Machine Design Databook Episode 3 part 4 docx

TABLE 23-76 Series designation Series Over Up to series Over Up to series Over Up to 1 Reserved for future use A Reserved for future use A Reserved for future use B r dφDφ E α T Download

General Plan Boundary Dimensions for Tapered Roller Bearings

There are four series in tapered roller bearings They are: (1) Angle series, (2) diameter series, (3) width series, (4) dimension series Dimension series is a combination of angle series, diameter series and width series Dimension series shall be designated by a combination of three symbols, for example 2BD The first symbol is a numeric character which represents a range of contact angles (angle series) The second symbol is an alphabetic character which represents range of numeric values for the outside diameter to bore relationship (diameter series) The third symbol is an alphabetic character which represents a range of numeric values of the width to section relationship (width series).

TABLE 23-76

Series designation

Series Over Up to series Over Up to series Over Up to

1 Reserved for future use A Reserved for future use A Reserved for future use

B

r

dφDφ

E

α

T

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TABLE 23-77

Dimensions for tapered roller bearings—Contact angle series 2

B

r

dφDφ

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TABLE 23-77 (Cont.)

B

r

dφDφ

Courtesy: Extracted from IS: 7461 (part 1) 1993

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TABLE 23-78

Dimensions for tapered roller bearings—Contact angle series 5

Courtesy: Extracted from IS: 7461 (part 1) 1993

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NA1012 RNA1012 Na1012 Na1012S/Bi 12 17.6 28 15 35 11280 9415 21600NA1015 RNA1015 Na1015 Na1015S/Bi 15 20.8 32 15 35 12600 10890 18300NA1017 RNA1017 Na1017 Na1017S/Bi 17 23.9 35 15 65 12260 12260 15900NA1020 RNA1020 Na1020 Na1020S/Bi 20 28.7 42 18 65 19610 18340 13200

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NA2015 RNA2015 Na2015 Na2015S/Bi 15 22.1 35 22 65 24320 21570 17200NA2020 RNA2020 Na2020 Na2020S/Bi 20 28.7 42 22 65 29220 26280 13200NA2025 RNA2025 Na2025 Na2025S/Bi 25 33.5 47 22 65 31580 31580 11100NA2030 RNA2030 Na2030 Na2030S/Bi 30 38.2 52 22 65 35700 35700 10000NA2035 RNA2035 Na2035 Na2035S/Bi 35 44 58 22 65 39230 40500 8600NA2040 RNA2040 Na2040 Na2040S/Bi 40 49.7 62 22 65 42950 45600 9600NA2045 RNA2045 Na2045 Na2045S/Bi 45 55.4 72 22 55 46580 50500 6900NA2050 RNA2050 Na2050 Na2050S/Bi 50 62.1 80 28 65 63740 74530 6100NA2055 RNA2055 Na2055 Na2055S/Bi 55 68.8 85 28 65 71100 82380 5500NA2060 RNA2060 Na2060 Na2060S/Bi 60 72.6 90 28 65 74040 84340 5200NA2065 RNA2065 Na2065 Na2065S/Bi 65 78.3 95 28 65 80410 95610 4900NA2070 RNA2070 Na2070 Na2070S/Bi 70 83.1 100 28 65 83360 101010 4500NA2075 RNA2075 Na2075 Na2075S/Bi 75 88 110 32 65 105910 131410 4300NA2080 RNA2080 Na2080 Na2080S/Bi 80 96 115 32 65 112780 143180 4000

Courtesy: IS: 4215, 1993

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NA3030 RNA3030 Na3030 Na3030S/Bi 30 44 62 30 0.65 35790 68160 8600NA3035 RNA3035 Na3035 Na3035S/Bi 35 49.7 72 36 0.65 91690 98070 7600NA3040 RNA3040 Na3040 Na3040S/Bi 40 55.4 80 36 0.65 102970 107870 6900NA3045 RNA3045 Na3045 Na3045S/Bi 45 62.1 85 38 0.85 106890 121600 6100NA3050 RNA3050 Na3050 Na3050S/Bi 50 68.8 90 38 0.65 115720 134350 5500NA3055 RNA3055 Na3055 Na3055S/Bi 55 72.6 95 38 0.65 119640 141220 5200NA3060 RNA3060 Na3060 Na3060S/Bi 60 78.3 100 38 0.65 126510 151026 4900NA3065 RNA3065 Na3065 Na3065S/Bi 65 83.1 105 38 0.65 131410 160830 4500NA3070 RNA3070 Na3070 Na3070S/Bi 70 88 110 38 0.65 137290 169650 4300NA3075 RNA3075 Na3075 Na3075S/Bi 75 96 120 38 0.65 140230 184360 4000NA3080 RNA3080 Na3680 Na3080S/Bi 80 99.5 125 38 0.65 149060 190250 3800NA3085 RNA3085 Na3085 Na3085S/Bi 85 104.7 130 38 0.65 153960 198090 3600

