Diffusion Theory Applied to Tool-Life Stochastic Modeling Under a Progressive Wear Process

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Marcello Braglia ◽  
Davide Castellano
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Tool Life ◽  
Diffusion Theory ◽  
Planck Equation ◽  
Life Distribution ◽  
Wear Process ◽  
Life Distributions ◽  
Useful Life ◽  
Fokker Planck

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.

Tool Life Distributions—Part 3: Mechanism of Single Injury Tool Failure and Tool Life Distribution in Interrupted Cutting

1978 ◽  
Vol 100 (2) ◽  
pp. 193-200 ◽  
Author(s):  
S. Ramalingam ◽  
Y. I. Peng ◽  
J. D. Watson
Keyword(s):  
Tool Life ◽  
Hazard Function ◽  
Rational Design ◽  
Tool Material ◽  
Distribution Functions ◽  
Life Distribution ◽  
Tool Failure ◽  
Interrupted Cutting ◽  
Life Distributions ◽  
Machining Lines

Tool life distribution under production machining conditions must be suitably accounted for in any rational design of large volume or automated machining lines. Reliable data on the type of distributions likely to be encountered are, however, unavailable. To remedy this, using relevent physical arguments, probabilistic models of tool failure which produce distribution functions germane to tool life scatter have been proposed and developed in earlier parts of this paper. An arbitrarily introduced hazard function was used to predict the life distributions likely to be obtained. The details of the mechanisms giving rise to tool failure were, however, not examined. Mechanistic questions connected with the single-injury tool failure (tool fracture) are examined in this part. The arbitrarily introduced hazard function is shown to have a physical basis. It is shown that the hazard function is determined by the interaction between the characteristics of the environment in which the tool operates and the mechanical properties of the tool material. The concepts outlined and the mechanistic model of tool failure proposed have been tested experimentally in interrupted cutting. It is shown that the predicted Weibull-distributed tool life is obtained when tool failure is due to a single injury and that the parameters of the Weibull distribution are governed by the properties of the tool material as well as those of the machining system.

Improving Tool-Life Stochastic Control Through a Tool-Life Model Based on Diffusion Theory

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Marcello Braglia ◽  
Davide Castellano
Keyword(s):  
Tool Wear ◽  
Tool Life ◽  
Diffusion Theory ◽  
Time Instant ◽  
Quality Level ◽  
Future Time ◽  
Wear Process ◽  
Current State ◽  
Life Model ◽  
Machined Parts

It is known that estimating the wear level at a future time instant and obtaining an updated evaluation of the tool-life density is essential to keeping machined parts at the desired quality level, reducing material waste, increasing machine availability, and guaranteeing the safety requirements. In this regard, the present paper aims at showing that the tool-life model that Braglia and Castellano (Braglia and Castellano, 2014, “Diffusion Theory Applied to Tool-Life Stochastic Modeling Under a Progressive Wear Process,” ASME J. Manuf. Sci. Eng., 136(3), p. 031010) developed can be successfully adopted to probabilistically predict the future tool wear and to update the tool-life density. Thanks to the peculiarities of a stochastic diffusion process, the approach presented allows deriving the density of the wear level at a future time instant, considering the information on the present tool wear. This makes it therefore possible updating the tool-life density given the information on the current state. The method proposed is then experimentally validated, where its capability to achieve a better exploitation of the tool useful life is also shown. The approach presented is based on a direct wear measurement. However, final considerations give cues for its application under an indirect wear estimate.

Diffusion coefficient for the Compton Fokker-Planck equation

1988 ◽  
Vol 40 (1) ◽  
pp. 29-38 ◽  
Author(s):  
M.K. Prasad ◽  
A.I. Shestakov ◽  
D.S. Kershaw ◽  
G.B. Zimmerman
Keyword(s):  
Diffusion Coefficient ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Tool-Life Distributions—Part 2: Multiple-Injury Tool-Life Model

1977 ◽  
Vol 99 (3) ◽  
pp. 523-528 ◽  
Author(s):  
S. Ramalingam
Keyword(s):  
Tool Life ◽  
Multiple Injury ◽  
Linear Wear ◽  
Life Distribution ◽  
Subsequent Work ◽  
Tool Failure ◽  
Linear Wear Rate ◽  
Life Model ◽  
Life Distributions ◽  
Log Normal

The single-injury tool-life model developed in Part 1 of this paper is extended to the case of tool failure due to a multitude of injuries. The expected tool-life distribution in the case of tool failure from multiple injuries due to constant, time-independent stochastic hazards is shown to be a gamma distribution. The result obtained is based on a linear wear-rate assumption. The model is further extended to ensure applicability in the nonlinear wear region. It is shown that the expectation of a log-normal tool-life distribution when tool failure is due to crater wear is not unrealistic. No specific mechanism of tool wear is used to develop the model. The nature of the hazards and the wear mechanisms that are consistent with the multiple-injury tool-life model will be discussed in a subsequent work.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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