and

expulsion of lubricant

Cavities filled with lubricant

remaining after solid-to-solid contact

Undeformed

surface

Solid-to-solid contact Lubricant film maintained byflow from adjacent cavities

FIGURE 7.24 Effect of roughness and asperity shape on survival of EHL films

b

FIGURE 7.25 Surface texture of the contacting surfaces; b is the semiaxis of the contact ellipse

in the direction of motion

The size of an asperity or a protuberance from the surface has a strong influence on the loadrequired for plastic deformation In simple terms, when an asperity becomes smaller, itscorresponding radius of curvature must also be reduced whatever the shape of the asperity.Applying the Hertzian theory of contact stresses, the load required to generate a constantstress in an asperity declines sharply with diminished radius of curvature For a surfacecomposed of asperities with a range of radii of curvature, a combined occurrence of limitedelastic deformation and severe plastic deformation is possible Returning to the concept ofsurface wavelength, an approximate proportionality between surface wavelength and radius

of curvature can be assumed and this observation was developed further in Sayles model as

is described below

The wavelengths smaller than the contact width constitute the surface features that can bedeformed elastically, while the fine surface texture forms the smaller features which can be

deformed plastically or even partially removed during metal-to-metal contact It is thoughtthat the elastic deformation of surface features forces them to conform to the opposingsurface and allows full EHL or micro-EHL lubrication to prevail despite the low λ values, e.g.

λ ≈ 1 Experiments conducted on an optical interferometry rig seem to confirm this theory[34] Studies of contacts generated between a glass disc and a steel ball deliberately roughened

by laser irradiation revealed that the elastic deformations taking place between the wavefeatures, which were smaller then the width of the contact, seemed to play a major role ininhibiting the metal-to-metal contacts under EHL conditions In such cases it is plausible thatmicro-EHL functions between these elastically deforming surface features The directionality

of roughness is also significant [35] Micro-EHL is favoured by alignment of the grooves or

‘lay’ of a surface roughness normal to the direction of rolling or sliding since thisarrangement creates a series of microscopic wedges It was also found that lubricating oilscontaining additives in high concentrations, such as ZnDDP, tend to influence the measuredEHL film thickness ZnDDP, in particular, was found to increase film thickness at low rollingspeeds where it is believed there is sufficient time between successive contacts for aprotective film to form on the worn surface [71]

The possible mechanism of micro-EHL is shown in Figure 7.26 where the asperities areseparated by transient squeeze films The high viscosity of oil in an EHL contact wouldensure that such squeeze forces are large enough to deform and flatten the asperities

Macroscopic value of hydrodynamic pressure

Micro-EHL pressure fields

Apparent squeeze

Apparent squeeze

Local EHL constriction

Local EHL constriction Rolling

Rolling

Undeformed

asperity

shape

FIGURE 7.26 Mechanism of micro-elastohydrodynamic lubrication

There are many different models of the micro-elastohydrodynamic lubrication regime [e.g.36-40] in which the lubrication film between a single asperity and a smooth surface in rolling,sliding and even collision between the asperities is considered

An example of such analysis is shown in the work of Houpert and Hamrock [41] where theproblem of a single asperity (surface bump) of approximately half the Hertzian contact width,passing through a rolling-sliding line contact was considered The results of the numericalsimulation are shown in Figure 7.27 It can be seen that under very high pressures, the shape

of the bump and the pressure profile change A large pressure spike is formed on the bumptraversing the contact

When the surface is covered with a series of small bumps and other imperfections there will

be a number of corresponding pressure peaks superimposed on the smooth macroscopicpressure distribution as these surface features pass through the contact representing the

micro-EHL pressure disturbances The size of these pressure peaks depends on the asperitywavelength and height Studies of the elastohydrodynamic lubrication of surfaces with suchwavy features seem to indicate that such pressure ripples can indeed develop on a nominallysmooth elastohydrodynamic pressure distribution [11,42] If the local pressure variation issufficiently large then elastic asperity deformation takes place and the micro-elastohydrodynamic lubricating films are generated inhibiting contact between the asperities.The generated local pressures can significantly affect the stress distribution underneath thedeforming asperities which can influence wear (i.e contact fatigue) It was found that underpractical loads the localized stress directly under the surface defect can often exceed the yieldstress of the material [11,43].

