Stability Lobe Diagram Research Articles

An updated tuning methodology of vibration absorber for machining chatter suppression

The Equal Real Troughs optimization criterion of vibration absorber improves unconditionally stable cutting depth of single-dimensional chatter vibration. However, the stability pockets within the lobes are decreased after tuning, which therefore causes the machining efficiency reduction at certain spindle speed. Noting that the spindle speed is preferred as a constant in the workshop once the assembly of machine tool/cutter/workpiece are determined, an updated optimization methodology is proposed to maximize the critical cutting depth within specified spindle speed range by utilizing the lobing effect. The optimization routine is formulated based on the boundary identification of stability lobe diagram (SLD), which is derived by the Zero-Order Analytical (ZOA) solution. The tuning methodology is validated on the design of vibration absorber in order to raise the machining stability of slender milling/turning cutter with large length-diameter ratio. The updated methodology enables the stability lobes relocation of single/two-dimensional chatter vibration for achieving higher critical cutting depth at specified spindle speed, and assures the stability width assignable considering the robustness of cutting parameter selection.

Assignment of the cutting mode when boring holes on CNC machine

Due to structural limitations, the processes of boring holes are performed in a low-rigidity machining system, which predetermines their susceptibility to vibrations. The article is devoted to the study of the process of boring holes on CNC machines, and the subject of the study is the effect of the cutting mode on the stability of the machining. The mathematical model of the machining system is presented in the form of a two-mass dynamic system, which forms a closed loop structure with negative feedback by elastic displacement. In addition, positive feedback is taken into account through the delay argument function, which represents machining along traces. It has been proven that this process provokes the emergence of regenerative oscillations in the machining system. The application of the system’s approach made it possible to obtain a mathematical model in the form of state variables, which is acceptable for the use of numerical modeling methods in both time and frequency space. An applied engineering program for determining the stability diagram in "cutting depth - spindle speed" coordinates has been created. The program uses a new criterion of stability of systems closed through positive feedback loop with a delay argument function. For the first time, the validity of such a criterion was proved for systems described by differential equations of the fourth order. The importance of taking into account the results of the study in the form of a stability lobes diagram when assigning a cutting mode, especially in the area of high speeds, is proven. Thus, according to the results of the experiments, a change in speed of only 7% from 2150 rpm to 2320 rpm with the same cutting depth of 0.4 mm allows the process to become stable. The use of the created program is possible in the system of automatic control of the online cutting mode when the machine is equipped with vibration sensors with appropriate systems for identifying the dynamic parameters of the machining system, which will significantly increase the machining efficiency.

Chatter reliability of high speed cylindrical grinding with uncertain parameters

Cylindrical grinding is commonly used as the final process of machining, but its quality and efficiency are often limited by chatter phenomenon. Many research show that the result from conventional chatter analysis by using the deterministic parameters is not consistent with the practical working condition and the chatter reliability prediction in high speed cylindrical grinding with uncertain parameters is studied in this paper. The dynamic model of the cylindrical grinding system is established, and uncertain parameters such as mass, stiffness and damping coefficient are introduced, and the stability lobe diagrams with uncertain parameters were obtained. The reliability model of the grinding system was established, and the reliability was solved by using the Monte Carlo simulation method, the improved first-order second-moment method and the second-order second-moment method, respectively. Then, the chatter-free reliability of the system was predicted by using the reliability lobe diagram. The accuracy of the grinding reliability prediction results is verified by the experiment results. Furthermore, the Monte Carlo sensitivity analysis method is used to study the influence of random parameters on the grinding system, and the results show that the variation of modal mass has the greatest influence on the reliability of the grinding system.

Virtual Dynamics Model for 5-axis Machining of Thin-Walled Blades

Abstract The five-axis ball-end milling dynamics of thin-walled blades is presented. The cutting forces are predicted from the ball end mill–blade geometry engagement maps along the tool path. The Frequency Response Function (FRF) of the thin-walled blade is predicted using Finite Element shell elements, and it is updated along the toolpath as the metal is removed. The predicted cutting forces are applied on both the workpiece and tool FRFs to predict the forced vibrations and chatter stability at each tool location. A simplified method to update the cutter–workpiece engagement (CWE) is used to obtain the three-dimensional stability lobe diagram at each desired point on the blade. The integrated model is used to simulate the 5-axis machining of thin-walled blades in the digital environment. The proposed digital model is experimentally validated by machining a series of thin-walled rectangular plates and a twisted fan blade.

