hw6.sol.Spring07

hw6.sol.Spring07 - 1 ME 452: Machine Design II Solution to...

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Unformatted text preview: 1 ME 452: Machine Design II Solution to Homework Set 6 Problem 1 (Problem 11-6, pate 591) Table 11-2, 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 (11-3), page 558, can be written as 60 = D D L L n The desired life of the single row 02-series deep groove ball bearing, supplied by Manufacturer 2, is specified in number of hours as 5000 hrs D L = and the inner-ring 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 (11-4), page 555, and Example 11-3, 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 (11-7), page 558, can be written as 1/ 10 1/ ( )(1 ) a D D b D x C F x x R = +-- (11-7) 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 11-7, 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 (11-7), 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 (11-6), page 557; i.e., 1/ 10 1/ ( )( 1/ ) = +- a D D b D x C F x x Ln R (11-6) Then the catalog load rating is 10 51.9 kN = C which is in good agreement with the previous calculation. Note that equation (11-7) is an approximation to equation (11-6) (see page 558)....
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hw6.sol.Spring07 - 1 ME 452: Machine Design II Solution to...

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