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Research Papers: FORMING

Residual Stresses Due to Rigid Cylinder Indentation and Rolling at a Very High Rolling Load

[+] Author and Article Information
M. Y. Ali

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: mdyusuf@umich.edu

J. Pan

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: jwo@umich.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received October 7, 2014; final manuscript received July 5, 2015; published online September 4, 2015. Assoc. Editor: Yannis Korkolis.

J. Manuf. Sci. Eng 137(5), 051005 (Sep 04, 2015) (13 pages) Paper No: MANU-14-1508; doi: 10.1115/1.4031067 History: Received October 07, 2014

In this paper, residual stresses due to indentation and rolling of a rigid cylinder on a finite plate at a very high rolling load with a relative peak pressure of 22 are examined by two-dimensional plane strain finite element analyses using abaqus for the first time. In the finite element analyses, the roller is modeled as rigid and has frictionless contact with the finite plate. The geometry of the finite plate and its boundary conditions are assigned to correspond to those of fillet rolling of crankshafts with the constraint in the rolling direction. Finite element analyses with different meshes for single indentation on an elastic flat plate under plane strain conditions are first carried out, and the results are benchmarked with those of the elastic Hertzian solutions to establish the requirement of the finite element meshes for acceptable numerical results. The results show that the accuracy of computational results is limited by the discretization of the finite element analysis by a plot of the contact width as a function of the load. For accurate peak pressure, a total of at least eight linear elements are needed. Finite element analyses with different meshes for single indentation on an elastic–plastic flat plate under plane strain conditions are then carried out. The plate material is modeled as an elastic–plastic power-law strain hardening material with a nonlinear kinematic hardening rule for loading and unloading. The computational results are compared to establish the requirement of the finite element meshes for acceptable numerical results within 4 mm distance to the rolling surface for the crankshaft fatigue analyses. The computational results for rolling at the relative peak pressure of 22 show that the symmetric Hertzian or modified Hertzian pressure distribution should not be used to represent the contact pressure distribution for rolling simulation, while the computational results for rolling at the relative peak pressure of 5 show that the symmetric Hertzian or modified Hertzian pressure distribution may be used to represent the contact pressure distribution for rolling simulation. The computational results for the rolling case also show a significantly higher longitudinal compressive residual stress and a lower out-of-plane compressive residual stress along the contact surface when compared to those for the single indentation case. The results suggest that the effects of rolling must be accounted for when two-dimensional finite element analyses of crankshaft sections are used to investigate the residual stresses due to fillet rolling of the crankshafts under the prescribed roller loads. Due to the boundary conditions of the finite plate, the compressive residual stresses are larger when compared to those when the boundary conditions of the finite plate are fully relaxed.

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Figures

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Fig. 1

The tensile stress–plastic strain curve of the plate material used in the finite element analyses

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Fig. 2

(a) A schematic view of the arrangement of a crankshaft journal, a primary roller, a portion of a secondary roller, and a support roller during the rolling process, (b) an illustration of the conical surface generated by the dashed line AB upon one revolution of the crankshaft journal, and (c) an auxiliary view of the primary roller and the conical surface shown in (b)

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Fig. 3

(a) A two-dimensional finite element model of a rigid cylinder rolling on a finite flat plate and magnified views of the finite element models for (b) mesh-1 with the element size of 0.4 mm and (c) mesh-2 with the element size of 0.1 mm

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Fig. 4

A comparison of the contact widths between the flat plate and the rigid roller obtained by the elastic Hertzian solution and the elastic finite element analysis as functions of the indentation load up to the maximum load of 3847 N/mm based on the fine mesh-2

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Fig. 5

A comparison of the results from the finite element analysis and the elastic Hertzian solution for contact between the elastic plate and the rigid roller directly under the roller. The stress distributions in the −y direction from the top surface for the top 5 mm of the plate for single indentation.

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Fig. 6

The contact pressure distributions on the plate surface based on the elastic Hertzian solution and the results of the elastic finite element analysis based on the fine mesh-2 with the element size of 0.1 mm due to single indentation by the rigid roller

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Fig. 7

(a) The contact pressure distributions, (b) the stress distributions, and (c) the residual stress distributions in the −y direction from the top surface based on mesh-1 and mesh-2 for single indentation on the elastic–plastic plate

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Fig. 8

The Mises stress distributions and the plastic zone sizes and shapes represented by the darker zone closer to the rolled surface due to the rolling when (a) the roller is moved down at the full rolling load, (b) the roller is rolled to the half rolling length, and (c) the roller is moved up after the rolling is completed

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Fig. 9

Contact pressure distributions for single indentation and during rolling based on a finer mesh size of 0.1 mm

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Fig. 10

The stress distributions of the upper surface during rolling at the half rolling length

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Fig. 11

(a) The stress distributions directly under the roller center in the −y direction from the top surface for single indentation and during rolling and (b) the contours of the longitudinal stress component σ11 for single indentation and during rolling

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Fig. 12

(a) The residual stress distributions in the −y direction from the top surface after the roller load is removed for the single indentation and rolling cases and (b) the distributions of the residual longitudinal stress σ11 after the roller load is removed for the single indentation and rolling cases

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Fig. 13

The residual stress distributions of the upper surface after the rolling is completed

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Fig. 14

The effects of the boundary conditions on the residual stresses at the marked locations (a) for the single indentation case and (b) at the half rolling length for the rolling case

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Fig. 15

Contact pressure distributions for single indentation and during rolling for a p0/k ratio of 5

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Fig. 16

(a) A portion of a three-dimensional finite element model of a crankshaft section under fillet rolling and (b) a magnified view near the contract zone between the crankshaft section and the primary roller

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Fig. 17

(a) The contact pressure distribution between the crankshaft section and the primary roller, (b) the contact pressure distributions for paths 1 and 2 as marked in (a), and (c) the contact pressure distributions for path 3 as marked in (a)

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Fig. 18

Magnified views of the finite element models near the rolling surfaces for (a) mesh-1 with the element size of 0.4 mm, (b) mesh-2 with the element size of 0.1 mm, (c) mesh-3 with the element size of 0.05 mm, and (d) mesh-4 with the element size of 0.025 mm

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Fig. 19

A comparison of the results from the finite element analyses and the elastic Hertzian solution for contact between the elastic plate and the rigid roller directly under the roller. The stress distributions in the −y direction from the top surface for the top 2 mm of the plate for single indentation.

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Fig. 20

The residual stress distributions in the −y direction from the top surface for the top 10 mm of the plate based on mesh-2 and mesh-4 for single indentation on the elastic–plastic plate

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