Stability Lobe Research Articles

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.

Proposal of novel chatter-free milling strategy utilizing extraordinarily numerous flute endmill and high-speed high-power machine tool

This paper proposes a novel chatter-free milling strategy that utilizes the infinite stable area, i.e., area below the high-speed part of the 0-th lobe, which has not been generally utilized to date. In the conventional methodology, the stable pockets are utilized to realize a high axial depth of cut. However, these pockets tend to shift, e.g., due to long-term deterioration of the spindle, and hence they sometimes cannot be utilized effectively. The proposed strategy combines an extraordinarily numerous flute endmill, e.g., 20 flutes, and a high-performance spindle, e.g., capable of a spindle speed of 33000 min−1, installed on a high-speed high-power machine tool. By increasing the number of flutes, the stability lobes shrink in inverse proportion to that number against the spindle speed and the depth of cut, and the infinite stable area can be utilized in the practical spindle speed zone of recent machine tools. A design method is proposed for the cutting tool and the cutting conditions to utilize this area effectively. Analyses and experiments are conducted to verify the effectiveness of the proposed milling strategy. In the experiments, the material removal rate reaches 2904 cc/min at the spindle speed of 33000 min−1 and the axial depth of cut of 110 mm with no chatter vibration. The infinite stable area is capable of much higher stability and machining ability than the conventionally utilized stable pockets.

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.

Nonlinear dynamics of friction-induced regenerative chatter in internal turning with process damping forces

Stability in internal turning operation depends on several factors such as cutting conditions, tool overhang, associated tool dynamics, regeneration, friction and process damping. In the present work, an improved friction-induced regenerative chatter mechanism is introduced for internal turning operations with the help of a two-degree of freedom (DOF) cutting tool model by considering structural nonlinearities and process damping effects. The model is initially validated with the existing linear stability analysis theory via the natural parameter continuation method. The stability lobes obtained from the proposed model predict the stable regions with good accuracy. Furthermore, the nonlinear behaviour of the cutting tool with Stribeck and regenerative effects under internal resonance and primary resonance conditions is investigated. The nonlinear dynamic responses and the cutting stability are predicted using the higher-order method of multiple time scales (MMTS). The effect of nonlinearities on the frequency response and stability is studied in detail and the system parameters for stable cutting operations are identified. In order to validate the cutting states of the stability diagrams, internal turning experiments are performed on AISI 1020 carbon steel workpieces and the stability conditions are found to be in good agreement.

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%.

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.

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.

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.

Investigation of tool flank wear effect on system stability prediction in the milling of Ti-6AI-4 V thin-walled workpiece

Excessive tool wear can shorten tool life and cause low machining surface quality and efficiency in the milling of Ti-6AI-4 V thin-walled workpieces. The influence mechanism between the tool flank wear and stability predication is of significant for its further development in milling Ti-6Al-4 V. However, the relationship between tool flank wear and stability predication needs to be further investigated as the effect of time-varying tool flank wear is ignored in conventional methods. In this work, a system stability prediction model considering time-varying tool flank wear effect in milling of Ti-6AI-4 V thin-walled workpiece is proposed. The tool flank wear region is discretized into differential elements, and then, the friction effect and process damping effect caused by extruding function between tool and workpiece are analyzed, and a time-varying milling force model is established. In this process, the relationship of cutting tool flank wear band width VB and section radius difference NB is determined, and the indentation volume between tool and workpiece is iteratively calculated, which is used to investigate process damping. After, the time-varying milling force coefficients are derived considering different tool flank wear status. Then, in modal space, the evolutionary process of stability lobe diagrams considering tool flank wear effect is determined. Subsequently, to effectively predict system stability, tool flank wear curves and dynamic cutting force coefficients are calibrated by slot milling, and the average errors between cutting force prediction values considering tool flank wear effect and experimental values in feed direction and normal direction are 7.3% and 12.1%, respectively. Finally, a series of machining tests are conducted to verify the effectiveness of tool flank wear on the machining stability in the milling of Ti-6AI-4 V thin-walled workpieces to some extent, and the experimental results show that the system stability prediction accuracy of the proposed method is improved by 23.8% compared with that using conventional method.

Stability analysis of milling process for multi-hardness splicing die

The tool bears the impact load and the alternating force load caused by the sudden change of hardness in the milling process of automobile panel splicing die, which aggravates the milling vibration and reduces the accuracy of die surface. According to the machining characteristics of automobile panel splicing die, the dynamic equation considering the impact of through-seam is established. The state item, the time-delay item and the periodic coefficient item in the state space form of dynamic equation were discretized by multi-order Lagrangian interpolation, and a fourth-order complete discretization method is proposed. Based on the proposed fourth-order complete discretization method, the multi-period milling stability lobe was obtained, and the milling stability lobe band in the splicing region was obtained by combining the maximum and minimum envelope method. The correctness of the dynamic model was verified by the time-frequency domain method such as Fourier transform and milling vibration and milling force data collected from the machining process. The research results can provide theoretical support for the selection and optimization of milling process parameters of splicing die.

