Engineering Tribology Episode 1 Part 8 pptx

Lubricant is then supplied through the hole to be distributedover a large fraction of the bearing length by the groove.. FIGURE 4.37 Typical lubricant supply grooves in journal bearings;

θ

O

W 1 R

FIGURE 4.30 Load components and pressure field acting in a journal bearing

Thus the load component acting along the line of centres is expressed by:

(4.104)

Substituting for ‘p’ (4.102) and separating variables gives:

Introducing a variable ‘∆’:

( )c R

D = 2R is the shaft diameter [m]

The Sommerfeld Number is a very important parameter in bearing design since it expressesthe bearing load characteristic as a function of eccentricity ratio Computed values ofSommerfeld number ‘∆’ versus eccentricity ratio ‘ε’ are shown in Figure 4.32 [3] The curveswere computed using the Reynolds boundary condition which is the more accurate Data forlong journal bearings which cannot be calculated from the above equations are also included.The data is also based on a bearing geometry where 180° of bearing sector on the unloadedside of the bearing has been removed Removal of the bearing shell at positions wherehydrodynamic pressure is negligible is a convenient means of reducing friction and thebearings are known as partial arc bearings The effect on load capacity is negligible except atextremely small eccentricity ratios An engineer can find from Figure 4.32 a value of

Sommerfeld number for a specific eccentricity and L/D ratio and then the bearing and

operating parameters can be selected to give an optimum performance It is usually assumedthat the optimum value of eccentricity ratio is close to:

S = π∆ Since:

U = 2πRN

substituting into equation (4.110) gives:

( )c R

∆ =

L η2πRN

Introducing ‘P’ [4]:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.01

0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1

2 3 4 5 6 8 10

20 30 40 50 60 80 100

L

D = ∞

= 1 1 2

=

1 4

=

1 8

=

0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1

2 3 4 5 6 8 10 20

0.004 0.005 0.006 0.008 0.01

1 8

∆ = N Pηπ 2

Thus:

( )c R

It can also be seen from Figure 4.30 that the attitude angle ‘β’ between the load line and the

line of centres can be determined directly from the load components ‘W 1 ’ and ‘W 2’ from thefollowing relation:

In journal bearings, the bottom surface is stationary whereas the top surface, the shaft, ismoving, i.e.:

dp + U h

It can be seen from equation (4.117) that when:

· the shaft and bush are concentric then:

e = 0 a n d ε = 0

and the value of the second term of equation (4.117) becomes unity The equation

now reduces to the first term only This is known as ‘Petroff friction’ since it was

first published by Petroff in 1883 [3]

· the shaft and bush are touching then:

e = c a n d ε = 1

which causes infinite friction according to the model of hydrodynamic lubrication

In practice the friction may not reach infinitely high values if the shaft and bushtouch but the friction will be much higher than that typical of hydrodynamiclubrication It is also true that as the eccentricity ratio approaches unity, the friction

coefficient rises The second term of (4.117) is known as the ‘Petroff multiplier’.

Figure 4.33 shows the relationship between the calculated Petroff multiplier andthe eccentricity ratio for infinitely long 360° journal bearings [8] The calculated

values are higher than those predicted from (1 - ε 2 ) -0.5 since the effects of pressure

on the shear stress of the lubricant are not included in equation (4.117) The effect

of cavitation, i.e the zero pressure region, does have a significant effect on frictionand this together with pressure effects are discussed in the next chapter on

As can be seen from equation (4.108) or from Figure 4.32 the load capacity rises sharply with

an increase in eccentricity ratio Friction force is relatively unaffected by changes in

0 0.2 0.4 0.6 0.8 1.0 Eccentricity

K

ε

1 2 3 4 5

FIGURE 4.33 Relationship between Petroff multiplier and eccentricity ratio for infinitely long

