Stability Lobe Diagram Research Articles

Vibration suppression of balls in different contact states during mirror milling of curved thin-walled parts based on magnetic follow-up support fixture

Milling of curved thin-walled parts is a critical step in the manufacturing of aircraft skins or rocket storage tanks. During the process of milling thin-walled parts using magnetic follow-up support fixture, the complex situation that the fixture balls in different contact states with the surface of the thin-walled parts occurs, leading to changes in the dynamic characteristics of the thin-walled parts, thereby causing machining vibration and even chatter, ultimately affecting machining quality. To this end, this paper focuses on the vibration of thin-walled parts under balls in different contact states. Firstly, the structure and function of the magnetic follow-up support fixture are illustrated. Then, a dynamical model of a mirror milling system that accurately reflects balls in different contact states is established using finite element technology, in order to explore the changing law of dynamic characteristics at milling points of thin-walled parts under balls in different contact states. To further investigate chatter under balls in different contact states of thin-walled parts, after obtaining modal parameters of the thin-walled parts through impact tests, three-dimensional stability lobe diagrams (3D-SLDs) of thin-walled parts under balls in different contact states are plotted using the full-discretization method, and chatter-free parameters are selected. Finally, the rationality of finite element analysis and stability analysis, as well as the practicality of the fixture, are verified through milling experiments. The experimental results show that after the fixture is applied, the dominant frequency of curved thin-walled parts can be increased by up to 6 times, its amplitude can be reduced by over 60 %, and the surface roughness can be reduced by up to 57.98 %.

Research on the influence of cutter overhang length on robotic milling chatter stability

Serial industrial robots are widely in demand in the field of large-scale component processing and manufacturing. However, the structure characteristic of serial robots makes it easy to generate chatter during milling and the overhang length of milling cutter has an important influence on the stability of robotic milling. Milling cutter overhang length refers to the length from the tip of the cutter to the protrusion of the spindle, to study the influence of milling cutter overhang length on the stability behavior of robotic milling, the modal parameters of milling cutter under different overhang length were obtained by hammer experiment, and its dynamic characteristics were analyzed. The stability behavior for robotic milling under different cutter overhang lengths was analyzed by using the stability lobe diagrams, and the stability lobe diagrams were verified by robotic milling experiments. The results show that the rigidity and natural frequency of milling cutter decrease with the increase of overhang length. There is a big gap between the stability lobe diagrams and the actual machining state when the cutter overhang length is short, and the low frequency vibration is easy to occur in the robotic milling process when the spindle speed is low, which is most probably because that the absorbed vibration energy by the cutter has been transferred to the robot body before the milling cutter vibrates. When the cutter overhang is increased and the feed direction is along the y-axis of the robot global coordinate system, the stability lobe diagrams by considering the multi-mode coupling effect is more consistent with the actual milling state.

Co-Kriging model-based multi-fidelity regression for refining milling stability predictions of variable tool overhang length using limited experimental data

Determining chatter-free machining parameters is critical in process planning since chatter vibrations significantly affect machining quality and production efficiency. Stability lobe diagram is essential in selecting chatter-free machining parameters, but its predictions confront challenges in both theoretical accuracy and experimental efficiency. To address this, the Co-Kriging modelling is introduced to predict the tool overhang length-dependent stability limits with limited experiments. First, tool tip dynamics and cutting force coefficients of a source overhang length are roughly identified to obtain sufficient low-fidelity (LF) theoretical stability limits. The entropy-based sampling and affine transformation are used to sequentially obtain high-fidelity (HF) experimental stability limits and update LF stability limits. HF and updated LF datasets are combined to train a multi-fidelity (MF) Co-Kriging model. For a target overhang length, MF stability limits of the source overhang length serve as LF data, and a minimum mean absolute percentage error (MAPE)-based sampling guides the acquisition of HF stability limits. Combining HF data and LF data processed by affine transformation to train a target Co-Kriging model. Case studies reveal that the proposed method exhibits lower MAPE values and significantly outperforms other comparison methods in predicting experimental stability limits, particularly when confronted with limited experimental data.

