Time Finite Element Analysis Research Articles

Improved dynamic simulation of end-milling process using time series analysis

Milling is a competitive manufacturing process that is widely used in automotive, aerospace, biomechanical and die/mould industries. Due to the complex geometry and intricate mechanics of milling, the realistic simulation of various milling processes is a challenging research task. Accurate simulation of the milling process requires a proper knowledge of its dynamics. In this paper, a method is developed for the accurate prediction of cutting forces and surface texture in the end-milling operation, based on Time Series Analysis (TSA). In the proposed approach, an equivalent damping ratio is defined for the cutting zone, while the damping ratio of the non-cutting zone is determined by experimental modal analysis. Using a correlation sum criterion, the simulation and experimental force signals are compared to anticipate the value of process damping inside the cutting zone, by assessing the variations in correlation dimensions for both signals. The simulation algorithm incorporates the Time Finite Element Analysis (TFEA) for predicting the dynamics of the milling system. It also takes into account the effect of cutter deflections and run out. The feasibility of the proposed algorithm is verified experimentally for the side wall machining of aluminum 7075-T6, using a High Speed Steel (HSS) helical end mill. The implemented model can accurately predict cutting forces and a 3D surface texture for low radial immersion cutting.

Anticipation of Stability Limits for Two Degree-of-Freedom Interrupted Milling

AbstractMilling is becoming an increasingly universal machining operation for producing parts used in aerospace, automotive, and life science engineering industries. The characteristics common to such parts are a high level of complexity and structural flexibility, both of which usually necessitate using low radial immersion milling operations. Low radial immersion milling operations involve interrupted cutting which induces chatter vibration under certain cutting conditions. The stability behavior of low immersion helical end milling processes is investigated in this paper. Time Finite Element Analysis (TFEA) is suggested for an approximate solution for delayed differential equations encountered during interrupted milling. An improved TFEA is proposed which includes the effects of helix angle variations on cutting force, cutting time and specific cutting force coefficients for a 2 DOF vibratory system. To verify the proposed method, experimental tests have been conducted which prove that the improved TFEA method accurately predicts the stability behavior of low immersion milling.

Limit cycles, bifurcations, and accuracy of the milling process

Time finite element analysis (TFEA) is used to determine the accuracy, stability, and limit cycle behavior of the milling process. Predictions are compared to traditional Euler simulation and experiments. The TFEA method forms an approximate solution by dividing the time in the cut into a finite number of elements. The approximate solution is then matched with the exact solution for free vibration to obtain a discrete linear map. Stability is then determined from the characteristic multipliers of the map. Map fixed points correspond to stable periodic solutions which are used to evaluate surface location error. Bifurcations and limit cycle behavior are predicted from a non-linear TFEA formulation. Experimental cutting tests are used to confirm theoretical predictions.