Novel calculation methods for geometrically accurate thread depth

In advanced manufacturing systems, particularly High-Mix Low-Volume (HMLV) environments, achieving first-pass conformity in threaded components remains challenging due to strict ISO tolerance requirements, non-standardized tool geometries, and reliance on gauge-based iterative corrections. These limitations not only reduce machining accuracy but also increase setup time, energy consumption, and material waste. This study introduces three fundamentally new calculation methods that enable precise geometrical determination of thread depth for CNC turning and milling of both external and internal metric threads. The methods integrate ISO-defined pitch-diameter tolerances, detailed tool geometry, and measured nose radius into a unified analytical framework, thereby enabling automatic and dimensionally accurate G-code generation. Method 1 addresses external thread turning using full-profile inserts. Method 2 provides a generalized model for external thread milling with free-form radii. Method 3 extends the approach to internal threads by incorporating pre-machined reference diameters. Industrial case studies demonstrates that the proposed methods can enhance precision manufacturing, eliminate trial-and-error adjustments. The results contribute to advanced and green manufacturing practices by improving automation readiness, shortening machine setup cycles, and enabling reliable production of atypical thread sizes and tolerance classes.