Machine Design Databook Episode 3 part 1 doc

23-9General 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 f

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 10
3 USCSU

SI Units,

10
9

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.

TABLE 23-3

Values of factorC1in Eq (23-23)

Oil, free drop (constant feed) Good Fairly good Favorable (ordinary condition) 2

Oil cup or grease (intermittent

Values of factorC2in Eq (23–23)

Rotating flat surfaces lubricated from the center to the circumference, such as annular step or pivot bearings 2

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

r + c2 w

FIGURE 23-8 Behaviour of a journal in its bearing.

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

FIGURE 23-9 Oil film pressure distribution in the full journal bearing.

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

TABLE 23-5

Allowable bearing pressure, reciprocating motion

Pressure, P

TABLE 23-6

Permissible Pv values

Values

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

oil-lubrication, maximum value

Mill shafting, self-aligning ring-oiled babbitt bearings, maximum 24,000 8.45 10 5

Self-aligning ring-oiled bearings, continuous load in one direction 35,000–40,000 12.3 10 5 to 14 10 5

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

TABLE 23-8

Abrasion pressures for bearings

Pressure

Hardened tool steel on lumen or phosphor bronze 10,000 68.8 Values applies to rigid, polished and accurately

fitted rubbing surface 0.50 C machine steel on lumen or phosphor bronze 8,000 55.0 When not worn to a fit or well lubricated reduce

to 4.22 kgf/mm2(41.4 MPa) Hardened tool steel on hardened tool steel 7,000 48.0

0.50 C machine steel or wrought iron on genuine

hard babbitt

Cast iron on cast iron (close grained or chilled) 4,500 31.0

Case-hardened machine steel on case-hardened

machine steel

0.30 C machine steel on cast iron (close-grained) 3,500 24.0

0.40 C machine steel on soft common babbitt 3,000 20.6

Soft machine steel on machine steel (not case- 2,000 13.8

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

reamed bronze or babbitt bearings; 0.4–0.8 mm rms

General machinery, intermittent or continuous motion, turned or

cold-rolled journal in reamed and bored bronze or babbitt

Lightly loaded bearing

Beyond this point

(a) Moderately and lightly loaded

bearing

(b) Heavily loaded bearing

FIGURE 23-10 Variation of attitude " of full journal bearing with characteristic number S [Radzimosvksy 4 ]

FIGURE 23-11 Position of minimum oil film thickness vs bearing characteristic number S for full journal bearing (Refer to Fig 23-9 for definition of ) [Boyd and Raimondi 5 ]

23.22

2nmin c

FIGURE 23-13 Variation of minimum oil film thickness variable  of full journal bearing with S.

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

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

FIGURE 23-15A Position of maximum oil film pressure and oil film termination versus bearing characteristic number S [Boyd and Raimondi24] (Refer to Fig 23-9 for definition of  P max , and  P 0 )

TABLE 23-11

Dimensionless performance parameters for full journal bearings with side flow

Values of 

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.

Lubri-TABLE 23-12

Dimensionless performance parameters for 1808 bearing centrally loaded with side flowa

Values of 

TABLE 23-13

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

Values of 

TABLE 23-14

Dimensionless performance parameters for 608 centrally loaded bearing with side flowa

Values of 

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

F
0 with Sommerfeld number S for

an idealized full journal bearing.

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

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

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

Lubricant feed rate Q

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

Coefficient of friction variable,

B/L = 2

/L 1 0

B/L = 1 0

/L 0

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

B/L = 4

Coefficient of friction variable,

B/L = 2

B/L = 3

B/L = 4

PARTIAL JOURNAL BEARING (Fig 23-25)

The resultant pressure distribution around the partial

journal bearing excluding, Pooil film pressure at the

FIGURE 23-24 Variation of the coefficient of friction variable 
¼
= with S for 3608 journal bearing [Boyd and Raimondi 5 ]

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 C
for variousvalues of B=L ratios

Trailing edge Line of centers

FIGURE 23-26 Variation of attitude " with S for an idealized offset

partial bearing having the maximum load capacity corresponding to a

given attitude.

0 0.1

10 20 30 40 50 60 70 80 90

ηn’ P

FIGURE 23-27 Variation of attitude angle with S for

an idealized offset partial bearing.

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

Refer to Fig 23-31 for CF for various attitudes"

B L

ratios under minimum friction [Kingsbury6]

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

∈=0 8

∈=0

6

∈=0 4

∈=0 2

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

=

FIGURE 23-31 Leakage factors for friction force for 120 8 centrally loaded partial journal bearings for various attitudes [Needs7]

= FIGURE 23-32 Friction correction factor for side flow [Boyd and Raimondi5]

P max P

=

FIGURE 23-33 The ratio of the maximum pressure (P max ) and the unit load Pð¼ P u Þ with B=L ratios for various attitudes for a

120 8 central partial bearing [Needs 7 ]

60 Partial journal bearings

180 Partial journal bearings

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

B/L = 0 B/L = 3 0

B/L = 0

B/L = 1 0 B/L =

B/L = 0

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

FIGURE 23-39 Friction curves illustrating boundary conditions.

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

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

& #34 ;2 ỵ & #34 ; cos ị sin 2 ỵ & #34 ;2? ?1 ỵ & #34 ; cos ị2



23- 36ị

W ẳUL2

22 ỵ & #34 ;2ịp2
... Analysis and Design? ??’ ASME, J cation Technol., Vol 10 4, pp 13 5 ? ?14 8, April 19 82.

Lubri-TABLE...

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

=

FIGURE 23- 31 Leakage factors