An effective investigation of chatter prediction system on Al6061 alloy in an end milling process

Visual examination of the surface topography, in conjunction with the other sensors, may confirm the existence of chatter. Online chatter detection during real machining operations is possible with the use of sensors, and the presence of noise in their output and restricted bandwidth are the major drawbacks of these sensors. Productivity drops and manufacturing costs go up when there is a lot of chatter in the machining process. In the present paper, an integrated spindle tool system is modeled using finite element method with Timoshenko beam theory including rotational and shear deformation effects. To maximize the average stable depth of cut in an end milling process while simultaneously minimizing the chatter vibration levels, real time and offline strategies have been investigated. Machining experiments performed on Al6061-alloy specimens provide an empirical confirmation of the stability boundaries. The surface topography methods such as scanning electron microscope (SEM) and optical microscope images along with vibration levels are considered, to identify chatter marks under various machining conditions, which helps to assure cutting process stability. Stability lobe diagrams are plotted with these derived conditions and observed at an incremental level in the axial depths of the cut. The methodology shown in this paper improves the machining stability of the end milling with the reduction in the tool tip vibrations.

Stability of Micro-Milling Tool Considering Tool Breakage

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 FRFs of the micro-milling tool are calculated by direct frequency response functions (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.

A novel approach of stability and topography prediction in five-axis ball-end milling process through workpiece-edge-coupling

By studying the workpiece-edge-coupling (WEC) in five-axis ball-end milling, the contact characteristics between the workpiece and edge curve are analyzed, and the chip model is extracted and simplified. The edge curve involved in the cutting process of each edge are calculated at each time and a new instantaneous numerical chip thickness model is established. Then the milling forces and stability lobe diagram (SLD) are calculated in following cut process with lead and tilt angle. The milling forces and SLD of lead angle at 15° and tilt angle at −15° are verified by comparing with Otzurk model as references, and it is found the SLD of WEC model can reflect the unstable points more properly than that of Otzurk model. Also the vibration in [Formula: see text] and [Formula: see text] directions show a divergence trend, which proves the high precision for the new algorithm adapted to the stability prediction of five-axis ball-end milling process. In addition, the surface topography is acquired considering lead and tilt angle as well as forced vibration, and the result is consistent with the experiment in the existing literature. It is found that the milling forces, SLD and surface topography show the same variation trend with the increase of lead and tilt angle. Besides, the stability region significantly expands and the surface topography improves by applying positive tilt angle other than the negative. Then, under the conditions of positive lead and tilt angle, increasing lead angle and decreasing tilt angle reduces the milling force, expands the stability region of SLD and improve the surface topography. The optimized tool posture is acquired by the coincident analysis of milling force, SLD and surface topography under different lead and tilt angle.

Influence of different position modal parameters on milling chatter stability of orthopedic surgery robots

This research is dedicated to exploring the dynamics of milling chatter stability in orthopedic surgery robots, focusing on the impact of position modal parameters on chatter stability. Initially, we develop a dynamic milling force model for the robotic milling process that integrates both modal coupling and regenerative effects. We then employ the zero-order frequency domain method to derive a chatter stability domain model, visually represented through stability lobe diagrams (SLDs). Through conducting hammer test experiments, we ascertain the robot's modal parameters at varying positions, enabling the precise generation of SLDs. This study also includes experimental validation of the chatter SLD analysis method, laying the groundwork for further examination of chatter stability across different positional modal parameters. Finally, our analysis of the variations in modal parameters on the stability of robot milling chatter yields a theoretical framework for optimizing cutting parameters and developing control strategies within the context of orthopedic surgery robots.

