Non-linear Model for Determining the Tools Life in the Wood Industry

A mathematical model was developed to determine the service life of saw blades during the wood cutting process, characterized by non-linear behavior represented by a function composed of a pseudo-logarithmic and an exponential term that describes the typical sigmoidal curve of abrasive wear. The proposed model achieved a reliability of 97%. The calculated inflection point was acceptably correlated with the effective tool life in industrial wood-cutting operations. Tool wear was evaluated as a function of the specific work performed (volume of sawn wood), revealing a constant increase in the initial cutting stages, followed by a stage where the edge wear increased exponentially. The wear rate rose from 2.2×10⁻² µm·m⁻³ to 4.4×10⁻² µm·m⁻³, reaching 9.9×10⁻² µm·m⁻³. The algorithm developed for non-linear modeling and for determining the inflection point through differential equations based on energy consumption and sawn wood volume provides valuable support for defining tool life under real industrial conditions. This approach enables the transition from a traditional and empirical methodology to an objective and data-driven one, based on the specific work performed by each saw. By associating the inflection point with the effective tool life, it is possible to prevent all the negative consequences associated with uncontrolled cutting processes. This reference point can therefore serve as a control limit for managing cutting operations in industrial sawmills.