Search Results (26)

Cast iron components are indispensable in aerospace and automotive systems, yet their milling operations are severely affected by regenerative chatter, which degrades machining quality and damages equipment. Although various chatter prediction methods have been reported, the optimal interpolation strategy of full-discretization methods (FDMs) for multi-factor coupled dynamic systems remains unclear. This study proposes an enhanced FDM to fill this research gap. A dynamic milling model accounting for regenerative effects, modal coupling and process damping is established, and an improved FDM based on Lagrange interpolation is further developed. A systematic single-factor analysis is carried out to examine the performance of 1st–4th-order interpolation for state, delay and periodic terms. Counter-intuitively, convergence analysis and stability lobe diagram (SLD) verification reveal that higher-order interpolation does not guarantee better performance. The optimal orders are identified as 2nd/3rd for state terms, 3rd for delay terms and 1st for periodic terms. Accordingly, the proposed 321-FDM (3rd-order state, 2nd-order delay, 1st-order periodic) exhibits higher accuracy and computational efficiency compared with benchmark methods, namely the semi-discretization method and Hermite-based 3rd-order FDM. Milling experiments on cast iron workpieces validate the established model and the 321-FDM, and the experimental stability thresholds agree well with numerical predictions. This work presents a validated, high-performance stability prediction tool for chatter avoidance in cast iron machining. Full article

The application of robotic milling manipulators demonstrates a promising method for the efficient manufacturing of large-scale structures. However, the cutting accuracy and efficiency of milling robots are predominantly subjected to their low stiffness, which may easily cause chatter during machining. Accurate prediction of chatter stability for robots is of practical importance and is challenging. This paper develops a dynamic model of flexible link elements by considering link flexibility and joint torsional deformation and then constructs a multi-link flexible coupled dynamic model using the receptance coupling substructure analysis (RCSA) method. Subsequently, the equivalent dynamic parameters are identified via the particle swarm optimization (PSO) algorithm. On this basis, the end-effector frequency response functions (FRFs) of the robot under different poses are predicted, and the stability lobe diagram (SLD) for milling is generated based on chatter theory. Finally, the predicted FRFs and stability regions are validated through modal tests and milling experiments. Experimental results demonstrate that the proposed model can predict the end-effector dynamic characteristics and chatter occurrence conditions under different poses, confirming its effectiveness in the analysis of milling chatter stability. Quantitative validation yields a maximum error of 3% for predicted first-order modal frequencies and relative modal amplitude errors below 10%, with experimentally confirmed critical depths of cut of 0.1–0.2 mm at 3000 rev/min and 0.5–0.6 mm at 5000 rev/min. Full article

This study proposes a methodology for selecting robust stable cutting conditions from a Receptance Coupling Substructure Analysis (RCSA)-based Stability Lobe Diagram (SLD) by considering tool clamping errors that may occur during operator tool setup. However, most existing RCSA studies have been conducted under the assumption of a constant tool clamping length and thus do not sufficiently reflect the clamping length variation observed in practical machining environments. Since the tool tip dynamic characteristics can be sensitive even to small variations in clamping length, operator-induced tool clamping errors in actual processes can introduce such variations and consequently degrade the prediction accuracy of the SLD. Moreover, uncertainty studies in milling stability have largely focused on variations in model parameters, such as cutting coefficients, damping, and modal parameters, whereas experimental quantification of operator-induced clamping length variability and its direct integration into RCSA-based tool tip Frequency Response Function (FRF) and SLD prediction has been relatively limited. Therefore, this study quantifies the distribution of tool clamping errors through clamping experiments and incorporates it into RCSA to derive an SLD band that accounts for tool clamping errors. The width of the SLD band is defined as a physical variation induced by clamping uncertainty, and the corresponding uncertainty range is set as an avoidance region. Robust cutting conditions are then selected from the remaining stable region while considering the physical variation width. The physical variation width was quantified as 60 rpm (minor axis) and 1.62 mm (major axis), representing the dispersion of the stability limit in the spindle speed and axial depth directions caused by clamping errors. As a result, stable cutting conditions that do not cross the stability limit can be determined even in the presence of process variations and disturbances. Full article

