Cutting force model considering tool edge geometry for micro end milling process

The analysis of the cutting force in micro end milling plays an important role in characterizing the cutting process, as the tool wear and surface texture depend on the cutting forces. Because the depth of cut is larger than the tool edge radius in conventional cutting, the effect of the tool edge radius can be ignored. However, in micro cutting, this radius has an influence on the cutting mechanism. In this study, an analytical cutting force model for micro end milling is proposed for predicting the cutting forces. The cutting force model, which considers the edge radius of the micro end mill, is simulated. The validity is investigated through the newly developed tool dynamometer for the micro end milling process. The predicted cutting forces were consistent with the experimental results.     

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 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.     

考虑犁切力的微铣削颤振稳定域建模与分析

以微结构铣削加工为研究对象,建立了微观尺度下考虑犁切效应的铣削动态铣削力模型和颤振稳定域解析模型。在微铣削加工实验的基础上,对应于刀齿的每一个瞬时转角,对微铣削颤振稳定域进行了时域求解,进而研究了犁切-剪切机制对微铣削颤振稳定域的影响。实验结果表明犁切效应对微细铣削过程的加工不稳定现象没有显著的影响。     

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.     

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.     

基于切削稳定性与表面质量约束的铣削工艺参数优化研究

铣削工艺系统的动态特性随着刀具夹持长度改变而变化,影响关联的铣削稳定性与加工表面质量,进而导致铣削加工的工艺规划具有不确定性.针对此问题,本文综合刀具悬伸量与传统铣削用量作为输入,分别建立极限切削深度与表面粗糙度的反向传播神经网络模型(BPNN),并进一步以其表达铣削稳定性与加工质量约束,构建以刀具悬伸量和粗/精加工阶...     

Chatter stability for micromilling processes with flat end mill

A mechanistic model is developed to predict micromilling forces with flat end mill for both shearing and ploughing-dominant cutting regimes. The model assumes that there is a critical chip thickness that determines whether a chip will form or not. Numerical method is extended to predict the chatter stability in micro end milling, which is performed based on the proposed cutting force model. The simulating procedure for predicting stability and cutting forces is presented in detail, and the stability diagram is constructed. The validation experiments are conducted to verify the simulation results. Both experimental cutting forces measured and machined workpiece surface scanned through digital microscope are analyzed and used to verify the proposed model.     

微细立铣削切削振动试验研究

基于45钢微细立铣削试验,分析了微细立铣削切削振动的基本特征,研究了直槽立铣加工时铣削参数对振动加速度和振动位移量影响的基本规律.研究结果表明:在同样的切削工况下,微细立铣削的切削振动远大于大直径立铣刀铣削的情况;铣削参数是振动加速度的主要影响因素,振动加速度随铣削参数的增加都呈上升趋势,但轴向切深H和转速n对振动加速度的影响比进给量f更显著;在一定的参数范围内,减小主轴转速n和增大轴向切深H能够减小振动位移量的大小.     

微铣削再生颤振动力学建模及稳定性分析

再生颤振是制约微铣削加工效率和加工质量的主要因素.以微铣削加工为研究对象,建立了考虑再生效应的微铣削颤振系统动力学模型和颤振稳定域解析模型,通过模态实验获得机床-刀具系统的频响函数,在此基础上综合使用铣削稳定性判据进行数值分析,获得了颤振稳定域解析解.最后进行了颤振稳定性加工实验,实验结果与仿真结果吻合良好,验证了建立的微铣削颤振系统动力学模型和颤振稳定域解析模型的正确性.     

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.     

Determining the stability regions in end milling

The stability regions of self-oscillation in the end milling of a rigidly fixed workpiece according to analytical calculations and simulation are compared. Possible explanations for the discrepancies are reported.     