Stability analysis of multi-insert rotating boring bar with stiffness variation

Manufacturing faces challenges in boring processes, critical for hole enlargement and finishing, due to low stiffness leading to static deflection and regenerative chatter. Stiffness variation has emerged as a promising solution for effectively suppressing chatter, while multi-insert rotating boring bars offer a viable approach to addressing static deflection in long and slender boring bars, enabling better tolerance with a large operational length-to-diameter ratio. However, integrating technological innovations to suppress chatter and prevent static deflection complicates the problem from a modeling and stability analysis perspective, making it challenging to find a comprehensive solution in the existing literature. This study explores the stability of multi-insert rotating boring bars with stiffness variation, providing insights into selecting optimal stiffness variation parameters. It introduces a novel extension of the multi-dimensional cutting force model to rotating boring tools with multiple inserts, employing the zero-order harmonic solution to analyze the stability of boring processes with time-varying dynamics. Experimental validation demonstrates the effectiveness of the proposed methodology, achieving 5 out of 6 matches in stability lobe diagrams for multi-insert rotating boring bars without stiffness variation. The model’s comprehensiveness is further demonstrated by comparing the results with those of existing studies in the literature for single-insert stationary boring bars. In the case without stiffness variation, the model successfully reproduces 4 out of 5 operating points, and with stiffness variation, it accurately predicts all 5 operating points. Sensitivity analyses guide the selection of optimal stiffness variation parameters for effective chatter suppression, favoring moderate frequencies and up to a 30% amplitude ratio.

Dynamic performance enhancement of machining center with epoxy granite base: Experiments and finite element simulations

Epoxy granite (EG) is used for machine building applications owing to excellent dynamic properties compared to cast iron (CI). Steel is preferred to reinforce with EG to improve the static stiffness of structures. The effects of addition of steel content on stiffness and damping properties of EG composite were assessed through a specimen level study. Subsequently, the base, which is a primary structure that affects the dynamics of the vertical machining center (VMC) was taken up for investigation. The novelty of the present work is the development of scaled down model of EG base with optimum reinforcement ratio to improve the dynamic response of VMC without compromising the static rigidity of the existing CI base. An experimental study was carried out to validate the assumption made in numerical analysis that EG is isotropic and homogeneous. The results of similitude relations revealed that the EG base exhibited sixteen times higher damping compared to CI base. The influence of EG base on the overall dynamics of VMC was assessed by performing pre-stressed finite element modal analysis and harmonic analysis. Upto seven-fold improvements in directional stiffnesses of VMC with the EG base were observed compared to VMC with CI base. The results of stability lobe diagram revealed a three-fold improvement in material removal rate for VMC with EG base compared to VMC with CI base. Thus, the proposed steel reinforced configuration of EG base has demonstrated a better dynamic performance of VMC without compromising static rigidity.

Stability Analysis of Milling Based on the Barycentric Rational Interpolation Differential Quadrature Method

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.

Chatter Identification in Milling of Titanium Alloy Using Machine Learning Approaches with Non-Linear Features of Cutting Force and Vibration Signatures

The generation of chatter during machining operations is extremely detrimental to the cutting tool life and the surface quality of the workpiece. The present study aims to identify chatter conditions during the end milling of Ti6Al4V alloy. Experimental modal analysis is carried out, and stability lobe diagrams (SLDs) are developed to identify machining parameters under stable and chatter conditions. Experiments are conducted to acquire cutting force and vibration signatures corresponding to machining conditions selected from the SLD. Non-linear chatter features, such as Approximate Entropy, Holder Exponent, and Lyapunov Exponent extracted from the sensor signatures, are used to build Machine Learning (ML) models to identify chatter using Decision Trees (DTs), Support Vector Machines (SVMs) and DT-based Ensembles. A feature-level fusion approach is adopted to improve the classification performance of the ML models. The DT-based Adaboost model trained using dominant non-linear features classifies chatter with an accuracy of 96.8%. The non-linear features extracted from the sensor signatures offer a direct indication of the chatter and are found to be effective in identifying the machining chatter with good accuracy.

Dynamic Modeling for Chatter Analysis in Micro-Milling by Integrating Effects of Centrifugal Force, Gyroscopic Moment, and Tool Runout.

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.