x b

x=

p

p max

0 0.5 1.0 1.5

Profile with bump Profile without bump

Undeformed bump

FIGURE 7.27 Pressure distribution and surface deformation of a single asperity passing

through the EHL contact, where W = 2.5 × 10-5, U = 1.3 × 10-11, G = 8000, slide to roll ratio U 2 /U 1 - 1 = 10, depth of the bump 1 [µm], width of the bump 0.5 [µm]

[41]

The phenomenon of micro-EHL is a very important research topic of many current andfuture studies The development of an accurate model of micro-EHL is fundamental totribology since it relates to the lubrication of real, rough surfaces

7.6 SURFACE TEMPERATURE AT THE CONJUNCTION BETWEEN CONTACTING SOLIDS AND ITS EFFECT ON EHL

Surface temperature has a strong effect on EHL, as is the case with hydrodynamic lubrication.Elevated temperatures lower the lubricating oil viscosity and usually decrease the pressure-viscosity coefficient ‘α’ A reduction in either of these parameters will reduce the EHL filmthickness which may cause lubricant failure Excessively high temperatures may alsointerfere with some auxiliary mechanisms of lubrication necessary for the stable functioning

of partial EHL Lubrication mechanisms auxiliary to partial EHL involve monomolecularfilms and are discussed in Chapter 8 on ‘Boundary and Extreme Pressure Lubrication’ Themaximum contact temperature is of particular engineering interest especially in predictingproblems associated with excessive surface temperatures which may lead to transitions in thelubrication mechanisms, changes in the wear rates through structural changes in the surfacelayers, and the consequent failure of the machinery

Calculation of Surface Conjunction Temperature

EHL is almost always found in concentrated contacts and in order to estimate thetemperature rise during sliding contact, it is convenient to model the contact as a point orlocalized source of heat as a first approximation In more detailed work, the variation oftemperature within the contact is also considered, but this is essentially a refinement only.Since the intense release of frictional heat occurs over the small area of a concentratedcontact, the resulting frictional temperatures within the contact are high, even when outsidetemperatures are close to ambient

The temperatures at the interface between contacting and mutually sliding solids is known

as the ‘surface conjunction temperature’ It is possible to calculate this temperature by

applying the laws of energy conservation and heat transfer Most of the energy dissipatedduring the process of friction is converted into heat, resulting in a significant local surfacetemperature rise For any specific part of the sliding surface, frictional temperature rises are

of very short duration and the temperatures generated are called ‘flash temperatures’ From

the engineering view point it is important to know the expected values of thesetemperatures since they can severely affect not only EHL but also wear and dry frictionthrough the formation of oxides, production of metallurgically transformed surface layers,alteration of local geometry caused by thermal expansion effects, or even surface melting [44]

As well as the transient ‘flash temperatures’ there is also a steady state ‘flash temperature rise’ at the sliding contact When the contact is efficiently lubricated, the transient flash

temperatures are relatively small and are superimposed on a large, steady-state temperaturepeak In dry friction, or where lubrication failure is imminent, the transient flashtemperatures may become larger than the steady-state component [45]

The flash temperature theory was originally formulated by Blok in 1937 [46] and developedfurther by Jaeger in 1944 [47] and Archard in 1958 [48] The theory provides a set of formulaefor the calculation of flash temperature for various velocity ranges and contact geometries.According to Blok, Jaeger and Archard's theory, the flash temperature is the temperature rise

above the temperature of the solids entering the contact which is called the ‘b u l k temperature’ The maximum contact temperature has therefore two components: the bulk

temperature of the contacting solids and the maximum flash temperature rise, i.e.:

where:

T c is the maximum surface contact temperature [°C];

T b is the bulk temperature of the contacting solids before entering the contact [°C];

T fmax is the maximum flash temperature [°C]

Evaluation of the flash temperature is basically a heat transfer problem where the frictionalheat generated in the contact is modelled as a heat source moving over the surface [46,47].The following simplifying assumptions are made for the analysis:

