OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 5 2 3 Fig. 5. Structural kinematic scheme of the hybrid metalworking system: the structural formula is 1 2 0 ( ) XYZ b w w Ñ It is obvious that the definition of the type of the parameter-oriented series structure has a significant impact on the stock of capabilities of its individual members. So, in order to ensure maximum efficiency of hybrid metal-cutting equipment, when designing it, it is necessary to strive for such a construction of a technological system in which the stock of its capabilities would have the least value. But this requirement is quite well fulfilled and is realized only in conditions of mass production. However, in the situation of small-scale and individual production, the factor of the necessary increase in the flexibility of technological equipment comes to the fore, forcing the creation of machines with an increased value of the allowed value of capabilities stock, which invariably leads to some decrease in its efficiency. The solution to this problem, i.e. finding the option of the most rational use of the range of universal machines is the equality of conditional average losses for all members of the parameter-oriented series: 1 2 const i m R R R R = = = = = = , (2) where m is the number of members of the size range. When forming the parameter-oriented series of metal-cutting machine tools, its main parameter is subjected to standardization. For example, for lathes, this is the machining diameter above the frame, and for milling metal-cutting equipment, it is the width of the table, etc. In this case, the ratio between the main parameters of neighboring members of the series will determine its normative capabilities stock. Taking this fact into account, dependence (1) can be transformed into an objective function of the form 1 1 (1 ) 1 min 1 m i i i i i R RC p = ϕ = − − Ψ ≤ → ϕ − ∑ , (3) where i i UC DC Ψ = – duty factor of metal-cutting machine capabilities stock. Since as the main parameter of the equipment grows, the reduced costs increase, it follows from the analysis of equation (3) that the equality of conditional average losses for all machines of the line can be ensured if the parameter-oriented series is built with a variable denominator [19, 71] 1 2 i m ϕ > ϕ > > ϕ > > ϕ (4) It should be noted that it is advisable to change the values of ϕi exponentially with the denominator d.
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