Chatter prediction for parallel mirror milling of thin-walled parts by dual-robot collaborative machining system

Thin-walled parts with double-sided features are widely used in the aerospace industry, but the machining of such parts still faces great challenges due to their weak rigid structure and the positioning errors caused by turning/re-clamping of the workpiece. For this purpose, a novel machining approach for parallel mirror robotic milling of thin-walled parts is proposed. Different from conventional single-sided milling, it can simultaneously machine both sides of the workpiece while avoiding the above problems and improving machining efficiency. However, the introduction of multiple cutting excitations makes the vibration behavior of the workpiece more complicated, thus making it difficult for the dynamic modeling of the dual-robot machining system. This paper aims to uncover the dynamic mechanism of chatter phenomenon in parallel mirror robotic milling process in consideration of the interaction of tool-workpiece-tool system. A dual-robot collaborative machining system is first developed for the milling of thin-walled workpiece, and the method of synchronous motion planning for dual robots is described. The slave robot synchronously follows the master robot and the two milling cutters mounted on tool flange of the robot are kept in mirror position. Over a tooth passing period, the engagement state of the cutters and the workpiece is analyzed considering the effect of rotation phase lag (RPL) between the twin cutters. After that, the vibration state and the corresponding instantaneous displacement of the workpiece can be expressed explicitly, then the dynamic resultant cutting force acting on the workpiece is calculated according to the mechanistic force model. Comprehensively considering the dynamic interaction of the tool-workpiece-tool system, multi-mode and position-dependent modal characteristics of thin-walled part, a time-varying delay differential equation is constructed and solved to explore the dynamical behavior of parallel mirror milling process. The predicted stability lobe diagram is validated by a series of parallel mirror milling tests on thin-walled PMMA plates. Comparisons of numerical and experimental results show that the dynamic model successfully predicts the chatter stability for the parallel mirror milling of thin-walled parts.

Study of optimization of blade non-uniform allowance process and chatter stability domain

In addressing the phenomenon of chatter during the machining of thin-walled components, a machining strategy involving the implementation of a continuous non-uniform toolpath has been proposed as a remedy for chatter suppression. The methodology commences with a meticulous determination of machining allowances, accomplished by utilizing fitting functions. Subsequently, the stiffness coefficients and natural frequencies inherent to the workpiece-tool system are extracted through modal analysis. A stability lobes diagram is formulated, employing the principles of regenerative chatter analysis. This diagram encompasses both uniform toolpath scenarios and non-uniform continuous toolpath scenarios, with the latter established via the least squares method. The resultant stability lobes diagram effectively delineates the boundaries within which chatter remains stable, under varying depths of cut. The stability lobes diagrams substantiate the effectiveness of the non-uniform continuous toolpath constructed via the least squares method in significantly augmenting the inherent stiffness coefficient of the workpiece-tool system, thereby mitigating chatter. This approach serves as a valuable guide for the manufacturing of intricate curved thin-walled components.

Determination of Chatter-Free Cutting Mode in End Milling

Chatter accompanies the cutting process and is the main obstacle to achieving precision and productivity in milling operations. To reduce the amplitude of vibrations, it was proposed to use a stability lobes diagram (SLD) when assigning cutting modes. The machining system in end milling was represented by a two-mass dynamic model in which each mass has two degrees of freedom. The behavior of such a system was described by a structure with two inputs, in-depth and cutting feed, and a delay in positive feedback on these inputs. A new criterion was applied to design the SLD based on an analysis of the location of the machining system Nyquist diagram on the complex plane. The algorithm for designing a stability chart was developed into an application program, a tool for the technologist-programmer when assigning cutting modes. A method for parameter identification necessary for designing the dynamic system “tool – workpiece” was proposed. The effectiveness of the developed method was proven experimentally when the choice of spindle speed during end milling allows one to reduce the roughness parameter Ra from 3.2 µm to 0.64 µm at the same feed rate of 650 mm/min.

Stability Analysis in Milling Based on the Localized Differential Quadrature Method.

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.

Milling Stability Prediction under Multi-effect Synergy

During the milling process, chatter vibration is prone to occur when the spindle, tool, and workpiece interact with each other under certain parameters, which seriously affects machining efficiency and reduces machining quality. Therefore, it is necessary to study the mechanism and influencing factors of chatter vibration, predict the stability of the milling system through a multi-effect synergistic dynamic model, and obtain the machining parameters of stable milling through analysis. Based on the traditional milling model, this article considered the regeneration effect, process damping effect, and modal coupling effect, and also considered the friction effect of the front cutting surface for friction-induced chatter, to make the model’s prediction range more accurate. Then, a milling dynamic model was established combining multiple effects, and its stability lobe diagrams were solved by the full-discretization method. The accuracy of the model was verified through milling stability experiments. The experimental results are basically consistent with the predicted stability lobe diagrams, indicating that the milling stability prediction model considering multi-factor coupling of the milling model is correct. Finally, the influence of various effects on milling stability was analyzed, with a focus on the influence of friction effects.