Stability enhancement and chatter suppression in continuous radial immersion milling

For continuous radial immersion milling operations, the dominant mode shape becomes difficult to determine when stiffness of the tool and workpiece are comparable, and this can pose a great challenge for ensuring machining processes stability. In this paper, we propose a rapid method to obtain time-varying modal parameters of the workpiece by combining experimental measurements with the receptance coupling method. Firstly, the contact parameters between the workpiece and vise were identified by a so-called dynamic coupling matrix. Then the mode shapes and the time-varying natural frequency of the workpiece were determined using the modal parameters of workpiece. Finally, the stability lobe diagrams (SLDs) were computed using the modal parameters and then were validated by undertaking immersion milling experiments. The experiments showed a more conservative and practical SLD for general workpiece under continuous radial immersion, where the workpiece mode had not always dominated the machining process. Based on the proposed method, we also explored two modifications in form of additional cylinder masses and passive support, to suppress chatter. Both modifications were effective in enhancing the minimum boundary of the conservative SLD, and the modification of passive support worked better. Although the modification of the workpiece could improve the stability boundary, it indirectly affected the dynamics of the milling tool through the interaction area between the workpiece and milling tool.

High efficiency and precision approach to milling stability prediction based on predictor-corrector linear multi-step method

Regenerative chatter is the most important factor affecting the stability of the milling process. It is core for suppressing chatter and improving production efficiency to accurately and efficiently identify the stable region of milling chatter. Therefore, according to the theory of predictor-corrector, three predictor–corrector methods (PCM) are, respectively, proposed for the milling stability region by applying the fourth-order Adams-Bashforth-Moulton formula, Simpson formula, and Hamming formula. Firstly, the regenerative chatter milling process is described as a second-order time-delay differential equation (DDE) with periodic coefficients. Thus, the forced vibration time can uniformly be discretized as a time node set. Secondly, the fourth-order Adams-Bashforth formula is used to predict the displacement at every time node, whereas the fourth-order Adams-Moulton formula can be employed to correct this predicted value. In addition, the fourth-order Simpson formula and Hamming formula can also correct the predicted value. Thus, a higher precision discrete prediction-correction expansion is constructed for the transformation of DDE into the state transition express. The Floquet theory can be depended on to present the judgment criterion of milling stability. Moreover, finally, under the same milling process parameters, comparisons of both the stability lobe curve and the local discrete error curve show that the PCM has a faster convergence rate than the 1st-SDM (first-order semi-discretization method) and 2nd-FDM (second-order full-discretization method). This shows that the PCM can obtain better computational accuracy under the same discrete number, whereas the PCM is significantly higher computational efficiency over 1st-SDM and 2nd-FDM. Meanwhile, considering the actual machining environment, helix angle effect and multiple modes effect of the tool are analyzed; experimental verification considering multiple modes with helix angle further indicates the applicability of the PCM.

Investigation of Machining Stability Considering Thermal and Rotation Effect: Effectiveness of Impact Excitation for a Rotating Spindle

This study investigates machining stability considering the rotational and thermal effects of a spindle-bearing system. Conventional method for analysis of machining stability only has regarded the static response of spindle system, which does not represent actual machining conditions as some investigations mentioned. Bearing stiffness change caused by a contact angle change is applied to the analytical approach for a dynamics of spindle system. At the same time, in a frequency response function (FRF) of rotating spindle, disturbance-induced signals are included such as a slip between hammer and tool, a spindle run-out and a noise due to insufficient impulse force. In this paper, a conventional impact exciting method which has been popular for characterization is refined in order to obtain dynamic characteristics of rotating spindle-bearing system on the consideration of coherence function. Those disturbances in the output signal are remarkably reduced through finding both the optimal conditions in terms of impulse force and the filtering of false responses. The proposed refined impact exciting tests, which can manage both rotational and thermal effects under rotating conditions, lead to provide FRFs matching more accurately. Stability lobe diagrams (SLDs) derived from FRFs obtained by experiments were derived to evaluate the effectiveness of the dynamic characteristic change in bearing-spindle systems. As a result, the axial depth of cut limitations at chatter occurrence points were well matched to actual depth limits with a deviation of 3% or less. Chatter vibration generation conditions can be well estimated, which proved that SLDs considering the dynamic characteristic of spindle-bearing system reveal the actual cutting condition since it includes thermal and rotation effects of spindle-bearing system during milling process.