This paper proposes an enhanced numerical integration technique for predicting milling stability. The underlying milling dynamics model incorporates regenerative chatter effects, formulated as a system of linear time-delay differential equations. The computational methodology begins by dividing the tool engagement period into the free vibration and forced vibration intervals, followed by uniform discretization of the forced vibration interval. A numerical integration method is primarily carried out using Simpson’s and Hermite’s rules. Thus, a discrete dynamic mapping that correlates the system’s current state with its previous state is constructed. Based on this, the milling stability is ultimately determined by applying Floquet theory. Furthermore, the mean squared error metric is introduced to quantify the prediction accuracy of stability lobe diagrams. Through comprehensive comparative analyses, the predicted efficiency and accuracy of the proposed method are systematically benchmarked against the conventional approaches. The simulated and experimental results demonstrate that the proposed method achieves high computational efficiency alongside good accuracy, and its engineering practicality is rigorously validated through milling experiments. Full article

Titanium alloy thin-walled components are extensively used in aerospace engineering, yet their milling stability remains a persistent challenge due to vibration-induced surface anomalies. This study develops an advanced dynamic model for the face milling of titanium alloy thin-walled structures, systematically integrating axial cutting dynamics with regenerative chatter mechanisms and nonlinear process damping phenomena. The proposed framework crucially accounts for time-varying tool–workpiece interactions and damping characteristics, enabling precise characterization of stability transitions under dynamically varying axial immersion conditions. A novel extension of the semi-discretization method is implemented to resolve multi-parameter stability solutions, establishing a computational paradigm for generating three-dimensional stability lobe diagrams (3D SLDs) that concurrently evaluate spindle speed, cutting position, and the axial depth of a cut. Comprehensive experimental validation through time-domain chatter tests demonstrates remarkable consistency between theoretical predictions and empirical chatter thresholds. The results reveal that process damping significantly suppresses chatter at low spindle speeds, while regenerative effects dominate instability at higher speeds. This work provides a systematic framework for optimizing machining parameters in thin-walled component manufacturing, offering improved accuracy in stability prediction compared to traditional two-dimensional SLD methods. The proposed methodology bridges the gap between theoretical dynamics and industrial applications, facilitating efficient high-precision machining of titanium alloys. Full article

Self-excited vibrations represent one of the most unfavorable phenomena in the cutting process because they can lead to the accelerated wear or breakage of the tool, a sudden deterioration in the quality of the machined surface, and an increase in noise and energy consumption. To avoid these negative effects, stability diagrams are used when defining the cutting regimes, which, depending on the main spindle speed and the cutting depth, show the border between the stable and unstable machine tool operation states from the aspect of self-excited vibrations. These diagrams, known as “stability lobe diagrams”, can be defined using mathematical models (analytical or numerical) or through experimental methods. However, when machining at relatively low main spindle revolutions, process damping occurs, which increases the system stability, i.e., enables a greater cutting depth limit. For the stability diagram to be effectively used for predicting the cutting depth limits at low machining speeds, it is necessary to take the effect of process damping into account. This paper introduces an experimental method for the determination of process damping and its integration into the mathematical framework of the Fourier series method, commonly utilized for the construction of stability lobe diagrams. Full article

Industrial robots are widely used in the field of processing because of their many advantages, such as their high flexibility and wide processing range, but the chatter phenomenon limits their application. In this study, a chatter model for the robot milling of natural marble is established that analyzes the effect of the milling parameters and position. The chatter stability model is first established based on the zeroth-order approximation method, in which the robot milling system is simplified into a vibration system with two degrees of freedom. The milling force coefficients are determined by robot milling experiments, and the modal parameters of the robot milling system are identified based on the single-point excitation and pickup methods, which are essential for the establishment of the chatter stability model. Second, robot milling experiments are conducted to verify the established model, proving its high prediction accuracy. Finally, the effect of the milling parameters and position on the chatter stability of the robot milling system is discussed. These conclusions can be references for the robot milling of natural marble. Full article

