In this paper, a novel approach to the derivation of the tool-life distribution, when the tool useful life ends after a progressive wear process, is presented. It is based on the diffusion theory and exploits the Fokker–Planck equation. The Fokker–Planck coefficients are derived on the basis of the injury theory assumptions. That is, tool-wear occurs by detachment of small particles from the tool working surfaces, which are assumed to be identical and time-independent. In addition, they are supposed to be small enough to consider the detachment process as continuous. The tool useful life ends when a specified total volume of material is thus removed. Tool-life distributions are derived in two situations: (i) both Fokker–Planck coefficients are time-dependent only and (ii) the diffusion coefficient is neglected and the drift is wear-dependent. Theoretical results are finally compared to experimental data concerning flank wear land in continuous turning of a C40 carbon steel bar adopting a P10 type sintered carbide insert. The adherence to the experimental data of the tool-life distributions derived exploiting the Fokker–Planck equation is satisfactory. Moreover, the tool-life distribution obtained, when the diffusion coefficient is neglected and the drift is wear-dependent, is able to well-represent the wear behavior at intermediate and later times.
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Università di Pisa,
Pisa 56126,
e-mail: marcello.braglia@dimnp.unipi.it
Università di Pisa,
Pisa 56126,
e-mail: davide.castellano@for.unipi.it
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June 2014
Research-Article
Diffusion Theory Applied to Tool-Life Stochastic Modeling Under a Progressive Wear Process
Marcello Braglia,
Università di Pisa,
Pisa 56126,
e-mail: marcello.braglia@dimnp.unipi.it
Marcello Braglia
Dipartimento di Ingegneria Civile e Industriale
,Università di Pisa,
Via Bonanno Pisano 25/B
,Pisa 56126,
Italy
e-mail: marcello.braglia@dimnp.unipi.it
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Davide Castellano
Università di Pisa,
Pisa 56126,
e-mail: davide.castellano@for.unipi.it
Davide Castellano
1
Dipartimento di Ingegneria Civile e Industriale
,Università di Pisa,
Via Bonanno Pisano 25/B
,Pisa 56126,
Italy
e-mail: davide.castellano@for.unipi.it
1Corresponding author.
Search for other works by this author on:
Marcello Braglia
Dipartimento di Ingegneria Civile e Industriale
,Università di Pisa,
Via Bonanno Pisano 25/B
,Pisa 56126,
Italy
e-mail: marcello.braglia@dimnp.unipi.it
Davide Castellano
Dipartimento di Ingegneria Civile e Industriale
,Università di Pisa,
Via Bonanno Pisano 25/B
,Pisa 56126,
Italy
e-mail: davide.castellano@for.unipi.it
1Corresponding author.
Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received June 11, 2013; final manuscript received February 7, 2014; published online March 26, 2014. Assoc. Editor: Allen Y. Yi.
J. Manuf. Sci. Eng. Jun 2014, 136(3): 031010 (12 pages)
Published Online: March 26, 2014
Article history
Received:
June 11, 2013
Revision Received:
February 7, 2014
Citation
Braglia, M., and Castellano, D. (March 26, 2014). "Diffusion Theory Applied to Tool-Life Stochastic Modeling Under a Progressive Wear Process." ASME. J. Manuf. Sci. Eng. June 2014; 136(3): 031010. https://doi.org/10.1115/1.4026841
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