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Unformatted text preview: 1 ME 452: Machine Design II Solution to Homework Set 6 Problem 1 (Problem 116, pate 591) Table 112, see page 561, will be used in the solution to this problem. Therefore, Manufacturer 2 (see note below the Table on page 591) is preferred over Manufacturer 1. The desired life of the bearing in revolutions, see Example (113), page 558, can be written as 60 = D D L L n The desired life of the single row 02series deep groove ball bearing, supplied by Manufacturer 2, is specified in number of hours as 5000 hrs D L = and the innerring rotation speed is specified as 900 rpm D n = Therefore, the desired life of the bearing in number of revolutions is 6 60 5000 900 270 10 revs L = = The desired dimensionless life measure, see Equation (114), page 555, and Example 113, page 558, can be written as 10 D L x L = From the Table on page 591, the 10 L life (or the rating life) for the bearings from Manufacturer 2 is 6 10 1 10 revs L = Therefore, the desired dimensionless life measure is 6 6 270 10 270 10 D x = = The dynamic load rating (or the catalog load rating) for the bearing, see Equation (117), page 558, can be written as 1/ 10 1/ ( )(1 ) a D D b D x C F x x R = + (117) where the desired value of the reliability is specified as 0.9 D R = 2 To make an initial selection of the bearing, the catalog load rating can be estimated using the radial load r F only (see Example 117, page 569). Therefore, the desired radial load is assumed to be the same as the specified radial load; i.e., 8 kN D r F F = = The Weibull parameters for the bearings from Manufacturer 2, see the Table on page 591, are specified as 0.02, 4.459 and 1.483 = = = x b where x is the minimum value of the dimensionless life, is the characteristic parameter and b is the shape parameter. For a ball bearing, the exponent a , see page 554, is specified as 3 a = Substituting the above values into Equation (117), the catalog load rating is 1/ 3 10 1/1.483 270 8 0.02 (4.459 0.02)(1 0.9) = + C Therefore, the catalog load rating is 10 52.4 kN = C Check. If the catalog load rating for the bearing is evaluated from Equation (116), page 557; i.e., 1/ 10 1/ ( )( 1/ ) = + a D D b D x C F x x Ln R (116) Then the catalog load rating is 10 51.9 kN = C which is in good agreement with the previous calculation. Note that equation (117) is an approximation to equation (116) (see page 558)....
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 Fall '08
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 Machine Design

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