Chatter failure comparison for high-speed milling of aerospace GH4099 with silicon nitride ceramic end mills: A laboratory scale investigation

Chatter generated in the high-speed cutting process can seriously limit the machining efficiency and affect the surface machining quality, which urgently needs to be controlled. Aiming at brittle ceramic end mills that are very sensitive to vibration, a strategy based on the modal experimental method is proposed to construct effective and accurate stability lobe diagram (SLD) for chatter prediction and failure analysis in this work. Firstly, the tool tip frequency response function (FRF) of four kinds of self-developed ceramic end mills and commercial cemented carbide end mills with the same structure are established by means of hammering modal experiments, and the modal parameters are solved and identified. Then, based on our established high-speed milling chatter prediction model, the milling force coefficients are obtained by linear regression analysis and calculation, thereby the milling SLDs of five end milling tools are developed. Finally, a series of high-speed side milling experiments are carried out using consistent cutting conditions. The results show that the constructed SLDs can effectively predict the chatter failure region and milling stability for five kinds of end mills, and four ceramic milling tools exhibit more excellent chatter suppression performance according to frequency domain analysis of vibration signals and the observation of workpiece surface vibration marks, in which the S4 ceramic milling tool presents the most significant high-speed milling stability.

Ensuring the stability of machining when using end mills

This paper reports a new approach to ensuring the stability of the end milling process, due to vibration-free cutting modes, which are determined from the stability lobes diagram of the dynamic machining system. An application program for automatic calculation of the stability lobes diagram in the coordinates «mill spindle speed – feed» has been developed, which is a tool for the technologist-programmer when designing control program for numerically controlled machines. The mathematical model underlying the application program represents a dynamic machining system as a single-mass system with two degrees of freedom, covered by negative feedback in the direction of two coordinates. The trailing machining is represented as positive feedback loops with a delay function in each. The mathematical model is given in the form of state variables, which allows applying numerical modeling methods to determine both transient and frequency responses. The software developed includes a separate module for automatic design of the stability lobes diagram whose algorithm uses the features of the location of the Nyquist diagram on the complex plane. Since the functioning of the developed program requires a priori information about the dynamic parameters of the machining system, a procedure for their experimental identification is presented. The stiffness of the machining system in two coordinates was determined with the help of a dynamometer, and the frequency responses were determined by the impulse response function, which was obtained with an impact hammer. The research results were confirmed experimentally both by computer simulation and milling on a machine tool and could be recommended for determining the cutting mode at end milling

Prediction of time-varying dynamics and chatter stability analysis for surface milling of thin-walled curved CFRP workpiece

Machining curved surfaces for thin-walled components is always challenging. Due to the strong anisotropic features of carbon fiber reinforced plastic (CFRP), new challenges, such as prediction accuracy loss, have emerged for avoiding the chatter of machining thin-walled curved CFRP workpieces. This paper studied the influence of the anisotropic properties of CFRP workpieces and time-varying dynamics on surface milling stability. An improved damping and time-varying dynamics prediction model was proposed integrated with FEA and numerical calculation considering the change of cutting position, the materials removed, and the anisotropic features of CFRP. Then, the 3D stability lobe diagram (SLD) was achieved by considering the dynamic change at each cutter point on the machining path and dynamic cutting forces based on the instantaneous fiber cutting angle. Based on the obtained 3D SLD, CFRP milling chatter could be accurately avoided, and machining efficiency could be improved. A case study of milling a thin-walled toroidal surface was conducted for validation. In the machining process of CFRP, unlike homogeneous materials such as metals, the natural frequency of CFRP fluctuates nonlinearly with the change curve of material removal within a specific range. Under a higher material removal rate, the surface roughness of the machined surface has been reduced by 74%, Ra below 2.35 µm, based on the selected process parameters of the novel-established SLD, compared to the surface roughness, Ra close to 9.21 µm, obtained by the previous method without considering the time-varying dynamics.