Актуальные проблемы в машиностроении. Том 13. № 1-2. 2026 Инновационные технологии в машиностроении ____________________________________________________________________ 29 MATHEMATICAL SUBSTANTIATION OF THE EFFECTIVENESS OF THE HYBRID GEAR‑SHAPING MACHINE MODEL 5111 WITH INTEGRATED HIGH‑FREQUENCY INDUCTION HEATING Popkov A.S., Post-graduate Student, junior researcher, e-mail: popkov.2016@stud.nstu.ru Novosibirsk State Technical University, 20 Prospekt K. Marksa, Novosibirsk, 630073, Russian Federation Abstract This paper presents a mathematical justification for the effectiveness of using hybrid technological equipment implemented on the basis of an upgraded gear‑shaping machine Model 5111 with an integrated surface heat treatment module using high‑energy high‑frequency current (HEH HFC) heating. The analysis is carried out from the standpoint of the fundamental principles of the theory of dimensional chains and the theory of technological locating. It is shown that the combination of gear machining and surface hardening in a single technological cycle without intermediate re‑clamping of the workpiece provides a significant reduction in the total machining error and an increase in the manufacturing accuracy of gears. Keywords gear machining, gears, heat treatment, hybrid equipment, modernization
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