Milling Mechanism and Chattering Stability of Nickel-Based Superalloy Inconel 718.

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.

Development of automated impact system for modal analysis of micro-end mill

The micro cutting tool used in micromilling process is highly susceptible to instability attributed to its low strength. A catastrophic failure of micro-end mill can occur if the chatter is not controlled during micromilling process, especially for micromilling of difficult-to-machine materials, like Ti and Ni alloys. Consequently, the control of chatter in micromilling process is necessary to manufacture the components with required dimensional and geometrical accuracy. Chatter can be avoided by selecting the stable process parameters from stability lobe diagram or by changing the process parameters during machining process by chatter onset identification. The both ways of chatter avoidance require the reliable identification of the modal parameters of the micro-end mill. Experimental modal analysis is most accurate method for identification of modal parameters owing to its ability of consideration of machine tool compliance. Hence, in the present work, automated impact system has been developed to impact the micro-end mill under both stationary and rotating conditions. The developed impact system has been found to be impacting the micro-end with maximum deviation of 2.6% in force amplitude due to repeated impacts. A maximum variation of 1.7% has been found in the natural frequency due to different impacts of the micro-end mill under both stationary and rotating conditions. The accurate estimation of frequency response function is expected to predict the stability of micromilling process with high reliability.

A Hybrid Full-Discretization Method of Multiple Interpolation Polynomials and Precise Integration for Milling Stability Prediction

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.

Prediction of Chatter Stability in Bull-Nose End Milling of Thin-Walled Cylindrical Parts Using Layered Cutting Force Coefficients

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.

Dynamics of the truncated conical thin-wall turning process

Dynamics of the rotational truncated conical thin-walled workpieces, which are widely used in predicting stability of turning process, was seldom reported. This article presents a systematical method to study the dynamic behaviors of these kinds of workpieces under the practical clamping conditions of their turning processes. Mathematical derivations, which consider the radius change along the conical direction, are detailed to predict the instantaneous dynamic characteristics of the workpieces by comprehensively considering the influence of rotation factor. The boundary condition of a clamping and free combination, which corresponds to the actual clamping requirement in turning, is well considered in the derivation. The frequencies and modal shapes of the workpiece under different rotating speeds are solved by the generalized differential quadrature algorithm. A series of modal impact tests, conducted with the workpiece under both static and rotating states, are used to confirm the method’s accuracy in predicting the in-process dynamic behavior. It is theoretically found that in contrast to the conventional turning processes, this thin-walled workpiece’s turning process undergoes clear multi-mode effects, which further significantly influence the process stability. After that, the aforementioned derivations are incorporated into the dynamic governing formulation of the turning process for solving the stability lobe diagrams (SLDs). Finally, actual truncated conical thin-wall turning tests confirm the reasonability of the proposed method, and find that the first three modes dominate the stability of the process but not only the first one.

Improved milling stability analysis for chatter-free machining parameters planning using a multi-fidelity surrogate model and transfer learning with limited experimental data

Decision-making on chatter-free machining parameters is essential for process planning since chatter significantly affects production quality and efficiency. Stability lobe diagram (SLD) is commonly used for selecting chatter-free machining parameters, but its analytical prediction often has poor accuracy and experiment-based prediction is time-consuming. This paper proposes a multi-fidelity (MF) surrogate model and transfer learning-based method to improve the milling stability analysis. Firstly, an analytical stability model is constructed to predict low-fidelity (LF) SLDs for key combinations of radial cutting width (a e) and feed rate per tooth (ft ). A few spindle speeds (n s) are selected from each key LF SLD to detect high-fidelity (HF) stability limits (ap lim) through milling experiments. Subsequently, sufficient LF and limited HF combinations of n s, a e, ft , and ap lim are taken to construct additive scaling function-based MF stability models. Predicted MF combinations of n s, a e, ft , and ap lim are combined with limited HF combinations to construct more accurate stability models through transfer learning. Then, a neural network is ultimately trained to predict ap lim values for arbitrary combinations of n s, a e, and ft . A detailed experimental validation indicates that the proposed method can provide more accurate lobe boundaries for machining parameters selection by introducing fewer experimental samples.

