Probability-statistical estimation method of feed influence on the tangential cutting force under turning

This research aims to develop the mathematical model and propose a method for estimating the feed stochasticity impact on the tangential cutting force during turning. The main reason for this research is that the existing models for determining the tangential component of the cutting force do not take into account the stochasticity of the feed rate. Measurements of tangential cutting force during turning on general-purpose lathes with known feed dispersion parameters were made. The mathematical model was developed, and dispersion characteristics (mean value, dispersion and mean square deviation) of the tangential cutting force component depending on the corresponding dispersion characteristics of the feed rate were obtained. The method of assessing the impact of stochasticity of the feed rate on the tangential cutting force is proposed. As the result of the carried-out investigations, it is proved that the stochasticity of the feed rate affects the dispersion of the tangential cutting force during turning. For specific conditions, the share of feed stochasticity in the dispersion of tangential cutting force component is from 40 to 60% and should be taken into account while prescribing rational cutting modes. The obtained results make it possible to adjust the cutting modes, particularly the amount of feed, under the conditions of real equipment to ensure certain power characteristics of the cutting process to prevent overloads during cutting. This investigation benefits to the establishment of additional factors affecting oscillations in the cutting process. The probabilistic-statistical approach is used in this investigation in order to prove that the stochasticity of the feed rate affects the dispersion of the tangential cutting force component.