Stability Lobe Diagram Research Articles

Modeling of Dynamic Instability Via Segmented Cutting Coefficients and Chatter Onset Detection in High-Speed Micromilling of Ti6Al4V

Miniature components with complex shape can be created by micromilling with excellent form and finish. However, for difficult-to-machine materials, such as Ti-alloys, failure of low-flexural stiffness microtools is a big limitation. High spindle speeds (20,000–100,000 rpm) can be used to reduce the undeformed chip thickness and the cutting forces to reduce the catastrophic failure of the tool. This reduced uncut chip thicknesses, in some cases lower than the cutting edge radius, can result in intermittent chip formation which can lead to dynamic variation in cutting forces. In addition, the run-out and the misalignment effects are amplified at higher rotational speeds which can induce dynamic force variation. These dynamic force variations coupled with low-flexural rigidity of micro end mill can render the process unstable. Consequently, accurate prediction of forces and stability is essential in high-speed micromilling. Most of the previous studies reported in the literature use constant cutting coefficients in the mechanistic cutting force model which does not yield accurate results. Recent work has shown significant improvement in the prediction of cutting forces with velocity–chip load dependent coefficients but a single-function velocity–chip model fails to predict the forces accurately at very high speeds (>80,000 rpm). This inaccurate force prediction affects the predicted stability boundary at those speeds. Hence, this paper presents a segmented approach, wherein a function is fit for a given range of speeds to determine the chip load dependent cutting coefficients. The segmented velocity–chip load dependent cutting coefficient improves the cutting force prediction at high speeds, which yields much accurate stability boundary. This paper employs two degrees-of-freedom (2DOF) model with forcing functions based on segmented velocity–chip load dependent cutting coefficients. Stability lobe diagram based on 2DOF model has been created for different speed ranges using Nyquist stability criterion. Chatter onset has been identified experimentally via accelerometer data and the power spectral density (PSD) analysis of the machined surface topography. Critical spatial chatter frequencies and magnitudes of PSD corresponding to onset of instability have also been determined for different conditions.

Milling stability prediction for flexible workpiece using dynamics of coupled machining system

An efficient machining is limited by the chatter of machining system including spindle and support, which would cause poor surface quality. This paper proposed an improved stability prediction method based on the dynamics of machine tool. Dynamics of the support are considered into the stability prediction of machining process. The spindle was modeled by the receptance coupling substructure analysis method to predict the dynamics at the tool point. The mathematical model of the closed manufacturing system (machine tool, spindle, holder, and tool) was given, as well as the details of joint contacts. The model was used to obtain the system characteristics, and the FRFs of the tool point were obtained from the model in frequency domain. Moreover, the stability limitation for machining system were developed to create the stability lobe diagram with the FRFs of both the spindle and support. Experimental results showed that the depths of improved stability lobes were smaller than those of the original ones, and the improved lobes were more accurate for the stability predictions. The machined surface quality showed that the stable machining system was beneficial to produce good surface. This improved method is helpful for the stability calculation and machining parameter selection especially when milling a thin-walled workpiece or a weak clamping fixture.

Passive and active strategies using embedded piezoelectric layers to improve the stability limit in turning/boring operations

Strategies for chatter modelling, monitoring and reduction are constantly under research, as chatter is well known for jeopardizing the industry productivity and the quality of machined parts. This research presents two different strategies to reduce chatter by improving the stability limit in turning/boring operations using piezoelectric layers embedded in the tool-holder. Both rely upon the fact that structural damping has a proportional relationship with the stability limit. Being so, the instability phenomenon can be significantly reduced by increasing the system’s structural damping either passively or actively. In the proposed passive strategy, the piezoelectric layers are connected to a dissipative inductive-resistive shunt circuit. In the proposed active strategy, the piezoelectric layers are connected to a velocity feedback control scheme. The effectiveness of both strategies is evaluated by the comparison of numerical and experimental driving point Frequency Response Functions (FRFs) of the free end of the tool holder and experimental Stability Lobe Diagrams (SLDs). This numerical evaluation is performed using multiphysical finite element models and dedicated simulation schemes. The viability and robustness of both strategies are also experimentally examined by emulating different tool-holder’s fixation conditions, which modify the system’s dynamic characteristics. Operational experiments with both control strategies are also performed. It can be concluded that both strategies can be good alternatives for improving the stability limit in turning/boring operations, since they are capable of increasing the structural damping. Nevertheless, the proposed passive strategy lacks robustness since it requires the fine-tuning of the electrical components of the shunt circuit according to the system’s dynamic characteristics. Finally, in spite of some technical difficulties, the proposed active strategy presents satisfactory performance and robustness for its practical implementation.

