Chatter stability prediction for high-speed milling through a novel experimental-analytical approach

Chatter prediction is crucial in high-speed milling, since at high speed, a significant increase of productivity can be achieved by selecting optimal set of chatter-free cutting parameters. However, chatter predictive models show reduced accuracy at high speed due to machine dynamics, acquired in stationary condition (i.e., without spindle rotating), but changing with spindle speed. This paper proposes a hybrid experimental-analytical approach to identify tool-tip frequency response functions during cutting operations, with the aim of improving chatter prediction at high speed. The method is composed of an efficient test and an analytical identification technique based on the inversion of chatter predictive model. The proposed technique requires few cutting tests and a microphone to calculate speed-dependent chatter stability in a wide range of spindle speed, without the need of stationary frequency response function (FRF) identification. Numerical and experimental validations are presented to show the method implementation and assess its accuracy. As proven in the paper, computed speed-dependent tool-tip FRF in a specific configuration (i.e., slotting) can be used to predict chatter occurrence in any other conditions with the same tool.     

Chatter prediction for milling of flexible pocket-structure

Flexible pocket-structures are widely used in engineering practice, especially in the aerospace industry. This paper presents a dynamic model which is suitable for predicting the chatter vibration during machining the thin bottom of flexible pocket-structures. The model is simplified as a three-degree-of-freedom (DOF) system, in which the cutter is considered to have two orthogonal degrees of freedom in its radial direction while the flexible component is considered to have one degree of freedom in the axial direction of the cutter. Modal analysis is implemented to obtain the system parameters. Thereafter, a semi-discretization method is used to plot the stability lobes. From the stability lobe, it is very easy to predict the appearance of the chatter vibration and thus decide the proper cutting conditions during milling the thin bottom of flexible pocket-structures. At the end of the paper, the developed model is demonstrated by a number of cutting experiments.     

Chatter reliability prediction of side milling aero-engine blisk

Reliability analysis of a dynamic structural system is applied to predict chatter of side milling system for machining blisk. Chatter reliability is defined as the probability of stability for processing. A reliability model of chatter was developed to forecast chatter vibration of side milling, where structure parameters and spindle speed are regarded as random variables and chatter frequency is considered as intermediate variable. The first-order second-moment method was used to work out the side milling system reliability model. Reliability lobe diagram (RLD) was applied to distinguish reliable regions of chatter instead of stability lobe diagram (SLD). One example is used to validate the effectiveness of the proposed method and compare with the Monte Carlo method. The results of the two approaches were consistent. Chatter reliability and RLD could be used to determine the probability of stability of side milling.

     

Chatter prediction utilizing stability lobes with process damping in finish milling of titanium alloy thin-walled workpiece

Machining chatter often becomes a big hindrance to high productivity and surface quality in actual milling process, especially for the thin-walled workpiece made of titanium alloy due to poor structural stiffness. Aiming at this issue, the stability lobes are usually employed to predict if chatter may occur in advance. For obtaining the stability lobes in milling to avoid chatter, this article introduces an extended dynamic model of milling system considering regeneration, helix angle, and process damping into the high-order time domain algorithm which can guarantee both high computational efficiency and accuracy. Via stability lobes, the reasonability and accuracy of the proposed method are verified globally utilizing specific examples in literature. More convincingly, the time-domain numerical simulation is also implemented to predict vibration displacement for partial stability verification. In this extended model, process damping is well-known as an effective approach to improve the stability at low spindle speeds, and particularly, titanium alloy as typical difficult-to-machine material is generally machined at low spindle speeds as well due to its poor machinability. Therefore, the proposed method can be employed to obtain the 3D stability lobes in finish milling of the thin-walled workpiece made of titanium alloy, Ti-6Al-4V. Verification experiments are also conducted and the results show a close agreement between the stability lobes and experiments.     

