Predictive framework for cutting force induced cylindricity error estimation in end milling of thin-walled components

The static deflections of cutting tool and workpiece are the primary source for the deviation of machined components from the design specifications during end milling of thin-walled geometries. The deviations are expressed as per the Geometric Dimensioning and Tolerancing (GD&T) principles using size, form, and orientation of the features. This paper proposes a computational framework to estimate cutting force induced cylindricity error during end milling of thin-walled circular components. The framework combines computational elements such as Mechanistic force model, Finite Element Analysis (FEA) based workpiece deflection model, Cantilever beam formulation based tool deflection model, and Particle Swarm Optimization (PSO) based cylindricity estimation algorithm. It has been observed that the static deflections of a cutting tool and thin-walled component influence the cylindricity error considerably. The inevitable aspects associated with the end milling of thin-walled circular components such as concave-convex side machining and workpiece rigidity are investigated subsequently. It was observed that the cylindricity error during concave side machining is considerably smaller due to geometric configuration imparting adequate stiffness to thin-walled components. The study also demonstrated that an appropriate combination of productive cutting conditions and the component thickness could reduce cylindricity error considerably. The outcomes of the present study are substantiated by conducting a set of computational simulations and end milling experiments over a wide range of cutting conditions. The computational framework proposed in the present study can assist process planners in selecting appropriate cutting conditions to manufacture thin-walled circular components within tolerance limits specified by the designer.     

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]     

数控机床几何误差的综合建模与补偿

对数控机床进行误差补偿是提高数控机床加工精度的有效方法.而建立快速准确的误差模型又是实施误差补偿的前提和基础.以三轴数控机床为对象,建立综合误差模型.     

关于逆向车削加工细长轴误差的力学分析

针对细长轴车削加工，分别在两种不同装夹条件下(一端卡盘夹紧、一端顶尖支承和两端顶尖支承)进行正向切削和逆向切削时的工件变形进行了力学分析，建立了正逆向切削工件在切削力作用下产生弯曲变形的解析模型。具体算例表明：逆向切削时工件的弯曲变形以及由此引起的加工误差远小于同等条件下正向切削的变形和误差。该模型及分析结果可用于细长轴加工的工艺设计。     

数控车削加工误差整体数学模型的建立

数控加工的精度是制造业所最终追求的目标和判别零件加工合格与否的重要指标之一,对形成数控车削加工误差的相关因素进行了分析,在误差敏感方向上,将多种影响加工精度的单项误差叠加起来,建立一种预测数控车削加工误差的算法,并在实际数控车削加工中得到应用。     

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.     

数控机床几何误差补偿器的实验研究

介绍一种由单片机控制的数控机床几何误差补偿器.误差补偿的原理主要是运用多体系统运动学理论建立机床几何误差模型,用单片机控制固化在程序存储器内的误差补偿程序完成补偿任务,并通过RS-232C实现数控机床与误差补偿器的通信与数据交换.     

A comprehensive error compensation system for correcting geometric, thermal, and cutting force-induced errors

A comprehensive error compensation system has been developed to correct geometric, thermal, and cutting force-induced errors on a turning centre. The basic approach to error compensation is proposed in this paper. The implementation of error compensation control and of hardware configuration of the system are also presented. A total of 11 geometric and thermal error components and 10 cutting force-induced error components can be compensated for using this system. Performance evaluations have been carried out using actual cutting tests. Experimental results show that the diameter accuracy of the part has been improved more than 5 times and taper accuracy of the part has been improved about 5 times.     

大型回转工作台安装调试中的误差分离与补偿技术的研究

首先建立了大型回转工作台的物理模型,根据这一模型建立了工作基面对地理坐标系的姿态变换矩阵,采用全微分法进行误差分离,推导得到了工作基面的姿态误差理论公式,并用一试验系统进行了验证。为大型回转工作台的校正提供了测试理论和方法。     

Relationship between geometric errors of thrust plates and error motions of hydrostatic thrust bearings under quasi-static condition

A new model using approximate formulas is established to predict the error motions of hydrostatic thrust bearings. Three different types of geometric errors of thrust plates are listed in this paper including tilt errors, saddle shaped errors and petal shaped errors. The influences of them on lateral tilt error motion, longitudinal tilt error motion and axial error motion are discussed. Definitions of averaging coefficients are made based on the approximate formulas. It is found that the time-varying tilt errors are the main reason for the error motions of hydrostatic thrust bearings. The thrust bearings with six pairs of recesses have priority over the thrust bearings with four and three pairs of recesses in the view of rotation accuracy. Experiments are done using a hydrostatic rotary table with an outer diameter of 2 m. It is found that the second harmonic errors are the main component of the radial run-out and the results agree well with the results calculated from the approximate formulas.     

