lecture5 bearings

77
ME 350 1 ME 350 Mechanical Design and Manufacturing II Transmission Support Bearings 轴轴

Upload: mahesh

Post on 16-Nov-2014

2.183 views

Category:

Documents


22 download

DESCRIPTION

bearing selection guide

TRANSCRIPT

Page 1: Lecture5 Bearings

ME 350

1

ME 350 Mechanical Design and

Manufacturing II

Transmission SupportBearings (轴承)

Page 2: Lecture5 Bearings

ME 350

2

Lectures

Power/Energy

Conversion(Electrical Motors)

Power/EnergyConversion

(Electrical Motors) Power/EnergyTransmission

(Gears, Belt Drives,

Power Screws)

TransmissionTransmissionSupportSupport

(Bearings)(Bearings)

Joints(Fasteners,

Connectors)StructuralSupport(FramesShaftsAxles

Spindles)

ToolsStress Analysis, Failure Theories

Dynamics, Statics, Etc….

Page 3: Lecture5 Bearings

ME 350

3

Why Bearings

Bearing is defined by Webster’s to be “a support or supporting part”

– In machine design, a bearing is a component that allows for relative motion between two bodies

Bearings are for:

reduce friction carry load guide of moving parts

Page 4: Lecture5 Bearings

ME 350

4

History

Page 5: Lecture5 Bearings

ME 350

5

Reconstruction of Old Bearing

Page 6: Lecture5 Bearings

ME 350

6

Development of the Bearing

700 B.C.

3500 B.C.

40 A.D.

1794 A.D.1869

1995

Page 7: Lecture5 Bearings

ME 350

7

Sliding or Rolling Bearings

Sliding bearings:

sliding friction µRolling bearings:

rolling frictionµ

Page 8: Lecture5 Bearings

ME 350

8

Principles of OperationRolling Friction (Rolling Bearing 滚动轴承 )

Roller/ball(滚子 / 球)Lubrication(润滑剂)

Outer Ring (外圈)

Inner Ring (内圈)

Sliding Friction (Sleeve Bearing 滑动轴承 )

Sleeve (轴瓦)

Lubrication

Circumferential pressure profile

Hydrodynamic lift is generated by fluid being dragged into gap by viscous shear

Page 9: Lecture5 Bearings

ME 350

9

Types of Antifriction BearingsBall Bearings

内径

外径

端面 外圈滚道

内圈滚道

保持架

Page 10: Lecture5 Bearings

ME 350

10

Bearings Components

Seal Rolling elements Inner ring Outer ring Cage Seal

Page 11: Lecture5 Bearings

ME 350

11

Types of Antifriction Bearings

Tapered Roller Bearings

保持架

•Components:Cone

=Inner ringCup

=Outer ringTapered

rollersCage

=Space retainer

Page 12: Lecture5 Bearings

ME 350

12

Types of Antifriction Bearings

Page 13: Lecture5 Bearings

ME 350

13

Roller and Ball Contact Area/Form

Page 14: Lecture5 Bearings

ME 350

14

Rolling Elements

Cylindrical

Needle

Taper

Ball Spherical Asymmetrical

Page 15: Lecture5 Bearings

ME 350

15

Types of Ball Bearings

深沟球 有装球缺口 角接触 带防尘盖 带密封圈

带球面外衬圈 双列球 双列自动调心 单向推力 单向推力带球面座圈

Page 16: Lecture5 Bearings

ME 350

16

Types of Ball Bearings• Single Row Deep Groove (Conrad) BB

(单列深沟球轴承) Spherical balls roll in deep groove in both races Space maintained by separators (retainers/cages) Ball radius smaller than groove radius Mostly take radial loads, some thrust load Theoretical point contact (actually a small circular area), so

high local contact stress Some permissible misalignment

Page 17: Lecture5 Bearings

ME 350

17

Types of Ball Bearings

• Double Row/Deep Groove BB(双列深沟球轴承)Add another row to increase load

capabilitiesGreater load capabilities than SRDGSmaller space requirement than 2 SRDGMore misalignment problems