· thermal properties of the contacting bodies are independent of temperature,

· the single area of contact is regarded as a plane source of heat,

· frictional heat is uniformly generated at the area of the contact,

· all heat produced is conducted into the contacting solids,

· the coefficient of friction between the contacting solids is known and attains somesteady value,

· a steady state condition (i.e ∂T/∂t = 0, the temperature is steady over time) isattained

Some of these assumptions appear to be dubious For example, the presence of the lubricant

in the contact will affect the heat transfer characteristics Although most of the heat producedwill be conducted into the solids, a portion of it will be convected away by the lubricantresulting in cooling of the surfaces An accurate value of the coefficient of friction is verydifficult, if not impossible, to obtain The friction coefficient is dependent on the level of theheat generated as well as many other variables such as the nature of the contacting surfaces,the lubricant used and the lubrication mechanism acting Even when an experimentalmeasurement of the friction coefficient is available, in many cases the friction coefficientcontinually varies over a wide range It is therefore necessary to calculate temperatures using

a minimum and maximum value of friction coefficient Temperatures at the beginning ofsliding movement should also be considered since flash temperatures do not forminstantaneously Flash temperatures tend to stabilize within a very short sliding distance butthe gradual accumulation of heat in the surrounding material and consequent slow rise inbulk temperature should not be overlooked

Not withstanding these assumptions, the analysis gives temperature predictions which,although not very precise, are a good indication of the temperatures that might be expectedbetween the operating surfaces

As already mentioned flash temperature calculations are based on the assumption that heatgenerated at the rate of:

q = Q/A

where:

Q is the generated heat [W];

A is the contact area [m2]

is conducted to the solids The frictional heat generated is expressed in terms of thecoefficient of friction, load and velocity, i.e.:

Q = µW|U A - U B |

where:

µ is the coefficient of friction;

W is the normal load [N];

U A is the surface velocity of the solid ‘A’ [m/s];

U B is the surface velocity of the solid ‘B’ [m/s].

There is no single algebraic equation giving the flash temperature for the whole range ofsurface velocities A non-dimensional measure of the speed at which the ‘heat source’

moves across the surface called the ‘Peclet number’ has been introduced as a criterion

allowing the differentiation between various speed regimes The Peclet number is defined as[47]:

L = Ua/2χ

where:

L is the Peclet number;

U is the velocity of a solid (‘A’ or ‘B’) [m/s];

a is the contact dimension [m], (i.e contact radius for circular contacts, half width

of the contact square for square contacts and the half width of the rectangle forlinear contacts);

χ is the thermal diffusivity [m2 /s], i.e χ = K/ρσ where:

K is the thermal conductivity [W/mK];

ρ is the density [kg/m3];

σ is the specific heat [J/kgK]

The Peclet number is an indicator of the heat penetration into the bulk of the contactingsolid, i.e it describes whether there is sufficient time for the surface temperature distribution

of the contact to diffuse into the stationary solid A higher Peclet number indicates a highersurface velocity for constant material characteristics

Since all frictional heat is generated in the contact, the contact is modelled and treated as aheat source in the analysis Flash temperature equations are derived, based on the

assumption that the contact area moves with some velocity ‘U’ over the flat surface of a body

2b

2b 2l

Body A Body B

FIGURE 7.28 Geometry of the circular, square and linear contacts

The heat transfer effects vary with the Peclet number as shown schematically in Figure 7.29.The following velocity ranges, defined by their Peclet number, are considered in flashtemperature analysis:

L < 0.1 one surface moves very slowly with respect to the other There is enough

time for the temperature distribution of the contact to be established inthe stationary body In this case, the situation closely approximates tosteady state conduction [44],

0.1 < L < 5 intermediate region One surface moves faster with respect to the other

and a slowly moving heat source model is assumed,

L > 5 one surface moves fast with respect to the other and is modelled by a fast

moving heat source There is insufficient time for the temperaturedistribution of the contact to be established in the stationary body and theequations of linear heat diffusion normal to the surface apply [44] Thedepth to which the heat penetrates into the stationary body is very smallcompared to the contact dimensions

Flash temperature equations are given in terms of the heat supply over the contact area, thevelocity, and the thermal properties of the material They are derived based on theassumption that the proportion of the total heat flowing into each contacting body is suchthat the average temperature over the contact area is the same for both bodies The flash

temperature equations were developed by Blok and Jaeger for linear and square contacts[46,47] and by Archard for circular contacts [48].