Courtesy: IS: 4215, 1993

TABLE 23-87

Hardness factors for needle-roller bearings

Maximum shear stress occurs below the contact

surface for ductile material

(ii) For cylinders

SELECTION OF FIT FOR BEARINGS

For selection of fit for housing seatings for radial and

thrust bearings

For selection of fit for shaft (solid) seatings for radial

and thrust bearings.

Refer to Table 23-91.

Refer to Table 23-92.

TABLE 23-88

Torrington needle-roller sizes

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TABLE 23-91

Selection of fit

(a) Housing seatings for radial bearings

Solid HousingsRotating outer-ring load

Heavy loads on bearings in thin walled housings;

heavy shock loads

Direction of loading indeterminate

Heavy and normal loads; axial mobility of outer ring

unnecessary

Normal and light loads; axial mobility of outer ring

desirable

Split or Solid HousingStationary outer-ring load

Solid HousingsArrangement of bearing very accurate

Accurate running and great rigidity under variable

load

Roller bearings D > 125 mmFor machine-tool D < 125 mm main spindles

N6M6Accurate running under light loads of indeterminate

direction

Ball bearings at work end of grinding spindle;

locating bearings in high-speed centrifugalcompressors

(b) Housing seatings for thrust bearings

Spherical roller thrust bearings where another bearingtakes care of the radial location

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TABLE 23-92

Selection of fit

(a) Shaft (solid) seatings for radial bearings

Shaft diameter, mm

Bearings with cylindrical boreStationary inner-ring load

Easy axial displacement of

inner ring on shaft

desirable

Easy axial displacement of

inner ring on shaft

unnecessary

Rotating inner-ring or direction of loading indeterminate

machine tools; pumps;

transport vehicles

1818–100100–200

—

4040-140140-200

—

4049-100100-200

h5j6k6m6

motors pumps; turbines;

gearing; wood workingmachines; and internal-combustion engines

1818–100100–140140–200200–280

—

4040–100100–140140–200200–400

—

4040–6565–100100–140140–280280–500

>500

j5k5m5m6n6p6r6r7

—

—

50–100100–140140–200200–500

n6p6r6r7

arrangements

Bearings with taper bore and sleeve

general; railway axle boxes

(b) Shaft seatings for thrust bearings

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23.3 FRICTION AND WEAR 1

SYMBOLS

exponent

junctions, kN (lbf )

which the surface layer must undergo under given abrasion condition, kN (lbf )

kN (lbf )

effective thickness of the worn-out surface layer, m (in)

number of repeated deformation as used in Eqs (23-256) to (23-258)

deformation

stress), MPa (psi)

flow pressure of material, MPa (psi)

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q friction work done corresponding to a simple stressing cycle

radius of circular junction (Fig 23-60), m (in)

m (in)

expressed in terms of their surface energies, N m (lbf in or lbf ft)

normal load per unit area, kN (lbf )

material, kN (lbf )

the absolute approach, m (in)

23-73

stress, MPa (psi)

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The general expression for force of friction

The total friction force

The real area of contact

The general expression for coefficient of friction

The total coefficient of friction

The coefficient of elastic friction when a rigid rough

surface is pressed against an elastically deformable

second surface

Greenwood and Tabor’s formula for coefficient of

Stiehl’s formula for coefficient of friction

Schutch’s formula for coefficient of friction for leather

sliding against slightly lubricated steel plate

9 64

Krumme’s formula for coefficient of friction in textile

machinery

Formula for coefficient of friction used in design of

brakes

Temperature of sliding surface

Mean temperature rise at the interface above the

v ¼ velocity of sliding, cm/s (ft/min)

r ¼ radius of the circular junction, cm, m (in)

Table 23-95

TABLE 23-94

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Simple and crude formula for the mean temperature

rise

The radius of a junction (Fig 23-60)

The load carried by each junction (Fig 23-60)

Mean temperature rise at the interface above the rest

of material

WEAR AND ABRASION

Linear wear rate

Steady state wear rate, depth per unit time

Volumetric wear rate

Energetic wear rate

The energetic and linear wear rate related by equation

The gravimetric wear rate

member, N/m (lbf/in) taken from Table 23-95

For a, b, c, d, e, refer to Table 23-103.

