20. Ball and Roller Bearings Introduction to Bearings Objectives • Recognize the different types of rolling contact bearings and applications where they may be suitable. Ball Bearings • Calculate equivalent load on Conrad-type ball – Radial and Thrust loads bearings and relationship of this load to expected lifetime of the bearing. Roller Bearings • Factor in effect of thrust loading on the equivalent – Radial and Thrust loads radial load in calculating the life of a bearing. Needle Bearings • Understand principles of roller bearings, tapered roller bearings, thrust bearings, and needle – Only radial loads bearings. • Select appropriate type of bearings and their sizes Augustfor 15, the 2007 design being undertaken. 1 August 15, 2007 2
Ball Bearings Single-row Ball Bearing Terminology
Terminology – Outer ring, which contains the outer raceway – Inner ring, which contains the inner raceway – Complement of balls – Two-piece separator (also called cage or retainer)
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Ball Bearing assembly Ball Bearings
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1 Ball Bearing nomenclature Ball Bearings
Width See the difference in the curvature of Corner the ball and the radius race)
Outside Bore diameter
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Life of Antifriction Bearings Life of Antifriction Bearings
They are subjected to repeated stress cycles and are likely to fail by fatigue.
B10 or L10 life is defined as the number of hours
e
f
i that 90% of the bearings tested will exceed. l
e
v
i The probability of failure is 10% at the L10 life. t
a
l
Average life is the number of hours that 50% of e the bearings exceed. R
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Fig. 20.1 Typical bearing failure curve Life of Bearings
The expected life of the bearing is L = T × n × 60 T = Hours of operation n = revolutions per minute
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2 Life of Bearings Life of Bearings
The life of the bearing decreases with an increase in the The equations can be rewritten as load. depending upon the variable to be k L ⎛ C ⎞ k = 3 for ball bearings calculated d = ⎜ d ⎟ L ⎜ P ⎟ = 10/3 for roller bearings c ⎝ d ⎠ 1/k k ⎛ Ld ⎞ ⎛ Cd ⎞ Ld = desired life C = P ⎜ ⎟ L = L ⎜ ⎟ d d ⎜ L ⎟ d c ⎜ P ⎟ Lc = life from the table (manufacturers catalog) ⎝ c ⎠ ⎝ d ⎠
Cd = dynamic rating from manufacturer
Pd = design load
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Life of Antifriction Bearings Example Problem 20-1: Life Expectancy of Ball Bearings • Table 12-1 lists the basic dynamic load for bearing number 6208 as 5050 pounds. • What would the expected life be for the bearing if it were subjected to a radial load of 2400 pounds? • If the shaft turns at 1750 rpm, how many hours
would bearing last based on L10 design life?
For a life of 1 million cycles August 15, 2007 15 August 15, 2007 16
Example Problem 20-1: Life Expectancy of Ball Example Problem 20-2: Life Expectancy of Ball Bearings Bearings
k ⎛ C ⎞ ⎜ d ⎟ 6 (20-5) • For conditions in the previous example problem, Ld = ⎜ ⎟ 10 ⎝ Pd ⎠ if an L10 life of 200 hours is needed, select a 3 bearing from Table 20-1 to meet criterion. ⎛ 5050 ⎞ 6 Ld = ⎜ ⎟ 10 ⎝ 2400 ⎠ 6 Ld = 9.3 x 10 rev 9.3 x 106 rev hr T = 1750 rev / min 60 min