Velocity of frictional heat source

High Peclet number

FIGURE 7.29 Frictional temperature profiles at low and high Peclet numbers

· Flash Temperature in Circular Contacts

In developing the flash temperature formulae for a circular contact, it was assumed that the

portion of the surface in contact is of height approximately equal to the contact radius ‘a’ The temperature at the distance ‘a’ from the surface is considered as a bulk temperature ‘T b’ of thebody This can be visualised as a cylinder of height equal to its radius with one end in contactand the other end maintained at the bulk temperature of the body The geometry of thecontact is shown in Figure 7.28

Average and maximum flash temperature formulae for circular contacts and variousvelocity ranges are summarized in Table 7.5 The average flash temperature corresponds tothe steady-state component of flash temperature, while the maximum value includes thetransient component The maximum flash temperature occurs when the maximum load isconcentrated at the smallest possible area, i.e when the load is carried by a plasticallydeformed contact [48]

· Flash Temperature in Square Contacts

Flash temperature equations for square contacts have been developed by Jaeger [47].Although square contacts are rather artificial the formulae might be of use in someapplications The geometry of the contact is shown in Figure 7.28 The formulae for various

velocity ranges are summarized in Table 7.6 Constants ‘C 1 ’ and ‘C 2’ required in flashtemperature calculations for the intermediate velocity range are determined from the chartshown in Figure 7.30 [47]

TABLE 7.5 Average and maximum flash temperature formulae for circular contacts.

number Average flash temperatureT fa

Maximum flash temperature

T f max qa

W

p y

or in general

where:

T fa is the average flash temperature [°C];

T fmax is the maximum flash temperature [°C];

µ is the coefficient of friction;

W is the normal load [N];

p y is the flow or yield stress of the material [Pa];

U A , U B are the surface velocities of solid ‘A’ and solid ‘B’ respectively [m/s];

U is the velocity of solid ‘A’ or ‘B’;

a is the radius of the contact circle [m] (Figure 7.28);

χ is the thermal diffusivity, χ = K/ρσ, [m2

N is the variable [°C], defined as:

N = πq/ρσU

where:

q = Q/πa 2 = µW|U A - U B |/πa 2

is the rate of heat supply per unit area (circular) [W/m2];

L ' is the variable defined as:

L' = U 2χ W πpy

number Average flash temperatureT fa

Maximum flash temperature

T f max qb

T fa = 0.266 µWU A − U B

K b U

2q K

T f max = 0.399 µWU A − U B

Kb πU

b is the half width of the contact square [m] (Figure 7.28);

L is the Peclet number; L = Ub/2χ;

q is the rate of heat supply per unit area (square) [W/m2];

q = Q/4b 2 = µW|U A - U B |/4b 2

The other variables are as already defined

· Flash Temperature in Line Contacts

Flash temperature formulae for line contacts for various velocity ranges are summarized inTable 7.7 [47] They are applicable in many practical cases such as gears, roller bearings, cutting

tools, etc The contact geometry is shown in Figure 7.28 and constants ‘C 3 ’ and ‘C 4’ required inflash temperature calculations for the intermediate velocity range are determined from thechart shown in Figure 7.30 [47]

TABLE 7.7 Average and maximum flash temperature formulae for line contacts

L < 0.1

T fa=or

Peclet

number Average flash temperatureT fa

Maximum flash temperature

T f max = 0.318 µWUA K l − UB

T f max = C4π2

or

χq KU

T f max = 0.159C 4 µWU A − U B

K l

C 4from Figure 7.30.

