Modelling of dimensional and geometric error prediction in turning of thin-walled components

In die-mold manufacturing and aircraft industry, many components that have thin-walled features are produced by turning operation. The major problem encountered during internal or external turning is cutting force induced deflection of workpiece along the periphery as well as axial length of a component. The present research work aims to develop a mathematical model for estimating dimensional and geometric errors during turning of thin-walled hollow cylinder qualitatively and quantitatively. In the proposed model, a mechanistic approach which is semi-analytical in nature is followed to achieve accuracy of the predicting results. First of all, process geometry model for thin-wall turning is developed based on process geometry variables such as uncut chip thickness, actual feed per revolution, actual depth of cut, peripheral cutting speed, effective cutting area etc. Using these process geometry variables and mechanistic cutting constants, a force model of turning is developed to estimate the tangential and radial force components. Later on, based on the predicted forces, tool-workpiece combined deflection model is developed to estimate radial, diametric and various geometric errors of the turned surface. The developed models are able to predict radial, diametric and various geometric errors such as straightness, circularly and cylindricity errors without conducting expensive actual machining operation. Hence, the present study will be helpful to take care of precautionary measures for controlling of dimensional and geometric errors more efficiently and reliably. Therefore, an attempt has been made to provide a basic platform to machining practitioners and process planners for in-depth comprehension and characterization of dimensional and geometric errors of the entire turned surface for varying machining conditions.     

Optimal fixture design in peripheral milling of thin-walled workpiece

In order to optimize the positions of the locators in peripheral milling of a thin-walled workpiece, a finite element model along with an accurate cutting forces model is proposed in this paper. The finite element model takes into account the thickness variations of the workpiece in peripheral milling. The locators on the secondary locating surface directly influence the surface errors in peripheral milling of thin-walled workpiece, so this paper deals with the optimization of the positions of the locators on the secondary locating surface. A method including two steps is presented. In the first step, the initial positions of the locators are determined by adding the locators at the position with the maximum deformation. In the second step, a heuristic algorithm is proposed to optimize the positions of the locators. Finally, a simulation example is used to illustrate the method.     

基于误差分离技术的几种圆柱度测量模型分析

对国内提出的四点法、五点法、两测头法等几种典型的基于误差分离技术的圆柱度测量模型分别进行了分析，探讨了这些测量模型中存在的一些问题。     

Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error

Measurement uncertainty is one of the most important concepts in geometrical product specification (GPS). The “Guide to the expression of uncertainty in measurement (GUM)” is the internationally accepted master document for the evaluation of uncertainty. The GUM method (GUMM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the mathematical model of measurand is strongly non-linear the use of this linear approximation may be inadequate. Supplement 1 to GUM (GUM S1) has recently been proposed based on the basis of probability density functions (PDFs) using the Monte Carlo method (MCM). In order to solve the problem that the number of Monte Carlo trials needs to be selected priori, adaptive Monte Carlo method (AMCM) described in GUM S1 is recommended to control over the quality of the numerical results provided by MCM.The measurement and evaluation of cylindricity errors are essential to ensure proper assembly and good performance. In this paper, the mathematical model of cylindricity error based on the minimum zone condition is established and a quasi particle swarm optimization algorithm (QPSO) is proposed for searching the cylindricity error. Because the model is non-linear, it is necessary to verify whether GUMM is valid for the evaluation of measurement uncertainty of cylindricity error. Then, AMCM and GUMM are developed to estimate the uncertainty. The procedure of AMCM scheme and the validation of GUMM using AMCM are given in detail. Practical example is illustrated and the result shows that GUMM is not completely valid for high-precision evaluation of the measurement uncertainty of cylindricity error if only the first-order terms in the Taylor series approximation are taken into account. Compared with conventional methods, not only the proposed QPSO method can search the minimum zone cylindricity error precisely and rapidly, but also the Monte Carlo simulation is adaptive and AMCM can provide control variables (i.e. expected value, standard uncertainty and lower and higher coverage interval endpoints) with an expected numerical tolerance. The methods can be extended to the evaluation of measurement uncertainty of other form errors such as roundness and sphericity errors.     

A real time machining error compensation method based on dynamic features for cutting force induced elastic deformation in flank milling

During the machining process, cutting forces cause deformation of thin-walled parts and cutting tools because of their low rigidity. Such deformation can lead to undercut and may result in defective parts. Since there are various unexpected factors that affect cutting forces during the machining process, the error compensation of cutting force induced deformation is deemed to be a very difficult issue. In order to address this challenge, this article proposes a novel real time deformation error compensation method based on dynamic features. A dynamic feature model is established for the evaluation of feature rigidity as well as the association between geometric information and real time cutting force information. Then the deformations are calculated based on the dynamic feature model. Eventually, the machining error compensation for elastic deformation is realized based on Function Blocks. A thin-walled feature is used as an example to validate the proposed approach. Machining experiment results show that the errors of calculated deformation with the monitored deformation is less than 10%, and the thickness errors were between ?0.05 mm and +0.06 mm, which can well satisfy the accuracy requirement of structural parts by NC (Numerical Control) machining.     