Chatter stability analysis for end milling via convolution modelling

This research discusses the methodology of developing a symbolic closed form solution that describes the dynamic stability of multiflute end milling. A solution of this nature facilitates machine tool design, machining parameter planning, process monitoring, diagnostics, and control. This study establishes a compliance feedback model that describes the dynamic behavior of regenerative chatter for multiflute tool-work interaction. The model formulates the machining dynamics based upon the interconnecting relationship of the tool geometry and the machining system compliance. The tool geometry characterises the cutting forces as a function of the process parameters and the material properties, while two independent vibratory modules, the milling tool and the workpiece, represent the machining system compliance. The compliance feedback model allows the development of a corresponding characteristic equation. By investigating the roots of the characteristic equation, this research symbolically expresses the stability of the system as a function of the cutting parameters, the tool geometry, the workpiece geometry, and the vibrational characteristics of the machine tool. Machining experimentation examining the fidelity of the regenerative chatter model is discussed. The dynamic cutting forces, cutting vibration, and surface finish of the machining process confirm the validity of the analytical prediction.Nomenclature b damping coefficient: mass-spring-damper representation - b _e equivalent damping coefficient: mass-spring-damper representation - C compliance element - CWD chip with density function - D diameter of cutter - d _a axial depth of cut - d _r radial depth of cut - average total cutting force - K _r radial specific cutting pressure constant - K _t tangential specific cutting pressure constant - k spring constant - k _e equivalent spring constant - m mass: mass-spring-damper representation - m _e equivalent mass: mass-spring-damper representation - n number of flutes on the cutter - p _x,y elemental cutting forces - P _1,2 elemental cutting force functions - R cutter radius - s Laplace variable - TS tooth sequencing function - chip thickness - t _c average chip thickness - t _x feed per tooth - helix angle - _x actual displacement of cutter tip - unit impulse function - _d damped circular frequency of vibration - damping ratio - spindle speed     

Chatter prediction based on frequency domain solution in CNC pocket milling

Chatter has been a problem in CNC machining process especially during pocket milling process using an end mill with low stiffness. Since an iterative time-domain chatter solution consumes a computing time along tool paths, a fast chatter prediction algorithm for pocket milling process is required by machine shop-floor for detecting chatter prior to real machining process. This paper proposes the systematic solution based on integration of a stability law in frequency domain with geometric information of material removal for a given set of tool paths. The change of immersion angle and spindle speed determines the variation of the stable cutting depth along cornering cut path. This proposed solution transforms the milling stability theory toward the practical methodology for the stability prediction over the NC pocket milling.     

Chatter and dynamic cutting force prediction in high-speed ball end milling

Machine tool chatter is a serious problem which deteriorates surface quality of machined parts and increases tool wear, noise, and even causes tool failure. In the present paper, machine tool chatter has been studied and a stability lobe diagram (SLD) has been developed for a two degrees of freedom system to identify stable and unstable zones using zeroth order approximation method. A dynamic cutting force model has been modeled in tangential and radial directions using regenerative uncut chip thickness. Uncut chip thickness has been modeled using trochoidal path traced by the cutting edge of the tool. Dynamic cutting force coefficients have been determined based on the average force method. Several experiments have been performed at different feed rates and axial depths of cut to determine the dynamic cutting force coefficients and have been used for predicting SLD. Several other experiments have been performed to validate the feasibility and effectiveness of the developed SLD. It is found that the proposed method is quite efficient in predicting the SLD. The cutting forces in stable and unstable cutting zone are in well agreement with the experimental cutting forces.     

Accurate and efficient stability prediction for milling operations using the Legendre-Chebyshev-based method

The International Journal of Advanced Manufacturing Technology - Stability prediction with both high computational accuracy and speed is still a challenging issue and has been attracting...     

