In this article, a new model of regenerative vibrations due to the deflection of the cutting tool in turning is proposed. The previous study reported chatter as a result of cutting a wavy surface of the previous cut. The proposed model takes into account cutting forces as the main factor of tool deflection. A cantilever beam model is used to establish a numerical model of the tool deflection. Three-dimensional finite element method is used to estimate the tool permissible deflection under the action of the cutting load. To analyze the system dynamic behavior, 1-degree-of-freedom model is used. MATLAB is used to compute the system time series from the initial value using fourth-order Runge-Kutta numerical integration. A straight hard turning with minimal fluid application experiment is used to obtain cutting forces under stable and chatter conditions. A single-point cutting tool made from high-speed steel is used for cutting. Experiment results showed that for the cutting parameters above 0.1mm/rev feed and 1:5mm depth of cut, the system develops fluctuations and higher chatter vibration frequency. Dynamic model vibration results showed that the cutting tool deflection induces chatter vibrations which transit from periodic, quasi-periodic, and chaotic type.

This article presents a new model of the flat surface grinding process vibration conditions. The study establishes a particular analysis and comparison between the influence of the normal and tangential components of grinding forces on the vibration conditions of the process. The bifurcation diagrams are used to examine the process vibration conditions for the depth of cut and the cutting speed as the bifurcation parameters. The workpiece is considered to be rigid and the grinding wheel is modeled as a nonlinear two-degrees-of-freedom mass-spring-damper oscillator. To verify the model, experiments are carried out to analyze in the frequency domain the normal and tangential dynamic grinding forces. The results of the process model simulation show that the vibration condition is more affected by the normal component than the tangential component of the grinding forces. The results of the tested experimental conditions indicate that the cutting speed of 30 m/s can permit grinding at the depth of cut up to 0.02 mm without sacrificing the process of vibration behavior.

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