In-process modelling of numerical control end milling

A computer-aided modelling system which can simulate the in-process cutting geometry and then calculate the corresponding dynamic cutting force in numerical control (NC) end milling is presented in the paper. In the developed system, the varying cutting geometry in end milling operations is simulated by a geometrical cutting simulation system using Boolean operations. Once the varying cutting geometry is identified, the dynamic cutting force can be calculated by a cutting process model. As a result, cutting performance in NC end milling can be verified through this developed system.     

Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

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.     

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.     

圆角铣削颤振稳定域建模与仿真研究

为避免在圆角铣削加工中产生颤振,建立考虑再生作用的圆角铣削动力学模型,推导其平均方向力系数计算公式。鉴于圆角铣削时主轴转速通常远大于圆角处的进给角速度,两者的平均方向力系数近似相等。因此,经典直线铣削颤振稳定域解析模型适用于圆角铣削,前提是需要用最大径向啮合角代替名义径向啮合角进行仿真。根据铣刀与工件的啮合情况,将圆角铣削分为均匀切宽圆角铣削和非均匀圆角切宽铣削两类,并分别推导出其最大径向啮合角计算公式。在动力学建模基础上开发圆角铣削颤振稳定域仿真模块,仿真结果得到了切削试验的验证,为圆角铣削切削参数的选择提供了一条有效途径。     

Calculations of chip thickness and cutting forces in flexible end milling

In the end milling process of a flexible workpiece, it is well recognized that the precise determination of the instantaneous uncut chip thickness (IUCT) is essential for the cutting force calculation. This paper will present a general method that incorporates simultaneously the cutter/workpiece deflections and the immersion angle variation into the calculation of the IUCT and cutting forces. Contributions are twofold. Firstly, considering the regeneration model, a new scheme for the IUCT calculation is determined based on the relative positions between two adjacent tooth path centers. Secondly, a general approach is established to perform numerical validations. On one hand, the engagement/separation of the cutter from the workpiece is instantaneously identified. On the other hand, the calculation of the IUCT is iteratively performed. To demonstrate the validity of the method, several examples are used to show the convergence history of the cutting force and the IUCT during the flexible end milling process. Both theoretical analyses and numerical results show that the regeneration mechanism is short lived and will disappear after several tooth periods in flexible static end milling process .     

A study on calibration of coefficients in end milling forces model

This paper presents an improved approach to calibrate the cutting coefficients in an end-milling model. In order to predict end-milling forces, lots of simulative models are established. In order to use them, coefficients in the models, for example, cutting pressure constants etc., must firstly be calibrated experimentally, and simulative precision and applicability of the models are influenced by them. For simplicity, using average forces to calibrate cutting parameters are widely adopted by lots of researchers. However, the existence of an instruments zero-drift, noise, etc., will have effect on the precision of experimental data, so, it is difficult to directly obtain exact average-cutting forces through experimental data. Aiming at the above problem, the paper investigates milling forces in the frequency domain, discusses the impact of experimental data at different frequencies on cutting force coefficients and the influence of sensitivity of error on experimental data at different frequencies on coefficients is studied. Based on the research, an improved method to calibrate the cutting coefficients is provided. Based on a series of experiments and numerical simulations, the validity of the method is confirmed. At the end of the paper, some useful conclusions are drawn.     

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.     

Wall thickness error prediction and compensation in end milling of thin-plate parts

