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The influence of shock loading can be taken into account by using the application factor, Ka, given in Table 65 for various degrees of shock loading The nominal load will be increased by the application factor By taking axial load and shock loading into consideration, the bearing life equation is further modified as [13]
C 3 L = K r LR Fe K a
Ft > 10, Fr
Fe = 1911 Ft
L 10 Creq = Fe K a K r LR
Table 65
Types of application
Application factor, Ka [13]
Ball bearings 10 10 13 12 15 15 20 20 30 Roller bearings 10 10 10 11 11 15 15 20
Uniform load, no impact Gearing Light impact Moderate impact Heavy impact
The service life of a given bearing in revolutions can now be calculated by using the following relationship:
C 3 Lrevolutions = K r L R Fe K a If the bearing works at constant speeds of nrpm, it is then possible to calculate the service life in hours by modifying the preceding equation as
1 C 3 Lhours = K r L R Fe K a nrpm 60
10 10
Precision Engineering
In cases when a certain amount of information is not available, Table 66 can serve as a guide for the design life of the bearing Table 66 Representative bearing design life [13]
Types of Application Design Life (thousands of hours) 01 05 4 8 8 14 14 20 20 30 50 60 100 200
Machines used intermittently, where service interruption is of minor importance Machines used intermittently, where reliability is of great importance Machines for an 8-hour service, but not every day Machines for an 8-hour service, every working day Machines for a continuous 24-hour service Machines for a continuous 24-hour service where reliability is of great importance
Example: Ball Bearing Selection Select a suitable ball bearing (radial ball bearing with a = 0 or an angular ball bearing with a = 25 ) based on the required rated capacity, Creq, using the following information [5]: Continuous operation of eight hours per day Rotation speed of 1800 RPM Radial load, Fr, = 12 kN Thrust load, Ft, = 15 kN Light to moderate impact Required reliability is 90% Kr = 1 (Figure 615) LR = 90 106 Ka = 15 (Figure 616) Lrev = 30,000 hours 1800 rpm 60 min/hour = 3240 106 revolutions For radial ball bearings: Fig 614: Illustration for selection of ball bearings [5] Ft/Fr = 125
F Fe = Fr 1 + 1115 t 035 = 24 kN Fr
L 10 Creq = Fe K a = 1055 kN K r LR
Rolling Element, Hydrodynamic and Hydrostatic Bearings For angular contact ball bearings (a = 25 ): Ft/Fr = 125
F Fe = Fr 1 + 0870 t 068 = 18 kN Fr
L 10 Cred = Fe K a = 781 kN K r LR
From most manufacturers catalogues and according to the values of Creq, the choice is either deep groove ball bearings or angular contact ball bearings The final decision of selection will be based on the cost of installation, including the shaft and the housing Example: Bearing Life Estimate the life of a radial contact ball bearing No 211 (C = 12 kN) for 90% reliability and the bearing reliability for 30,000 hours life based on [5] The application factor is 15 for light to moderate impact Radial load, Fr = 12 kN and thrust load, Ft = 15 kN Ft/Fr = 125
F Fe = Fr 1 + 1115 t 035 = 24 kN Fr The bearing life for 90% reliability, Kr = 1 1 C 3 Lhours = K r L R = 45920 h Fe K a nrpm 60
The bearing reliability for a 30000 hour life Lrev = 30000 h 1800 rpm 60 min/h = 3240 106 revolutions Kr =
Lrev
C 3 LR Fe K a
= 065
From Figure 615, reliability for Kr = 065 is estimated as 95% It may be seen that for 90% reliability, the bearing life is 45920 hours However, for 95% reliability, the bearing life reduces to 30000 hours
Precision Engineering
Fig 615: Illustration for calculation of the life of a bearing [5]
63 LUBRICATED SLIDING BEARINGS
In sliding bearings, the bearing elements are usually separated by a film of lubricant that can be either a solid or a liquid and in which the sliding motion is the predominant element [6] This type of bearing is used whenever there is the need for long life, low cost, high-speed characteristics and noise-free operation Going back in time, the slider bearing was the first type of bearing to be used Figure 616 shows that the concept of lubrication for a sliding bearing existed during the ancient Egyptian era
Fig 616: Egyptians used lubrication to ease the movement of Colossus, 1880 BC [5]
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