Influence of frictional mechanism on chatter vibrations in the cutting process\u2013analytical approach

The paper examines a nonlinear one-degree-of-freedom model of the cutting process. The classical regenerative mechanism of chatter is enriched by an additional friction phenomenon which generates frictional chatter. Additionally, the nonlinear cubic stiffness of the tool is taken into account. The aim of the paper is to investigate interactions between regeneration and the frictional effect. The proposed model is solved by the multi-time scale method. The cutting process stability (trivial solution) is determined in order to produce stability lobe diagrams and determine the influence of friction on the process. Finally, the maps of chatter amplitudes are presented and new frictional stability lobe diagrams are proposed to analyse the influence of friction.

Milling Stability Analysis Based on Chebyshev Segmentation

Chebyshev segmentation method was used to discretize the time period contained in delay differential equation, then the Newton second-order difference quotient method was used to calculate the cutter motion vector at each time endpoint, and the Floquet theory was used to determine the stability of the milling system after getting the transfer matrix of milling system. Using the above methods, a two degree of freedom milling system stability issues were investigated, and system stability lobe diagrams were got. The results showed that the proposed methods have the following advantages. Firstly, with the same calculation accuracy, the points needed to represent the time period are less by the Chebyshev Segmentation than those of the average segmentation, and the computational efficiency of the Chebyshev Segmentation is higher. Secondly, if the time period is divided into the same parts, the stability lobe diagrams got by Chebyshev segmentation method are more accurate than those of the average segmentation.

A complete methodology for identifying dynamics of heavy machine tool through operational modal analysis

Heavy machine tool work under such high-load conditions that chatter vibrations are prone to occur, which significantly diminishes the machining efficiency and quality. Stability lobe diagrams are commonly used to select appropriate spindle speed and axial depth of cut to get rid of chatter and maximize the material removal rate. However, this needs precise identification of the dynamics of the entire machine tool structure, especially in the low-frequency range. Operational modal analysis has been the proven technique for estimating dynamic characteristics of machine tool structures in operation conditions. In this article, a complete methodology was presented for employing operational modal analysis for heavy machine tool in machining conditions. A random cutting exciting method originally presented by Minis is modified which generates pseudorandom impulse force to excite a heavy vertical lathe structure. And the excitation signal of random cutting force was modeled to analyze the effect of cutting parameters on energy and frequency band of the excitation. One operational modal analysis method, the pLSCF (referred to as PolyMAX) method, was employed to estimate modal parameters during machining. It was also observed in chatter tests that the operational modal analysis results are more accurate than the traditional impact test results in characterizing the dynamics of machine tool structure in machining.

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2 ABSTRACT: Stability lobe diagram (SLD) helps in avoiding chatter in high speed machining. The stability lobe diagram has been predicted for the spindle of 32kW and 25,000 rpm. The spindle was modelled with beam elements using FEA tool. The natural frequency of the system was found to be 921Hz by modal analysis. A parametric study involving bearing preload, bearing spacing, span, material of spindle, diameter of spindle was done. An experiment was conducted to verify the variation in natural frequency of the system due to the change in spacing. A substantial shift in frequency was observed by altering the spacing. The cumulative effect of all the design variables resulted in a frequency enhancement from 921Hz to 1300 Hz. The variation of spindle stiffness and natural frequency with speed was plotted for various bearing preloads and design variables. A regression analysis is done to develop an empirical relation to predict the natural frequency of the spindle. Pareto chart was plotted to find the most influencing factor among the design variables. The frequency response function of the spindle system was found by Harmonic analysis. Stability lobe diagram was predicted using MATLAB. Real time machining was done to validate the stability lobe. Parametric study of stability lobe has been done and a significant increase in permissible depth of cut has been observed from stability lobe diagram due to the increase in natural frequency.

