PSI - Issue 81

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

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which allows determining the required plate thickness that ensures the specified reliability level. The parameter γ \ gammaγ in this case reflects the safety factor associated with reliability requirements. The economic feasibility limit corresponds to a reliability level of γ=0.9 . This value provides a compromise between the increase in manufacturing costs associated with increasing the strength of the plate and the reduction in operating costs due to the reduction in the number of failures. Thus, the resulting ratio allows determining the optimal plate thickness that ensures the necessary reliability and economic efficiency in heavy turning processes. 3.4. Research on the maintainability and durability of turning tools for heavy-duty machines The maintainability of assembled turning tools is one of the key factors determining their reliability and operational efficiency in heavy cutting conditions. Maintainability is understood as the adaptability of a tool to restore its working condition, which includes the possibility of maintenance, condition monitoring and failure elimination without significant time expenditure. Experimental studies have shown that the time required to restore a tool depends significantly on the stability of its cutting properties and the load on the cutting elements. An increase in stability dispersion and the frequency of sudden failures leads to an increase in downtime. The proportion of downtime associated with tool maintenance averages 6 – 10% of the total system operating time or up to 27% of the downtime. The distribution of recovery time for S and H type tools, obtained from statistical data processing, is shown in Fig. 6. The curves have a normal distribution, which confirms the random nature of the recovery processes. For S-type tools, the average recovery time is slightly less than for H-type tools, which is explained by the simplified design of the fasteners and the lower labour intensity of replacing the inserts.

f(  )

0,08 0,07 0,06 0,05 0,04 0,02 0

1

2

1 2 3 4 5 6 7 8 9

τ ,

min

Fig. 6. Distribution of the recovery time for turning tools for designs: 1 – type S, 2 – type H.

The average experimental values of the restoration time confirm that the least time is spent on replacing the cutting insert (≈39 s ), and the most time is spent on restoring the body (≈80 s). The average coefficient of variation for these processes is V = 0.25 – 0.32, which indicates sufficient stability of maintenance operations. Durability analysis showed that for type H prefabricated cutters, the overall reliability level is about 0.64, while for cutting plates it is 0.75 – 0.82. Further increasing the reliability level leads to an unjustified increase in costs, so these values are reasonable for practical application. 4. Discussion The results obtained are consistent with the conclusions of previous studies, which emphasise the stochastic nature of tool wear and the need to use probabilistic models to predict its reliability. Previous work has shown that traditional exponential and deterministic approaches do not provide sufficient accuracy in describing the real variability of tool stability indicators under severe cutting conditions. In contrast, the Polmark model proposed in this study allows for non-exponential distributions of failure and recovery times, which provides a more adequate reflection of the dynamics of the tool operation process. A comparison of experimental and calculated data showed that the proposed model reliably describes both the average failure free operating time and the average recovery time obtained during the tests. The calculated values of the readiness coefficient and maintainability indicators are in good agreement with the empirical results for different types of cutter designs. This confirms the feasibility of using the Polmark model to assess the reliability of complex technical systems, in particular prefabricated turning cutters for heavy machine tools. From a practical point of view, the developed methodology has significant advantages for machine-building enterprises. The introduction of regulated tool replacement based on the gamma-percentage stability period allows maintaining a rational level of reliability (approximately 0.64 for the entire cutter system) and preventing unscheduled downtime. This approach provides an optimal balance between maintenance costs and production efficiency. In addition, the probabilistic estimate of recovery time can be used for maintenance planning, in particular for optimising inspection schedules, replacements and management of spare parts for tools. An important advantage of the Polmark model is its ability to describe real stochastic wear processes, taking into account variations in mechanical loads, cutting forces and material properties. Unlike classical reliability models, this approach reflects the