End milling has been widely adopted to machine the thin-plate parts that play increasingly important role in the aerospace industry, due to the advantages of high machining accuracy and fine machined surface quality. In this paper, a systematic method is proposed to predict and compensate the wall thickness errors in end milling of thin-plate parts. The errors are caused by the static deflections induced by the varying cutting force imposed on the weakly rigid part. To improve the efficiency of computing the part deformation, a novel FE model is firstly developed by combing the methods of substructure analysis, special mesh generation and structural static stiffness modification. Then, the time- and position-dependent deformations of the part are calculated based on the proposed FE model to predict the wall thickness errors left on the finished part. It reveals for the first time that the surface topography of the finished thin-plate part is formed by the repeated cutting with the bottom edge of the cutter (BEC) in end milling. Owing to the coupling between the axial cutting depth (ACD) and the force-induced deflection, the modified ACDs for compensation of the static wall thickness errors are finally determined by an iterative adjustment method. The proposed method is verified by three-axis end milling experiments. The experiment results show that the predicted wall thickness errors match well with the really measured ones, and the errors are reduced by 77.18% with the help of the proposed compensation method. Moreover, the proposed FE model reduces the computational time elapsed for error prediction by 67.44% as compared with the benchmark FE model.     

Chatter vibration surveillance by the optimal-linear spindle speed control

The paper concerns self-excited chatter vibration during high speed slender ball-end milling. Non-stationary cutting process, with inclusion of various approaches towards dynamic characteristics of the process, is described. Dynamic analysis of the milling process is performed and dynamics of controlled closed loop system with time-delay is presented. In order to reduce vibration level, instantaneous change in the spindle speed appears as a control command, and thus—the method of vibration surveillance by the spindle speed optimal-linear control is developed. Presented cutting models have been applied for the proposed method and procedure of the chatter vibration surveillance with a use of variable spindle speed has been developed. Computer simulations are performed for selected cases of ball-end milling at constant and variable spindle speed. The results of them are successfully confirmed by experimental investigations on the Alcera Gambin 120CR milling machine equipped with the S2M high speed electrospindle.     

Identifying bifurcation behavior during machining process for an irregular milling tool geometry

High-productivity machining processes cause tool and material defects and even damages in machine spindles. The onset of self-excited vibration, known as chatter, limits this high material removal rate. This chatter vibration refers to machining instability during cutting processes, which results in bifurcation behavior or nonlinear effect wherein the tool and the workpiece are not engaged with each other. In particular, bifurcation for low-radial immersion conditions can be easily promoted and identified. In this study, an experiment on an irregular milling tool as a variable helix and variable pitch geometry was conducted under a flexible workpiece condition. The bifurcation behavior from regenerative chatter was identified and quantified from displacement sensor and inductive sensor measurements. A series of cutting tests was used to measure the vibration signals, which were then analyzed based on the frequency spectrum, the one-per-revolution effect, and the Poincaré section. According to results, Hopf bifurcation and period-one bifurcation instabilities apparently occurred to validate chatter stability prediction through a semi-discretization method. However, period-doubling bifurcation was only determined during the unstable cutting of a uniform tool that was not in variable helix/pitch or an irregular milling tool. An irregular tool geometry caused the modulation of the regenerative effect to suppress chatter, and period-doubling instability could not be exhibited during cutting as a regular tool behavior. This period-one chatter instability of an irregular milling tool should be identified and avoided by practitioners to achieve high productivity in machining using the aforementioned irregular milling tools.     

A grey-fuzzy modeling for evaluating surface roughness and material removal rate of coated end milling insert

The prime factor for selecting equipment is its performance capability and reliability without compromising on quality. Materials for aerospace application such as aluminum and its alloys have limited applications because of their complications in machining, effectively and economically. There is no further development in raising the effectiveness above the optimal level in cutting tool materials. The surface roughness influences the determination of the quality of the product. The present study focuses on finding optimal end milling process parameters by considering multiple performance characteristics using grey fuzzy approach. In this work, Aluminum Alloy 6082T6 (AA6082T6) is used as workpiece material which was end milled using Aluminum Chromo Nitride (AP3) coated milling insert. Three process performance parameters namely Centre Line Average Roughness (Ra), Root Mean Square Roughness (Rq) and Material Removal Rate (MRR) were optimized. The grey output is fuzzified into five membership functions and also with twenty-seven rules. Grey Fuzzy Reasoning Grade (GFRG) is developed and the optimal values were found out from the Grey relational grade. The result of the Analysis of Variances (ANOVA) shows that the maximum contribution in the depth cut is (31.785%) followed by feed (28.212%). Moreover, Adaptive Neuro-Fuzzy Inference System (ANFIS) model has been developed with the help of the same input values compared to the performance of the fuzzy logic model. With the help of detailed analysis, it has been found that the fuzzy logic based model gives more reasonable results when compared to ANFIS model.     