Investigation and prediction of chip geometry in diamond turning

Management of the chips generated in diamond turning is often critical, because contact between chips and the workpiece can result in superficial damage to the finished surface. Controlling chip motion is not a trivial process as the proper positioning of an oil or air stream requires an understanding of the dynamics of a diamond turned chip and the machining parameters that affect it. Work has been performed to investigate the effects of cutting speed, depth of cut, tool geometry, tool wear, and workpiece material properties on chip motion and geometry. Utilizing radius of curvature data from cutting experiments, a parameter has been proposed that can be used to predict chip radius of curvature for a wide range of machining conditions. This chip curvature parameter, χ, exhibits a power law relationship with chip radius of curvature as a function of tool geometry, depth of cut, cutting speed, and both elastic and plastic properties of the workpiece material.     

Five axis machine tool volumetric error prediction through an indirect estimation of intra- and inter-axis error parameters by probing facets on a scale enriched uncalibrated indigenous artefact

The volumetric accuracy of five-axis machine tools is affected by intra-axis geometric errors (error motions) and inter-axis geometric errors (axes relative position and orientation errors). Self-probing of uncalibrated facets on the existing machine tool table is proposed to provide the necessary data for the self-calibration of the machine error parameters and of the artefact geometry using an indirect approach. A set of 86 non-confounded coefficients are selected from the ordinary cubic polynomials used to model both the intra- and inter-axis errors. A scale bar is added to provide the isotropic scale factor. The estimated model is then used to predict the actual tool to workpiece position. Experimental trials are conducted on a five-axis horizontal machining centre using its original unmodified machine table as an artefact. For validation purposes only, the estimated artefact geometry is compared to accurate coordinate measuring machine (CMM) measurements. A study of the volumetric error predictive capability of the model for selected subsets of estimated error coefficients is also conducted.     

Volumetric performance evaluation of a laser scanner based on geometric error model

We discuss a geometric error model for those large volume laser scanners that have the laser source and a spinning prism mirror mounted on a platform that can rotate about the vertical axis. We describe the terms that constitute the model, address their effect on measured range and angles, and discuss the sensitivity of different two-face and volumetric length tests to each term in the model. We report on experiments performed using commercially available contrast targets to assess the validity of the proposed model. Geometric error models are important not only in improving the accuracy of laser scanners, but also in facilitating the identification of test procedures for performance evaluation of these instruments and therefore in the development of documentary Standards. The work described in this paper lays the foundation for such efforts.     

数控机床空间几何误差测量研究进展

数控机床是衡量国家制造装配业水平的重要标志,数控机床的加工精度是反映其性能和水平的一个关键指标。误差补偿是提高数控机床加工精度的一个主要途径和发展趋势,数控机床空间误差快速、精确测量是进行误差补偿、提高数控机床精度的前提与关键。如何快速准确测量数控机床各种误差成为国内外测量域的一个研究热点和重点,出现了很多不同类型的测量方法和仪器。按测量仪方法及仪器与测量策略这两条主线,对现有数控机床空间几何误差测量方法进行较全面介绍,分析了各种方法的优缺点,讨论了其发展趋势。     

Machining accuracy improvement for a dual-spindle ultra-precision drum roll lathe based on geometric error analysis and calibration

This paper performs a comprehensive analysis and calibration on the geometric error of the ultra-precision drum roll lathe with dual-spindle symmetrical structure and cross slider layout. Firstly, the volumetric error model which contains all geometric errors of the dual-spindle ultra-precision drum roll lathe (DSUPDRL) is developed based on the combination of the homogenous transfer matrix (HTM) and multi-body system (MBS) theory. Secondly, sensitivity analysis for the volumetric error model is conducted to identify the sensitive geometric error components of the DSUPDRL using an improved Sobol method based on the quasi-Monte Carlo algorithm. The result of sensitivity analysis laid the foundation for the subsequent geometric error calibration. Then, some sensitive error components along the X and Z directions are calibrated using a laser interferometer and a pair of inductance displacement probes. Besides the volumetric error model, the concentricity error caused by dual-spindle symmetrical structure is proposed and calibrated by the on-machine measurement using a classic reversal method. Finally, a large-scale roller mold with a diameter of 250 mm and a length of 600 mm is machined using the DSUPDRL after calibration. The experimental result shows that 1.4 μm/600 mm generatrix accuracy is obtained, which validate the effectiveness of the geometric error analysis and calibration.     

