Catastrophe Modeling Of Chip Flow Angle In Oblique Cutting Of Straight Double-Edged Lathe Tool

It was found that the catastrophe of chip flow angle is a cutting phenomenon with great application potential from experiments.However,people lack sufficient understanding of its mechanism.The establishment of a mathematical model describing the catastrophe of chip flow angle is the fundamental way to explore the mechanism and the law of the catastrophe of chip flow angle in essence.It has important theoretical and practical significance.Derived the cutting plane area and cutting power calculation function in oblique cutting for the main edge of a straight double-edged lathe tool.Using the cutting power function as the potential function,the cutting width and the cutting depth as the control variables,a mathematical model(cusp catastrophe mode)was established to describe the catastrophe of chip flow angle by using the catastrophe theory.A method of fitting the explicit expression of the bifurcation set equation from the drawing of the bifurcation sets was proposed.The model was programmed on the Maple platform,and a set of critical conditions for the catastrophe of chip flow angle was obtainedThe cutting experiment on a cone-shape end face of a group of 6061 aluminum alloy workpiece with straight double-edged lathe tools was designed and completed.A method of capturing the catastrophe of chip flow angle and obtaining the critical condition of catastrophe by the filmed chip flow video and the measured cutting force waveform diagram were proposed,and the validity of the previous mathematical model of the catastrophe of chip flow angle and the accuracy of the accuracy of the forecast results were verified.In order to explore the effects of the mechanical properties of the workpiece material on the catastrophe of chip flow angle,an empirical model for calculating the parameters of the 6061 aluminum alloy based on the cutting conditions was established by the finite element simulation experimental data of the orthogonal cutting process of the single point tool.According to the empirical model,a mathematical model in which the mechanical properties of the workpiece material are considered was established to describe the catastrophe of chip flow angle when turning with straight double-edged lathe tools(?n?0o??s?0o),and a set of critical conditions and the chip flow angle before and after the catastrophe were obtained.The cutting experiment on a concave-shape end face of a group of 6061 aluminum alloy workpiece with straight double-edged lathe tools was designed and completed.The experimental data of the critical conditions and the chip flow angle before and after the catastrophe were obtained.The validity of the foregoing mathematical model and the accuracy of the forecast results are verified.A series of repetitive experiments have been completed.It is proved that the catastrophe of chip flow angle is repeatable.The above researches explain the mechanism of the catastrophe of chip flow angle in essence,reveal its inherent law,and preliminarily lay the foundation for the rational use and control of it.