Investigation of surface integrity in end milling of 55NiCrMoV7 die steel under the cryogenic environments

Abstract

Cryogenic assisted machining is experiencing growing popularity and acceptance as a toxic-free, eco-friendly, hazardless process producing improved structural components. This article deals with the analysis of 3D and 2D roughness profiles, surface morphology, residual stress and microhardness of 55NiCrMoV7 die steel after end milling operation under dry, wet, cryogenic CO₂ and LN₂ cooling environments. Among different cooling methods, the cryogenic CO₂ was seen enhancing the surface topography and morphology due to the presence of minimal wear track. The result indicates the production of an insignificant amount of residual stress in the machined surface by the cooling environments at a spindle speed of 1989?rpm and feed rate of 0.02?mm/rev. The surface microhardness values were higher under cryogenic conditions compared to dry and wet conditions. Cryogenic LN₂ provided the highest microhardness value among the four cooling methods.     

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.     

数控铣床加工端面螺纹的方法

利用数控铣床的宏程序功能与端面螺纹的阿基米德螺旋线特性来加工端面螺纹,具有工艺设计简单,程序编制简单,经济性好的特点;通过对端面螺纹加工的工艺分析和宏程序编制方法的详细论述,介绍了端面螺纹在数控铣床上的加工过程。     

Optimum surface roughness in end milling Inconel 718 by coupling neural network model and genetic algorithm

In this study, optimum cutting parameters of Inconel 718 are determined to enable minimum surface roughness under the constraints of roughness and material removal rate. In doing this, advantages of statistical experimental design technique, experimental measurements, artificial neural network and genetic optimization method are exploited in an integrated manner. Cutting experiments are designed based on statistical three-level full factorial experimental design technique. A predictive model for surface roughness is created using a feed forward artificial neural network exploiting experimental data. Neural network model and analytical definition of material removal rate are employed in the construction of optimization problem. The optimization problem was solved by an effective genetic algorithm for variety of constraint limits. Additional experiments have been conducted to compare optimum values and their corresponding roughness and material removal rate values predicted from the genetic algorithm. Generally a good correlation is observed between the predicted optimum and the experimental measurements. The neural network model coupled with genetic algorithm can be effectively utilized to find the best or optimum cutting parameter values for a specific cutting condition in end milling Inconel 718.     

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.     

球头铣刀数控加工表面形貌几何仿真的研究

几何仿真是建立铣削力预测模型的基础,而传统的几何仿真只考虑刀具的平动而忽略其转动。本文在同时考虑刀具平动和转动的基础上,利用工件Z-Map表示模型和刀刃离散表示法,提出了一种球头铣刀三轴数控铣削的微观几何仿真算法。该算法鲁棒性好、适用范围广,不仅能高效而准确地仿真铣削表面形貌,而且能准确提供切屑的轮廓,为建立精确的切削力预测模型提供了重要的几何参数。     

A Novel Artificial Neural Networks Force Model for End Milling

The physical process of multipoint metal cutting depends on a large number of parameters that are strongly interlinked. A number of empirical and semimechanistic models are described in the literature. This paper uses the artificial neural networks (ANNs) approach to evolve a comprehensive model for critical process parameters, such as cutting force, based on a set of input machining conditions. A set of eight input variables is chosen to represent the machining conditions, and process parameters (such as maximum force and mean force) are predicted. Exhaustive experimentation is conducted to develop the model and to validate it. The model is tested for a typical machining scenario found in industry, namely pocket-milling. Excellent agreement between the simulated and experimental forces is found.