Swept surface determination for five-axis numerical control machining

This paper presents a closed-form solution of the swept profile of a generalized cutter in five-axis numerical control (NC) machining. The machine configurations and tool movements defined in NC programs are considered to model the true machine tool trajectory, which includes the linearly translational and rotational movements. Based on the machine tool trajectory and the cutter geometry, the cutter’s instantaneous swept profile is determined. By integrating the intermediate swept profiles, the cutter’s swept envelope can be constructed and applied to NC verification. The proposed method provides the explicit solution of the swept profile of a generalized cutter, which is important but not possible in the existing methods for five-axis NC verification. The computer implementations show that the approach developed is superior to the traditional methods.     

基于开放式系统的曲面加工误差动态补偿控制

将基于传感器信息的智能型开放加工系统应用于曲面的高精度加工,提出了曲面加工误差的动态补偿方法。为预测加工误差的补偿量,建立了刀具弯曲模型,分析了刀具弯曲对加工误差的影响。实验结果表明,本系统可有效地提高加工精度,使加工误差降低1／3－1／4。     

High-precision machining by measurement and compensation of motion error

This paper describes a systematic method to model and compensate geometric errors of machine tools. In order to separate geometric errors from other errors, measured errors are analyzed in the frequency domain by using the Fourier series. Then, the frequency components corresponding to geometric errors are selected based on the repeatability of their wavelength. Finally, the components are reconstructed and forwarded for the compensation by a fine motion drive. A CNC machine tool with a fine motion mechanism on the Z-axis was developed to compensate the error components in the Z direction on the XY plane. A flat surface machining with non-rotational cutting tools was tested to validate our approach. On the plane of 45 mm×70 mm, the fluctuation of the relative displacement was reduced from 1.3 to 0.5 μm P-V. Machining experiments with a single-crystal diamond tool were also carried out and the straightness of the profile curve was reduced from 1.0 to 0.4 μm. The result of the experiments showed that the geometric errors were compensated separately from the vibration due to the bending mode of the machine column.     

Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path

This paper presents an approach to predict cutting force in 3-axis ball end milling of sculptured surface with Z-level contouring tool path. The variable feed turning angle is proposed to denote the angular position of feed direction within tool axis perpendicular plane. In order to precisely describe the variation of feed turning angle and cutter engagement, the whole process of sculptured surface milling is discretized at intervals of feed per tooth along tool path. Each segmented process is considered as a small steady-state cutting. For each segmented cutting, the feed turning angle is determined according to the position of its start/end points, and the cutter engagement is obtained using a new efficient Z-map method. Both the chip thickness model and cutting force model for steady-state machining are improved for involving the effect of varying feed turning angle and cutter engagement in sculptured surface machining. In validation experiment, a practical 3-axis ball end milling of sculptured surface with Z-level contouring tool path is operated. Comparisons of the predicted cutting forces and the measurements show the reliability of the proposed approach.     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 2: Surface generation model and experimental verification

This paper presents a surface generation model for sculptured surface productions using the ball-end milling process. In this model, machining errors caused by tool deflections are studied. As shown in Part 1 of this paper, instantaneous horizontal cutting forces can be evaluated from the cutting geometries using mechanistic force models. In this paper, a tool deflection model is developed to calculate the corresponding horizontal tool deflection at the surface generation points on the cutter. The sensitivity of the machining errors to tool deflections, both in magnitude and direction, has been analyzed via the deflection sensitivity of the surface geometry. Machining errors are then determined from the tool deflection and the deflection sensitivity of the designed surface. The ability of this model in predicting dimensional errors for sculptured surfaces produced by the ball-end milling process has been verified by a machining experiment. In addition to providing a means to predict dimensional accuracy prior to actual cutting, this surface generation model can also be used as a tool for quality control and machining planning.     

虚拟加工设备的建模和加工过程物理仿真

介绍了虚拟加工设备建模的常用软件，并对虚拟数控机床和刀具的建模进行了讨论。着重研究了虚拟加工过程物理仿真，利用有限元（FEM）法建立了切削力仿真模型，利用多体系统运动学理论建立了虚拟数控机床的运动模型。最后，提出虚拟加工物理仿真技术发展中存在的问题以及未来的研究方向。     

An accurate,efficient envelope approach to modeling the geometric deviation of the machined surface for a specific five-axis CNC machine tool