Wear index is given by abradability, 

The coefficient of abrasion resistance as per work in

the former Soviet Union

For surface roughness as obtained by different

machining processes

Work done during wear

Volume of transferred fragments formed in sliding a

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Another formula for volume of transferred fragment

formed in sliding a distance

The primary equation of wear according to Archard,

Burwell, and Strang

Abrasion wear

The mean diameter of loose wear particles which are

produced at a smooth interface

The ratio of half mean diameter of the area of contact

to mean radius of the curvature at the tip of the

For K, refer to Table 23-100.

W

Volumetric wear rate

Half the mean diameter of the area of contact for

The spacing s between ridges in the elastomer surface

of closely packed hemisphere so that d ¼ 2R

Fatigue wear

Volume of surface layer removed under fatigue

The required sliding length during abrasion cycle

under the given abrasion conditions before failure

and separation occurs

The total work of friction

The coefficient of abrasion resistance

The Hertzian relationship for the average depth of

penetration for single spheres

The depth penetration

R ¼ asperity tips radius, cm, m (in)

E ¼ Young’s modulus for rubber, GPa (psi)

W ¼ applied load per asperity

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The number of asperities

The effective thickness of the surface layer of

elastomer

The coefficient of abrasion resistance

The ratio of abrasion resistance to coefficient of

sliding friction

The fatigue resistance of rubber taking into

con-sideration tensile strength, geometry of the base

surface, and the loading conditions

The ratio of abrasion resistance to coefficient of

friction

The relationship between fatigue index b and 

Roll formation

The coefficient of abrasion resistance

The main condition which determines the probable

occurrence of roll formation

The more general form of the equation for volumetric

wear rate which dependence on abrasion by load

ð23-306Þ where b ¼ index which is characteristic of the material

where K ¼ constant

where

C ¼ constant taken from Table 23-101

P ¼ interfacial pressure, MPa (psi)

 is obtained from Table 23-101.

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Tread rubber

The shearing stress for tread rubber

The critical shearing stress for tread rubber

Specific wear by mass

Specific wear by volume

Specific wear by volume based on the geometry of the

aspirities arising out of the surface treatment

where P ¼ normal pressure, MPa (psi)

The fatigue wear predominates.

Either wear through roll formation or abrasive wear occurs.

The wear is due to surface fatigue.

Other forms of wear predominate.

can be obtained from Table 23-102 and the

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The absolute approach

An expression for modified specific wear

Modified specific wear formula during microcutting

Modified specific wear formula during plastic contact

ð23-316Þ where

2 ¼ diameter of contact spot, cm

 ¼ tangent to the smoothness of the surface equal

to the derivative of approach over the contact

Radii of curvature asperities for different methods of surface preparation

Modified specific wear formula during elastic contact

GENERAL

For values of wear rate correction factors; physical and

mechanical properties of clutch facings; mechanical

properties, performance and allowable operating

conditions for various materials; physical and

mechan-ical properties of materials for sliding faces; rubbing

bearing materials and applications and allowable

working conditions and frictions for various clutch

"

ð23-320aÞ where

8

ffiffiffi

 p

r

b 2

Approximate values of wear rate correction factors

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TABLE 23-104

Physical and mechanical properties of clutch facings

kgf/mm2

106

N

=m2MPa

kgf/mm2

106

N

=m2MPa

kgf/mm2

106

N

=m2MPa

kgf/mm2

106

N

=m2MPa

Wearrateat1008C,mm3/J

MaximumMaximumoperating

kgf/mm2

10

3

103N/m2

10

3

MPa

kgf/mm2

106

N

=m2MPa

23.169

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Hardness, H

kcal/mh 8C W/mK kcal/mh W/m

23.170

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Hardness, H

kcal/mh 8C W/mK kcal/mh W/m

23.171

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6 Kingsbury, A., ‘Optimum Conditions in Journal Bearing,’ Trans ASME, Vol 54, 1932.

7 Needs, S J., ‘Effect of Side Leakage in 120-degree Centrally Supported Journal Bearings,’ Trans ASME, Vol 56, 1934; Vol 51, 1935.