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3 Example Problem 20-2: Life Expectancy of Ball Bearings Equivalent combined radial load T n 60 m L = 106 hr 200 hr 1750 rev 60 m For combined radial and thrust loads L = (20-1) 6 10 min hr P = V X R + Y Ft L = 21 x 106 revolutions P = equivalent radial load (lb) l / k ⎛ L ⎞ ⎜ d ⎟ Cd = Pd ⎜ ⎟ R = actual radial load (lb) ⎝ Lc ⎠ (20-3) 1/3 F = actual thrust load (lb) ⎛ 21⎞ t Cd = 2400 lb ⎜ ⎟ ⎝ 1 ⎠ X = radial factor (usually 0.56) Cd = 6622 lb V = 1.0 for inner race rotating • Bearing number 6211 has a dynamic load rating of 7500 pounds. = 1.2 for outer race rotating • This bearing would be acceptable. • If bearing bore is too large, a heavier series could be substituted. Thrust factor Y is obtained from Table 20.2 August 15, 2007 19 August 15, 2007 20
Table 20.2 Thrust factor for Deep-groove ball Example Problem 20-3: Ball Bearing Selection bearings • Select a bearing from Table 20-1 to meet following criteria: Ft/Cs 0.014 0.028 0.056 0.084 0.11 0.17 0.28 0.42 0.56 – R = 1200 pounds Y 2.3 1.99 1.71 1.55 1.45 1.31 1.15 1.04 1.00 –Ft = 500 pounds – n = 1500 rpm - shaft rotates
–L10 = 5000 hours Ft = Thrust force on the bearing
Cs = Static rating of the bearing (Manufacturer’s catalog)
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Example Problem 20-3: Ball Bearing Selection Example Problem 20-3: Ball Bearing Selection (cont’d.) l / k •To select bearing, assume thrust factor of Y = 1.6 (average of table): ⎛ L ⎞ – Adjust rating for life: C = P ⎜ d ⎟ d d ⎜ ⎟ (20-3) (20-6) L P = .56 R + Y Ft ⎝ c ⎠ 1/3 P = .56 1200 lb + 1.6 500 lb ⎛ 450 ⎞ Cd =1472 lb ⎜ ⎟ P = 1472 lb ⎝ 1 ⎠
– Find life: Cd = 11,280 lb – From Table 20-1:
Bearing Number 6215 Cd = 11,400 1500 rpm 5000 hr 60 min C = 9,700 L = s 106 hr – Verify assumption for Y: Ft 500 6 = = .0515 (20-7) L = 450 10 revolutions Cs 9700 – Interpolate to find factor:
⎛ .056 − .0515 ⎞ Y = ⎜ ⎟ (1.99 − 1.71) + 1.71 ⎝ .056 − .028 ⎠ August 15, 2007 23 August 15, 2007 Y = 1.76 24
4 Example Problem 20-3: Ball Bearing Selection Example Problem 20-3: Ball Bearing Selection (cont’d.) (cont’d.)
–Verify: P = .56 R + Y Ft P = .56 (1200) + 1.76 (500) – Interpolate: P = 1550 lb 1/ k ⎛ .056 − .048 ⎞ ⎛ Ld ⎞ Y = ⎜ ⎟ (1.99 − 1.71) + 1.71 C = P ⎜ ⎟ ⎝ .056 − .028 ⎠ d d ⎜ L ⎟ ⎝ c ⎠ Y = 1.79 1/3 ⎛ 450 ⎞ P = .56 (1200 lb) + 1.79 (500 lb) Cd =1550 ⎜ ⎟ ⎝ 1 ⎠ P = 1567 lb 1/3 C = 11,875 lb ⎛ 450 ⎞ d Cd = 1567 ⎜ ⎟ • This is not acceptable. ⎝ 1 ⎠
• Try next larger size bearing. Try bearing number 6216. Cd = 12,005 lb
F 500 – Bearing number 6216 meets design criteria. t = = .048 Cs 10,500
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Example Problem 20-4: Life Expectancy of Ball Example Problem 20-4: Life Expectancy of Ball Bearings Bearings
– Find thrust factor as bearing is known: • Estimate life for a 6200 series bearing that has an F 300 inside diameter of 30 mm on a stationary shaft t = = .129 C 2320 where outside race rotates. s (20-7) • There is a radial load of 1,000 pounds and a thrust – Interpolate from Table 20-2: load of 300 pounds. ⎛ .17 − .129 ⎞ Y = ⎜ ⎟ (1.45 −1.31) + 1.31 ⎝ .17− .11 ⎠ Y = 1.41
P =V X R + Y Ft (20-6) P =1.2 (.56) 1000 + 1.41(300) P =1095 lb
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Example Problem 20-4: Life Expectancy of Ball Bearings (cont’d.) Static strength capacity
k It is defined as the maximum load that can (20-5) ⎛ Cd ⎞ 6 Ld = ⎜ ⎟ 10 be applied without bearing damage when ⎜ P ⎟ ⎝ d ⎠ neither race is moving. 3 ⎛ 3350 ⎞ L = ⎜ ⎟ 106 The permanent deformation does not d 1095 ⎝ ⎠ exceed 0.0001 in. per in. of diameter of the L = 28.6 x 106 revolutions d rolling element.
