Machine Design Databook 2010 Part 11 potx

23-8and 23-9 The diametral clearance ratio or relative clearance Attitude or eccentricity ratio or eccentricity coeﬃcient Oil ﬁlm thickness at any position For position of minimum oil th

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TABLE 23-2

Journal bearing design practices

Bearing modulus (minimum) Diameter

Maximum pressure, P clearance Viscosity, 1 Viscosity, S 00 ¼1Pn S 00 ¼ nP0

ratio Machinery Bearing kgf/mm 2 kpsi MPa ¼dc Ratio L

d cP Pa s 103 USCSU

SI Units,

109

and aircraft Crankpin 1.06–2.47 1.5–3.5 10.40–24.40 0.7–1.4 to to 10 24.2

Gas and oil Main 0.49–0.85 0.7–1.2 4.85–8.35 0.001 0.6–2.0 20 20 20 48.4 engines (four- Crankpin 0.90–1.27 1.4–1.8 8.80–12.40 <0.001 0.6–1.5 to to 10 24.2 stroke) Wrist pin 1.27–1.55 1.8–2.2 12.40–15.20 <0.001 1.5–2.0 65 65 5 12.1 Gas and oil Main 0.35–0.56 0.5–0.8 3.42–5.50 0.001 0.6–2.0 20 20 25 60.4 engines (two- Crankpin 0.70–1.06 1.0–1.5 6.85–10.40 <0.001 0.6–1.5 to to 12 29.0 stroke) Wrist pin 0.85–1.07 1.2–1.8 8.35–12.50 <0.001 1.5–2.0 65 65 10 24.2

Steam Main 0.07–0.19 0.1–0.275 0.69–1.87 0.001 1.0–2.0 2–16 2–16 100 241.8 turbines

Generators, Rotor 0.07-0.14 0.1-0.2 0.69-1.37 0.0013 1.0–2.0 25 25 200 483.5 motors,

machine

Key: ð1Þ ¼ absolute viscosity, Pa s (cP); n ¼ speed, rpm; n 0 ¼ speed, rps; P ¼ pressure, N/m 2

or MPa (psi); MPa ¼ megapascal ¼ 10 6

N/m2; Pa ¼ Pascal ¼ 1 N/m 2 ; 1 psi ¼ 6894.757 Pa; 1 kpsi ¼ 6.89475 MPa; USCSU ¼ US Customary System units.

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

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TABLE 23-3

Values of factorC1in Eq (23-23)

Oil cup or grease (intermittent

Values of factorC2in Eq (23–23)

Sliding ﬂat surfaces wiping over the guide ends, such as reciprocating crossheads; use 2 for relatively long

guides and 3 for short guides

2–3

Sliding or wiping surfaces lubricated from the periphery or outer wiping edge, such as marine thrust bearings

and worm gears

B A

D

E e

r + c2 w

(b) At start (c) Running

DESIGN OF BEARINGS AND TRIBOLOGY

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BEARING PRESSURE (Fig 23-9)

General Electric Company’s formula for bearing

pressure in the design of motor and generator bearing

Victor Tatarinoﬀ’s equation for safe operating load

Victor Tatarinoﬀ’s equation for permissible unit

Pa¼ 15:5p3ffiffiffiffiffiffivm

USCS ð23-24bÞwhere Pain psi and vmin ft/min

Pa¼ 0:0635p3ffiffiffiffiffiffivm

Customary Metric ð23-24cÞwhere Pain kgf/mm2and vmin m/s

W ¼ 1nd3ðL=dÞ2

127ð106Þh

1þLd

L þ d

USCS ð23-26aÞwhere P in psi, 1in cP, n in rpm, L and d in in

P ¼ 13:5n0

2

L

L þ d

SI ð23-26bÞwhere P in Pa, in Pa s, n0in rps, and L and d in m

With groove

Line of centers or line joining 0 (centre

of bearing) and 0’

(centre of jouurnal) I

θ

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H F Moore’s equation for critical pressure

The critical unit pressure for any given velocity should

not exceed according to Louis Illmer

Stribeck’s equation for the critical pressure when the

speed does not exceed 2.5 m/s (500 ft/min)

Stribeck’s equation for the critical pressure when the

speed exceeds 2.5 m/s (500 ft/min)