Development of Chatter Threshold Determination Methodology in Milling Process by Using Inclined Workpiece

Machined product quality depends on its dimension and surface quality. The dimension quality depends on machine tool accuracy while the surface quality depends on machining system stiffness. A low machining system stiffness will shift spindle shaft-tool resonance frequencies to low frequencies. When one of these frequencies coincides with spindle rotational speed or its harmonics, chatter will be generated which in turn worsen the workpiece surface roughness. In addition to increasing machining system stiffness, chatter can be eliminated by decreasing the axial depth of cut as well. Maximum axial depth at certain spindle rotational speed which will not generate chatter is called as chatter threshold. A diagram describing chatter thresholds for certain range of spindle rotational speed is called as a SLD (stability lobe diagram). The diagram is very useful for selecting a maximum depth of cut at certain rotational speed in order to obtain chatter-free machining process. The SLD can be generated theoretically or experimentally. The theoretical one is fast and cheap but it is not guaranteed to be correct. On the other hand, although the experimental one will produce exact values but it is long, cumbersome and expensive, because for certain rotational speed many machining with different axial depth of cut must be conducted until chatter threshold is reached. The same process is then repeated for other rotational speeds. This paper deals with a new method in determining the chatter threshold or SLD experimentally, by using inclined workpiece, by which it only needs one time machining-test for each rotational speed. In this method, during machining process, chatter occurrence is detected by using accelerometer and validated by its surface roughness afterwards. It is shown in this paper that the new method works well for machining aluminium workpiece in vertical machining center.

A model for predicting chatter stability considering contact characteristic between milling cutter and workpiece

It has been demonstrated that chatter has a negative effect on machined surface quality during milling process. The identification of chatter is crucial for reducing its influence on machining integrity, especially for the milling process of curved surface. Change of cutter position will cause chip thickness to vary in milling process. Therefore, different contact characteristic between milling cutter and workpiece will be brought out. Compared with the traditional predictive model, a model for predicting chatter stability considering this contact characteristic is proposed in this study. Stability lobe diagrams at different cutter positions are proposed to predict milling stability by employing full-discrete method. A series of experiments are carried out to calibrate and verify the stable lobe diagram. The predicting result is in good agreement with experimental investigation for the stability characterization of curved surface milling process. The model proposed in this study could be used to improve machined quality for curved surface.

Stability analysis of machine tool spindle under uncertainty

Chatter is a harmful machining vibration that occurs between the workpiece and the cutting tool, usually resulting in irregular flaw streaks on the finished surface and severe tool wear. Stability lobe diagrams could predict chatter by providing graphical representations of the stable combinations of the axial depth of the cut and spindle speed. In this article, the analytical model of a spindle system is constructed, including a Timoshenko beam rotating shaft model and double sets of angular contact ball bearings with 5 degrees of freedom. Then, the stability lobe diagram of the model is developed according to its dynamic properties. The Monte Carlo method is applied to analyse the bearing preload influence on the system stability with uncertainty taken into account.

Development and analysis of a consciously designed Joint Interface Module for improvement of a machining system’s dynamic performance

Machining vibrations and dynamic instability of machine tools is an important consideration in machining systems. Common approaches for improving their dynamic performance target either the process, or intelligent, yet complex control systems with actuators. Given that machine tools’ dynamic characteristics are largely defined by the characteristics of the joints, this article proposes a novel concept, attempting to create a new paradigm for improving the dynamic behaviour of machine tools—introducing modular machine tools components (Joint Interface Modules—JIMs) with joints deliberately designed for increasing dynamic stiffness and enhancing damping with the use of viscoelastic materials. Through a systematic model-based design process, a prototype replicating a reference tool holder was constructed exploiting viscoelastic materials and the dynamic response of the machining system was improved as a result of its introduction; in machining experiments, the stability limit was increased from around 2 mm depth of cut to 4 mm depth of cut, without compromising the rigidity of the system or changing the process parameters. The article also includes the results of investigations regarding the introduction of such prototypes in a machine tool and discusses the shortcomings of the stability lobe diagrams as a method for evaluating the performance of machine tool components with viscoelastically treated joints.