360° bearings [8]

eccentricity ratio until an eccentricity ratio of about 0.8 is reached Although the operation of

bearings at the highest possible levels of Sommerfeld number and eccentricity ratio willallow minimum bearing dimensions and oil consumption, the optimum value of theeccentricity ratio, as already mentioned, is approximately ε = 0.7 Interestingly the optimal

ratio of maximum to minimum film thickness for journal bearings is much higher than forpad bearings as is shown below:

at θ = 0 where film thickness is a maximum, h 1 = c (1 + ε) and

at θ = π where film thickness is a minimum, h 0 = c (1 - ε)

so that the optimal inlet/outlet film thickness ratio for journal bearings is

h 1

h 0

= 1 + ε

1 - ε = 1 + 0.7 1 - 0.7 = 5.67.This ratio is higher than for linear pad bearings for which it is

equal to 2.2 There is a noticeable discrepancy in optimum ratios of maximum to minimum

film thickness but strictly speaking these two ratios are not comparable In the case of linearpad bearings classical theory predicts a maximum load capacity while for journal bearingsthere is no maximum theoretical capacity, instead a limit is imposed by theoreticalconsiderations When cavitation effects are ignored, the friction coefficient for a bearing withthe Half-Sommerfeld condition is:

µ = 8Rc(1− ε2 ) 1.5

· Lubricant Flow Rate

For narrow bearings, the flow equation (4.18) is simplified since ∂p/∂x ≈ 0 and is expressed inthe form:

UhL 2 Substituting for ‘h’ from (4.99), gives the flow in the bearing:

θ = 0 and h = h 1 and out of the bearing at θ = π and h = h0

Substituting the above boundary conditions into (4.120) it is found that the lubricant flowrate into the bearing is:

Lubricant outflow

h 1

FIGURE 4.34 Unwrapped oil film in a journal bearing

and the lubricant flow rate out of the bearing is:

Lubricant must be supplied at this rate to the bearing for sustained operation If this

requirement is not met, ‘lubricant starvation’ will occur.

For long bearings and eccentricity ratios approaching unity, the effect of hydrodynamicpressure gradients becomes significant and the above equation (4.121) loses accuracy.Lubricant flow rates for some finite bearings as a function of eccentricity ratio are shown inFigures 4.35 and 4.36 [8] The data is computed using the Reynolds boundary condition,values for a 360° arc or complete journal bearing are shown in Figure 4.35 and similar datafor a 180° arc or partial journal bearing are shown in Figure 4.36

FIGURE 4.36 Lubricant leakage rate versus eccentricity ratio for some finite 180° bearings [8]

Practical and Operational Aspects of Journal Bearings

Journal bearings are commonly incorporated as integral parts of various machinery with awide range of design requirements Thus there are some problems associated with practicalimplementation and operation of journal bearings For example, in many practicalapplications the lubricant is fed under pressure into the bearing or there are some criticalresonant shaft speeds to be avoided The shaft is usually misaligned and there are almostalways some effects of cavitation for liquid lubricants Elastic deformation of the bearing willcertainly occur but this is usually less significant than for pad bearings All of these issues willaffect the performance of a bearing to some extent and allowance should be made during thedesign and operation of the bearing Some of these problems will be addressed in this sectionand some will be discussed later in the next chapter on ‘Computational Hydrodynamics’

· Lubricant Supply

In almost all bearings, a hole and groove are cut into the bush at a position remote from thepoint directly beneath the load Lubricant is then supplied through the hole to be distributedover a large fraction of the bearing length by the groove Ideally, the groove should be thesame length as the bearing but this would cause all the lubricant to leak from the sides of thegroove As a compromise the groove length is usually about half the length of the bearing.Unless the groove and oil hole are deliberately positioned beneath the load there is littleeffect of groove geometry on load capacity Circumferential grooves in the middle of thebearing are useful for applications where the load changes direction but have the effect ofconverting a bearing into two narrow bearings These grooves are mostly used in crankcasebearings where the load rotates Typical groove shapes are shown in Figure 4.37 The edges ofgrooves are usually recessed to prevent debris accumulating

FIGURE 4.37 Typical lubricant supply grooves in journal bearings; a) single hole, b) short

angle groove, c) large angle grove, d) circumferential groove (adapted from [19])