Chatter detection in milling processes using frequency-domain Rényi entropy

Chatter is a kind of self-excited vibration and causes negative effects in machining processes. This paper presents a practical method to identify the chatter with cutting force signals in milling processes. Since the spectrum of the chatter signal exhibits discrete spectral lines around the chatter frequencies and the Rényi entropy is an effective index to characterize the randomness of data series, the frequency-domain Rényi entropy is proposed as a chatter indicator. As the chatter severity level grows, the signal components at the chatter frequencies become more and more significant, which means a reduction of the randomness of the spectral series. As a result, the value of the Rényi entropy-based indicator decreases rapidly at the onset of the chatter. In order to eliminate the interference of the normal signal components, i.e., the spindle speed-related frequency components, the spectrum is preprocessed to filter out those components first. Various milling experiments are conducted. The results show that the value of the proposed indicator changes sharply at the onset of chatter in various milling conditions with different spindle speeds and cutting depths. Also, the proposed indicator is compared with the commonly used Shannon entropy-based indicator and verified to have a larger difference between the stable and chatter statuses and is higher sensitivity to the chatter.     

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.     

Three-dimensional process stability prediction of thin-walled workpiece in milling operation

High-speed machining of thin-walled workpiece is widely used in aerospace industry. To optimize the machining parameters in milling operations, the related process stability is required to be predicted. Compared to the existing two-dimensional (2D) milling stability model, a more completed three-dimensional (3D) regenerative process stability prediction model of thin-walled workpiece is presented based on the newly developed dynamic model. The efficiency and accuracy of the regenerative milling stability can be improved in the presented 3D model. The analysis procedure of the stability of flexible dynamic milling is developed in details. The 3D stability lobes are calculated according to the full discretization method and direct integration scheme. To verify the accuracy of presented 3D stability model, the thin-walled workpiece milling sound pressure signal and surface quality are determined in experiments.     

Three degrees of freedom chatter stability prediction in the milling process

Journal of Mechanical Science and Technology - Chatter in the cutting process has a great influence on workpiece surface quality, machining efficiency, and service life of the machine tool. This...     

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.     

A time-space discretization method in milling stability prediction of thin-walled component

The stability prediction of thin-walled workpiece milling is an awkward problem due to the time variant of dynamic characteristics during milling process. Integrating the time discretization method for stability prediction mentioned in many articles, a novel time-space discretization method for thin-walled component milling stability prediction is proposed based on thin plate theory and mode superposition principle, which includes the effects of the engagement position between cutter and workpiece and multi-modes of the system. The results show that the method presented is very reliable and efficient, and its accuracy is also in good agreement with experimental results. Additionally, the method can be used to handle various complex boundary conditions by means of the updated Rayleigh-Ritz solutions together with the penalty method. Two case studies are performed to explain the validation of the method as well as milling experiments of a half-clamped thin plate.     

Chatter prevention for milling process by acoustic signal feedback

This paper presents how real-time chatter prevention can be realized by feedback of acoustic cutting signal, and the efficacy of the proposed adaptive spindle speed tuning algorithm is verified as well. The conventional approach to avoid chatter is to select a few appropriate operating points according to the stability lobes by experiments and then always use these preset cutting conditions. For most cases, the tremble measurement, obtained by accelerometers or dynamometers, is merely to monitor spindle vibration or detect the cutting force, respectively. In fact, these on-line measures can be more useful, instead of always being passive. Furthermore, most of these old-fashioned methodologies are invasive, expensive, and cumbersome at the milling stations. On the contrary, the acoustic cutting signal, which is fed into the data acquisition interface, Module DS1104 by dSPACE, so that an active feedback loop for spindle speed compensation can be easily established in this research, is non-invasive, inexpensive, and convenient to facilitate. In this research, both the acoustic chatter signal index (ACSI) and spindle-speed compensation strategy (SSCS) are proposed to quantify the acoustic signal and compensate the spindle speed, respectively. By converting the acoustic feedback signal into ACSI, an appropriate spindle speed compensation rate (SSCR) can be determined by SSCS based on real-time chatter level. Accordingly, the compensation command, referred to as added-on voltage (AOV), is applied to actively tune the spindle motor speed. By employing commercial software MATLAB/Simulink and DS1104 interface module to implement the intelligent controller, the proposed chatter prevention algorithm is practically verified by intensive experiments. By inspection on the precision and quality of the workpiece surface after milling, the efficacy of the real-time chatter prevention strategy via acoustic signal feedback is further examined and definitely assured.     

