Friction and Lubrication in Mechanical Design Episode 1 Part 7 pdf

Thermal Considerations in Tribology 135 5.5 HEAT PARTITION A N D TRANSIENT TEMPERATURE DISTRIBUTION IN LAYERED LUBRICATED CONTACTS This section briefly describes a generalized and effi

of the effect of applying the same total quantity of heat input with a trian- gular flux with the same maximum value but with different slopes, S1 and

S2, during the increase and decrease phases respectively Using the integra- tion approach, therefore:

Thermal Considerations in Tribology 131

Figures 5.7-5.11 show plots of the surface temperature history for

S1/S2 = 9, 4,1, b, and 4, respectively

Figure 5.12 shows the maximum surface temperature as a function of

S1/S2 for the same total heat flow qmax It can be seen from Fig 5.12 that the

highest surface temperature rise occurs as the ratio SI/S2 decreases

If the heat flux function is determined from experimental data and is difficult to integrate, the temperature rise can be obtained by summing the effects of incremental steps that are constructed to convolute the function as illustrated in Fig 5.13 Better accuracy can be obtained as the number of steps increases

The temperature rise at the surface for this case can be calculated as:

1 1 2

t = t 2 + t 3 , A T = - & E41 4 = T + ( 4 2 - 4 1 ) 4 = T

Time (sec)

Figure 5.1 Temperature rise on the surface of a steel slab due to a total heat input

q applied at different rates ( t O / t l = 0.1)

0 2 4 6 8 10

Time (sec) Figure 5.8 Temperature rise on the surface due to a total heat input q applied

Figure 5.10 Temperature rise on the surface due to a total heat input q applied at different rates (lo/tl = 0.8)

the slope ratio for the triangular heat input Dimensionless surface temperature rise as a function of the rate of

Figure 5.1 3 Convolution integration for a general heat input function

Thermal Considerations in Tribology 135

5.5 HEAT PARTITION A N D TRANSIENT TEMPERATURE

DISTRIBUTION IN LAYERED LUBRICATED CONTACTS

This section briefly describes a generalized and efficient computer- based model developed by Rashid and Seireg [23], for the evaluation of heat

partition and transient temperatures in dry and lubricated layered concen- trated contacts The program utilizes finite differences with the alternating direction implicit method

The program is capable of treating the transient heat transfer problem

in lubricated layered contacts with any arbitrary distribution of layer prop- erties and thicknesses It takes into consideration the time variation in speeds, load, friction coefficient, fluid film thickness between surfaces, and the effective radius of curvature of contacting solids It calculates the surface temperature distribution in the layered solids in lubricant film Also, the role

of the chemical layer on surface and film temperatures in lubricated con- centrated contacts can be evaluated Furthermore, the transient operating conditions, which are associated with the performance of such systems, are incorporated in temperature calculations

A general model for the contact zone in sliding/rolling conditions can be approximated by two moving semi-infinite solids separated by a lubricant

film, as shown in Fig 5.14 The heat generation distribution inside the

lubricant film is controlled by the rheological behavior of the lubricant under different pressures, temperatures, and rolling and sliding speed

In many concentrated contact problems, the moving solids may have different thermal properties, speeds, bulk temperatures and different chemi- cal layers on their surface All these variables are introduced in the model, as well as any considered heat generation condition in the lubricant film The boundary conditions for this problem are based on the fact that the temperature gradient diminishes away from the heat generation zone

Figure 5.1 4 Model for heat transfer in layered lubricated contacts

The temperature field around the contact zone is represented by a rec- tangular grid containing appropriately distributed nodal points in the two solids and the lubricant tilni normal to the flow and in the flow direction The size of each division c m be changed in such ;i manner that the boundary conditions c m be satisfied for a particular problem without increasing the number o f nodes A larger number o f divisions are used

;icross the lubricant film to xcommodate the rapid chringe in both tempera- ture and velocity across the film

The niesh size is progressively expanded in each moving solid with the distances of the node from the heat generation zone

The developed program hiis the following special features:

1 The use of finite difference with the alternating direction implicit method provides considerable inodeling flexibility and computing efficiency