Chatter stability of micro end milling by considering process nonlinearities and process damping

The micro end milling uses the miniature tools to fabricate complexity microstructures at high rotational speeds. The regenerative chatter, which causes tool wear and poor machining quality, is one of the challenges needed to be solved in the micro end milling process. In order to predict the chatter stability of micro end milling, this paper proposes a cutting forces model taking into account the process nonlinearities caused by tool run-out, trajectory of tool tip and intermittency of chip formation, and the process damping effect in the ploughing-dominant and shearing-dominant regimes. Since the elasto-plastic deformation of micro end milling leads to large process damping which will affect the process stability, the process damping is also included in the cutting forces model. The micro end milling process is modeled as a two degrees of freedom system with the dynamic parameters of tool-machine system obtained by the receptance coupling method. According to the calculated cutting forces, the time-domain simulation method is extended to predict the chatter stability lobes diagrams. Finally, the micro end milling experiments of cutting forces and machined surface quality have been investigated to validate the accuracy of the proposed model.

Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface

To identify stable cutting conditions with a high depth of cut, stability lobe diagrams are used. In order to predict these diagrams, frequency response functions (FRF) at the tool tip are required for every tool, holder and machine combination. To reduce the number of experimental tests, receptance coupling substructure analysis (RSCA) is proposed in the literature. In order to take full advantage of this method, contact parameters between holder and tool must be known. To identify these parameters this paper presents a new method based on free-free measurements. The obtained contact parameters led to good results for various tool lengths. Based on this, an extensive investigation is performed for the ER32 holder interface. Afterwards, the RCSA method is tested. Therefore, different spindle–holder–tool assemblies are modeled for two machine tools. Prediction and measurement of obtained tool-tip FRF shows a good match, especially for the frequency position.

Chatter Identification of Face Milling Operation via Time-Frequency and Fourier Analysis

Chatter is generally defined as self-generated vibrations from the interaction between tool and workpiece. It is the most critical vibration in machining operations and can decrease the surface quality and cause the premature tool wear. Chatter creates erroneous vibrations on the workpiece surface. However, even though the spatial response of chatter is still bounded, its frequency response would become unstably broadband, emitting high-pitched sounds. The deterioration in both time and frequency domains implies that chatter is a route-to-chaos process. To capture the time-frequency characteristics of chatter, instantaneous frequency is applied to extract the relevant force vibration of machining chatter, and the energy ratio approach is used to develop a discrete stability lobe diagram of a face-milling operation. The proposed method is validated by measuring the surface roughness of the workpiece.

Stability prediction of thin-walled workpiece made of Al7075 in milling based on shifted Chebyshev polynomials

With the rapid development of aerospace technology, Al7075 has been widely used for structural components. High-speed milling is one of the most effective ways to improve machining efficiency of Al7075. During the milling process, regenerative chatter which restricts the milling quality and productivity often occurs. With the aim of avoiding regenerative chatter, stability lobe diagram (SLD) is widely used to obtain chatter-free parameters. This work presents a stability prediction method by using shifted Chebyshev polynomials. The milling dynamics with consideration of the regenerative effect is described by time periodic delay-differential equations (DDEs). The transition matrix of the milling system is constructed with the help of Chebyshev–Gauss–Lobatto (CGL) points. In order to demonstrate the accuracy of the proposed method, the rate of convergence of the proposed method is compared with that of the classical benchmark methods. On the other hand, in the process of thin-walled workpiece milling, the dynamic behavior of the workpiece depends on the tool position. To study the influence of the tool position dependent dynamics on the chatter stability of the thin-walled workpiece, a three-dimensional SLD is obtained. The verification experiments are conducted to verify the reliability of the proposed method. The results show that the experimental results are consistent with the predicted results.

Estimation of the Bistable Zone for Machining Operations for the Case of a Distributed Cutting-Force Model

Regenerative machine tool chatter is investigated for a single-degree-of-freedom model of turning processes. The cutting force is modeled as the resultant of a force system distributed along the rake face of the tool, whose magnitude is a nonlinear function of the chip thickness. Thus, the process is described by a nonlinear delay-differential equation, where a short distributed delay is superimposed on the regenerative point delay. The corresponding stability lobe diagrams are computed and are shown numerically that a subcritical Hopf bifurcation occurs along the stability boundaries for realistic cutting-force distributions. Therefore, a bistable region exists near the stability boundaries, where large-amplitude vibrations (chatter) may arise for large perturbations. Analytical formulas are obtained to estimate the size of the bistable region based on center manifold reduction and normal form calculations for the governing distributed-delay equation. The locally and globally stable parameter regions are computed numerically as well using the continuation algorithm implemented in dde-biftool. The results can be considered as an extension of the bifurcation analysis of machining operations with point delay.