A prediction method of milling chatter stability for complex surface mold

This paper proposes a kind of milling chatter stability prediction method used for the stability of milling free-form surface based on the time-domain. Firstly, a dynamic equation is established by considering the influence of mold surface curvature and cutting tool lead angle on dynamic chip thickness without deformation. Then, the multi-delay milling system vibration displacement, which is given by the ratio of dynamic chip thickness and the static chip thickness as the threshold, was calculated based on the numerical method. Finally, the chatter stability domain based on the full-discretization method of milling chatter stability domain is compared to analyze the influence of the characteristics of free surface curvature on the chatter stability domain. The results of the experiment show that the time-domain simulation method can reveal the influence of different processing areas of free-form surface mold on the instability mechanism of the system. The change trend of milling chatter stability domain was found to be consistent with the experimental results.     

Accurate and efficient prediction of milling stability with updated full-discretization method

The study of the time domain method for milling stability prediction mainly focuses on the prediction accuracy and efficiency. The state item of the full-discretization formulations is usually approximated through the higher-order Lagrange polynomial interpolation for the higher prediction accuracy of milling stability. However, the time-delay term has not been considered. This paper proposes an updated full-discretization method for milling stability prediction based on the high-order interpolation of both the state item and the time-delay term and investigates the effect of the high-order interpolation of the time-delay term on accuracy of milling stability prediction. The state transition matrix on one time period is established directly to compensate the computational time expense of the high-order interpolation. By analyzing the convergence feature and lobes of benchmark examples, the high-order interpolation of both the state item and the time-delay term is proven to be more effective than only the higher-order interpolation of the state item, and the direct establishment of the state transition matrix can achieve the purpose of saving computational time.     

Fast prediction of chatter stability lobe diagram for milling process using frequency response function or modal parameters

Prediction of chatter stability is important for planning and optimization of machining process in order to improve machining efficiency and reduce machining damage. Based on the classical analytical solution of chatter stability for milling process and in-depth analysis of the impact of modal parameters on the stability lobe diagram, a straight forward procedure for fast predicting stability lobe diagram directly using modal parameters of machining system was put forward. In consideration of the fact that the modal parameters of milling system can be estimated directly from the frequency response function using single DOF modal parameter estimation method, stability lobe diagram can be plotted directly using the tool tip’s frequency response function. The machining performances of a machining center with three different cutting tools were evaluated and the corresponding optimized cutting conditions were determined. The correctness of the proposed method was validated by good agreement of the predicted stability lobe diagram with that using the classical analytical method, and simulation results show that its calculation speed had been improved by 2–3 orders of magnitude. As a result, the proposed method of plotting stability lobe diagram using frequency response function can be utilized as an effective tool to select chatter-free cutting conditions in shop floor applications.     

A novel Chebyshev-wavelet-based approach for accurate and fast prediction of milling stability

Currently, semi-analytical stability analysis methods for milling processes focus on improving prediction accuracy and simultaneously reducing computing time. This paper presents a Chebyshev-wavelet-based method for improved milling stability prediction. When including regenerative effect, the milling dynamics model can be concluded as periodic delay differential equations, and is re-presented as state equation forms via matrix transformation. After divide the period of the coefficient matrix into two subintervals, the forced vibration time interval is mapped equivalently to the definition interval of the second kind Chebyshev wavelets. Thereafter, the explicit Chebyshev–Gauss–Lobatto points are utilized for discretization. To construct the Floquet transition matrix, the state term is approximated by finite series second kind Chebyshev wavelets, while its derivative is acquired with a simple and explicit operational matrix of derivative. Finally, the milling stability can be semi-analytically predicted using Floquet theory. The effectiveness and superiority of the presented approach are verified by two benchmark milling models and comparisons with the representative existing methods. The results demonstrate that the presented approach is highly accurate, fast and easy to implement. Meanwhile, it is shown that the presented approach achieves high stability prediction accuracy and efficiency for both large and low radial-immersion milling operations.