Micro-milling, widely employed across various fields, faces significant challenges due to the small diameter and limited stiffness of its tools, making the process highly susceptible to cutting chatter and premature tool breakage. Ensuring stable and safe cutting processes necessitates the prediction of chatter by considering the tool breakage. Crucially, the modal parameters of the spindle–holder–tool system are important prerequisites for such stability prediction. In this paper, the frequency response functions (FRFs) of the micro-milling tool are calculated by direct FRFs of the micro-milling cutter and cross FRFs between a point on the shank and one on the tool tip. Additionally, by utilizing a cutting force model specific to micro-milling, the bending stress experienced by the tool is computed, and the tool breakage curve is subsequently determined based on the material’s permissible maximum allowable stress. The FRFs of the micro-milling tool, alongside the tool breakage curve, are then integrated to generate the final stability lobe diagrams (SLDs). The effectiveness and reliability of the proposed methodology are confirmed through a comprehensive series of numerical and experimental validations. Full article

Chatter causes great damage to the machining process, and the selection of appropriate process parameters through chatter stability analysis is of great significance for achieving chatter-free machining. This article proposes a milling stability analysis method based on the barycentric rational interpolation differential quadrature method (DQM). The dynamics of the milling process considering the regeneration effect is first modelled as a time-delay differential equation (DDE). When adjacent pitch angles of the milling cutter are symmetric, the milling dynamic equation contains a single time delay. Otherwise, when adjacent pitch angles are asymmetric, the dynamic equation contains multiple time delays. The barycentric rational interpolation DQM is then used to approximate the differential and delay terms of the milling dynamics equation, and to construct a state transition matrix between adjacent milling periods. Finally, the chatter stability lobe diagram (SLD) is obtained based on the Floquet theory. According to the SLD, the appropriate spindle speed can be selected to obtain the maximum stable axial depth of cutting, thereby effectively improving the material removal rate. The accuracy and efficiency of the proposed method have been validated by two widely used milling models, and the results show that the proposed method has good accuracy and computational efficiency. Full article

During machining, the surface of the machined materials is damaged and tool wear occurs, sometimes even to complete failure. Machining of thin-walled parts is generally cumbersome due to their low structural rigidity. The study deals with the effect of the feed rate and the thickness of the thin-walled part on the dynamic behavior and stability of the turning process during the roughing and finishing of thin-walled tubular workpieces made of steel alloy 42CrMo4. At the same time, the cutting forces and deformations of the workpiece were also evaluated via numerical and experimental approaches. The numerical study is based on a three-dimensional (3D) finite element model (FEM) developed using the ABAQUS/Explicit frame. In the model, the workpiece material is governed by the behavior law of Johnson–Cook. Numerical and experimental results show that the cutting forces and the quality of the machined surface depend not only on the choice of cutting parameters but also on the dynamic behavior of thin-walled parts due to their low rigidity and low structural damping during the machining operation. Cutting forces are proportional to the feed rate and inversely proportional to the thickness of the part. Their variations around the average values are low for roughing tests where the wall-part thickness is higher or equal to 3.5 mm. However, these variations intensify for finishing tests where the wall thickness is less or equal to 1.5 mm. Indeed, the recorded FFT spectra for a finishing operation show several harmonics that occurred at around 550 Hz, and the amplitude of the peaks, which describes the level of power contained in the signals, shows an increase similar to that of the amplitudes of the temporal signal. The flexibility of the part generates instability in the cutting process, but the frequencies of the vibrations are higher than the frequency of rotation of the part. Full article

During micro-milling, regenerative chatter will decrease the machining accuracy, destabilize the micro-milling process, shorten the life of the micro-mill, and increase machining failures. Establishing a mathematical model of chatter vibration is essential to suppressing the adverse impact of chatter. The mathematical model must include the dynamic motions of the cutting system with the spindle–holder–tool assembly and tool runout. In this study, an integrated model was developed by considering the centrifugal force induced by rotational speeds, the gyroscopic effect introduced by high speeds, and the tool runout caused by uncertain factors. The tool-tip frequency-response functions (FRFs) obtained by theoretical calculations and the results predicted by simulation experiments were compared to verify the developed model. And stability lobe diagrams (SLDs) and time-domain responses are depicted and analyzed. Furthermore, experiments on tool-tip FRFs and micro-milling were conducted. The results validate the effectiveness of the integrated model, which can calculate the tool-tip FRFs, SLDs, and time responses to analyze chatter stability by considering the centrifugal force, gyroscopic effect, and tool runout. Full article