Improved calculation of the cutting force in end milling

Determination of the cutting force in end milling on the basis of the Johnson–Cook phenomenological model is described. The numerical results obtained by this method are compared with experimental data.     

An enhanced method for cutting force estimation in peripheral milling

A new model for cutting force estimation is presented in this paper. It is based on the specific cutting force coefficient, which is defined as a function of chip thickness. The distinguishing feature of the proposed cutting force model is the use of average chip thickness for cutting force calculation on each position of the cutting tool, in such a way that only one iteration is needed on every angular position of the tool. This model is based on the actual workpiece–tool interaction which provides information about the real position of the cutting edge. It provides an alternative to other studies in scientific literature commonly based on numerical integrations. With this model, it is possible to estimate the cutting forces not only under steady-state conditions but also under variable machining conditions of axial and radial depth of cut.     

Tool wear monitoring system for CNC end milling using a hybrid approach to cutting force regulation

A tool wear monitoring system is indispensable for better machining productivity, with the guarantee of machining safety by informing of the time due for changing a tool in automated and unmanned CNC machining. Different from monitoring methods using other signals, the monitoring of the spindle current has been used without requiring additional sensors on the machine tools. For reliable tool wear monitoring, only the current signal from tool wear should be extracted from the other parameters to avoid exhaustive analyses on signals in which all of the parameters are fused together. In this paper, the influences of force components from different parameters on the measured spindle current are investigated, and a hybrid approach to cutting force regulation is employed for tool wear signal extraction from the spindle current. Finally, wear levels are verified with experimental results by means of real-time feedrate aspects, varied to regulate the force component from tool wear.     

Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.     

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.     

Prediction of cutting forces and machining error in ball end milling of curved surfaces -II experimental verification

This paper presents the results of a series of experiments performed to examine the validity of a theoretical model for evaluation of cutting forces and machining error in ball end milling of curved surfaces. The experiments are carried out at various cutting conditions, for both contouring and ramping of convex and concave surfaces. A high precision machining center is used in the cutting tests. In contouring, the machining error is measured with an electric micrometer, while in ramping it is measured on a 3-coordinate measuring machine. The results show that in contouring, the cutting force component that influences the machining error decreases with an increase in milling position angle, while in ramping, the two force components that influence the machining error are hardly affected by the milling position angle. Moreover, in contouring, high machining accuracy is achieved in “Up cross-feed, Up cut” and “Down cross-feed, Down cut” modes, while in ramping, high machining accuracy is achieved in “Left cross-feed, Downward cut” and “Right cross-feed, Upward cut” modes. The theoretical and experimental results show reasonably good agreement.     

矩形薄板侧铣加工变形预测与补偿技术研究

针对目前薄壁件加工的高精度要求与铣削加工变形之间的矛盾,基于ABAQUS建立了2Al2铝合金薄壁板侧铣加工变形的有限元预测模型,得到2Al2薄壁板的加工变形曲线,并据此提出一种通过在进给方向上刀心位置偏置和刀具轴向方向偏摆来同时进行补偿的方案.最后,用试验验证了有限元预测变形的可靠性和补偿策略的有效性.     

In-process estimation of radial immersion angle using cutting force in face milling

In this paper, a on-line estimation method of the radial immersion angle using cutting force is presented. The ratio of cutting forces in feed and cross-feed directions acting on the single tooth at the immersion angle is a function of the immersion angle and the ratio of radial to tangential cutting force. It is found that the ratio of radial to tangential cutting force is not affected by cutting conditions and axial rake angle, which implies that the ratio determined by one preliminary experiment can be used regardless of the cutting conditions for a given tool and workpiece material. Using the measured cutting force during machining and predetermined ratio, the radial immersion ratio is estimated in process. Various experimental results show that the proposed method works within5% error range.     