For permissible Pv values

For values S00 for various combinations of journal

bearing materials, abrasion pressure for bearings,

allowable bearing pressures for semi-ﬂuid lubricants

and diametral clearances in bearing dimensions

Pc¼ 7:23 105 ffiffiffi

v

p

SI ð23-27aÞwhere Pcin N/m2and v in m/s

Pc¼ 0:0737pffiffiffiv

Customary Metric ð23-27bÞwhere Pcin kgf/mm2and v in m/s

Pc¼ 7:5pffiffiffiv

USCS ð23-27cÞwhere Pcin psi and v in ft/min

Pc¼ 9:7 105 ffiffiffi

v

p

SI ð23-28dÞwhere Pcin N/m2and v in m/s

Pc¼ 10pffiffiffiv

USCS ð23-28eÞwhere Pcin psi and v in ft/min

Pc¼ 0:0986pffiffiffiv

Customary Metric ð23-28fÞwhere Pcin kgf/mm2and v in m/s

Pc¼ 2:9 106 ffiffiffi

v

p

SI ð23-28gÞwhere Pcin N/m2and v in m/s

Pc¼ 30pffiffiffiv

USCS ð23-28hÞwhere Pcin psi and v in ft/min

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TABLE 23-5

Allowable bearing pressure, reciprocating motion

TABLE 23-6

Permissible Pv values

Values

Mill shafting, with self-aligning cast-iron bearings, grease, or imperfect

oil-lubrication, maximum value

Key : US Customary unit: P ¼ pressure, psi, v ¼ velocity, ft/s; SI unit: P ¼ pressure, N/m 2 , v ¼ velocity, m/s

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TABLE 23-8

Abrasion pressures for bearings

Pressure

ﬁtted rubbing surface

0.50 C machine steel or wrought iron on genuine

hard babbitt

Case-hardened machine steel on case-hardened

machine steel

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IDEALIZED JOURNAL BEARING (Figs 23-8

and 23-9)

The diametral clearance ratio or relative clearance

Attitude or eccentricity ratio or eccentricity coeﬃcient

Oil ﬁlm thickness at any position

For position of minimum oil thickness and max oil

ﬁlm pressure

Minimum oil ﬁlm thickness

The minimum oil ﬁlm thickness variable

Precision spindle, hardened and ground steel, lapped into bronze

Electric motors and generators, ground journals in broached or

General machinery, intermittent or continuous motion, turned or

cold-rolled journal in reamed and bored bronze or babbitt

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Lightly loaded bearing

Beyond this point

S = 159.36

Bearing characteristic number, S =ηnP ψ12

(a) Moderately and lightly loaded

bearing

Bearing characteristic number, S =ηn’P ψ12

(b) Heavily loaded bearing

Bearing Characteristic Number, S = ηn’ P ψ12

23.22

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23.23Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

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The safe oil ﬁlm thickness for a bearing in good

condition and vm 1 m/s (200 ft/min)

The thickness of oil ﬁlm where the pressure is

maxi-mum or minimaxi-mum

The resultant pressure distribution around a journal

bearing excluding Po the oil ﬁlm pressure at the

point where

The pressure at any point (Figs 23-8 and 23-9)

The load carrying capacity of the bearing [Fig 23-8

hmin¼ 0:0015v0:4

m A0:2 Customary Metric ð23-34bÞwhere hminin mm, A in mm2, and vmin m/s

"ð2 þ " cos Þ sin ð2 þ "2Þð1 þ " cos Þ2

ð23-36Þ

W ¼UL2

2ð2 þ "2Þpffiffiffiffiffiffiffiffiffiffiffiffiffi2 "2

!