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5 Some useful facts Some useful facts If the load of roller bearing is doubled, the fatigue Load carrying capacity is roughly proportional to life is reduced by a factor of 10. the diameter of the rolling elements. Deformation is the cause of rolling resistance. Roller bearings have much grater load-carrying Hence harden all surfaces to about Rc 58. capacity than ball bearings. Wheel bearing of automobile is designed for L10 Bearings are subjected to repeated stress cycles life of 100,000 miles, 10% of the bearing may fail with max compressive stress of approx 150,000 before 100,000 miles are reached. psi. This cause fatigue failure. For properly loaded bearings force required to pull Load of a ball bearing is doubled, fatigue life is a load of 1 ton: reduced by a factor of 8. – 1.6 lb for ball bearing – 3.0 lb for roller bearing August 15, 2007 31 August 15, 2007 32
Maximum capacity Ball Bearings Type of Rolling Contact Bearings Maximum number of balls can be inserted
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Maximum capacity Ball Bearings Ball Bearing with shields
Maximum number of balls can be inserted Greater radial load carrying capacity
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6 Angular contact Bearings Angular contact Bearings
Balls are inserted by thermally expanding the outer ring. Can take greater thrust load than the maximum capacity ball bearing from only one direction.
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Double row angular contact Bearings Double row angular contact Bearings
Takes thrust in both directions
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2-piece inner-ring Ball Bearings 2-piece inner-ring Ball Bearings Large number of balls – higher load- Advantages carrying capacity – The maximum complement of balls makes for Deep ball raceway - higher load carrying capacity. Higher thrust load capacity – The very deep ball raceway shoulder makes for high thrust-load capacity. Thrust loads from both directions – Thrust loads can be handled in both directions.
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7 Roller Bearings Roller Bearings
Because of the line contact, they can take greater loads They also have more rolling resistance (0.0015 for roller and 0.0008 for ball bearing) Types of roller bearings – Cylindrical – Tapered – Spherical
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Tapered Roller Bearings Needle Bearings
Use large number of small diameter rollers. There is no space between rollers (needles). No cage required. Drawn cup type is very thin and compact because of the design. Used for lighter loads.
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Needle Bearings Needle Bearings Some types rollers contact directly the shaft (Fig. 4.21) without any inner race. The shaft should be hardened (Rc 58) for proper operation (Fig. 4.22). They have large load-capacity/size ratio. It requires very little radial space. One application is the roller type cam follower (Fig. 4.23). They have higher coefficient of friction. Typical value is 0.0025 compared to 0.0015 for roller bearings. They have lower max speed limit.
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8 Needle Bearings – cam follower Thrust Bearings
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Cylindrical roller Thrust Bearings Conical Thrust Bearings
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Lubrication of Antifriction Bearings Advantages
Provide a lubricating film between the rolling elements and the separator at the areas of contact Journal bearings or Plain surface bearings Dissipate heat caused by deformation of the – Requires little radial space rolling elements and raceways as well as heat – Run quietly caused by the sliding contact between the rolling – Have a longer life span elements and the separator – Are less sensitive to contamination Prevent corrosion of bearing components – Are less costly Aid in preventing dirt and other contamination – Can better sustain shock loads from entering the critical areas of the bearing – Requires less precise mounting where sliding or rolling contact takes place – Are available in split halves
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9 Advantages
Antifriction bearings – Have less friction – Requires no wearing-in period – Requires less axial space – Can run at higher speeds – Have fewer maintenance problems – Have fewer lubrication difficulties – Allow for considerable misalignment – Are easy to replace – Allow for greater precision – Readily available in large varieties
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Summary Summary
Antifriction bearings operate with rolling contact. Bearings fail because of fatigue. There are a number of ways in which the balls Load capacity of a bearing can be calculated are loaded into a ball bearing. using the supplied formulae. Roller bearings take larger loads than ball Lubrication in bearings serve a number of functions such as dissipating heat, prevent bearings because of the line contact. corrosion and forming a film between rolling Needle bearings requires little space. element and the raceway. Tapered roller bearings can take axial as well as Pre-mounted bearings are complete bearing radial loads. assemblies.
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