shigley 9e si chap12

8/16/2019 Shigley 9E SI Chap12

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Chapter 12

ubrication and

Journal Bearings

Copyright © 2011 by The McGraw-Hill Companies, Inc. ermission re!"ire# $or repro#"ction or #isplay.

%higley&s Mechanical 'ngineering (esign

)th '#ition in %I "nits

*ichar# G. +"#ynas an# . eith isbett

Prepared by

"ei-/"an Chanssociate ro$essor o$ Mechanical 'ngineering

ational Cheng "ng niersity


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12 3"brication an# o"rnal +earings

ChapterOutline

12-1 Types of Lubrication

12-2 Viscosity

12-3 Petroff’s Equation

12-4 Stable Lubrication

12-5 Thick-Film Lubrication

12-6 Hydrodynamic Theory

12-7 Design Considerations

12-8 The Relations of the Variables

12-9 Steady-State Conditions in Self-Contained Bearings

12-10 Clearance

12-11 Pressure-Fed Bearings

12-12 Loads and Materials

1213 Bearing Types

12-14 Thrust Bearings

12-15 Boundary-Lubricated Bearings


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3

Introduction

• The object of lubrication is to reduce friction, wear, and heating ofmachine parts that move relative to each other.

• The field of application for journal bearings is immense.

The crankshaft and connecting-rod bearings of an automotive enginemust operate for thousands of miles at high temperatures and under varing load conditions.

The journal bearings used in the steam turbines of power-generating stations are said to have reliabilities approaching.

• In the stud of lubrication and journal bearings, additional fundamental studies, such as chemistr, fluid mechanics, thermodnamics, and heat transfer, must be utili!ed in developing the material.


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4

Tpes of Lubrication

• "ive distinct forms of lubrication ma be identified#

$drodnamic #the load-carring surfaces of the bearing are separated b a relativel thick film of lubricant.

$drostatic #does not re%uire motion of one surface relative to another is obtained b introducing the lubricant, which is sometimes air or water, into the load-bearing area at a pressure high enough to separate the surfaces with a relativel thick film of lubricant.

&lastohdrodnamic #the phenomenon that occurs when a lubricant is introduced between surfaces that are in rolling contact.

Boundar # has the highest asperities ma be separated b lubricant films onlseveral molecular dimensions in thickness from insufficient surface area, a dropin the velocit of the moving surface, a lessening in the %uantit of lubricant deli

vered to a bearing, an increase in the bearing load, or an increase in lubricant temperature resulting in a decrease in viscosit

'olid film # (hen bearings must be operated at e)treme temperatures, a solid-film lubricant such as graphite or molbdenum disulfide must be used because the ordinar mineral oils are not satisfactor.


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5

*iscosit

• Let a plate + be moving with a velocit on a film of lubricant of thickness h and imagine the film as composedof a series of hori!ontal laers and the force " causing these laers to deform or slide on one another just like a deck of cards.

• ewtons viscous effect states that the shear stress in th

e fluid is proportional to the rate of change of velocit with respect to .

where / is the constant of proportionalit and definesabsolut

e viscosit , also called dnamic viscosit.

• "or most lubricating fluids, the rate of shear is constant,and du 0d 1 0h .

• "luids e)hibiting are said to be ewtonianfluids.

• The absolute viscosit is measured b the pascal-second23a 4 s5 in 'I.


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6

3etroffs &%uation

• + vertical shaft rotating in a guide bearing carring a ver small load. The cl

earance space is completel filled with oil with negligible leakage.• The shearing stress in the lubricant is e%ual to the velocit gradient times t

he viscosit. The force re%uired to shear the film is the stress times the area. The tor%ue is the force times the lever arm r .

• If we now designate a small force on the bearing b ( , in ewtons, then the pressure 3 , in 3ascal, is 3 1 ( 06rl . The frictional force is f ( , where f is the coefficient of friction, and so the frictional tor%ue is

• The coefficient of friction can then be solved as

• Thebearing characteristic number , or the 'ommerfeld number , is defi

ned

(here the %uantit r 0c is called the radial clearance ratio


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7

'table Lubrication

• 3etroffs bearing model predicts that f is proportional to /- 03 , that is, a straight line to the right of point 7 .

• 3etroffs model presumes thick-film lubrication without metal-to-metal contact. + design constraint to keep thick film lubrication is to

be sure that

• The region to the right of line B + defines stable lubrication because variations are self-correcting and the region to the left of line B+ represents unstable lubrication.

•

The diference between boundary andhydrodynamic lubrication can beexplained rom the data generated bythe McKee brother in an actual tet oriction o the change in the coe!ciento riction "eru the bearing

characteritic #$ %&.


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'

Thick-"ilm Lubrication

• 'uppose a lubricant is introduced into the top of the bearing as sh

own a minimum film thickness h 8 occurs, not at the bottom of the journal, but displaced clockwise from the bottom. This is e)plained b the fact that a film pressure in the converging half of the filmreaches a ma)imum somewhere to the left of the bearing center.