ð23-38Þ

S ¼n0P

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The constant of the bearing or bearing modulus

The calculation of minimum oil ﬁlm thickness from

Figs 23-14 and 23-16

The bearing characteristic number or Sommerfeld

number as a function of attitude

The angular positions of points where the maximum

or minimum pressure in the oil ﬁlm occur [Fig 23-8c

and Fig 23-9]

For positions of maximum oil ﬁlm pressure and oil

ﬁlm termination vs bearing characteristic number S

S00¼n

where in Pa s (cP)Refer to Table 23-7 for bearing modulus

Hint: S is determined from Eq (23-39) and CL fromFig 23-16 for a given ðL=dÞ ratio Calculate60S=ðCL106Þ Knowing 60S=ðCL106Þ, you can thenobtain the minimum ﬁlm thickness variable fromFig 23-14 From and Eq (23-33), you can thendetermine the minimum oil ﬁlm thickness

1 2

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TABLE 23-11

Dimensionless performance parameters for full journal bearings with side ﬂow

Key : Qs ¼ ﬂow of lubricant with side ﬂow, cm 3

/s; ¼ weight per unit volume of lubricant whose speciﬁc gravity is 0.90 ¼ 8.83 kN/m 3

(0.0325 lbf/

in 3 ); csp¼ specific heat of the lubricant, kJ/NK (Btu/lbf 8F) ¼ 0.19 kJ/NK (0.42 Btu/lbf 8F); T0 ¼ difference in temperature, 8C.

Source: A A Raimondi and J Boyd, ‘‘A Solution for the Finite Journal Bearings and Its Applications to Analysis and Design’’ ASME, J cation Technol., Vol 104, pp 135–148, April 1982.

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TABLE 23-12

Dimensionless performance parameters for 1808 bearing centrally loaded with side ﬂowa

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TABLE 23-13

Dimensionless performance parameters for 1208 for centrally loaded bearing with side ﬂowa

a See Key and Source under Table 23-11.

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TABLE 23-14

Dimensionless performance parameters for 608 centrally loaded bearing with side ﬂowa

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The total frictional resistance on an idealized journal

bearing surface

The total frictional resistance on an idealized lightly

loaded journal bearing

For the relation between dimensionless quantity

an idealized full journal bearing.

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The relation between coeﬃcient of friction and

bear-ing characteristic number

The relation between the coeﬃcient of friction and

Average coeﬃcient of friction at very high pressure

Angular displacement, deg

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INFLUENCE OF MISALIGNMENT OF

SHAFT IN BEARING

Minimum oil ﬁlm thickness corresponding to the

materials factor (km), the surface roughnesses (Rp)

and amount of misalignment of the journal and

Turned or rough ground

Ground or ﬁne bored

Lapped or polished

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Bearing load capacity number

The required grease supply rate per hour for grease

lubricated bearing

The coeﬃcient of friction

The diameter of journal bearing for speeds below

Values of factorkgfor grease lubrication at

various rotational speeds

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60 Partial journal bearings

01 52 0

Coefficient of friction variable,

B/L = 3

B/L = 2

B/L = 1 0

B/L = 4

B/L = 3

B/L = 2

B/L = 1 0

B/L = 2

/L 1 0

B/L = 1 0

/L 0

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B/L = 0 B/L = 1 0 B/L = 2 0 B/L = 3

B/L = 4

B/L = 2

B/L = 3

B/L = 4

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PARTIAL JOURNAL BEARING (Fig 23-25)

The resultant pressure distribution around the partial

journal bearing excluding, Pooil ﬁlm pressure at the

Bearing Characteristic Number, S = ηn’ ( )ψ12

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Pressure at any point in a partial journal bearing

To determine the attitude" and attitude angle for

various values of S and for an idealized oﬀset partial

bearing having the maximum load capacity

corre-sponding to a given attitude

INFLUENCE OF END LEAKAGE

Leakage factors CW, CF, and C

Refer to Figs 23-26 and 23-27 respectively

Refer to Fig 23-28 for CW, CF, and Cfor variousvalues of B=L ratios

Trailing edge Line of centers

ho = hmin

Pmaxh’max

partial bearing having the maximum load capacity corresponding to a

given attitude.

0 0.1

0.2 0.3 0.4 0.5 0.6 10

20 30 40 50 60 70 80 90

ηn’ P Bearing characteristic number, S = ψ12

an idealized oﬀset partial bearing.