Bayesian updating of modal parameters for modeling chatter in turning

Variations in the mechanics and dynamics of the machining process under operational conditions cause inaccuracies in chatter model predictions. The parameters of chatter models therefore require re-calibration based on experimental observations during machining. This paper presents a new Bayesian method for the in-process calibration of chatter model parameters in turning. The new method comprises two stages. First, we identify the dominant closed-loop poles of the machining system from in-process vibration signals; then, we use those poles in a Bayesian model updating method to determine the probability distributions of the model parameters. Compared to existing methods, which require experimental observations under both stable and unstable conditions, the presented method requires a limited set of vibration measurements during stable conditions only. Moreover, the updated probability distributions are used to establish credibility bounds around the Stability Lobe Diagrams (SLD). An experimental example is presented to demonstrate the efficiency and effectiveness of the presented method in enhancing the accuracy of chatter predictions in turning.

Research on Milling Characteristics of Titanium Alloy TC4 with Variable Helical End Milling Cutter

The application of variable helical end mills to the milling of titanium alloys can suppress the regeneration effect during the machining process and ensure the stability of milling. However, due to their special geometry, their milling characteristics are also different. In this paper, the process of milling titanium alloy with a variable helix end mill is taken as the research object, and the milling force, milling stability and machining effect during the machining process are deeply studied. Firstly, the feed per tooth and cutting thickness model of the variable helical end mill were established, the milling force prediction model of the variable helical end mill was deduced, and the instantaneous milling force and its variation law were obtained by solution. Secondly, the finite element analysis model of the variable helix end mill for machining titanium alloy was established, and the influence of the variable helix angle structure on the milling force was obtained. Then, the dynamic equation of milling with a variable helix end mill was established, the stability lobe diagram of variable helix milling is was and drawn, and the influence of variable helix angle on milling stability was analyzed. Lastly, a variable helix end mill milling experiment was designed to verify the accuracy of the theoretical model and finite element simulation; the influence of the variable helix angle structure on the surface roughness was analyzed, and the influence of machining parameters on the milling force when using a variable helix end mill was investigated.

Investigation of robotic milling chatter stability prediction under different cutter orientations by an updated full-discretization method

Chatter can easily occur during robotic milling owing to the low rigidity of serial robots. Chatter affects the quality of the workpiece surface and damages the robot equipment, which is a bottleneck that hinders the application of robotic milling. An effective way to ensure milling stability is to rationally select the cutting parameters using high-precision stability lobe diagrams (SLDs). In this study, an updated full-discretization chatter stability prediction method based on the fourth-order Hermite and third-order Newton interpolation polynomial was proposed. A dynamical model of robotic milling was established by considering the regenerative effect, cutter structure modal coupling effect, and the influence of cutter orientations. Based on the established robotic milling dynamic model and the proposed full-discretization method, SLDs related to the axial depth of cut, spindle speed, lead angle, and tilt angle were generated. The dominant influencing factors of the robotic milling chatter stability under different robot postures and cutter orientations were analysed. The robotic milling experiment results show that the dynamic characteristics of the robot are different in each direction. When the milling cutter feeding direction is parallel to the x-axis direction of the global coordinate system, the regenerative effect is dominant. When the feed direction of the milling cutter is parallel to the y-axis of the global coordinate system, the cutter structure modal coupling effect is more obvious. This is possibly because the dynamic characteristics of the tool tip change during the milling process under different robot postures. However, the milling process becomes more stable with an increase in the lead or tilt angle. This is mainly because when the cutting depth is constant, the cutter–workpiece engagement area gradually decreases with an increase in the tool angle.

Optimizing the micro-texture and cutting parameters of ball-end milling cutters to achieve milling stability

The machining of titanium alloy can lead to serious tool wear, with this resulting in a lack of milling system stability and chatter. This paper looks at the relationship between milling stability and the use of micro-texturing on cutter surfaces, which aims to reduce tool wear. A stability lobe diagram is first drawn that is based on a dynamic model of the milling of titanium alloy by a ball-end milling cutter. This provides the cutting parameters for a stable domain. A micro-texture distribution model is then established for different cutting depths and the influence of micro-texture parameters on the milling performance of cutting tools according to various cutting parameters studied. The parameters are then optimized using an artificial bee colony algorithm, with the milling force, machined surface quality, and tool wear being adopted as the principal evaluation indicators. This provides a theoretical basis for the future selection of optimal cutting and micro-texture parameters.