Prediction and Analysis of Milling Stability Under Multi-effect Synergy

In the milling process is often accompanied by a lot of vibration, these vibrations will lead to the instability of the processing process resulting in the occurrence of chatter, chatter in the process will seriously affect the processing efficiency, reduce the quality of processing, so the mechanism of chatter and influencing factors to study, and through the analysis of stable milling processing parameters, to achieve efficient precision machining is very important. In this paper, based on the traditional milling model, the regeneration effect, process damping effect and modal coupling effect are taken into account, and the friction effect of the front cutter face is also taken into account for frictional chatter to make the prediction range of the model more accurate. Then, a milling dynamic model was established combining various effects, and the stability lobe diagram was solved by the fully discrete method. The influence of each effect on milling stability was analyzed and the influence of friction effect was emphatically discussed. Finally, the accuracy of the model was verified by the milling stability experiment.

Tool vibration isolation in hard turning process with magnetorheological fluid damper

Tool vibration in metal cutting significantly influences the surface finish and machining stability. Suppressing the tool vibration to enhance the finished product quality is the need of the hour. The current study proposes the augmentation of a Magnetorheological (MR) fluid damper to suppress tool vibration in hard tuning with easy installation without structural modification. The MR fluid damper changes its damping coefficient with the magnetic field to regulate variable cutting conditions. An optimal composition of MR fluid has been prepared in-house to be used in the damper. The in-house MR fluid is compared with commercial MR fluid. The comparison shows that in-house prepared MR fluid performs equally well compared to commercial fluid. The MR damper effectively damps high-amplitude vibration at aggressive cutting conditions. The L9 Taguchi design of the experiment opted to arrive at minimal machining parameters to evaluate the damper's performance in machining two workpiece materials, namely oil-hardened nickel steel (OHNS) and high carbon high chromium (HCHCR D2) die steel. The surface roughness and tool vibration are reduced with the damper. It is noted that in-house MR fluid performed equally well as commercial MR fluid. The tool wear study is also carried out to monitor the influence of external damping over tool life. The stability lobe diagram is obtained analytically with experimental validation to mark the stability limit of the machining condition. The stability boundary increases with the damper enabling aggressive cutting conditions.

Machinability analysis of micro-milling thin-walled Ti-6Al-4V micro parts under dry, lubrication, and chatter mitigation conditions

Micro-milling technology is an efficient method for machining titanium alloy thin-walled micro parts. However, the machinability of thin-walled microstructures can be greatly affected by chatters due to their weak stiffness, especially in difficult-to-machine materials like titanium alloys. In order to obtain high-quality thin-walled micro parts, a chatter mitigation strategy is presented and its mechanism is analyzed in this paper. The titanium alloy workpiece is submerged into a kind of high-viscosity fluid, which can improve machining stability by increasing the damping of the micro-milling process. The stability lobe diagrams (SLD) are established, and the machinability is analyzed and compared under different machining conditions. The cutting force, surface roughness, micro-tool wear, and dimension accuracy of thin-walled micro parts are selected as the evaluation criteria for the machinability assessment. Well-designed micro-milling experiments are carried out under dry, lubrication, and chatter mitigation conditions using the same cutting process parameters. The results show that the use of cutting fluid can effectively improve machinability under stable cutting processes, but the effect of cutting fluid is weakened under chatter machining. The proposed chatter mitigation strategy can suppress regenerative chatter throughout the micro-milling process for thin-walled micro parts and improve their machinability comprehensively.

