Working limit of the circular saws in the cutting of high density fiberboard (HDF) through a nonlinear model and differential equations

The wood industries focus their efforts on improving the productivity and efficiency of their operations to increase their competitiveness. There is a notable interest in the model development to assist autonomous control systems within the operations of the wood industry. For this, it is very important to know the behavior of the different outputs in the production process, such as the power consumption during cutting, since it provides vital information on the state of the wear of the cutting tools even when they are in operation. This allows knowing when to change the cutting tool in advance to avoid any negative effects on the products. In this article, a non-linear fit composed of a modeled function with quasi-logarithmic behavior and an exponential part of the power consumption based on a cutting length in circular saws in high density fiberboard (HDF) is presented. The working limit of the cutting tools was determined by means of differential equations identifying the inflection point in the function. The theoretical model was experimentally corroborated in a multi-objective way by relating the results of power consumption, the surface and the dimensional quality of the boards, the cutting length and the calculated inflection point. It can be affirmed that the developed non-linear model presents a good approximation towards the final part of the function (region of practical interest), the moment when it is necessary to change the cutting tools. By applying the suggested methodology, it is possible to avoid all the described negative consequences of an uncontrolled machining process in an adaptive way to the natural variability of a real industrial production.