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Load leakage factor according to Kingsbury6

Load leakage factor CWas a function of B=L ratio for

a slider bearing having q ¼ ðh1=h2Þ 1 ¼ 1 or

h1¼ 2h2

Load leakage factor for 1208, centrally loaded partial

bearing according to Needs7

Load correction factor for side ﬂow according to

Boyd and Raimondi24

Coeﬃcient of friction leakage factor according to

Kingsbury6

Friction leakage factor according to Kingsbury6

Friction leakage factor for 1208, centrally loaded

partial bearing according to Needs7

CW ¼ W

Refer to Fig 23-28 for CW.Refer to Table 23-16

Refer to Fig 23-29 for CW for various attitudes"

Refer to Fig 23-30 for CW for various minimum oilﬁlm thickness variables

B L 2.0 2.5 3.0 2.5 4.0

TABLE 23-16Load leakage factorCWas a function ofB=L ratiofor a slider bearing having the qualityq equal tounity

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∈=0 8

∈=0

6

∈=0 4

∈=0 2

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Friction correction factor for side ﬂow according to

Boyd and Raimondi5

The ratios of the maximum pressure in the oil ﬁlm

Pmax, and the unit load, P, with B=L ratios for various

values of attitude,", for 1208 central partial journal

bearing according to Needs7

The variation of attitude,", with bearing

characteris-tic number, S, for various values of B=L ratios for 608,

1208, 1808 partial and full journal bearings

The variation of coeﬃcient of friction variable,

¼ = , with bearing characteristic number, S, for

various values of B=L ratios for 608, 1208, 1808,

par-tial and full journal bearing

The friction curves illustrating boundary conditions

Refer to Fig 23-32 for CF for various minimum oilﬁlm thickness variables and B=L ratios

Refer to Fig 23-33 for Pmax=P and Fig 23-34 forP=Pmaxfor various values of B=L ratios and attitudes

=

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0

B/L = 2 0 B/L = 1 0 B/L =

0

B/L = 4 0 B/L = 3 0 B/L = 2 0 B/L = 1 0

B/L = 0

0 B/L = 3 0

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FRICTION IN A FULL JOURNAL BEARING

WITH END LEAKAGE FROM BEARING

The total friction force acting on the surface of a full

journal bearing with end ﬂow

The coeﬃcient of friction variable

Petroff

Representative experimental

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Lasche’s equation for the coeﬃcient of friction which

may be used for bearing subjected to pressure varying

from 0.103 MPa (15 psi) to 1.55 MPa (225 psi) and

speed varying from 2.5 to 18 m/s and temperature

varying from 30 to 1008C

The coeﬃcient of friction according to Illmer when

bearing is subjected to pressure varying from

0.23 MPa (35 psi) to 0.7 MPa (100 psi) and speed

vary-ing from 0.5 m/s to 1.5 m/s (100 ft/min to 300 ft/min)

The coeﬃcient of friction according to Tower tests

P ¼ 0:02=t Customary Metric ð23-57bÞwhere P in kgf/mm2and t in 8C

where P in psi and t in 8F

¼23;126

P ﬃﬃt

where P in N/m2and t in K

¼0:00236

P ﬃﬃt

where P in kgf/mm2and t in 8C

¼ 4:5

P ﬃﬃt

¼

vp

20 ffiffiffiffiffiPt

where P in psi, v in ft/min, and t in 8F

¼144;204:5P

ffiffiffivt

r

SI ð23-60aÞwhere P in N/m2, v in m/s, and t in K

¼0:0147P

ffiffiffivt

r

Customary Metric ð23-60bÞwhere P in kgf/mm2, v in m/s, and t in 8C

¼2P

ffiffiffivt

r

USCS ð23-60cÞwhere P in psi, v in ft/min, and t in 8F

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The coeﬃcient of friction according to Lasche when

the speed exceeds 2.5 m/s (500 ft/min)

OIL FLOW THROUGH JOURNAL

BEARING

Oil ﬂow through bearing

Oil ﬂow through a central groove of bearing from one

end

Total oil ﬂow through a central groove of bearing

from both ends

Total oil ﬂow through a central groove for lightly

loaded bearing [From Eq (23-65) as" ! 0]

Total oil ﬂow through a central groove for heavily

loaded bearing [From Eq (23-65) as" ! 1]

Oil ﬂow through a single hole

¼24:73ffiffiffiffiffiPt

where P in N/m2and t in K

¼0:0079ffiffiffiffiffiPt

where P in kgf/mm2and t in 8C

¼ 0:4ffiffiffiffiffiPt

Q ’3

ð23-68Þ

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The ratio of Qg to Qh in the unloaded region of

bearing from Eq (23-65) and (23-68)

