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Research Papers: Elastohydrodynamic Lubrication

Multitude of Objectives Based Optimum Designs of Cylindrical Roller Bearings With Evolutionary Methods

[+] Author and Article Information
Rajiv Tiwari

Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, India
e-mail: rtiwari@iitg.ernet.in

Rahul M. P. Chandran

Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati 781039, India

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 17, 2014; final manuscript received March 5, 2015; published online May 11, 2015. Assoc. Editor: Xiaolan Ai.

J. Tribol 137(4), 041504 (Oct 01, 2015) (12 pages) Paper No: TRIB-14-1170; doi: 10.1115/1.4030166 History: Received July 17, 2014; Revised March 05, 2015; Online May 11, 2015

In the design of cylindrical roller bearings (CRBs), a long life is one of the most essential criteria. However, the life of bearings depends on the multitude of factors that includes the fatigue, lubrication, and thermal characteristics in bearings. In the present work, three primary objectives namely, the dynamic capacity, the elastohydrodynamic lubrication (EHL) minimum film-thickness, and the maximum temperature have been optimized, sequentially. Some of these objectives may be contradicting to each other. The optimum bearing design has been attempted by first deriving a constrained nonlinear formulation and then optimizing it with an evolutionary algorithm. Constraint violations study has been performed to have assessment of the effectiveness of each of the constraints. A convergence study has been carried out to ensure the near global optimum point in the design. In terms of the basic dynamic capacity of the bearing, there is an excellent conformity among the optimized and customary bearings. A sensitivity study of various geometric design variables has been performed to see changes in objective functions and results show that geometric variables have hardly any undesirable influence.

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Figures

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Fig. 1

Internal geometries of a CRB

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Fig. 2

Temperature node systems of the housing and bearing

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Fig. 3

Rolling element-lubricant-inner raceway ring temperature node system

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Fig. 4

A flow diagram of the optimum design of CRBs with the ABC algorithm

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Fig. 5

Variation of the best Cd with number of generations

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Fig. 6

Variation of the best fitness with number of generations

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Fig. 7

Variation of the best fitness with number of generations

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Fig. 8

Variation of pitch diameter with number of generations

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Fig. 9

Variation of number of rollers with generations

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Fig. 10

Constraint violations with population numbers for the last generation: (a) Constraint 7, (b) Constraint 8, (c) Constraint 9, (d) Constraint 10, and (e) Constraint 17

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Fig. 11

Geometric study on constraints for the optimized bearing NU 202: (a) optimized bearing basic geometry, (b) various constraints for Dm overlapped on optimized bearing geometry (hatched area represents bounds for Dm; roller is shown by dotted lines; arrows direction shows bound direction), (c) various constraints for Dr overlapped on optimized bearing geometry, and (d) various constraints for le overlapped on optimized bearing geometry (Cn represents nth constraint)

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