Stiffness modeling technique for five-axis milling process system with thin-walled parts

The manufacturing industry is witnessing increasing precision requirements for thin-walled components, such as turbine blades and casings, in the field of aerospace engines. This is because these components suffer high material removal rates and poor machining performance, resulting in extreme changes in cutting forces during machining and the formation of chatter marks on the machined surface, leading to decreased surface quality. The relative vibration between the cutting edge and workpiece surface is mainly influenced by the milling forces and stiffness of various parts of the process system. Therefore, modeling of stiffness and analysis of such process systems are crucial for increasing the machining accuracy.

Based on the research on machine tool modeling using cutting tools, casings, and fixtures available domestically and internationally, simulation calculations and process system analyses were conducted under typical working conditions. A large amount of data was generated through hammering and vibration excitation experiments, and an eXtreme Gradient Boosting (XGBoost) algorithm was employed to establish a stiffness model for a cradle-type AC rotary table structure machine tool; furthermore, this model includes pose information. The stiffness model of the machine tool was integrated with the tool, workpiece, and fixture models obtained via the finite element method using a stiffness series formula and the spatial coordinate transformation method for developing the stiffness model of the process system. The stiffness model's accuracy was increased through iterative updates. First, the harmonic response of the tool, casing, and fixture was calculated through the finite element simulation. Second, a suspended measurement device for measuring the dynamic stiffness of the machine tool was proposed using an electromagnetic exciter. The device offers the advantages of high excitation power, high measurement signal-to-noise ratio, and measurement ability in different machine tool poses. Subsequently, the dynamic stiffness values of the machine tool in different poses were measured using the exciter. After obtaining the stiffness models of the tool, fixture, and workpiece systems through the finite element method, the overall stiffness modeling of the process system was completed through the stiffness series theory and spatial coordinate transformation. Finally, the calibration and iteration mechanism of the stiffness model of the process system were established. An XGBoost algorithm was established to estimate the dynamic stiffness of the process system using milling force and surface topography information measured through milling experiments. An adaptive undersampling technique for discrete data with equal chord height was proposed to address the severe imbalance between the amounts of dynamic stiffness data obtained through the abovementioned model and vibration excitation test data.

1) After comparing the measurement results of the hammering experiment with simulation result, the maximum error of the dynamic stiffness obtained through the finite element simulation was < 10% and the average error was < 6%, indicating that relatively accurate tool and casing models can be obtained through this simulation. 2) After measuring the dynamic stiffness of the machine tool at different poses by using the electromagnetic exciter, the error rate of the machine tool stiffness model established using XGBoost algorithm meets the 3σ criterion. 3)The average error of the XGBoost algorithm for measuring the process system stiffness through milling force and surface topography is less than 13%, with a maximum value of no more than 18%.

The undersampled vibration excitation test data and stiffness data obtained through the cutting experiments were used for calibrating and iterating the stiffness model of the process system, ensuring that the error rate of the model meets the 3σ criterion.