• The dimension c is the radial clearance and is the difference in th

e radii of the bushing and journal. The distance between these centers is theeccentricit and is denoted b e . The minimum film th

ickness is designated b h 8, and it occurs at the line of centers. Th

e film thickness at an other point is designated b h . (e also define an eccentricit ratio as(

• The bearing hown in the )gure i *nown a apartial bearing+ , the radiu o the buhing ithe ame a the radiu o the -ournal. it i*nown a a )tted bearing+ , the buhing

encloe the -ournal. a indicated by thedahed line. it become a ull bearing+


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/

$drodnamic Theor #Background and assumption• The present theor of hdrodnamic lubrication originated in the laborator of

Beauchamp Tower in the earl 9::8s in &ngland. The results obtained b Towerhad such regularit that ;sborne


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01

$drodnamic Theor # >evelopment

• 'elect an element of lubricant in the film of dimensions d) ,d , and

d! , and compute the forces that act on the sides of this element.• 'umming the forces in the ) direction with ewtons viscous effect

we obtain

• +ssume that there is no slip between the lubricant and the boundar surfaces. This gives two sets of boundar conditions

• The velocit distribution across the is obtained b superposing a parabolic distribution onto a linear distribution.

• >efine ? as the volume of lubricant flowing in the ) direction per u

nit time.

the assumption of an incompressible lubricant

results in the classical


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00

>esign 7onsiderations

• The group of variables whose values are either given or under the control of the designer are

The viscosit / The load per unit of projected bearing area, 3 The speed - The bearing dimensions r , c , @, and l

• The second group of variables are dependent that the designer cannot control

The coefficient of friction f The temperature rise T

The volume flow rate of oil ? The minimum film thickness h 8

• The angular speed - that is significant to hdrodnamic film bearing performance is

where- j 1 journal angular speed, rev0s- b 1 bearing angular speed, rev0s- f 1 load vector angular speed,

rev0s

• Trumplers >esign 7riteria for Journal Bearings


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02

The viscosit 7harts

• The assumption that viscosit of the lubricant is constant as it passes through the beari

ng might not hold since the temperature of theoil is higher when it leaves the loading !one than it was on entr.

• >efine temperature that is the average of the inlet and outlet temperatures

where T 9 is the inlet temperature and T is the temper

ature rise of the lubricant from inlet to outlet. The viscosit used in the analsis must correspond to T av.


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03

*iscosit-Temperature 7hart for Aultiviscosit Lubricants


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04

Ainimum "ilm Thickness 7hart


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05

7oefficient of "riction 7hart


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06

Lubricant "low 7hart


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07

"ilm 3ressure 7hart


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0'

Lubricant Temperature


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0/

• elcontained i called bearing becaue the lubricant ump i

within the bearing houing and the lubricant i cooled within thehouing+

• The heat gi"en up by the bearing houing may be etimated romthe euation

'tead-'tate 7onditions in'elf-7ontained Bearings

• >efines T f as the average film temperature

• "inding the e%uilibrium temperatures is an iterative process wherein a trial average film temperature 2and the corresponding viscosit5 is used to compare the heat generation rate and theheat loss rate. +n adjustment is made to bring

these two heat rates into agreement.


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21

7learance

• In designing a journal bearing for thick-film lubricati

on, the engineer must select the grade of oil to be used, together with suitable values for 3 , - , r , c , and l .

• The radial clearance c is difficult to hold accurate during manufacture, and it ma increase because of wear.

• The performance of a particular bearing is calculated

for a whole range of radial clearances and is plottedwith clearance as the independent variable.

• If the clearance is too tight, the temperature will be too high and the minimum film thickness too low.

• The range of clearances for the free-running fit is about twice that of the close-running fit.

•

(hen both the production tolerance and the futurewear on the bearing are considered, it is seen, that the best compromise is a clearance range slightl to the left of the top of the minimum-film-thickness curve.


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22

3ressure-"ed Bearings 27ont.5

• The amount of lubricant that flows out both ends at an position N is

where d+ is the elemental area.

• Integrating around the bearing gives the total side flow as

•

The characteristic pressure in each of the two bearings that constitute the pressure-fed bearing assembl 3 is given b

• The heat gain of the fluid passing through the bearing is

• +t stead state, the rate at which the journal does frictional work on the fluid fil

m is

• (ith 'ommerfeld number and using J 1 FFE lbf 4 in0Btu, D 1 8.8F99 lbm0inF, and7 p 1 8.O6 Btu02lbm 4 "5, we find

where T " is T in ".


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23

Loads and Aaterials

• The diameter and length of a bearing depend u

pon the unit load.• + long bearing 2large l 0d ratio5 reduces the coef

ficient of friction and the side flow of oil and therefore is desirable where thin-film or boundar-value lubrication is present. ;n the other hand,where forced-feed or positive lubrication is present, the l 0d ratio should be relativel small.

• The two conflicting re%uirements of a good bearing material are that it must have a satisfactorcompressive and fatigue strength to resist the e)ternall applied loads and that it must be soft

and have a low melting point and a low modulus of elasticit.

• +dditional considerations in the selection of a good bearing material are its abilit to resist corrosion and, of course, the cost of producing thebearing.


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24

Bearing Tpes

• Two tpes of bushings. The solid bushing is made b casting, b dr

awing and machining, or b using a powder-metallurg process. The lined bushing is usuall a split tpe.

• 'ome tpical groove patterns are shown. In general, the lubricantma be brought in from the end of the bushing, through the shaft,or through the bushing.


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25

Thrust Bearings

• + fi)ed-pad thrust bearing consisting essentiall of a runner sliding

over a fi)ed pad is shown.• "ull-film, or hdrodnamic, lubrication is obtained if the speed of t

he runner is continuous and sufficientl high, if the lubricant has the correct viscosit, and if it is supplied in sufficient %uantit.

• Bearings are fre%uentl made with a flange that positions the beari

ng in the housing and also takes a thrust load.


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shigley 9e si chap12

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