Chatter stability analysis is an effective way to optimize the cutting parameters and achieve chatter-free machining. This paper proposes a milling chatter stability analysis method based on the localized differential quadrature method (LDQM), which has the advantages of simple principle, easy application, and high computational efficiency. The milling process, considering the regeneration effect, is modeled using linear periodic delay differential equations (DDE), then the state transition matrix during the adjacent cutting period is constructed based on the LDQM, and finally, the stability of the milling process is obtained based on the Floquet theory. The accuracy and computation efficiency of the proposed method are verified through two benchmark milling models. The simulation results demonstrate that the proposed method in this paper can accurately and quickly obtain the chatter stability lobe diagram (SLD) of the milling process, which will provide guidance for optimizing the process parameters. Full article

Nickel-based superalloy Inconel 718 is widely used in the aerospace industry for its excellent high-temperature strength and thermal stability. However, milling Inconel 718 presents challenges because of the significantly increased cutting force and vibration, since Inconel 718 is a typical difficult-to-machine material. This paper takes the milling process of Inconel 718 as the research object, initially, and a milling force model of Inconel 718 is established. Subsequently, the finite element analysis method is used to analyze the stress field, temperature field, and milling force in the milling process of Inconel 718. Building upon this, a dynamic equation of the milling of Inconel 718 is established, and based on the modal experiment, stability lobe diagrams are drawn. Furthermore, milling experiments on Inconel 718 are designed, and the results calculated using the milling force model and finite element analysis are verified through comparison to the experimental results; then, the fmincon optimization algorithm is used to optimize the processing parameters of Inconel 718. Eventually, the results of the multi-objective optimization illustrate that the best processing parameters are a spindle speed of 3199.2 rpm and a feed speed of 80 mm/min with an axial depth of cut of 0.25 mm. Based on this, the best machining parameters are determined, which point towards an improvement of the machining efficiency and quality of Inconel 718. Full article

As milling chatter can lead to poor machining quality and limit the efficiency of productivity, it is of great significance to learn about milling chatter stability and research the effective and fast prediction of milling stability. In this study, a hybrid full-discretization method of multiple interpolation polynomials and precise integration (HFDM) is proposed for milling stability prediction. Firstly, the third-order Newton interpolation polynomial, third-order Hermite interpolation polynomial and linear interpolation are applied to approximate the state term, delay term and periodic coefficient matrix, respectively. Meanwhile, the matrix exponentials can be calculated based on the precise integration algorithm, which can improve computational accuracy and efficiency. The numerical simulation results indicate that the proposed method can not only effectively generate a stability lobe diagram (SLD) but also obtain better prediction accuracy and computation efficiency. A milling experiment is offered to demonstrate the feasibility of the method. Full article

During the bull-nose end milling operations of thin-walled structures, chatter usually occurs and adversely affects cutter performance, finished surface quality, and production efficiency. To accurately predict chatter stability, a suitable dynamic model with effective system parameters is required. In this article, a three-degree-of-freedom (3-DOF) dynamic model is developed to analyze the milling stability of the thin-walled cylinders, in which the dynamics of the bull-nose end mill along the x-axis and y-axis directions and the dynamic of the workpiece along the z-axis direction are taken into account. Then, the cutter-workpiece engagement (CWE) is extracted by employing a slice-intersection-based approach. And the layered cutting force coefficients are identified by considering the influences of varying cutter diameters on the cutting speed. Thereafter, the semi-discretization method (SDM) is adopted to compute the stability lobe diagram (SLD). In the end, a group of milling tests are carried out on a thin-walled cylinder to validate the accuracy and reliability of the proposed model, and the results show that the model predictions agree well with the experimental data. Full article