8 Shigley, J E., Mechanical Engineering Design, First Metric Edition, McGraw-Hill Book Company, New York, 1986.

9 Edwards, K S., Jr., and R B McKee, Fundamentals of Mechanical Component Design, McGraw-Hill Book company, 1991.

10 Shaw, M C., and F Macks, Analysis and Lubrication of Bearings, McGraw-Hill Book Company, New York, 1949.

11 Lingaiah, K., Machine Design Data Handbook, McGraw-Hill Publishing Company, New York, U.S.A., 1994.

12 FAG Rolling bearings, Catalog WL 41520EI, 1995 edition, FAG Precision Bearings Ltd., Maneja, Vadodara, India.

TABLE 23-108

Allowable working conditions and friction for various clutch facing materials

Temperature

Working pressure

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13 SKF Rolling Bearings, Catalog 4000E 1989, SKF Rolling Bearings, India Ltd., Mumbai, India.

14 Bureau of Indian Standards, Manak Bhavan, 9 Bahadur Shah Marg, New Delhi 110 002, India.

15 Neale, M J., Editor, Tribology Handbook, Butterworth, London, 1973.

16 International Organization for Standards, 1, rue de Varembe, Case Postale 56, CH 1211, Geneve 20, Switzerland.

17 New Departure-Hyatt Bearing Division, General Motor Corporation, USA.

18 NSK Corporation (Corporate), Automotive Products Bearing Division, 3861 Research Park Drive, Ann Arbor, Michigan 48100-1507, USA.

19 The Torrington Company, 59 Field Street, Torrington, Conn 06790, USA.

20 Antifriction Bearing Manufacturers Association, USA.

21 Black, P H., and O E Adams, Jr., Machine Design, McGraw-Hill Publishing Company, New York, 1968.

BIBLIOGRAPHY

ASME Standards.

Baumeister, T., ed., Marks’ Handbook for Mechanical Engineers, McGraw-Hill Book Company, New York, 1978 Black, P H., and O E Adams, Jr., Machine Design, McGraw-Hill Book Company, New York, 1968.

Boswall, R O., The Theory of Film Lubrication, Longmans, Green and Company, New York, 1928.

Bureau of Indian Standards.

O’Connor, J J ed., Standard Handbook of Lubricating Engineering, McGraw-Hill Book Company, New York, 1968.

Fuller, D P., The Theory and Practice of Lubrication for Engineers, John Wiley and Sons, New York, 1956 Niemann, G., Machine Elements—Design and Calculations in Mechanical Engineering, Vol II, Springer-Verlag, Berlin, 1950; Student Edition, Allied Publishers Private Ltd Bangalore, India, 1979.

Niemann, G., Maschinenelemente, Springer-Verlag, Berlin, Erster Band, 1963.

Niemann, G., Maschinenelemente, Springer-Verlag, Berlin, Zweiter Band, 1965.

Hyland, P H., and J B Kommers, Machine Design, McGraw-Hill Book Company, New York, 1943.

ISO Standards

Lansdown, A R., Lubrication: A Practical Guide to Lubricant Selection, Pergamon Press, New York, 1982 Leutwiler, O A., Elements of Machine Design, McGraw-Hill Book Company, New York, 1917.

Michell, A G M., Lubrication—Its Principles and Practice, Blackie and Son, London, 1950.

Neale, M J., ed., Tribology Handbook, Butterworth, London, 1973.

Norman, C A., E S Ault, and I F Zarobsky, Fundamentals of Machine Design, The Macmillan Company, New York, 1951.

Norton, A E., Lubrication, McGraw-Hill Book Company, New York, 1942.

Slaymaker, R R., Bearing Lubrication Analysis, John Wiley and Sons, New York, 1955.

Rippel, H C., ‘‘Design of Hydrostatic Bearings,’’ Machine Design, Parts 1 to 16, Aug 1 to Dec 5, 1963 SAE Handbook, 1957.

Shigley, J E., Machine Design, McGraw-Hill Book Company, New York, 1962.

Shigley, J E., and C R Mischke, Standard Handbook of Machine Design, McGraw-Hill Book Company, New York, 1986.

Shigley, J E., and C R Mischke, Mechanical Engineering Design, McGraw-Hill Book Company, New York, 1989.

Vallance, A., and V L Doughtie, Design of Machine Members, McGraw-Hill Book Company, New York, 1951 Wilcock, D F., and E R Booser, Bearing Design and Application, McGraw-Hill Book Company, New York, 1957.

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