A time-frequency approach to ensuring stability of machining by turning

This paper reports a new approach to ensuring the stability of the turning process, which is based on the frequency-time characteristics of the technological machining system (TMS). The approach uses a mathematical model of the turning process as a single-mass system with one degree of freedom, taking into account negative feedback on the normal coordinate and positive feedback with a delay in cutting depth. A new criterion for the stability of the cutting process as a system with a delay in positive feedback is proposed, based on the analysis of frequency characteristics in the form of a Nyquist diagram. It is proved that such a system will be stable when the chart of its Nyquist diagram does not cover a point with coordinates [+1, 0] on the complex plane. The validity of the new criterion has been confirmed by comparing the simulation results in the time range with the location of the Nyquist diagram on the complex plane. Based on the new criterion of stability, an algorithm for automatic construction of a Stability Lobes Diagram (SLD) has been developed. The necessary a priori parameters of TMS, the ranges of frequency change, and the calculation step for constructing such a characteristic in the coordinates "cutting depth – spindle rotational speed" have been determined. The adequacy of the obtained results is confirmed by a full-scale experiment to assess the roughness of machined parts under cutting modes that fall into the area of stability and instability on the SLD chart. The full-scale experiment proved the possibility of a significant reduction in roughness according to the Rz parameter, from 43 µm to 18 µm, while increasing productivity by 1.28 times. The use of a stability lobes diagram is especially effective when programming CNC lathes where it is possible to select the spindle speed in a wide range.

An improved time-varying stability analysis of micro milling considering tool wear

Micro-milling is widely used to process micro-parts and structures, which has the advantages of high material removal rate, high precision and high flexibility of applicable materials. The chatter in micro-milling process seriously reduces the machining efficiency and surface quality. The existing researches are focusing on a selection of appropriate process parameters to suppress the occurrence of chatter, while the influence of tool wear has rarely been considered. In this work, an improved time-varying stability analysis of micro milling considering tool wear was studied. A modified force model taking tool wear, bottom edge milling force, tool runout, and size effect into consideration was established. The dynamic forces due to regenerative undeformed chip thickness in both the shearing region and the transition region were investigated. A dynamic equation which combined the modified force model and the dynamic forces was developed and solved for stability analysis. Experiments on micro-milling of Ti-6Al-4 V titanium alloy with coated micro-milling tools, were carried out to verify the improved time-varying stability analysis model. The results showed that the modified force model had relatively high prediction accuracy, and the calculated stability lobe diagram (SLD) of micro-milling considering tool wear was verified. This work offers theoretical and technical guidance toward the improvement of chatter stability and the development of process online monitoring in micro-milling.

Development of a generalized extended harmonic solution for analyzing the combination of chatter suppression techniques in milling

In this paper a comprehensive and structured analysis of the stabilizing properties linked to the combination of different chatter suppression techniques in milling was carried out. Specifically, the spindle speed variation, the stiffness variation and the usage of tools with variable pitch and variable helixangles were considered.For this purpose, a unique, general and efficient frequency domain formulation (extended harmonic solution) was developed. It is suitable for dealing with differential delayed equations characterized by multiple and distributed time dependent delays and time periodic dynamics. It was demonstrated that the developed solution converges to the reference cases, which were studied in literature through semi-discretization and its extensions. Moreover, by selecting a proper number of considered harmonics, the computation time was reduced of one order of magnitude, in the face of a slight reduction of accuracy with respect to time domain approaches.The computed stability lobe diagrams demonstrated that the combination of multi-chatter suppression techniques allows exploiting the best features of each methodology. The simultaneous use of the spindle speed variation and the stiffness variation was studied for the first time. The absolute limit of stability increased up to 204%, much more than by adopting the techniques in a separate manner. If the enlargement of the stability region is considered as the reference target, the best results were granted by the combination of all the three strategies. Indeed, the improvement with respect to the use of only two techniques was at least 10%.