A hybrid deep learning model for robust prediction of the dimensional accuracy in precision milling of thin-walled structural components

The use of artificial intelligence to process sensor data and predict the dimensional accuracy of machined parts is of great interest to the manufacturing community and can facilitate the intelligent production of many key engineering components. In this study, we develop a predictive model of the dimensional accuracy for precision milling of thin-walled structural components. The aim is to classify three typical features of a structural component—squares, slots, and holes—into various categories based on their dimensional errors (i.e., “high precision,” “pass,” and “unqualified”). Two different types of classification schemes have been considered in this study: those that perform feature extraction by using the convolutional neural networks and those based on an explicit feature extraction procedure. The classification accuracy of the popular machine learning methods has been evaluated in comparison with the proposed deep learning model. Based on the experimental data collected during the milling experiments, the proposed model proved to be capable of predicting dimensional accuracy using cutting parameters (i.e., “static features”) and cutting-force data (i.e., “dynamic features”). The average classification accuracy obtained using the proposed deep learning model was 9.55% higher than the best machine learning algorithm considered in this paper. Moreover, the robustness of the hybrid model has been studied by considering the white Gaussian and coherent noises. Hence, the proposed hybrid model provides an efficient way of fusing different sources of process data and can be adopted for prediction of the machining quality in noisy environments.     

自适应模糊系统在车削工件直径误差预测中的应用研究

根据车削过程中工件直径误差的特点,提出了用自适应模糊系统预测由弹性变形等因素引起的工件直径误差的思路,通过梯度下降算法训练M amdan i型模糊系统,以确定合理的系统参数。根据工件直径误差与切削深度、进给量等的关系,进行车削实验,得到训练数据和测试数据,用训练数据训练模糊系统,进而用测试数据进行测试,得到结果合理,从而验证了利用自适应模糊系统进行工件直径误差预测的可行性。和回归分析的预测值进行比较,比较结果显示了自适应模糊系统在车削工件直径误差预测方面的应用具有优势。     

Experimental investigation of surface roughness and cutting ratio in a spraying cryogenic turning process

Abstract

Surface roughness is one of the most common criteria indicating the surface finish of the part, which depends on various factors including cutting parameters, geometry of the tool, and cutting fluid. One of the goals of using cutting fluids in machining processes is to achieve improved surface finish. In addition to high costs, commonly used cutting fluids cause dermal and respiratory problems to the operators as well as environmental pollution. The present article aims at investigating the effect of spray cryogenic cooling via liquid nitrogen on surface roughness and cutting ratio in turning process of AISI 304 stainless steel. Through conducting experimental tests, the effects of cutting speed, feed rate, and depth of cut on surface roughness and cutting ratio have been compared in dry and cryogenic turning. A total number of 72 tests have been carried out. Results show that cryogenic turning of AISI 304 stainless steel reduces surface roughness 1%–27% (13% on the average), compared to dry turning. The obtained results showed that the cutting ratio in cryogenic turning is averagely increased by 32% in comparison with dry turning, also that chip breakage is improved in cryogenic turning.     

ARX Modelling and Compensation of Roundness Errors in Taper Turning

The forecasting compensatory control (FCC) strategy is successfully applied to the taper turning process to improve the roundness accuracy of the workpiece during cutting. This strategy, which is based on active error sensing, stochastic modelling and forecasting control, is capable of compensating both repeatable and non-repeatable errors. In the stochastic modelling, the effect of cutting force is considered, thus yielding an autoregressive model with exogeneous input (ARX). The resultant force is obtained from the outputs of the piezoelectric force sensor while the relative motion error between the tool and the workpiece is determined by means of a master taper and a capacitive sensor. The forecast error is sent to a piezoelectric actuator that moves the cutter to compensate for the error motion. Practical tests were performed on an experimental lathe with the FCC system using models with different orders and forgetting factors. A maximum improvement of 33% can be achieved by this FCC strategy using ARX (3,3) and forgetting factor of 0.997.     

Forced-based tool deviation induced form error identification in single-point diamond turning of optical spherical surfaces

In the single-point diamond turning (SPDT) of optical spherical/aspheric surface, tool deviating from the spindle rotation center significantly deteriorates the form accuracy of the spherical/aspherical surface and its optical performance. In this study, the influence of tool deviation on the form accuracy of a convex spherical surface and the cutting force forms during the turning process were studied first, following which a force-based tool deviation model was derived to identify the tool deviation using cutting force. Finally, by analyzing the influence of tool deviation on the three-dimensional (3D) form of residual structures at the center of the convex spherical surface, the 3D form of the convex spherical surface was predicted online. Results indicate the existence of a mapping relation between the tool deviation and the cutting force form, which could be further used to online predict the 3D form of the machined convex spherical surface in SPDT through the established geometric model.