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TECHNICAL PAPERS

Numerical Simulation of a Heat-Treated Ring Gear Blank

[+] Author and Article Information
C. Mgbokwere

Scientific Research Laboratory, Ford Motor Company, Dearborn, MI 48121

M. Callabresi

MLC Technical Consultant, Livermore, CA 94550

J. Eng. Mater. Technol 122(3), 305-314 (Mar 02, 2000) (10 pages) doi:10.1115/1.482802 History: Received December 01, 1999; Revised March 02, 2000
Copyright © 2000 by ASME
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References

Mgbokwere, C., Dowling, W., Smith, D., Copple, W., and Mack C., 1999, “2D-Simulation of a 211 Ring gear Blank,” The Third International Conference on Quenching and Control Distortion, ASM, pp. 234–253.
Ishigawa,  H. J., 1978, “Phase Transformation in Steels,” J. Thermal Stress., 1, pp. 211–222.
Burmett,  J. A., and Padovan,  J., 1979, “Residual Stress Fields in Heat-Treated Case-Hardened Cylinders,” J. Thermal Stress., 2, pp. 251–263.
Rammerstorfer,  F. G., Fischer,  W., Mitter,  K., Bathe,  J., and Snyder,  M. D., 1981, “On Thermo-Elastic-Plastic Analysis of Heat-Treatment Processes Including Creep and Phase Changes,” Comput. Struct., 13, pp. 771–779.
Leblond,  J. B., Devaux,  J., and Devaux,  J. C., 1989, “Mathematical Modeling of Transformation Plasticity in Steels I: case of Ideal-Plastic Phases,” Int. J. Plast., 5, pp. 573–591.
VonBergen, R. T., 1992, “The Effects of Quenchant Media Selection and Control on the Distortion of Engineered Steel Parts,” First International Conference on Quenching and Distortion Control, G. E. Totten, ed., pp. 275–282.
Roberts,  C. S., 1953, “Effects of Carbon on the Volume Fractions and Lattice Parameters of Retained Austenite and Martensite,” Trans. AIME, 197, p. 203.
Kirkaldy, J. S., and Venugopalan, D., 1984, “Phase Transformation in Ferrous Alloys,” AIME Publications, Marder, A. R., and Goldenstein, J. I., eds., p. 125.
Watt,  D. F., Coon,  L., Bibby,  M., Goldak,  J., and Henwood,  C., 1988, “An Algorithm for Modelling Microstructural Development in Weld Heat-Affected Zones. Part A. Reaction Kinetics,” Acta Metall., 36, pp. 3029–3035.
Asby,  M. F., and Easterling,  K. E., 1982, “First Report on Diagrams for Grain Growth in Welds,” Acta Metall., 30, pp. 1969–1978.
Lusk, M., Krauss, G., and Jou, H., 1995, “A New Balance Principle for Modeling Phase Transformation Kinetics,” International Conference on Martensite Transformations, pp. 123–131.
Bammann, D. J., Prantil, V. C., and Lathrop, J. F., 1995, “A Model of Phase Transformation Plasticity,” Modelling of Casting, Welding and Advanced Solidification Processes VII, Cross, M., and Campbell, J., eds., pp. 275–285.
Fischer,  F. D., Sun,  Q-P., and Tanaka,  K., 1996, “Transformation-Induced Plasticity (TRIP),” Appl. Mech. Rev., 49, pp. 317–364.
Krauss, G., 1992, “Heat Treatment, Microstructures, and Residual Stresses in Carburized Steels,” First International Conference on Quenching and Distortion Control, G. E. Totten, ed., pp. 181–191.
Das, S., Upadhya, G., and Chandra, U., 1992, “Prediction of Macro- and Micro-Residual Stress in Quenching using Phase Transformation Kinetics,” First International Conference on Quenching and Distortion Control, G. E. Totten, ed., pp. 229–234.

Figures

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Ring gear blank used for simulation
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Heat treat process model schematic
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(a) Illustration of regions where heat transfer coefficient is applied. (b) Location of thermocouples on the gear blank.
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Two-dimensional mesh used in the simulation
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Results of the carbon diffusion analysis. (a) Carbon contour plot and (b) carbon gradient from bottom inside diameter inward.
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Optimum distribution of the ten heat transfer coefficient
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Comparison of measured and calculated time-temperature profile
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Temperature distribution at four different time intervals
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(a) Contour plot of phase volume fraction at 12.8 s. (b) Contour plot of phase volume fraction at 44.5 s. (c) Contour plot of phase volume fraction at 240 s. (d) Contour plot of phase volume fraction at 780 s.
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Contour plot of the hardness with the Rockwell C conversion in parenthesis. Also shown are four locations of the phase volume fraction at 780 s.
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Calculated phase volume fraction from the surface of the blank to the core
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Optical micrographs of center core sections (a) bottom and (b) top. The bottom microstructure is a bainite formed at a higher temperature with more ferrite than the top microstructure which consists of bainite and martensite.
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Evolution of volume fraction in the bottom core (a) and from the bottom inside surface (b) as a function of time with corresponding calculated cooling curve
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Calculated stress and temperature profile as a function of time at four different locations. (a) Stress in the longitudinal direction (b) stress in the hoop direction.
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Contour plot of stresses and plastic strain
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Comparison between computed and measured stresses. (a) Current simulation (b) previous simulation.
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Illustration of the computed and measured displacement. (a) Current simulation (b) previous simulation.

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