Prediction of specific force coefficients from a FEM cutting model

This paper presents a method to obtain the specific cutting coefficients needed to predict the milling forces using a mechanistic model of the process. The specific coefficients depend on the tool–material couple and the geometry of the tool, usually being calculated from a series of experimental tests. In this case, the experimental work is substituted for virtual experiments, carried out using a finite element method model of the cutting process. Through this approach, the main drawbacks of both types of models are solved; it is possible to simulate end milling operations with complex tool geometries using fast mechanistic models and replacing the experimental work by virtual machining, a more general and cheap way to do it. This methodology has been validated for end milling operations in AISI 4340 steel.     

基于切削电流系数的铣刀磨损状态监测

基于切削力系数的铣刀磨损状态监测方法提出了与切削参数独立的刀具磨损指标。由于存在干扰机床正常加工、实时性不佳、传感器安装不便和成本过高等问题,限制了其在实际工业环境中的应用。针对上述问题,结合切削力与主轴电流的关系,提出一种基于主轴切削电流系数的铣刀磨损状态监测方法。首先,融合切削力系数和主轴电流的优点,建立铣削电流模型;其次,根据切削电流模型进行切削电流系数辨识,记录新刀状态下切削系数;然后,使用切削系数实时估计相同加工工况下新刀切削电流,监测实际切削电流偏离估计值的程度,判断铣刀磨损状态;最后,通过实验与力信号对比验证该方法的正确性。实验结果表明,该方法可以替代基于切削力系数的磨损状态监测方法,能有效、实时、无干扰、便利和低成本地识别新刀、正常和严重3种磨损状态。     

CORRELATION-BASED ESTIMATION OF CUTTING FORCE COEFFICIENTS FOR BALL-END MILLING

This article presents a methodology to estimate cutting force coefficients based on the least squares approximation using correlation factor between the estimated and measured cutting forces in order to determine the corresponding tool angular position. This method can be applied on measured cutting force data over any small interval of time that need not contain information of the time instant when the cutting tool enters the workpiece, which has been the main requirement in the conventional method. This allows a quick estimation of the cutting force coefficients regardless of the chosen cutting conditions and tool-workpiece material, which is often the case in industrial machining processes. This proposed method has been validated by comparison of cutting force coefficients obtained using conventional estimation technique for a slot ball-end milling test. Besides being useful for predictive evaluation of forces, such estimation of cutting force coefficients of the cutting force model can be useful for understanding variations in cutting process over the tool life and can assist in online monitoring and process optimization.     

Modelling the cutting forces in micro-end-milling using a hybrid approach

This paper presents the development of a cutting force model for the micro-end-milling processes under various cutting conditions using a hybrid approach. Firstly, a finite element (FE) model of orthogonal micro-cutting with a round cutting edge is developed for medium-carbon steel. A number of finite element analyses (FEA) are performed at different uncut chip thicknesses and velocities. Based on the FEA results, the cutting force coefficients are extracted through a nonlinear algorithm to establish a relationship with the uncut chip thickness and cutting speed. Then, the cutting force coefficients are integrated into a mechanistic cutting force model, which can predict cutting forces under different cutting conditions. In order to account for the cutting edge effect, an effective rake angle is employed for the determination of the cutting force. A comparison of the prediction and experimental measured cutting forces has shown that the developed method provides accurate results.     

Improved dynamic cutting force model in ball-end milling. Part I: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper.     

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.     

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.     

An Improved Method for the Determination of 3D Cutting Force Coefficients and Runout Parameters in End Milling

A simple improved method is suggested for determining constant cutting force coefficients, irrespective of the cutting condition and cutter rotation angle. This can be achieved through the combination of experimentally deternimed cutting forces with those from simulation, performed by a mechanistic cutting force model and a geometric uncut chip thickness model. Additionally, this study presents an approach that estimates runout-related parameters, and the runout offset and its location angle, using only one measurement of cutting force. This method of estimating 3D end milling force coefficients was experimentally verified for a wide range of cutting conditions, and gave significantly better predictions of cutting forces than any other methods. The estimated value of the runout offset also agreed well with the measured value.     

3D FE MODELLING OF SUPERFICIAL RESIDUAL STRESSES IN TURNING OPERATIONS

In this paper, the residual stresses on workpiece surface after cutting operations are studied by means of 3D finite element method (FEM) simulations and the results are compared with the experiments. In particular, the effects of feed rate and tool nose radius on the final workpiece residual stresses when turning AISI 1045 steel bars were analyzed; two different approaches were utilized for the simulative models. In the first approach incremental Lagrangian and Eulerian solvers were coupled to reach both mechanical and thermal steady state conditions performing a single cutting pass, while the second approach consisted of an incremental Lagrangian simulation in which consecutive turning passes were considered in order to reach mechanical and thermal steady state. The simulation results were finally compared with the experimental ones: the agreement between them is satisfactory even if the numerical errors are, in some cases, remarkable.     