In-process estimation of radial immersion ratio in face milling using cutting force

In order to prevent tool breakage in milling, maximum total cutting force is regulated at a specific constant level, or threshold, through feed rate control. Since the threshold is a function of the immersion ratio, an estimation of the immersion ratio is necessary to flexibly determine the threshold. In this paper, a method of in-process estimation of the radial immersion ratio in face milling is presented. When an insert finishes sweeping, a sudden drop in cutting forces occurs. These force drops are equal to the cutting forces that act upon a single insert at the swept cutting angle and they can be acquired from cutting force signals in the feed and cross-feed directions. Average cutting forces per tooth period can also be calculated from the cutting force signals in two directions. The ratio of cutting forces acting upon a single insert at the swept angle of cut and the ratio of average cutting forces per tooth period are functions of the swept angle of cut and the ratio of radial to tangential cutting force. Using these parameters, the radial immersion ratio is estimated. Various experiments are performed to verify the proposed method. The results show that the radial immersion ratio can be estimated by this method regardless of other cutting conditions.Nomenclature F_T, F_R tangential and radial forces - F_X, F_Y cutting forces in feed direction and cross feed direction - dF_X, dF_Y cutting force differences before and after the immersion angle in X and Y direction - K_s specific cutting pressure - a depth of cut - r ratio between tangential force and radial force - s_t feed per tooth - instantaneous angle of cut - _s swept angle of cut - _T tooth spacing angle - w radial width of cut - R cutter radius - z number of inserts     

The estimation of the diameter error in bar turning: a comparison among three cutting force models

Machining accuracy is considerably affected by the deflection of the machine-tool-workpiece system under the action of the cutting force. A new model to estimate a bar diameter error due to the deflection of the tool, of the workpiece-holder and of the workpiece was defined by the authors, starting from a cutting force model. This work deals with a comparison among the bar diameter errors that are calculated by means of the developed model involving three different cutting force models. The considered cutting force models were the specific cutting resistance, the Kronenberg cutting force and the unified-generalised mechanics of the cutting force model developed by Armarego. The numerical results were compared with those obtained by experimental tests carried out through a parallel lathe. The results show that the Armarego's cutting force model provides values of the force components and, therefore, the values of the resulting bar diameter errors are closest to the experimental ones.Nomenclature a The longitudinal position of the tool, [mm] - a_pn The nominal depth of cut, [mm] - a_p The real depth of cut, [mm] - b The width of area of cut, [mm] - A The tool-workpiece interference area of cut, [mm²] - AB The generalised cutting edge vector - A_r The area of the workpiece cross section, [mm²] - c_s The spindle compliance, [mm/N] - c_t The tailstock compliance, [mm/N] - c_tht The tangential toolholder compliance, [mm/N] - c_thr The radial toolholder compliance, [mm/N] - D The workpiece diameter, [mm] - E The modulus of elasticity, [N/mm²] - f The feed, [mm/r] - F_rad The radial component of the cutting force, [N] - F_feed The feed component of the cutting force, [N] - F_{tan g} The tangential component of the cutting force, [N] - F_i The resultant of F_feed and F_{tan g}, [N] - G The shear modulus, [N/m²] - h The thickness of the area of the cut, [mm] - I The workpiece moment of inertia, [mm⁴] - L The workpiece length, [mm] - P_i The plane containing the inflected curve of the workpiece - P_f The tool assumed working plane - P_n The cutting edge normal plane - P_nG The generalised cutting edge normal plane - P_r The tool reference plane - r_l The chip length ratio - R The workpiece radius, [mm] - R_b The tailstock reaction force, [N] - R_s The spindle reaction force, [N] - S The shape factor - v_c The cutting speed, [mm/min] - v_e The resultant cutting speed, [mm/min] - v_f The feed speed, [mm/min] - v_ch The chip speed, [mm/min] - v_sh The shear speed, [mm/min] - w(z) The total deflection of the workpiece axis, [mm] - w_a The total displacement of the workpiece axis from z reference axis measured in P_i plane, [mm] - (z) The orientation of P_i with respect to F_rad and F_{tan g}, [degree] - The friction angle, [degree] - _n The normal friction angle, [degree] - _nG The generalised normal friction angle, [degree] - The shear factor - _n The normal shear angle, [degree] - _NG The generalised normal shear angle, [degree] - _f The tool side angle, [degree] - _n The tool normal rake angle, [degree] - _nG The generalised tool normal rake, [degree] - _P The tool back angle, [degree] - _c The chip flow angle, [degree] - _cG The generalised chip flow angle, [degree] - _r The tool cutting edge angle, [degree] - _rG The generalised tool cutting edge angle, [degree] - _s1 The tool cutting edge inclination, [degree] - _s2 The inclination of the secondary tool cutting edge [degree] - _sG The generalised tool cutting edge inclination, [degree] - The friction coefficient - The work material shear stress, [MPa] - _r The tool approach angle, [degree] - The approach angle of the secondary cutting edge, [degree]     

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

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.     

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.