Page 18: Lecture5 Bearings

ME 350

18

• Angular Contact BB (角接触球轴承)One side of race is higher Can accommodate a larger thrustForce resultant preferred between

15º and 40º

Types of Ball Bearings

Page 19: Lecture5 Bearings

ME 350

19

• Self-aligning BB (自动调心球轴承)

Types of Ball Bearings

Spherically ground outer race

allows for alignment flexibility

Reduced load bearing

capabilities, with minimal thrust

loading

Page 20: Lecture5 Bearings

ME 350

20

Types of Ball Bearings

•Thrust BB (推力球轴承)Large axial loading capabilities

Shaft speeds must be kept low because of centrifugal forces

Page 21: Lecture5 Bearings

ME 350

21

Types of Roller BearingsA)Cylindrical(圆柱滚子)

B) Spherical(球面滚子)

C) Tapered Roller, Thrust (推力圆锥滚子)

D) Needle(滚针)

E) Tapered Roller ( 圆锥滚子 )

F) Steep-angle Tapered Roller(大锥角圆锥滚子)

Page 22: Lecture5 Bearings

ME 350

22

Types of Roller Bearings

Cylindrical (Straight)RB (圆柱滚子轴承)Greater radial load capacityTheoretical line contact (actually a

rectangle), so lower contact stresses

Do not use for thrust - causes rubbing not rolling外圈无挡边 内圈无挡边 内圈单挡边 内圈单挡边

并带斜挡圈内圈单挡边并带平挡圈

Page 23: Lecture5 Bearings

ME 350

23

Needle RB (滚针轴承)Roller with small diameterSmall d, makes them radially

compact, good for large radial loads at high speeds

Thrust capabilities and misalignment poor

Types of Roller Bearings

Page 24: Lecture5 Bearings

ME 350

24

Types of Roller Bearings• Spherical RB (球面滚子轴承)One type of self-aligningIf misaligned - relative rotation of

outer race to rollers and inner raceLoad capability increased

• Thrust RB (推力滚子轴承)Only resist thrustSeveral types: rollers, tapered

rollers

Page 25: Lecture5 Bearings

ME 350

25

• Tapered RB( 圆锥滚子轴承 )

Combine advantages of straight roller and ball type bearings

Can accommodate radial and axial loading

High load bearing capabilities

Types of Roller Bearings

Page 26: Lecture5 Bearings

ME 350

26

Overview of Design

• Failure Theory for antifriction bearings is not fully developed

• Bearing selection is based on life testing and reliability models

• Tabulated load ratings for AFBMA (Anti-Friction Bearing Manufacturers Association)

• Design Requirements converted to required catalog load ratings

Page 27: Lecture5 Bearings

ME 350

27

How Bearings Fail

• Static stressStatic Load Rating, Co (额定静载荷)

=Load that bearing can withstand w/o permanent deformation

Balls will indent races, cause pitting, lead to noise, rapid wear

• Fatigue stressLife, Reliability and Load relationsWill happen due to high contact

stressesMore likely than static failureSpalling or pitting in area of contact

Page 28: Lecture5 Bearings

ME 350

28

Life v. ReliabilityLife TestingL = life = # of cycles of revolutionF = applied load, fixed for life tests

After some operating period, t=LReliability = % of surviving bearingsLife is different under different reliabilityL10 life = life at 10% failure (90% Reliability)Described with a Weibull Probability Distribution

Page 29: Lecture5 Bearings

ME 350

29

• L10 life is usually used as the Rating(or minimum) Life (额定寿命)

Life v. Reliability

Page 30: Lecture5 Bearings

ME 350

30

Load v. Life

•For 2 groups of identical bearings tested under different loads F1 and F2, the respective lives L1 and L2 are related by

a

FF

LL

1

2

2

1

a = 3 for ball bearings

a = 10/3 for roller bearings

Page 31: Lecture5 Bearings

ME 350

31

Load v. Life

C = basic load rating ( 基本额定动载荷 , life = 1 millions of revolutions )

•The Basic Load Rating (C) is The constant radial load which a group of

apparently identical bearings can endure for a rating life of 106 revolutions of the inner ring (stationary load and stationary outer ring)

CFL a /1

F = rated load of bearing under life LL = life of bearing in millions of revolutions

= 90 for 90106 revolutionsa = 3 for ball bearinga = 10/3 for roller bearings

Page 32: Lecture5 Bearings

ME 350

32

Load vs. Life

•Supposing a company rates its bearings for 3000 hrs at 500 rpm.