Flow variable (dimensionless)

Oil ﬂow through a bearing with side leakage

Oil flow ratio Qs

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THERMAL EQUILIBRIUM OF JOURNAL

¼ ðPLdÞd

2! ¼ ðPLdÞv SI ðUSCSÞ ð23-72aÞwhere Hgin J/s (Btu/s), Mtin N m (lbf in), W in

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δ = 0 05

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The heat generated can also be found by knowing the

temperature rise of lubricant oil which is used to carry

away heat generated in the bearing

Temperature rise of the lubricant ﬁlm variableT

The temperature rise of the lubricant ﬁlm due to heat

generated which is to be carried away by the

lubri-cant, can be found from Eq (23-66c)

If the end ﬂow is also taken into consideration then

the temperature rise of the ﬂow Q Qeldue to heat

generated, isT and the temperature rise of end

leak-age isT=2, which is the average of the inlet and the

¼ weight per unit volume of lubricant whoseaverage speciﬁc gravity is 0.90

¼ 8:83 kN/m3(0.0325 lbf/in3)

Csp¼ speciﬁc heat of lubricant, kJ/N K (Btu/lbf 8F)

¼ 0.19 kJ/N K (0.42 Btu/lbf 8F)

Q in m3/s;T in 8CRefer to Fig 23-44 forT

T ¼ 78P

Q

¼ 78ð= ÞP4Q=d2n0L ¼ 19:5 P

Q=d2n0LCustomary Metric ð23-74bÞwhere P in kgf/mm2, d in mm, L in mm, Q in mm3/s,

in rps, andT in 8F

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n0in rps, andT in K

For L = 1 d

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The temperature rise of the lubricant ﬁlm due to heat

generated in pressure fed bearings

Heat dissipated by self-contained bearings

Another formula for the heat dissipated in bearing in

terms of average lubricant oil ﬁlm temperature

The heat dissipating capacity of bearing based on

projected area of bearing

Pederson’s equation for heat radiating capacity of

bearing due to friction between journal and bearing

T ¼16ð1 þ 1:5" 106ð= ÞSW2ÞP 2

where W in N, PSin N/m2, d in m, and T in K

T ¼ 9:7ð= ÞSW2ð1 þ 1:5"2ÞPSd4 Customary Metricð23-76bÞwhere W in kgf, PSin kgf/mm2, d in mm, and T

in8C

where

C ¼ combined coeﬃcient of radiation and convection

¼ 9:6 103kW/m2K (1.7 Btu/ft2h8F) when thebearing located in still air and oil bath

¼ 11:36 103kW/m2K (2 Btu/ft2h8F) when thebearing located in air circulation and in oil bath

¼ 15:36 103kW/m2K (2.7 Btu/ft2h8F) foraverage design practice

¼ 33:5 103kW/m2K (5.9 Btu/ft2h8F) when theair velocity over the bearing is 2.5 m/s (500 ft/min)

A ¼ eﬀective surface area of bearing housing

¼ (25 104dL) in m2for bearing masses of metal

as in a ring oil bearing (25 dL in in2)

¼ (6 104dL) in m2for light construction (6 dL in

in2)

tb¼ surface temperature of bearing housing, 8C (8F)

ta¼ temperature of surrounding air, 8C (8F)

Hd¼ CA

where m can be assumed as constant whichdepends on the lubrication system and it istaken from Table 23-17a, tois lubricant ﬁlmtemperatures,8C

C and A are as given under Eq (23-67a)

and Hdin J/s

¼ k < dðtb taÞ USCS ð23-68cÞwhere kðtb taÞ in ft-lbf/min/in2/8F values can betaken from Fig 23-45(b)

Hd¼ðT þ 18Þ2

TABLE 23-17a

Values of factor,m in Equation (23-67b)

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an idealized oﬀset partial bearing.

DESIGN OF BEARINGS... (www.digitalengineeringlibrary.com)

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Tiêu đề	Design of Bearings and Tribology
Trường học	McGraw-Hill Education
Chuyên ngành	Mechanical Engineering
Thể loại	Textbook
Năm xuất bản	2010
Thành phố	New York

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