COMBINED EFFECTS OF FLANK AND CRATER WEAR ON CUTTING FORCE MODELING IN ORTHOGONAL MACHINING—PART II: BAYESIAN APPROACH-BASED MODEL VALIDATION

Flank and crater wear are the primary tool wear patterns during the progressive tool wear in metal cutting. Cutting forces may increase or decrease, depending on the combined contribution from the flank and/or crater wear. A two-dimensional (2D) slip-line field based analytical model has been proposed to model the force contributions from both the flank and crater wear. To validate the proposed force model, the Bayesian linear regression is implemented with credible intervals to evaluate the force model performance in orthogonal cutting of CK45 steels. In this study, the proposed analytical worn tool force model-based predictions fall well within the 75% credible intervals determined by the Bayesian approach, implying a satisfactory modeling capability of the proposed model. Based on the parametric study using the proposed force model, it is found that cutting forces decrease with the increasing crater wear depth but increase with the increasing flank wear length. Also, the predicted cutting forces are affected noticeably by the friction coefficients along the rake and flank faces and the ratio of crater sticking region to sliding region, and better knowledge of such friction coefficients and ratio is expected to further improve worn tool force modeling accuracy. Compared with the finite element approach, the proposed analytical approach is efficient and easy to extend to three-dimensional worn tool cutting configurations.     

Prediction of cutting forces in helical milling process

The prediction of cutting forces is important for the planning and optimization of machining process in order to reduce machining damage. Helical milling is a kind of hole-machining technique with a milling tool feeding on a helical path into the workpiece, and thus, both the periphery cutting edges and the bottom cutting edges all participated in the machining process. In order to investigate the characteristics of discontinuous milling resulting in the time varying undeformed chip thickness and cutting forces direction, this paper establishes a novel analytic cutting force model of the helical milling based on the helical milling principle. Dynamic cutting forces are measured and analyzed under different cutting parameters for the titanium alloy (Ti–6Al–4V). Cutting force coefficients are identified and discussed based on the experimental test. Analytical model prediction is compared with experiment testing. It is noted that the analytical results are in good agreement with the experimental data; thus, the established cutting force model can be utilized as an effective tool to predict the change of cutting forces in helical milling process under different cutting conditions.     

A separate-edge force coefficients’ calibration method using specific condition for cutters with variable helix and pitch angles combining the runout effect

Classical ways of computing cutting force coefficients cannot be used by the cutters with non-uniform helix and pitch angles. So, this paper presents a novel separate-edge-forecast method to compute cutting force coefficients for any kind of flank-end cutter, especially for cutters with non-uniform helix and pitch angles. Using this method, the cutter runout can be combined into the cutting force coefficients without computing the cutter runout parameters. Simultaneously, the method predicts the cutting force coefficients for every cutter edge. Firstly, a series of three-axis machining experiments, which must satisfy the specific condition that only one cutter edge is removing materials at any time, is conducted. Then, the cutting force-curves are divided into N force lobes. Each lobe is assigned to the corresponding cutter edge using an algorithm. Subsequently, the cutter edge and the corresponding cutting force lobe are used to determine the cutting force coefficients. This means N cutter edges have N groups of cutting force coefficients, correspondingly. Finally, in order to verify the validity and correctness of the proposed method, a cutter with non-uniform helix and pitch angle is utilized to predict cutting force coefficients based on which the cutting forces are also computed. The results demonstrate that the cutting forces predicted agree well with the data measured. Simultaneously, it can be observed that the method can predict the coefficients considering the cutter runout effect.     

STABILITY LOBES PREDICTION FOR CORNER RADIUS END MILL USING NONLINEAR CUTTING FORCE COEFFICIENTS

There are a vast number of different types of end mill tools used in the manufacturing industry, each type with a unique shape. These tool shapes have a direct influence on the cutting force it generates during machining. This article presents a more accurate approach to predicting the stability margin in machining by considering the cutting force coefficients and axial immersion angle as variables along the axial depth of cut. A numerical approach to obtaining a converged solution to the stability model is presented. The results obtained are validated using experimental results and a very good agreement is seen.     

Precision radial turning of AISI D2 steel

This paper compares finite element model (FEM) simulations with experimental and analytical findings concerning precision radial turning of AISI D2 steel. FEM machining simulation employs a Lagrangian finite element-based machining model applied to predict cutting and thrust forces, cutting temperature and plastic strain distribution. The results show that the difference between the experimental and simulated cutting force is near 20%, irrespectively of the friction coefficient used in the simulation work (approximately 19.8% for a friction of 0.25% and 18.4% for the Coulomb approach). Concerning the thrust force, differences of about 22.4% when using a friction coefficient of μ?=?0.25 and about 56.9% when using the Coulomb friction coefficient (μ?=?0.378) were found. The maximum cutting temperature obtained using the analytical model is 494.07°C and the difference between experimentation and simulation methods is 15.2% when using a friction coefficient of 0.25 and when using the Coulomb friction only 3.1%. Regarding the plastic strain, the differences between analytical calculations and FEM simulations (for the presented friction values) suggest that the finite element method is capable of predictions with reasonable precision.     

