Advanced regression model fitting to experimental results in case of the effect of grinding conditions on a cutting force with the planer technical knives

• Multi-step procedure for establishing regression functions was presented. • One-, two- and three-factor analyses were performed to eliminate redundant factors. • Analyses of variance and Tukey, Levene and Brown-Forsythe tests were used. • Nonlinear models were worked out by comparing the distribution of residuals. • Akaike Information Criterion, Cook’s distance and Variance Inflation Factor were also used. The use of well-fit models enables users to make better decisions and draw accurate insights, so in this article a multi-step procedure for establishing regression functions for experimental data is presented. This was inspired by the need to determine well-fitted models for the results of the study of the relationship between the input factors of the grinding process of planer knives and the measured grinding power, as well as in relation to the knife cutting force. The sharpening process was carried out under various conditions, making it possible to assess their influence on the results and select the most favorable technological parameters to prepare the knives for operation. The equations adjusted by Excel or other basic methods require additional verification if the mathematical formula and values of the model coefficients correspond to the data and the physical meaning. For this purpose, one-, two- and three-factor analyses were performed to eliminate redundant factors and introduce significant interactions between input parameters. Additional analyses of variance and Tukey, Levene and Brown-Forsythe tests were used to determine the general form of the model. Detailed form of nonlinear models was worked out by comparing the distribution of residuals, looking for outliers and evidence of the presence or absence of collinearity, as well as by determining the values of additional model quality indicators, such as Akaike Information Criterion, Cook’s distance and Variance Inflation Factor. The models presented include a categorization variable (grinding type) and are presented graphically in the form of surface plots. With reference to the technological processes studied, a discussion of the physical significance of the developed models and the influence of the input factors on the model output value was conducted. The analyzes additionally include an evaluation of the model factors using prediction slice plots.