•Suppose one of the bearings has a rated radial load of 2140 lb.

•Then the corresponding L10 life is

revrevh

hL 610 1090

min500min60)3000(

•And the basic load rating is

lbLFC aR 8263902140 10/3/1

Page 33: Lecture5 Bearings

ME 350

33

Load v. Life

F = actual loadL = actual lifetime FR = load rating/catalog loadLR = rated lifetime (at test load)a = 3 for ball bearinga = 10/3 for roller bearings

LLRFRF

a

CFL a /1

Page 34: Lecture5 Bearings

ME 350

34

Load v. Life

LLRFRF

a

• Works for FIXED reliability

• Rated life standard LR = L10 life

• AFBMA uses L10 life of 106 revolutionsHave tables of bearing load ratingsActually extrapolated from tests for use in

calculations, actually FR ratings are not applied to bearings & would cause early failure

Page 35: Lecture5 Bearings

ME 350

35

ExampleA catalog lists the basic dynamic load rating for a BB to be 7,050 lb for a rated life of 1 million rev.

What would be the expected L10 life of the bearing if it were subjected to a load of 3,500 lb?

Page 36: Lecture5 Bearings

ME 350

36

Example - Solution

ThusL = LR*(FR/F)a = 106*(7050/3500)3

= 8.17*106 revs

LLRFRF

a

Page 37: Lecture5 Bearings

ME 350

37

Load v. Life – Different Speeds

aa

RHR

DHDD

R

DDR nL

nLFLLFF

11

•If a bearing is going to be subjected to a load FD for a life LHD*nD

•And the catalog specifies a life of LHR*nR

•The bearing to be selected has to have a radial load rating equal to or greater than FR

Page 38: Lecture5 Bearings

ME 350

38

Reliability/Life Equations

If FD=FR, then the reliability at different life is:

• Ball Bearings & Straight RB

4831

4394020

exp 10

.LL

..

R

• Tapered RB

5.1

48.4exp 10L

L

R

Page 39: Lecture5 Bearings

ME 350

39

If FD≠FR(or C10), the Extant Reliability:

Reliability/Life Equations

R gives a predicted reliability for bearings that are more than adequately sized

Page 40: Lecture5 Bearings

ME 350

40

If we want a different reliability:

Reliability/Life Equations

RD = Desired reliability

Page 41: Lecture5 Bearings

ME 350

41

Reliability/Life Equations

Combining life terms and Load/Life equation gives

1

1/1.48310.02 4.439(ln( ))

a

D

HD D

HR RR D

R

L nL n

F F

LR = LRhnR = “3000 hrs @ 500 rpm”

= 90 * 106 revs

Page 42: Lecture5 Bearings

ME 350

42

Reliability/Life Equations1

1/1.48310.02 4.439(ln( ))

a

D

HD D

HR RR D

R

L nL n

F F

FR (C10) = catalog radial load rating corresponding to LHR hours of life at the rated speed of nR rpm.

FD = design radial load corresponding to the required life of LHD hours at a design speed of nD rpm and a reliability of RD

Page 43: Lecture5 Bearings

ME 350

43

ExampleA ball bearing is to be selected to withstand a radial load of 4 kN and have an L10 life of 1200 h at a speed of 600 rev/min. The bearing maker's catalog rating sheets are based on an L10 life of 3800 h at 500 rev/min.

a. What load should be used to enter the catalog?b. What is the reliability of this application if the catalog rating is 3.8 kN?