I t is capable of handling transient variations in geometry loud, spccd, and material properties

2

Thermal Considerations in Tribology 137

The program as developed would be useful in investigating the effect of the different parameters on the temperature distribution in line contacts It can provide a valuable guide for performing experimental studies to generate empirical design equations for layered surfaces It can also be utilized to develop empirical equations for lubricated layered contacts applicable to specific regimens of materials and operating conditions The results for any application can be considerably enhanced by incorporating an appro- priate rheological model for the lubricant This would enable the prediction

of traction, velocity, profile in the film, and the heat generation distribution

in the contact zone

138 Chapter 5

4 The heat of compression in the lubricant film and the moving solids

has a negligible effect on the temperature rise inside the contact zone

Because the lubricant film thickness and the Hertzian contact with (x-direction) are small in comparison to the cylinder width (z-direc- tion), the temperature gradient in the z-direction is expected to be small in comparison with those across and along the film Therefore, the conduction in the z-direction is neglected

5

The thermal properties of the surface layers in lubricated contacts cover a wide material spectrum There are some cases where the surface layer has low thermal conductivity in comparison with the lubricant film (for exam- ple, paraffinic and the organic surface layers as compared with oil) At the same time, there are some types of coatings, like silicon carbide (Sic), which are much more conductive than any common lubricant The thermal resis- tance at the interface between the surface layer and the bulk solid should also be taken into consideration if the thermal boundary layer penetrates the surface layer inside the solid

The developed program is utilized to study the variation in maximum film temperature versus oil film thickness for several surface layer thick- nesses The attached surface layer to each moving solid is assumed to be identical and the distribution of heat generation is assumed to be uniform across the film (w = h) For the considered example:

the lubricant film The results as plotted in Fig 5.15 show a gradual reduc-

tion in the influence of the layer thickness on the lubricant film temperature

as the film thickness increases for the same friction heat level, as demon- strated by the upper two curves in the figure All the temperature curves for the layered contacts have the tendency to converge to a common level as the lubricant film thickness increases in magnitude

This is represented in more detail in Fig 5.16, which shows the depen-

dency of the maximum film temperature upon a wider range of surface layer

on surface layer thickness for thin and thick film lubrication The same argument can explain the increase in lubricant film thickness If the lubri- cant film is less conductive than the surface layer, then the lubricant film thickness has much less influence on the maximum film temperature, as shown in Fig 5.17

Figure 5.18 shows the variation in surface layer temperature versus oil film thickness for different insulative layer thicknesses It should be noted that as the fluid film decreases in thickness, the same friction level will result

in a higher surface film temperature Thus, chemical activity may increase to

a significant level before bearing asperity surfaces actually achieve contact

This has been confirmed experimentally by Klaus [20] such experimental

lubricated contacts (conductive layers, K J / K F = 1 /6)

Maximum film temperature versus oil film thickness for layered

Thermal Considerations in Tribology 141

In the case of boundary lubrication, in which the asperity interaction with the solid surfaces plays a major role, the temperature level becomes even more sensitive to surface layer thickness The small contact width between the asperities generates a shallow temperature penetration across the surface layer, which increases the temperature level even for a very thin layer The following can be concluded from the investigated conditions:

1 In the case of an insulative surface layer, the maximum rise in film temperature is strongly dependent on the surface layer thickness, whereas this is not the case for the conductive surface layer (see Figs 5.15 and 5.17)

In both cases, the surface layer temperature decreases with the increase in lubricant film thickness This is attributed to the con-

lubricated contacts (conductive layers, K 3 / K F = 1 /6)

Maximum surface temperature versus oil film thickness for layered

3

vection effects (see Figs 5.18 and 5.19) It should be noted here that this result occurs for the considered smooth surfaces without any asperity interaction This illustrates the importance of the surface layers on convection and consequently, the surface temperatures

As can be seen in Fig 5.16, there appears to be a surface layer

thickness, for each oil film thickness, beyond which the layer thick- ness will have no effect on the maximum temperature in the lubri- cant film