Geometric deviation, defined as the difference between the nominal surface and the simulation model of the machined surface, is the fundamental concern of five-axis tool path planning. Since the machined surface is part of the cutter envelope surface generated by the cutter motion, it is necessary to calculate the envelope surface in order to obtain the geometric deviation. In the stage of tool path planning, current approaches calculate the cutter envelope surface by using the cutter motion along the given tool path. However, the cutter motion of practical machining on a specific five-axis CNC machine tool is different from the given tool path. Moreover, the computation is very challenging when the accurate cutter motion of practical machining is applied to calculate the envelope surface. To overcome these two problems, a geometric envelope approach with two major distinctions is proposed in this paper. First, the envelope surface of the cutter undergoing a general motion is efficiently obtained as a closed-form vector expression. Second, the accurate cutter motion, which is determined by machine kinematic and interpolation scheme in practical machining, can be easily applied to calculate the accurate envelope surface. With the envelope surface, the geometric deviation is calculated to estimate the overcut or undercut in five-axis milling. An example is given to demonstrate the validity of the proposed method.     

Identification and compensation of geometric errors of rotary axes on five-axis machine by on-machine measurement

The geometric errors of rotary axes are the fundamental errors of a five-axis machine tool. They directly affect the machining accuracy, and require periodical measurement, identification and compensation. In this paper, a precise calibration and compensation method for the geometric errors of rotary axes on a five-axis machine tool is proposed. The automated measurement is realized by using an on-the-machine touch-trigger technology and an artifact. A calibration algorithm is proposed to calibrate geometric errors of rotary axes based on the relative displacement of the measured reference point. The geometric errors are individually separated and the coupling effect of the geometric errors of two rotary axes can be avoided. The geometry error of the artifact as well as its setup error has little influence on geometric error calibration results. Then a geometric error compensation algorithm is developed by modifying the numeric control (NC) source file. All the geometric errors of the rotary errors are compensated to improve the machining accuracy. The algorithm can be conveniently integrated into the post process. At last, an experiment on a five-axis machine tool with table A-axis and head B-axis structure validates the feasibility of the proposed method.     

Fast calibration and modeling of thermally-induced machine tool errors in real machining

Calibration and modeling of thermally induced errors is a critical part of enhancing machine accuracy by software error compensation. In most applications, parametric thermal errors of a machine tool are calibrated and modeled individually by air-cutting experiments. Calibrating thermal errors individually is time-consuming and may neglect thermal interaction among thermal sources. The accuracy of the air-cutting model in real machining is also questionable. In this report, thermal errors of multiple machine axes in real cutting were calibrated simultaneously by a quick set-up measurement system consisting of on-machine probes and artifacts. Characteristics of thermal errors in real cutting under different cutting conditions, cutting paths and workpiece materials were investigated. It was found that thermal errors in real machining were distinct from those in air cutting.     

Milling error prediction and compensation in machining of low-rigidity parts

The paper reports on a new integrated methodology for modelling and prediction of surface errors caused by deflection during machining of low-rigidity components. The proposed approach is based on identifying and modelling key processing characteristics that influence part deflection, predicting the workpiece deflection through an adaptive flexible theoretical force-FEA deflection model and providing an input for downstream decision making on error compensation. A new analytical flexible force model suitable for static machining error prediction of low-rigidity components is proposed. The model is based on an extended perfect plastic layer model integrated with a FE model for prediction of part deflection. At each computational step, the flexible force is calculated by taking into account the changes of the immersion angles of the engaged teeth. The material removal process at any infinitesimal segment of the milling cutter teeth is considered as oblique cutting, for which the cutting force is calculated using an orthogonal–oblique transformation. This study aims to increase the understanding of the causes of poor geometric accuracy by considering the impact of the machining forces on the deflection of thin-wall structures. The reported work is a part of an ongoing research for developing an adaptive machining planning environment for surface error modelling and prediction and selection of process and tool path parameters for rapid machining of complex low-rigidity high-accuracy parts.     

螺旋锥齿轮数控铣齿加工过程几何仿真研究

利用面相对象技术和CAD系统的三维建模功能及其ObjectARX技术，根据螺旋锥齿轮的加工原理，提出了CNC铣齿机、齿坯和刀具三维模型的构建方法以及基于全局光照明的加工环境光照计算的具体方法。利用齿坯实体模型和刀具实体模型做布尔减运算，来实现模拟工件材料的去除过程；同时，采用全局光照明模型建立了具有真实感的数控加工虚拟现实环境。实际应用表明，该系统不但实现了螺旋锥齿轮的计算机辅助铣齿，提高了加工效率，降低了加工成本；而且还提供了非常真实的仿真效果。所获仿真结果可为齿面接触分析、有限元应力分析、齿轮的数控加工等提供精确的三维几何模型。     

