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

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.

1977 ◽  
Vol 99 (3) ◽  
pp. 519-522 ◽  
Author(s):  
S. Ramalingam ◽  
J. D. Watson

The statistical variability of tool life in production machining must be accounted for in any rational design of large-volume or automated manufacturing systems. The probabilistic approach needed for such a design is presently limited by lack of data on tool-life distributions and by lack of knowledge of the underlying causes giving rise to tool-life scatter. Given these circumstances, on the basis of relevant physical arguments one may construct probabilistic models that produce distribution functions germane to the problem of tool-life scatter. This paper is concerned with such a study. This first part presents the results obtained on the assumption that the useful life of a tool is terminated by a single, catastrophic injury. Cases where resistance to tool failure is time-independent and time-dependent are examined. The case of tool failure caused by multiple injuries will be presented in Part 2.


1977 ◽  
Vol 99 (3) ◽  
pp. 523-528 ◽  
Author(s):  
S. Ramalingam

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.


Author(s):  
Marcello Braglia ◽  
Davide Castellano

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.


2011 ◽  
Vol 25 (2) ◽  
pp. 251-263 ◽  
Author(s):  
Broderick O. Oluyede

In this article notions of exponential dominance and uncertainty for weighted and unweighted distributions are explored and used to compare values of the informational energy function and the differential entropy. Stochastic inequalities and bounds for cross-discrimination and uncertainty measures in weighted and unweighted residual life distribution functions and related reliability measures are presented. Moment-type inequalities for the comparisons of weighted and unweighted residual life distributions are also presented.


1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.


Author(s):  
Vladimir A. Avakov

Abstract In the previous publication [2], the transformation between fatigue life and strength distribution was established using double-logarithmic coordinate system (lnN-lnS). Here, a similar transformation is established using a semi logarithmic (lnN-S) coordinate system. With the aid of the developed orthogonal relations, lognormal, Weibull and three-parameter logweibull life distributions have been transformed into normal, asymptotic type 1 of smallest value, and three-parameter Weibull strength distributions, respectively. This procedure may be applied to other types of fatigue life distribution.


1982 ◽  
Vol 10 (3) ◽  
pp. 773-779 ◽  
Author(s):  
Naftali A. Langberg ◽  
Moshe Shaked

1976 ◽  
Vol 98 (1) ◽  
pp. 183-188 ◽  
Author(s):  
H. A. Elmaraghy ◽  
J. N. Siddall

This paper presents a Monte Carlo simulation method for fatigue failure, by which the randomness of two material properties as well as that of the applied load can be incorporated into a stochastic model using an appropriate failure criterion to predict the statistical characteristics of fatigue life under constant and random amplitude cyclic loading conditions. In this technique, both the endurance limit Se and the fatigue strength coefficient Sf′ are treated as stochastic variables. The combined effect of the randomness of Se, Sf′, and the applied stress on the statistical characteristics of fatigue lives is predicted analytically using digital simulation of fatique tests. The life distributions and their statistical characteristics are found to be in good agreement with those obtained from analyzing the experimental results, indicating that the proposed technique and the underlying assumptions and hypotheses are adequate. The suggested method is believed to be an effective, fast, and easy-to-use design tool which is suitable for use on electronic computers. It is ideal for parametric studies compared with the costly and time-consuming laboratory fatigue tests. Minimum experimental data are needed as a basis for the analysis. New results are presented which show the effect of the randomness of the loads and material properties on the randomness of fatigue life distribution.


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