Stability analysis in milling of thin-walled workpieces with emphasis on the structural effect

In aerospace industry, thin-walled workpieces are widely used in order to reduce the weight and to fulfill the high demands of their later applications. These workpieces are usually highly sophisticated and difficult to machine according to their geometry and material choice. In this paper, influence of material removal within the thin-walled workpiece machining operation on the dynamic properties of the workpiece and the machining process system is discussed. Aiming at learning about dynamic properties evolution during the machining operation, different milling processes of thin-walled plate are studied. Numerical simulation methods are employed in the study to investigate the dynamic properties evolution and machining stability with the material removal process in the milling process of thin-walled workpiece. The investigation results are expected to be used for designing optimized material removal sequence, which will guarantee highly material removal rate as well as highly machining accuracy of thin-walled workpiece.

In order to control the cutting chatter in machining of thin-walled workpieces, the dynamic milling model of thin-walled workpieces is analyzed and built based on the analysis of degrees in two perpendicular directions of tool-workpiece system. In high speed milling of 2A12 aluminum alloy, the compensation method based on the modification of inertia effect was proposed and accurate cutting force coefficients were obtained. Modal parameters of tool-workpiece system were acquired via modal analysis tests. The stable lobe for high speed milling of 2A12 aluminum alloy thin-walled workpieces and limit cutting axial-depth at different cutting radial-depth were obtained. The results were verified with cutting tests. The method can be used in milling of thin-walled workpieces to select cutting parameters properly. All these work lay a reliable foundation to the further studies on the cutting chatter rules of thin-walled workpieces.

Chatter vibration in milling has been one crucial factor hindering the realization of high-performance machining. The corresponding stability analysis is of great significance for obtaining chatter-free machining parameters. Based on the predictor-corrector scheme, this paper develops an accurate and efficient holistic-discretization method for the stability analysis of milling processes. According to the system state equation, the period of the time-periodic coefficient matrix is divided into two time intervals. The forced vibration time period is then equidistantly discretized. Working as a holistic unit, the time-periodic parameter matrix, the state term, and the delay term are approximated over two different subintervals by the second-order Lagrange interpolations. Finally, the Floquet transition matrix can be constructed by taking advantage of the predictor-corrector scheme, and the milling stability can be semi-analytically determined by utilizing the Floquet theory. The computational accuracy of the proposed method is analyzed theoretically and illustrated by making comparisons with the first-order semi-discretization method (1st SDM), the second-order, and the third-order updated full-discretization methods (2nd UFDM and 3rd UFDM). The stability lobes for two benchmark milling models and the computational efficiency of these methods are presented to further verify the effectiveness of the proposed method. Theoretical analysis and numerical results validate that the proposed predictor-corrector-based holistic-discretization method achieves both high computational accuracy and efficiency for milling stability analysis. In conclusion, the proposed semi-analytical algorithm has a high potential for industrial applications.

Systematic simulation procedure of peripheral milling process of thin-walled workpiece

Fuzzy stability analysis of regenerative chatter in milling

An accurate analytical model for regenerative chatter vibration in plunge cutting is proposed. Effects of the cross transfer function and the cutting force ratio on chatter stability are considered in the proposed model. Equivalent transfer function is defined, which is useful to understand those effects on chatter stability. Basic plunge cutting experiments were conducted to verify the proposed model. Although the critical widths of cut in the CW and CCW rotation processes were significantly different from each other in the experiment, even when the other conditions were the same, chatter stability limits were predicted accurately by the proposed model as compared with the conventional model.

Operational modal analysis based dynamic parameters identification in milling of thin-walled workpiece

When machining thin-walled workpieces like turbine blades, the parts are prone to be bent by the cutting forces due to its low rigidity. The workpiece deflection during the machining process of the thin-walled workpiece is a critical issue that is likely to jeopardize the finish surface quality. Traditionally, in order to control the machining error caused by deflections, conservative machining parameters are adopted as constants for each cutter locations which are determined by simply taking the weakest spot as the reference. As the residual thickness left on the thin-walled part surface usually cannot be removed with a single cut, multi-pass machining is necessary to be used by removing the residual thickness with several rounds of cuts. For a given thin-walled workpiece, the primary objective in this thesis research is to develop optimized process planning strategies for five-axis machining including both end milling and flank milling aiming at improving the machining time efficiency to educe the total machining time while maintaining the acceptable machining errors. For five-axis end milling, the optimization process to achieve this goal is divided into two parts. Firstly, the optimization of machining parameters for thin-walled workpiece is accomplished by a novel variable depth-of-cut machining strategy for semi-finish and finish machining based on the workpiece deflection constraints. It strives to maximize the depth-of-cut locally for each cutter contact (CC) point while respecting a calibrated threshold of the normal cutting force 𝐹<sub>𝑛</sub> which is the major cause of the workpiece deflection. The maximum allowed depth-of-cut 𝑑<sub>𝑚𝑎𝑥</sub> of each CC point is determined adaptively according to the calibrated maximum allowed 𝐹<sub>𝑛</sub> of the thin-walled workpiece. The multi-pass semi-finishing tool path is generated by offsetting the finishing tool path with the computed variable depth-of-cut. Next, we integrate the optimization of finishing tool path and machining parameters together to further improve the machining efficiency of the multi-pass machining for the thin-walled workpiece. A five-axis tool path generation method is developed to automatically generate a finishing tool path that reduces the total machining time of the multi-pass tool path expanded from the generated finishing tool path for an arbitrary thin-walled workpiece. A cutting area potential field on the given part surface of a thin-walled workpiece is first established to indicate the principle feed direction for any point on the part surface. Based on this field, the finishing tool path is planned through the iso-scallop height tool path expansion scheme. For the flank milling of thin-walled workpieces, a new multi-pass adaptive machining parameters optimization method for flank milling of thin-walled workpiece is developed that generates the multi-pass tool path from an input finishing tool path, with the optimized radial depth-of-cut and feedrate assigned to each cutter location. Both radial depth-of-cut and feedrate are simultaneously optimized by solving a minimization problem formulated based on the cutting force model subject to the deflection constraints and machine’s kinematical constraints. Finally, computer simulations and physical cutting experiments are reported to clarify the improvements achieved in machining efficiency by the proposed strategies.