An improved cutting force model for micro milling considering machining dynamics

Micro milling, as a versatile micro machining process, is kinematically similar to conventional milling; however, it is significantly different from conventional milling with respect to chip formation mechanisms and uncut chip thickness modelling, due to the comparable size of the edge radius to the chip thickness, and the small per-tooth feeding. Considering tool runout and dynamic displacement between the tool and the workpiece, the contour of the workpiece left by previous tool paths is typically in a wavy form, and the wavy surface provides a feedback mechanism to cutting force generation because the instantaneous uncut chip thickness changes with both the vibration during the current tool path and the surface left by the previous tool paths. In this study, a more accurate uncut chip thickness model was established including the precise trochoidal trajectory of the cutting edge, tool runout and dynamic modulation caused by the machine tool system vibration. The dynamic regenerative effect is taken into account by considering the influence of all the previous cutting trajectories using numerical iteration; thus, the multiple time delays (MTD) are considered in this model. It is found that transient separation of the tool-workpiece occurring at a low feed per tooth, caused by MTD and the existing cutting force models, is no longer applicable when transient tool-workpiece separation occurs. Based on the proposed uncut chip thickness model, an improved cutting force model of micro milling is developed by full consideration of the ploughing effect and elastic recovery of the workpiece material. The proposed cutting force model is verified by micro end milling experiments, and the results show that the proposed model is capable of producing more accurate cutting force prediction than other existing models, particularly at small feed per tooth.     

Investigation on chatter stability of thin-walled parts in milling based on process damping with relative transfer functions

Chatter usually occurs in cutting of thin-walled workpiece due to poor structural stiffness, which results in poor surface quality and damaged tool. Aiming at process damping caused by interference between a tool flank face and a machined surface of thin-walled part, the dynamic model and critical condition of stability are proposed by the relative transfer functions, when both the tool structure and the machined workpiece have similar dynamic behaviors in this paper. Using the frequency method to solve the stability of the cutting chatter, it can be seen that the process damping can significantly improve the stability of the low speed region. Moreover, the stability domain is different and more exact than the one that derives from the simple superposition of the tool and the workpiece lobe diagrams. The correctness of the model is validated by experiments. These conclusions provide a theoretical foundation and reference for the milling mechanism research.     

Prediction of surface roughness in end face milling based on Gaussian process regression and cause analysis considering tool vibration

Surface roughness is a technical requirement for machined products and one of the main product quality specifications. In order to avoid the costly trial-and-error process in machining parameters determination, the Gaussian process regression (GPR) was proposed for modeling and predicting the surface roughness in end face milling. Cutting experiments on C45E4 steel were conducted and the results were used for training and verifying the GPR model. Three parameters, spindle speed, feed rate, and depth of cut were considered; the experiment results showed that depth of cut is the main factor affecting the surface roughness and regression results showed that the GPR model has a good precision in predicting the surface roughness in different cutting conditions. The prediction accuracy was nearly about 84.3 %. Based on the GPR prediction model, 3D-maps of surface roughness under various cutting parameters could be obtained. It is very concise and useful to select the appropriate cutting parameters according to the maps. As experimental results did not conform to the empirical knowledge, frequency spectrums of the tool were analyzed according to the 3D-maps, it was found that tool vibration is also a crucial factor affecting the machined surface quality.     

Extension of process damping to milling with low radial immersion

This paper investigates the stabilizing effect of process damping at low cutting speeds for regenerative machine tool vibrations of milling processes. The process damping is induced by a velocity-dependent cutting force model, which takes into account that the actual cutting velocity is different from the nominal one during machine tool vibrations. The chip thickness and the cutting force are calculated according to the direction of the actual cutting velocity. This results in an additional damping term in the governing delay-differential equation, which is time-periodic for milling and inversely proportional to the cutting speed. In the literature, this term is often assumed to be constant and is considered to improve stability properties at low spindle speeds. In this paper, it is shown that the velocity-dependent cutting force model captures the improvement in the low-speed stability only for turning operations and milling with large radial immersion, while it results in a negative process damping term for low-immersion milling. Consequently, an extended process damping model is needed to explain the low-speed stability improvement for low radial immersion milling.     

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.