Process Optimization of Non-Holonomic Surface Milling for Al-Si7Mg Component

Milling process enhancement for an aluminium alloy component with a large bore and variable wall thickness for incomplete circular surfaces, research on the optimization of milling process parameters based on machining stability and machining deformation control was carried out. Analysis of the formation mechanism of the regeneration effect caused by casting defects in cast aluminium parts, the stability lobe diagrams are plotted by the zero-order frequency domain analysis method, and the effects of radial depth of cut, cis-reverse milling and the dynamics parameters of the milling system on the boundary range of the stability lobe diagram were investigated. By orthogonal simulation analysis of milling deformation, determine the primary and secondary relationship between the influence of each process parameter on the machining deformation and the optimal combination of each process parameter in the test range. The results show that in the milling process, reducing the radial depth of cut, using a more rigid milling cutter and reverse milling can all be effective in improving the stability of the process; The significant influence of process parameters on the amount of machining distortion is: radial depth of cut > feed rate > cutter’s speed, the optimal combination of process parameters is: cutter’s speed 600 r/min, radial depth of cut 0.2 mm, feed rate 150 mm/min.The process parameters are used for machining verification, the surface roughness of the annular hole was improved from 6.3 to 3.2 before the optimization, and the coaxiality was improved from 0.12mm to 0.05mm before the optimization. The results show that Optimised milling process parameters improve part quality.

Regenerative Effects of Orthogonal Chip Dimensions on Turning Stability of Thin-Wall Workpiece-Tool Coupled Dynamics

Machining stability of thin-wall (flexible) components plays an important role in manufacturing efficiency and final product qualities, where machining dynamics are characterized by infinite degrees of freedom distributed in both the time and spatial domains. This article presents a distributed parameter method to model the coupled workpiece-cutting tool (WP-CT) dynamics and investigate the regenerative effects of both depth and width of cut on turning stability. By accounting for the regenerative effects in both radial and axial directions of a flexible disk component, this method relaxes a commonly made assumption that the regenerative chip of the coupled WP/CT dynamics varies in the direction of chip thickness. Formulated using the energy method, the dynamic model that requires only a few dominant modes is developed to construct 3-D stability lobe diagrams in terms of width/depth of cut, rotational speed, and cutting position. The proposed modeling method, which offers a means to identify parameters of a coupled WP-CT system and predict the spatially distributed vibrations and their effects on machining stability, has been analyzed in simulation and validated with experiments.

Generalized mechanics and dynamics of modulated turning

This paper presents a generalized cutting force and regenerative chatter stability prediction for the modulated turning (MT) process. Uncut chip thickness is modeled by considering current tool kinematics and undulated (previously generated) surface topography for any given modulation condition in the feed direction. It is found that chip formation is governed by the undulated surface generated in multiple past spindle rotations. Uncut chip thickness is computed analytically in the form of trigonometric functions, and cutting forces are predicted by making use of orthogonal cutting mechanics. Regenerative chatter stability of the process is also modelled. Analytical semi-discretization-based solution is developed to accurately predict the stability lobe diagrams (SLDs) of the MT process. Predicted stability lobes are validated through numerical time-domain simulations and experimentally via orthogonal (plunge) turning tests. It is found that as compared to conventional single-point continuous turning, regenerative stability of MT exhibits multiple (3) regenerative delay loops and long out-of-cut duration in-between tool engagement stabilizes the process to reach up to 2x higher stable widths/depths as compared to the conventional continuous turning.

THEORETICAL STUDY OF NONLINEAR CHATTER STABILITY ANALYSIS BASED ON SYNTHESIS OF LINEARIZATIONS IN OPERATING POINTS FOR DIFFERENT TURNING CONDITIONS

This paper deals with an approach to study nonlinear chatter analysis, which is based on the synthesis of linear theory for different turning conditions. Mainly, contact nonlinearities play a crucial role in the behavior of the machine tool and the stability of turning operation. However, the analysis of nonlinear systems is challenging because nonlinear system analyzes are often limited to a linearized solution, which may be insufficient to reveal the stability lobe diagram. The presented study proposes a theoretical approach which is based on a synthesis of linearization in the operating point. This approach provides several solutions of stability lobe diagrams which are strongly depending on the loading conditions of the nonlinear system and all solutions are integrated to the final stability lobe diagram. The presented method is applied to a simplified 2D structure between two supports with nonlinear contact stiffness. Resulted analysis of the lobe diagram are compared with results of the time-domine simulations and it shows a good match. This paper shows that the presented approach offers an effective solution for refining the stability estimate for nonlinear mechanical systems.