T f max=or

2q K

T f max = 0.399 µWUA K l − UB

b is the half width of the contact rectangle [m] (Figure 7.28);

l is the half length of the contact rectangle [m] (Figure 7.28);

L is the Peclet number; L = Ub/2χ;

q is the rate of heat supply per unit area (rectangle) [W/m2];

q = Q/4bl = µW|U A - U B |/4bl

The other variables are as already defined

It can be seen from Tables 7.5 and 7.6, that the average flash temperature equations forcircular and square contacts are identical apart from a small difference in the proportionalityconstant The shape of the contact, with the exception of elongated contacts, has a small effect

on flash temperature and the average flash temperature formulae for square sources can beused for most irregular shapes of sources [47]

L

Peclet number 0

1 2 3 4 5 6 7

FIGURE 7.30 Diagram for evaluation of constants ‘C ’ required in flash temperature

calculations for the intermediate velocity range [47]

True Flash Temperature Rise

The heat generated in frictional contacts is divided between the contacting solids Theproportion of the total heat flowing to each body is determined on the basis that the averagesurface temperature is the same for both bodies [48] A simple way of estimating the truetemperature rise in the contact is to initially assume that all the heat generated is supplied to

body ‘A’ The appropriate flash temperature equation for a given speed and contact geometry conditions is then selected and a flash temperature ‘T fA ’ calculated The next step in the calculation procedure is to assume that all the heat generated is transferred to body ‘B’ The

appropriate flash temperature equation for this second model is then selected and the

corresponding flash temperature ‘T fB’ calculated It should be noted that for each body, theflash temperature equations adequate for their speed conditions must be selected Forexample, both surfaces of meshing gears move with high velocity thus equations for Peclet

number L > 5 apply to both bodies ‘A’ and ‘B’ On the other hand, in some applications where only one of the surfaces moves fast and the other moves very slowly, the equations for L > 5 and L < 0.1 should be applied consecutively In such cases the flash temperatures are

calculated assuming that initially all frictional energy is conducted to the moving surface andthen that all frictional energy is conducted to the stationary surface The true flashtemperature rise must be the same for both solids in contact and is calculated from:

For example, for two fast moving surfaces in line contact, the maximum temperature rise of

the conjunction ‘T fmaxc’ is given by the expression:

Substituting the expressions for maximum flash temperature from Table 7.7 for L > 5, the

commonly used equations for maximum temperature rise in line contacts are obtained, i.e.:

T f maxc= 1.11µWUA − UB

If the contacting solids are of the same material then their thermal constants are also thesame and the above equation can be written as:

R ' is the reduced radius of curvature of the undeformed surfaces [m]

or in terms of maximum contact pressure as:

T f maxc= 2.45 µpmax (Kρσ) 1.5 UA 0.5 0.5 − UB 0.5

E'

(7.42)

where:

p max is the maximum contact pressure [Pa]

Although the procedure outlined does not always provide precise values of the temperaturedistribution over the entire interface between contacting solids it greatly facilitates thephysical interpretation of frictional temperatures For example, consider a pin-on-discmachine with the pin and the disc manufactured from the same material Since the pin isstationary, low speed conditions of heat transfer apply, whereas high speed conditions apply

to the disc The interfacial temperature of the disc will be very much lower than that of thepin since the disc is constantly presenting fresh cool material to the interface Hence thetemperature distribution at the interface will be mostly determined by the heat flowequations in the disc [44,49] Another example of this effect which is more closely related toEHL is the difference in frictional temperatures between a large and a small gear-wheel whenmeshed together

The maximum flash temperature rise is located towards the trailing region of the contact andits location depends on the Peclet number as shown in Figure 7.31 [47]

The maximum flash temperature distribution for high speed conditions in circular contacts

is shown in Figure 7.32 [44] It can be seen that the maximum temperature is about

T fmax = 1.64T fa and occurs at the centre of the trailing edge of the contact

It should be noted that the heat source considered in the analysis was treated as uniform, i.e.the frictional energy generated is uniformly distributed over the contact area It has beenfound that for the non-uniform heat sources arising from the Hertzian pressure distribution,

the value of ‘q max ’ is almost unaffected by the non-uniform distribution of ‘q’ [44,49].

However, it was found that the maximum temperature for a circular contact is increased by16% compared to the uniform heat source, and its location is moved inward from thetrailing edge [44]