Three-dimensional stability prediction and chatter analysis in milling of thin-walled plate

Stability lobe diagram can be used for selecting proper milling parameters to perform chatter-free operations and improve productivity during milling of thin-walled plates. This paper studies the machining stability in milling of thin-walled plates and develops a three-dimensional stability lobe diagram of the spindle speed, tool position, and axial depth of cut. The workpiece-holder system is modeled as a 2-degree-of-freedom system considering that the tool system is much more rigid than the thin-walled plate, and dynamic equations of motion described for the workpiece-holder system are solved numerically in time domain to compute the dynamic displacements of the thin-walled plate. Statistical variances of the dynamic displacements are then employed as a chatter detection criterion to acquire the stability lobe diagram. The experimentally obtained stability limits correspond well with the predicted stability limits. In addition, influence of feed rate on stability limits is also investigated. By performing frequency analysis of the measured cutting forces to judge if chatter occurs, it is found that feed per tooth has little influence on the stability limits. However, feed per tooth impacts the machined surface quality. The results show that the surface quality drops by increasing feed per tooth.

Improved predictions of the stability lobes for milling cutting operations of thin-wall components by considering ultra-miniature accelerometer mass effects

In this work, we study how the mass and the lightweight connecting cable of an ultra-miniature accelerometer sensor (ACC) influence the frequency response function (FRF) of thin-wall aluminum workpieces, and its influence over the stability analysis of the milling process. To address these effects, experimental FRF measurements were performed by using a noncontact laser Doppler vibrometer (LDV) system to compare its collected data with those obtained by using the ACC. To correlate the discrepancies observed between measurements, we have used the structural modification method and finite element simulations to quantify the accelerometer mass and its connecting cable effects. Then, we computed the stability lobes diagram by using the enhanced, multistage homotopy perturbation method (EMHPM) to determine stable cutting parameters. It was found that the predicted stability lobes agree well with experimental data if the structural modification method is used to compensate the accelerometer measurements. This methodology could help researches and machinist with limited access to LDV equipment to perform reliable experimental dynamic measurements in cases where the cable and accelerometer mass could affect data accuracy.

Electromagnetic actuator for determining frequency response functions of dynamic modal testing on milling tool

Machine tools are the main driving forces of industrialization of a country. However, poor machinability because of chatter vibration results in poor surface quality, excessive noise, and reduced material removal rate. Modal testing is a useful method to investigate dynamic properties of a cutting tool system and improve material removal rate. However, at present, modal testing using impact hammer is limited by certain problems. This paper developed a non-contacting electromagnetic actuator (EMA) to determine frequency response functions (FRFs) under amplitude and speed dependencies of cutting milling tools. The geometry was designed using magnetic circuit analysis and generalized machined theory before finite element analysis was conducted using magnetostatic-ansys software. Next, EMA was used as a contacting and non-contacting exciter of a conventional milling machine to determine the FRFs and dynamic properties of milling tool with amplitude and speed dependencies including comparison with static FRFs. Subsequently, dynamic properties and FRFs are used to establish stability lobe diagram. Stability lobe diagram also shows an improvement of up to 5% of depth of cut at lower spindle speed. In conclusion, by generating force that applies to static and dynamic modal testing, an EMA can determine dynamic properties and stability lobe diagram for increasing material removal rate and production rate.

Prediction of Dynamic Milling Stability considering Time Variation of Deflection and Dynamic Characteristics in Thin-Walled Component Milling Process

The milling stability of thin-walled component is an important problem in the aviation manufacturing industry. The milling stability is influenced by both deflection characteristic and dynamic characteristic of workpiece. Moreover, in the material removal, the deflection and dynamic characteristics of workpiece are time-variant on the change of machining positions. Thus, the milling stability is also time-variant. In order to investigate the time variation of deflection and dynamic characteristics of workpiece, a new computational model was established in this paper. Based on the influences of the deflection and the dynamic characteristics of workpiece, a new stability lobes diagram which can show different stability domains and chatter domains in different process positions was obtained. Experimental testing has been conducted to validate the established new model.