Page 44: Lecture5 Bearings

ME 350

44

Example – Solution (a)

a

RHR

DHDDR nL

nLFF1

31

500*60*3800600*60*1200*4

kN 89.2

Page 45: Lecture5 Bearings

ME 350

45

Example – Solution (b)

379.0500603800

600601200

10

L

LD

97.0

48.3

439.4

48.3

02.0379.0exp

439.4

02.0/

exp

483.1

3

3

483.1

10

1010

a

D

a

DD

FC

FC

LL

R

Page 46: Lecture5 Bearings

ME 350

46

Bearing Selection Process• Select the type of bearing• Find the equivalent radial load ( 当量径向载荷 ),

Fe Accounts for any thrust/axial load

• Apply a load factor, Ka , such that

FD = Ka Fe

• Determine the minimum acceptable shaft diameter that limits the bore size

• Determine the design life

LD = (hours)(rpm)(60min/hr)

Page 47: Lecture5 Bearings

ME 350

47

Bearing Selection Process• Compute the dynamic load rating, FR

(C10)

• Identify candidate bearings with required rating

• Select bearing with most convenient geometry, also considering cost and availability

• Determine mounting conditions

Page 48: Lecture5 Bearings

ME 350

48

Bearing Type Selection

Page 49: Lecture5 Bearings

ME 350

49

Bearing Type SelectionCriteria:• Type of load: radial, thrust,

combination of both, steady or shock

• Magnitude of load• Rotation speed• Shaft misalignment• Diameter of both shaft and housing• Packaging constraints• Desired life• Maintenance requirements

Page 50: Lecture5 Bearings

ME 350

50

Bearing Type Selection

Page 51: Lecture5 Bearings

ME 350

51

Axial, radial and combine loads

Axial load

radial loadCombine load

Page 52: Lecture5 Bearings

ME 350

52

Thrust bearings

Cylindrical thrust:

Spherical roller thrust bearingThrust ball

Thrust:Thrust ballThrust ball:

Page 53: Lecture5 Bearings

ME 350

53

Recap of Bearing Types

Page 54: Lecture5 Bearings

ME 350

54

Speed rates

Oil lub.

Grease lubMax rotating speed

r/min

Page 55: Lecture5 Bearings

ME 350

55

Equivalent LoadsRadial bearings with thrust (axial) loads must have the load transformed into equivalent radial load (Fe) for bearing design

Fr = applied radial load

Fa = applied thrust load

V = rotation factor = 1.0 when inner race rotates,

=1.2 when outer race rotates

Page 56: Lecture5 Bearings

ME 350

56

Equivalent Loads

X = radial factor (径向载荷系数) (Table 11-1)Y = thrust factor (轴向载荷系数) (Table 11-1)These depend on the geometry of the bearing.Determined by ratio of:

Fa – thrust componentC0 – basic static load rating (Table 11-

2,3)e – variable reference value

Note: This requires iteration, since the basic

static load rating C0 is not known until bearing is selected

Page 57: Lecture5 Bearings

ME 350

57

Equivalent Loads

Page 58: Lecture5 Bearings

ME 350

58

Equivalent Loads

Page 59: Lecture5 Bearings

ME 350

59

Determine the Thrust Load of Tapered Roller Bearings

•Thrust component, Fa(180), due to pure radial load, Fr, is given by

K

FF ra

47.0)180(

K =0.389cot, ratio of radial rating of bearing to thrust rating( Figure 11-17)Can be approximated in the preliminary selection process as: = 1.5 for radial bearings = 0.75 for steep-angle bearings

N

Page 60: Lecture5 Bearings

ME 350

60

Determine the Thrust Load of Tapered Roller Bearings

Fae

Page 61: Lecture5 Bearings

ME 350

61

Fre

FaeFrA FrB

Fa180A Fa180B

Fae

FreFa180A

FrA FrB

Fa180B

Indirect mounting (m=-1)

Direct mounting (m=1)