In this paper, a method to optimize the location of tuned mass damper (TMD) for enhancing chatter stability limits of thin-walled workpiece by using numerical techniques is proposed with due consideration to mass effect of TMD. The dominant mode of workpiece is identified from the simulated and measured frequency response functions of the workpiece. Two TMDs each having single degree of freedom are designed and a finite element model to predict the response of the workpiece-damper system is developed. The effect of damper location on the chatter stability of the thin-walled workpiece is investigated. Further, the locations for TMDs are optimized for enhanced chatter stability of workpiece by using response surface methodology. Milling tests were performed on workpiece with and without TMDs. A three-fold improvement in minimum stable depth of cut is realized after incorporating the TMDs at their optimal locations on thin-walled workpiece.

Chatter is the most obscuring phenomenon and significant amount of research has been documented regarding prediction, control and elimination of chatter. Chatter is still a main hindrance in achieving good surface finish and productivity. This paper presents the influence of helix angle of milling cutter in down-milling, up-milling and slotting operation. Altintas multi-frequency solution (MFS) is advanced by adding the impact of helix angle in milling forces. A comparison is made for stability lobes diagram based on the helix angle model for different helix angles against the Altintas multi-frequency solution model (MFS) and zero order approximation (ZOA) model. The comparison shows that for small helix angle the stability lobes follow the Altintas (MFS) model and for high helix angle the stability lobes follow the Altintas (ZOA) model. The experimental results prove the simulations. Introduction

Enhancing stiffness of thin-walled workpieces is essential to suppress chatter during milling, and applying pre-bending on workpieces is an effective method to achieve this. A semi-analytical dynamic model based on the variational method is developed to uncover how pre-bending curvature and direction modulate dynamic stiffness and milling stability. A fixture-based pre-bending technique is then applied to maintain the workpiece in its bent configuration during milling. Numerical analysis confirms the stiffness enhancement is generally applicable across various geometries, with the first natural frequency increased in all simulated cases and the increase exceeding 110% in high aspect ratio cases. Stability simulations indicate that pre-bending expands the stable spindle-speed range, easing parameter selection under uncertainty. Experimental results show a transition from an unstable to a stable milling state at a spindle speed of 8000 rpm. The results validate the established dynamic model and demonstrate that applying pre-bending technique, with theoretically guided selection of curvature and direction, significantly improves milling stability.

A New Approach to Build a Heat Flux Model of Milling Processes

This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays, and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method, especially for the low radial immersion cases with multiple delays. First, the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases, respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary, and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.

Flexible parts are widely used in the aeronautic and power industries which have high machining accuracy requirement. However, the flexible part is apt to vibrate in cutting processes due to its low structure stiffness and damping. Accurate approximation of cutting stability boundary of flexible part is difficult, because traditional stability analysis simplifies the complex dynamic system and some parameters still have large vibrations and can cause bad surface accuracy even when they are predicted to be located in the stable zone. To better evaluate the stability in flexible part milling, a synthetical stability method is proposed to calculate the boundary which can assure both the cutting stability and the surface location accuracy. To exclude other factors which may have great effect on cutting stability, such as multiple structure modes and structure mode coupling, etc, a flexible support platform is designed to test the validity of the classical local stability analysis. After the comparison between the local stability prediction and the experimental results, it is found that the local stability analysis is defective for the stability prediction of the flexible part milling. Therefore, the dynamical equation is improved and both the periodical excitation and the regenerative excitation are considered. The stability boundary is calculated by using the time-domain numerical method, with the radial immersion and cutting entrance angle’s variation originated from forced vibration being considered. The simulation based on the synthetical stability analysis has a good agreement with the experimental results, which verifies the validity of the presented method.

The influence of cryogenic cooling on milling stability