5.6 DIMENSIONLESS RELATIONSHIPS FOR TRANSIENT

TEMPERATURE A N D HEAT PARTITION

The use of dimensional analysis in defining interactions in a complex phe-

nomenon is a well-recognized art Any dimensional analysis problem raises

two main questions:

Thermal Considerations in Tribology 143

Case 1: Heat Source Moving over a Semi-Infinite Solid (Fig 5.20)

This problem is used to check the validity of the modeling approach since an analytical solution by Blok [S] and Jaeger [6] is available for this case The

derived equation for the maximum rise in surface temperature is obtained by using a series approximation as:

Ts - TB = 1.128 5

Figure 5.20 Moving semi-infinite solid under a stationary heat source

(5.7)

which is in general agreement with the analytically derived relationship The differences in the constant can be attributed to the numerical approximation

in the computer model

Case 2: Sliding/Rolling Dry Contacts (see Fig 5.21)

The maximum temperatures on the contacting surfaces can be developed from Eq (5.7) as:

Thermal Considerations in Tribology I45

Figure 5.21 Two cylinders under dry sliding condition

Tsl = Ts2 in this case, therefore, the heat partition coefficient a can be calculated for equal bulk temperatures as:

Blok [2] derived an identical equation for the flash temperature The contact

in Blok's equation is determined analytically as 1.1 1 instead of 1.03 deter- mined from the developed program

Case 3: Heat Source with a Hertzian Distribution Moving over a

Layered Semi-Infinite Solid (Fig 5.22)

In this case, the relationship for the maximum rise in the solid surface temperature can be obtained using the 7t theorem as:

By using the value of the penetration depth D in the solid at the trailing edge

[26], Eq (5.12) can be rewritten as:

I46 Chapter 5

L

Figur

U -

I

5.22 Layered semi-infinite solid moving under a stationary heat source

Similarly, the maximum rise in the surface layer temperature is derived as:

or by using the penetration depth concept:

where

D = = temperature penetration depth at the trailing edge

1 UhipocO required entry distance for temperature penetration across the

“=5-= k0

film

Thermal Considerations in Tribology 147

Tso = maximum rise in the solid surface temperatue for unlayered semi-infinite

Ts = maximum rise in the solid surface temperature for unlayered semi-infinite solids for the same heat input

solids for the same heat input

Case 4: Lubricated Rolling/Sliding Contacts

The temperature distribution and heat partition in heavily loaded lubricated contacts is not yet fully understood due to the ill-defined boundary condi- tions and the modeling complexities in the problem In this part of the work,

a number of dimensionless equations are derived for predicting both the maximum film temperature and the heat partition between the contacting solids

The model to be analyzed is shown in Fig 5.23 It represents two roll- inglsliding cylinders having different radii, thermal properties, and bulk temperatures, which are separated by lubricant film thickness h Because the lubricant is subjected to extremely high pressures and shear stresses, which only act for a very short time, the assumption that the lubricant behaves as Newtonian liquid is not valid Experiments demonstrated that typical lubricants exhibit liquid-solid transitions in elastohydrodynamic

contacts [4] and that this transition depends on both pressure and tempera-

ture The heat source depth w in the model represents the liquid region where the lubricant undergoes a high shear rate This region ranges between 0.1 and 0.4h At moderate to high sliding speeds, the magnitude of w is

approxiamtely 0 lh In order to simplify the derivation of dimensionless equations for this case, w is initially assumed to be equal to zero Now

Figure 5.23 Lubricated, heavily loaded sliding/rolling cylinder

148 Chapter 5

the partition of heat in lubricated rollinglsliding contacts can be predicted

by using Eqs (5.12) and (5.13) In the practical range of different material

combinations and bulk temperature difference, the heat generation zone in Fig 5.23 is assumed to be at the center of the film Accordingly, by referring

to Fig 5.14, which represents two layered cylinders rubbing against each other, we can assume that:

By assuming that the amount of heat flowing to the upper semi-infinite layered solid is aq,, then the lower one receives (1 - a)q, Since the max- imum temperature rise inside the heat generation zone is the same for the two layered semi-infinite solids, then according to Eq (5.9), let: