Chatter stability prediction in milling using time-varying uncertainties

The chatter stability in milling severely affects productivity and quality of machining. Tool wear causes both the cutting coefficient and the process damping coefficient, but also other parameters to change with cutting time. This variation greatly reduces the accuracy of chatter prediction using conventional methods. To solve this problem, we consider the cutting coefficients of the milling system to be both random and time-varying variables and we use the gamma process to predict cutting coefficients for different cutting times. In this paper, a time-varying reliability analysis is introduced to predict chatter stability and chatter reliability in milling. The relationship between stability and reliability is investigated for given depths and spindle speeds in the milling process. We also study the time-varying chatter stability and time-varying chatter reliability methods theoretically and with experiments. The results of this study show that the proposed method can be used to predict chatter with high accuracy for different cutting times.     

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.     

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.     

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.     

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 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 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.     

Life prediction system using a tool’s geometric shape for high-speed milling

In recent years, machinery and tool technology has been developing rapidly. The accuracy of operations have also become more and more exact. Elsewhere, raw materials have also been honed, hoping to provide more useful properties than previously. Thus, how to find the best way to prolong the life of a tool subjected to hardened material cutting is the target of this research. Three kinds of tool angle of the endmill are used in this research; clearance angle, rake angle, and helical angle. The cutting conditions are the same; we only change the tool angle for all the cases studied. We attempt to discover better tool geometrical angles for the high-speed milling of NAK80 mold steel. The tool wear rate was measured through a toolmaker’s microscope and the roughness of the machined surface was measured by the roughness-measuring instruments after several complete surface layers were removed from the workpiece in the experiment. Also, a noise-mediator was used to detect the level of cutting noise during each surface layer workpiece removal of the high-speed milling process, and different noise levels were then compared with the tool wear rates for identifying noise characteristics in the case of an over-worn tool state. An abductive network was applied to synthesize the data sets measured from the experiments and the prediction models are established for tool-life estimation and over-worn situation alert under various combinations of different tool geometrical angles. Through the identification of tool wear and its related cutting noise, we hope to consequently construct an automatic tool wear monitoring system by noise detection during a high-speed cutting process to judge whether the tool is still good or not, and, so, the cost of milling can be reduced.     

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.     

Tool system for high-speed milling

A model of the tool system for the high-speed milling of high-technology components is developed. The influence of the dimensions of the system components on the roughness of the machined surface is studied. The formulas obtained permit assessment of the milling productivity for the dimensional parameters of the tool system and the roughness, specified for a specific technological process.     

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.     

薄壁零件的高速铣削稳定性研究

薄壁结构零件在加工过程中极易发生变形和切削振动,这对提高加工质量和加工效率十分不利.在考虑刀具和工件两个方向自由度的基础上,分析了薄壁零件的动态铣削模型.针对2A12铝合金薄壁结构零件,利用MIKRON UCPDUR0800 高速加工中心和相关仪器、软件,通过铣削力辨识实验和模态实验,进行了高速铣削薄壁零件的稳定域分析和实验验证.     

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.     

Multidisciplinary design optimization of a milling cutter for high-speed milling of stainless steel

The milling cutter’s fracture strength is more important than its chemical stability and thermal conductivity in high-speed milling. The multidisciplinary design optimization (MDO) method is employed to optimize the fracture-resistant performance of a milling cutter in this work. An experimental study on high-speed milling of the martensitic stainless steel 0Cr13Ni4Mo is conducted. The cutting forces and cutting temperature in the milling process are measured to provide initial data for the structural optimization of the milling cutter. The mathematical models of cutting force and cutting temperature are studied. Considering that the induced stress in the milling cutter is generated by thermomechanical coupling, the thermoelastic–plastic governing equation in the milling process is introduced in this work. The sensitivity of the structural parameters to the maximum equivalent stress of the milling cutter is calculated, and the structural parameters that have the greatest effects on the maximum equivalent stress are determined as design variables for the cutters’ optimization. The MDO procedure for the cutter’s optimization consists of updating of solid model, finite element analysis of thermomechanical coupling, postprocessing, and optimization algorithm. The MDO results show that the optimized milling cutter has a better fracture-resistant performance than the initial one. The maximum deformation, overall equivalent stress, and deformation are decreased.     

An approach for analyzing and controlling residual stress generation during high-speed circular milling

In the rapid development of the modern high-speed milling industry, particularly in the aerospace field, machined residual stress is an important evaluation indicator of the quality, and whether it can be controlled or not is critical. In this article, experimental data of residual stress in feed direction and vertical feed direction validated with finite element (FE) simulation, which resulted in the finding that residual stress distribution is nonuniform in varied machined circular areas. The maximum residual tensile stress in different directions changes with coordinates. It is well known that uncut chip thickness (UCT) will influence the cutting force and temperature, but the relation between UCT and residual stress is still difficult to understand and explicate. Traditional measurement of residual stresses in the feed and vertical feed direction is difficult to explain. Based on the UCT model which is a function of feed rate and tool diameter, by measuring residual tangential and radial stress, it is observed that residual tangential stress is influenced by the UCT. Moreover, residual radial stress, under high feed rate, is distributed with wave change, and residual radial stress under smaller feed rate is still affected by the UCT. These results indicate that it is possible to optimize the residual stress distribution by controlling UCT (feed rate and tool diameter) with high-speed milling.     

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...     

New predictor-corrector methods based on piecewise polynomial interpolation for milling stability prediction

Abstract

Chatter frequently occurs during cutting operations, which seriously restricts the machining productivity and workpiece accuracy. Consequently, accurate and efficient stability prediction is of great significance to determine stable machining parameters. A cubic Hermite–Newton approximation method which can determine the chatter stability boundaries more efficiently is presented in this paper. The milling dynamic system can be expressed as time-periodic delay differential equations (DDEs) with consideration of the regeneration effect. A typical benchmark example is provided to assess the convergence feature and stability lobes of the cubic Hermite–Newton approximation method and several existing methods. The results indicate that the cubic Hermite–Newton approximation method can achieve satisfactory results. For the sake of developing the cubic Hermite–Newton approximation method with higher convergence rate and computational efficiency, the tooth-passing period is further separated into two distinct phases according to whether the value of coefficient matrix equals to zero. Meanwhile, the linear interpolation polynomial is used to predict milling stability, and then piecewise polynomial interpolation was utilized in two adjacent time intervals to correct this prediction. By adopting the two benchmark examples, the effectiveness of the two new methods can be analyzed using existing methods. The results demonstrate that the two new methods have superior accuracy and efficiency.     

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.     

高速铣削加工的数学模型建立和实验研究

在高速铣削机理研究中,铣削参数的应用实验研究是至关重要的.通过单因素和多因素实验,研究高速铣削参数对已加工工件表面粗糙度和表层残余应力的影响规律.实验表明,高速铣削能够获得较好的工件表面质量.