螺旋锥齿轮端铣加工刀位计算方法

针对螺旋锥齿轮在数控加工中心上加工效率低的问题,提出利用盘状铣刀对螺旋锥齿轮进行端铣的加工方法.由螺旋锥齿轮齿面及刀具的几何特征,调整铣刀与被加工齿面的相对位置,使齿面与刀具包络面的法截面相对法曲率最小,增大切削带宽,同时控制刀轴矢量调整切削深度避免加工干涉.最后将规划的加工刀位转化到数控机床轴上,利用VERICUT进行加工仿真验证该方法的可行性与正确性.     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1: Chip geometry analysis and cutting force prediction

The study of machining errors caused by tool deflection in the balkend milling process involves four issues, namely the chip geometry, the cutting force, the tool deflection and the deflection sensitivity of the surface geometry. In this paper, chip geometry and cutting force are investigated. The study on chip geometry includes the undeformed radial chip thickness, the chip engagement surface and the relationship between feed boundary and feed angle. For cutting force prediction, a rigid force model and a flexible force model are developed. Instantaneous cutting forces of a machining experiment for two 2D sculptured surfaces produced by the ball-end milling process are simulated using these force models and are verified by force measurements. This information is used in Part 2 of this paper, together with a tool deflection model and the deflection sensitivity of the surface geometry, to predict the machining errors of the machined sculptured surfaces.     

基于多体系统理论的车铣中心空间误差模型分析

数控机床的误差建模是进行机床运动设计、精度分析和误差补偿的关键技术,也是保证机床加工精度的重要环节.本文利用多体系统理论来构建超精密数控机床的几何误差模型,该模型简便、明确,不受机床结构和运动复杂程度的限制,为计算机床误差、实现误差补偿和修正控制指令提供了理论依据.在机床实际应用中,可以利用由精密机床误差建模所推导出的几何位置误差来修正理想加工指令,控制机床的实际运动,从而实现几何误差补偿,提高机床加工精度.     

Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool

This paper proposes an efficient and automated scheme to predict and identify the position and motion errors of rotary axes on a non-orthogonal five-axis machining centre using the double ball bar (DBB) system. Based on the Denavit-Hartenberg theory, a motion deviations model for the tilting rotary axis B and rotary C of a non-orthogonal five-axis NC machine tool is established, which considers tilting rotary axis B and rotary C static deviations and dynamic deviations that total 24. After analysing the mathematical expression of the motion deviations model, the QC20 double ball bar (DBB) from the Renishaw Company is used to measure and identify the motion errors of rotary axes B and C, and a measurement scheme is designed. With the measured results, the 24 geometric deviations of rotary axes B and C can be identified intuitively and efficiently. This method provides a reference for the error identification of the non-orthogonal five-axis NC machine tool.     

Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics

Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. By synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool–workpiece interface for error compensation.     

并联机床数控加工的刀具瞬时包络面轮廓线研究

文章对用并联机床进行曲面加工,处于两个加工刀位之间的刀具的平移和旋转的运动速度进行了分析.通过引入在一般运动情况下(包括旋转和平移),通用锥形刀具的瞬时包络面轮廓线的求解公式,得到了用并联机床数控加工中刀具的瞬时包络面轮廓线的解法.对这些轮廓线进行放样处理就可以创建刀具的包络面体.应用上述研究成果可以模拟并联机床曲面加工中已加工表面的形状,文中最后给出了计算实例并进行了验证.     

The form error prediction in side wall machining considering tool deflection

In this research, an effective method for the form error prediction in side wall machining with a flat end mill is suggested. The form error is predicted directly from the tool deflection without surface generation by cutting edge locus with time simulation. The developed model can predict the surface form error accurately about 300 times faster than the previous method. Cutting forces and tool deflection are calculated considering tool geometry, tool setting error and machine tool stiffness. The characteristics and the difference of generated surface shape in up milling and down milling are discussed. The usefulness of the presented method is verified from a set of experiments under various cutting conditions generally used in die and mold manufacturing. This study contributes to real time surface shape estimation and cutting process planning for the improvement of form accuracy.     

准双曲面齿轮数控加工仿真系统设计

根据准双曲面齿轮数控加工原理,提出了CNC铣齿机、齿轮毛坯和盘铣刀实体模型的具体构建方法;利用简化的齿轮毛坯实体模型和盘铣刀实体模型做布尔减运算,在计算机上实现了模拟工件材料的去除过程;通过加工仿真结果和实际加工结果对比,验证了加工仿真方法的正确性.所获得的仿真结果可为齿面接触分析和有限元应力分析提供精确的实体模型.