The idealized lubricant supply conditions assumed previously for load capacity analysis donot cause significant error except for certain cases such as the circumferential groove Thecalculation of lubricant flow from grooves requires computation for accurate values and isdescribed in the next chapter Only a simple method of estimating lubricant flow is described

in this section With careful design, grooves and lubricant holes can be more than just ameans of lubricant supply but can also be used to manipulate friction levels and bearingstability

Lubricant can be supplied to the bearing either pressurized or unpressurized The advantage

of unpressurized lubricant supply is that it is simpler, and for many small bearings a can oflubricant positioned above the bearing and connected by a tube is sufficient for several hoursoperation The bearing draws in lubricant efficiently and there is no absolute necessity for

pressurized supply Pressurization of lubricant supply does, however, provide certainadvantages which are:

· high pressure lubricant can be supplied close to the load line to suppress lubricant

heating and viscosity loss This practice is known as ‘cold jacking’,

· for large bearings, pressurized lubricant supply close to the load line prevents shaft

to bush contact during starting and stopping This is a form of hydrostaticlubrication,

· lubricant pressurization can be used to modify vibrational stability of a bearing,

· cavitation can be suppressed if the lubricant is supplied to a cavitated region by asuitably located groove Alternatively the groove can be enlarged, so that almost all

of the cavitated region is covered, which prevents cavitation within it

For design purposes it is necessary to calculate the flow of lubricant through the groove It isundesirable to try to force the bearing to function on less than the lubricant flow dictated byhydrodynamic lubrication since the bearing can exert a strong suction effect on the lubricant

in such circumstances When the bearing is rotating, the movement of the shaft entrains anyavailable fluid into the clearance space It is not possible for the bearing to rotate at anysignificant speed without some flow through the groove or supply hole If lubricant flow isrestricted then suction may cause the lubricant to cavitate in the supply line which causespockets of air to pass down the supply line and into the bearing or the groove may becomepartially cavitated When the latter occurs there is no guarantee that the lubricant flow fromthe groove will remain stable, and instead lubricant may be released in pulses In either case,the hydrodynamic lubrication would suffer periodic failure with severe damage to thebearing

There are two components of total flow ‘Q’ from a groove or supply hole into a bearing; the net Couette flow ‘Q c’ due to the difference in film thickness between the upstream and down-

stream side of the groove/hole and the imposed flow ‘Q p’ from the externally pressurizedlubricant, i.e.:

Q = Q c + Q p

An expression for the net Couette flow is:

where:

Q c is the net Couette flow [m3/s];

U is the sliding velocity [m/s];

l is the axial width of the groove/hole [m];

h d is the film thickness on the downstream side of the groove/hole [m], as shown

in Figure 4.38;

h u is either the film thickness on the upstream side of the groove or the film

thickness at the position of cavitation if the bearing is cavitated [m], as shown inFigure 4.38

Note that ‘h d’ depends on the position at which the groove is located and can be calculatedfrom the bearing geometry On the other hand, when cavitation occurs a generous estimate

for ‘h u ’ is the minimum film thickness, i.e h u = h 0 = c(1 - ε) The net Couette flow is the

minimum flow of lubricant that should pass through the groove/hole even if the lubricantsupply is not pressurized If this flow is not maintained then the problems of suction andintermittent supply described above will occur

FIGURE 4.38 Couette flow at the entry and the exit of the groove.

However, even the net Couette flow may not be sufficient to prevent starvation of lubricantparticularly if the groove/hole is small compared to the bearing length For smallgrooves/holes and for circumferential grooves, pressurization of lubricant is necessary forcorrect functioning of the bearing In fact the Couette flow in bearings with circumferential

grooves is equal to zero, i.e Q c = 0 The pressurized flow of lubricant from a groove has been

summarized in a series of formulae [19] These formulae supersede earlier estimates ofpressurized flow [3] which contain certain inaccuracies Formulae for pressurized flow from asingle circular oil hole, rectangular feed groove (small angular extent), rectangular feedgroove (large angular extent) and a circumferential groove are summarized in Table 4.4 [19]

Coefficients ‘f 1 ’ and ‘f 2’ required or the calculations of lubricant flow from a rectangulargroove of large angular extent are determined from the chart shown in Figure 4.39

TABLE 4.4 Formulae for the calculation of lubricant flow through typical grooves (adapted