Determine the Thrust Load of Tapered Roller Bearings

Page 62: Lecture5 Bearings

ME 350

62

ae

B

rBArAeA mF

K

FKFF

47.04.0

•Equivalent radial load on bearing A and B is

•Fae = external thrust loadrBeB FF

aeB

rB

A

rA mFK

F

K

F

47.047.0

B

rBaBae

B

rBaA K

FFmF

K

FF

47.0,

47.0

So

Then

If

Determine the Thrust Load of Tapered Roller Bearings

Page 63: Lecture5 Bearings

ME 350

63

ae

A

rABrBeB mF

K

FKFF

47.04.0

•Equivalent radial load on bearing A and B is

rAeA FF

aeB

rB

A

rA mFK

F

K

F

47.047.0

aeA

rAaB

A

rAaA mF

K

FF

K

FF

47.0,

47.0

So

Then

If

Determine the Thrust Load of Tapered Roller Bearings

Page 64: Lecture5 Bearings

ME 350

64

Load FactorsModify the design load to account for the type of application before looking up in catalog:

eaD FKF Ka : Load Application Factor, Table 11-5FD: Design load

Page 65: Lecture5 Bearings

ME 350

65

Load Factors

5

Page 66: Lecture5 Bearings

ME 350

66

Dimension-series

Dimension-series code (尺寸系列代号)

Page 67: Lecture5 Bearings

ME 350

67

Dimension-series

Page 68: Lecture5 Bearings

ME 350

68

Bearing-Life Recommendations(Table 11-4)

Page 69: Lecture5 Bearings

ME 350

69

Rated load

aa

RHR

DHDD

R

DDRre nL

nLF

L

LFF

11

FR : Catalog rated load

(sometimes C0 in catalogs)

Calculate the required rated load of the application:

RreF

RreR FF

Page 70: Lecture5 Bearings

ME 350

70

Lubrication

The most common lubricants have traditionally been grease and oil.

Newer lubricants can be used to withstand higher temperatures, decrease the friction coefficient, etc. However, this is not typical in roller bearings.

Page 71: Lecture5 Bearings

ME 350

71

ExampleA countershaft is supported by roller bearings using indirect mounting. The radial bearing loads are 1120 lb for the left-hand bearing and 2190 lb for the right-hand bearing. The shaft rotates at 400 rev/min and is to have an L10 life of 40 kh and an application factor of 1.4.Assume K = 1.5, and find the required radial rating for each bearing, the rating life is 3 kh at 500 rev/min.

Page 72: Lecture5 Bearings

ME 350

72

Example – Solution

No external thrust. Thus

B

rBArAeA K

FKFF 47.04.0

lb14775.12190*47.05.11120*4.0

lbFF rBeB 2190

Page 73: Lecture5 Bearings

ME 350

73

Example – Solution

Thus

lbFDA 206814774.1

lbFDB 306621904.1

lbFRA 4207500*3000

400*10*40*206810

33

lbFRB 6237500*3000

400*10*40*3066

103

3

Page 74: Lecture5 Bearings

ME 350

74

Summary

• Nomenclature of Ball bearing and Roller Bearing

• Performance of Various Types of Bearings• Life/Reliability Trade-off at Constant Load• Life/Load Trade-off at Constant Reliability• Load-Life-Reliability Trade-off• Bearing Selection Criteria• Equivalent Radial Load

Page 75: Lecture5 Bearings

ME 350

75

Mounting

Page 76: Lecture5 Bearings

ME 350

76

11-13

A gear-reduction unit uses the countershaft shown in the figure. Find the two bearing reactions.These bearings are to be plain radial ball bearings, selected for an L10 life of 40 kh corresponding to a shaft speed of 400 rev/min. Use 1.2 for the application factor and specify the bearings selected.

Page 77: Lecture5 Bearings

ME 350

77

11-14The worm shaft shown in part a of the figure transmits 1.35 hp at 600 rev/min. A static force analysis gave the results shown in part b of the figure. Bearing A is to be an angular-contact ball bearing mounted to take the 555lb thrust load. The bearing at B is to take only the raidal load and so a straight bearing will be employed. Use an application factor of 1.3 and a life of 25kh corresponding to a reliability of 99% and specify each bearing.