Prediction of cutting forces in mill turning through process simulation using a five-axis machining center

Mill turning is a process applied in the milling of a curved surface while the workpiece rotates around its center. Depending on the eccentricity of the tool, when a flat-end mill tool performs a curved trajectory perpendicular to the rotation axis of the tool, its bottom part is engaged in removing material. In order to optimize the process, the cutting force needs to be predicted. Hence, in this work, an approach to simulating the cutting force in mill turning is presented. The case of non-eccentricity of the tool is considered. The undeformed chip geometry is modeling as a function of the tool engagement considering the process kinematics. Experiments were conducted on a five-axis machining center enabling the measurement of the X–Y and Z components of the cutting forces. In order to verify the influence of the bottom part of the tool on the cutting forces, experiments were carried out using three different cutting depths. Numerical cutting simulations and experimental test results are compared to validate the proposed approach.     

OPTIMIZATION OF THE CUTTING EDGE GEOMETRY OF COATED CARBIDE TOOLS IN DRY TURNING OF STEELS USING A FINITE ELEMENT ANALYSIS

This paper investigates the effects of edge radius of a round-edge coated carbide tool on chip formation, cutting forces, and tool stresses in orthogonal cutting of an alloy steel 42CrMo₄ (AISI 4142H). A comprehensive experimental study by end turning of thin-walled tubes is conducted, using advanced coated tools with well-defined cutting edge radii ranging from 5 to 68 microns. In parallel, 2-D finite element cutting simulations based on Lagrangian thermo-viscoplastic formulation are used to predict the cutting temperatures and tool-stress distributions within the tool coating and substrate. The results obtained from this study provide a fundamental understanding of the cutting mechanics for the coated carbide tool used, and can assist in the optimization of tool edge design for more complex geometries, such as chamfered edge. Specifically, the results obtained from the experiments and simulations of this study demonstrated that finite element analysis can significantly help in optimizing the design of coated cutting tools through the prediction of tool stresses and temperatures, especially within the coating layer.     

A new approach to the analysis of high-speed milling in the case of chipped inserts

High-speed milling permits to machine materials with increased productivity. For a reliable application of this strategy, it is crucial to avoid tool chipping during the machining; in practice, this implies underestimating tool life. The formation of chipping induces vibrations, high temperature on tool nose, and poor surface quality. This is a problem when it represents the last operation. A better comprehension of how a damaged insert works is useful to design a reliable monitoring system. More researches use several sensors to monitor the health state of the milling tool, like force signal, current signal, acceleration, acoustic emission, etc., and complex elaboration systems have been considered. The objective of this paper is the proposal of a model to analyze the chipping of multi-tooth milling tool. First milling tests are carried out on a milling center and cutting forces are measured. The experimental data were elaborated and a suitable model is set up. The finite element method (FEM) is considered and simulations were performed using SFTC Deform 2D^TM, a Lagrangian implicit solutor. The material model and the friction law are calibrated following an appropriate procedure. In this work, face milling using multi-tooth milling tool is considered. Face milling are very common operations in several industrial sectors. The results show the FEM model is able to simulate the standard deviation of feed force during the chipping. A regression model between chipping scar dimension and feed cutting force is presented in order to summarize the obtained results.     

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.     

Condition-based tool management for small batch production

This paper presents a novel tool management concept for cutting processes which integrates tool relevant information, such as distribution data, tool orders, tool condition, and allocation data, within a centralized information cycle. The developed tool management approach uses decentralized identification and storage technologies, enabling an autonomous cooperation of tools and machine tools within a production. The first part of the paper is focused on the assessment of tool condition in a flexible job shop production. A tool wear monitoring system based on cutting force coefficients is developed and demonstrated by an exemplary milling operation. Thereby, it is shown that cutting force coefficients are suitable for wear monitoring and prediction, even for varying cutting conditions. For the online assessment of the current tool condition and for the prediction of residual tool life, an empirical tool wear model is demonstrated. This is applied to a novel condition-based tool management strategy which enables the optimum exploitation of the life time and performance of the cutting tool. The developed condition-based tool management concept is finally demonstrated by a software demonstrator.     

CALCULATION OF THE SPECIFIC CUTTING COEFFICIENTS AND GEOMETRICAL ASPECTS IN SCULPTURED SURFACE MACHINING

This article presents a method for obtaining the shear and ploughing specific cutting coefficients for a ball-end milling cutting force model. Thus, by using the proposed calculation method, the need for introducing variable shear cutting coefficients has been identified. This fact is due to the dependency among the specific cutting coefficients and the cutting edge inclination angle, which is variable in ball-end mills. Linear, quadratic and cubic polynomial shear cutting coefficients have been calculated, and the degree of adjustment obtained in each approach has been analyzed. At the same time, the expressions of the ploughing specific coefficients have been analyzed. The proposed calculation method has been applied to the following materials: a 7075-T6 aluminum alloy and a 52HRC AISI H13 tool steel. The results obtained from the validation demonstrate how the obtained coefficients are capable of predicting cutting forces over a wide range of cutting conditions. Finally, the results from applying the coefficients calculated in horizontal slot milling tests have been introduced in a model capable of calculating cutting forces in slope milling cases, which validates the calculation method proposed as a generic method for estimation of cutting coefficients.