Single rectangular groove

with small angular extent

( β < 5°)

Single rectangular groove

with large angular extent

Q p is the pressurized lubricant flow from the hole or groove [m3/s];

p s is the oil supply pressure [Pa];

η is the dynamic viscosity of the lubricant [Pas];

h g is the film thickness at the position of the groove [m];

c is the radial clearance [m];

d h is the diameter of the hole [m];

L is the axial length of the bearing [m] (In the case of bearings with a

circumferential groove it is the sum of two land lengths as shown in Figure 4.37.Note that in this case the bearing is split into two bearings.)

l is the axial length of the groove [m];

b is the width of the groove in the sliding direction [m];

D is the diameter of the bush [m];

ε is the eccentricity ratio;

f 1 , f 2 are the coefficients determined from Figure 4.39

The grooves are centred on the load line but positioned at 180° to the point where the loadvector intersects the shaft and bush The transition between ‘large angular extent’ and ‘small

angular extent’ depends on the L/D ratio; e.g for L/D = 1, 180° is the transition point whereas for L/D ≤ 0.5 the limit is at 270° For angular extents greater than 90° it is recommended,

however, that both calculation methods be applied to check accuracy

It should be noted that the pressurized flow of large angular extent bearings is significantlyinfluenced by eccentricity so that it is necessary to calculate the value of this parameter first.For small grooves/holes, the lubricant supply pressure may be determined from the amount

of pressurized flow required to compensate for the difference between Couette flow and thelubricant consumption of full hydrodynamic lubrication At very low eccentricities someexcess flow may be required to induce replenishment of lubricant since the hydrodynamiclubricant flow rate declines to zero with decreasing eccentricity If this precaution is notapplied, progressive overheating of the lubricant and loss of viscosity may result particularly

as low eccentricity is characteristic of high bearing speed, e.g 10,000 [rpm] [20]

· Cavitation

As discussed already, large negative pressures in the hydrodynamic film are predicted whensurfaces move apart or mutually sliding surfaces move in a divergent direction For gases, anegative pressure does not exist and for most liquids a phenomenon known as cavitationoccurs when the pressure falls below atmospheric pressure The reason for this is that mostliquids contain dissolved air and minute dirt particles When the pressure becomes sub-atmospheric, bubbles of previously dissolved air nucleate on pits, cracks and other surfaceirregularities on the sliding surfaces and also on dirt particles It has been shown that veryclean fluids containing a minimum of dissolved gas can support negative pressures but thishas limited relevance to lubricants which are usually rich in wear particles and are regularlyaerated by churning If there is a significant drop in pressure, the operating temperature can

be sufficient for the lubricant to evaporate The lubricant vapour accumulates in the bubblesand their sudden collapse is the cause of most cavitation damage The critical differencebetween ‘gaseous cavitation’, i.e cavitation involving bubbles of dissolved air, and ‘vaporouscavitation’ is that with the latter, sudden bubble collapse is possible When a bubble collapsesagainst a solid surface very high stresses, reaching 0.5 [GPa] in some cases, are generated andthis will usually cause wear Wear caused by vaporous cavitation progressively damages thebearing until it ceases to function effectively The risk of vaporous cavitation occurringincreases with elevation of bearing speeds and loads [21] Cavitation in bearings is alsoreferred to as ‘film rupture’ but this term is old fashion and is usually avoided

Cavitation occurs in liquid lubricated journal bearings, in elastohydrodynamics and inapplications other than bearings such as propeller blades In journal bearings, cavitationcauses a series of ‘streamers’ to form in the film space The lubricant feed pressure has someability to reduce the cavitation in the area adjacent to the groove [22], as shown in Figure 4.40

FIGURE 4.40 Cavitation in a journal bearing; a) oil fed under low pressure, b) oil fed under

high pressure (adapted from [22])

Large lubricant supply grooves can be used to suppress negative hydrodynamic filmpressures and so prevent cavitation This practice is similar to using partial arc bearings andhas the disadvantage of raising the lubricant flow rate and the precise location of thecavitation front varies with eccentricity This means that cavitation might only be prevented