PSI - Issue 81

Viktor Kovalov et al. / Procedia Structural Integrity 81 (2026) 297–304

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Based on these probabilities, the stationary probabilities of the system states are calculated = ∫ ∑ ( ) 0 ∞ ∑ ∫ ∑ ( ) 0 ∞ , as well as the tool readiness coefficient

K G =π 1 +π 2 , which characterises the probability that the system is in an operational state at any given moment in time. Two distribution laws are used to quantitatively describe the processes of wear and recovery. The Weibull distribution is used to model the failure-free operating time of a carbide plate: ( ) = −( ) where η — is the scale parameter (characteristic service life), and β — is the shape parameter that determines the type of failure ( β > 1 corresponds to wear failures). The process of restoring operability after repair or replacement is described by an exponential law: ( ) = λ −λt where λ=1/T rel — recovery intensity, inverse to the average repair time. The combination of Weibull distributions and the exponential law within the semi-Markov model allows for the reproduction of both gradual and sudden tool failures, as well as the random duration of repair and restoration processes. The proposed probabilistic model provides the ability to quantitatively assess the reliability of a prefabricated cutter, take into account the influence of stochastic loads and cutting modes, and forms the basis for determining an economically feasible level of reliability. 2.3. Experimental verification of the model To confirm the reliability of the developed mathematical model of the reliability of the assembled turning tool, experimental studies were carried out in conditions as close as possible to production conditions. The experiments were carried out on lathes equipped with cutters with replaceable carbide inserts of types S and H. The materials processed were steels 40X and 45, hardened to a hardness of 40 – 45 HRC, which ensured high thermomechanical loads characteristic of heavy turning conditions. During the research, the following cutting modes were used: cutting depth a p =10 – 19 мм , feed f=0.8 – 1.0 mm/rev, cuttingspeed v=75 – 110 m/min. For each combination of parameters, at least twenty tests were performed with recording of the time to tool failure, i.e. the moment of complete wear or destruction of the cutting edge, as well as the time to restore performance after replacing the carbide insert. The experimental data obtained were used for statistical evaluation of the Weibull distribution parameters and the exponential law, which formed the basis of the probabilistic reliability model. To verify the conformity of the theoretical distributions with the experimental data obtained, the Kolmogorov – Smirnov criterion was applied, which allows testing the hypothesis of the consistency of the empirical distribution function F n (x) and the theoretical function F(x) . The results of the calculations show that the statistical deviation does not exceed the critical value at a significance level of α=0.05 , which confirms the adequacy of the model. A comparative analysis showed that the error between the experimental and calculated values of the probability of failure-free operation of the cutter does not exceed 10%, and the average deviation of the reliability function is about 8%, which is acceptable for practical calculations. Thus, the results obtained confirm the adequacy of the proposed stochastic reliability model for a prefabricated turning tool. A graphical comparison of the failure-free functions based on experimental data and theoretical calculations according to Weibull's law showed a high convergence of the curves, which indicates the correctness of the selected distribution type and the validity of using a semi-Markov model to describe real operating processes. Thus, the model can be used to predict the service life of tools, plan scheduled replacements, and optimise the maintenance system in production conditions. 3. Research results 3.1. Reliability and Tool Life Analysis Based on the described methodology, which combines experimental testing and probabilistic modelling, quantitative results were obtained that allow the reliability of the assembled turning tool to be assessed under severe operating conditions. The failure free function of the cutting part of the tool is described by Weibull's law with parameters η=115 хв and β=1.6 , which corresponds