Machineability in NURBS interpolator considering constant material removal rate

Increasing demands on precision machining of three-dimensional free-form surfaces have necessitated that the tool move smoothly and at varying feedrates. To achieve this, parametric interpolators, such as the Non-Uniform Rational B-Spline (NURBS) interpolator, have been introduced in CNC machining systems. Such interpolators reduce the data burden in the Numerical Control (NC) code, increase data transfer rate into the NC controller, and finally give smooth motion while machining. In this research, a new concept to control cutting load in a NURBS interpolator based on the degree of curvature was tried. This protects the cutting tool and improves machineability. To prove the system, cutting force and surface topography were evaluated. From the experimental results, the interpolator is adequate for machining a free-form surface.     

Fast real-time NURBS path interpolation for CNC machine tools

In this paper, a novel fast real-time non-uniform rational B-spline (NURBS) path interpolation method is presented. This method efficiently integrates the data processing of a NURBS path in a CNC controller, from pre-processing to real-time interpolation. In the calculation of the total length of the NURBS path, the numerical adaptive quadrature method adapts to the integrand, i.e. the first derivative of the length function, automatically, dividing the parameter interval into subintervals with fine or coarse spacing according to the varying condition of the integrand. This new method takes full advantage of the subdivision scheme. The key point is to generate inverse length functions (ILF) for each resulting subinterval. In the real-time NURBS path interpolation, the new setting path parameter can be calculated directly using the ILF without the need for any time-consuming computation of NURBS derivatives and iteration. The proposed method is extremely fast, accurate and suitable for real-time implementation, and simulations and practical tests proved its effectiveness.     

NURBS曲线与圆弧求交的剪刀迭代法

提出了一种剪刀迭代算法,用于CAD／CAM／CNC系统中NURBS曲线段与圆弧之交点的求取。该方法从几何的观点出发,像剪刀一样将两段曲线的两端不断剪短,经多次迭代后,最终得到交点。该方法从数学上将高次方程降阶为低次方程,特别适用于3次NURBS曲线与圆弧的求交。     

NURBS在平面异形玻璃切割系统中的应用

根据AutoCAD中样条曲线的生成原理,结合AutoCAD的DXF图形交换文件的结构形式以及DXF文件有效信息的提取方法,给出了构造样条曲线参数方程的方法.然后针对给定参数方程的曲线,提出一种圆弧拟和的实用算法.该算法在保证产品加工精度的同时,可尽量减少曲线的分割段数,从而降低了NC程序的规模,提高了加工效率.该项技术已被应用到所开发的玻璃切割系统中,使得该系统能够高效率地切割任意外形的玻璃制品.     

The material removal mechanism in mechanical lapping of diamond cutting tools

In order to reveal the surface layer removal nature and explain the anisotropy of material removal rate in mechanical lapping single crystal diamond cutting tools, a brittle-ductile transition lapping mechanism is proposed. And then, the dynamic critical depths of cut for brittle-ductile transition in different directions on different planes can be calculated. The lapped surface layer of diamond cutting tool will be removed in plastic mode as long as the embedding depth of diamond grit into the lapped surface is less than the corresponding critical depth of cut. Lapping experiments on the named (110) plane and (100) plane are carried out and the lapped surfaces are measured with atomic force microscope (AFM). The results show that all the lapped surfaces of diamond cutting tools consist of plastic grooves in nanometric scale and the maximal groove depths have prominent anisotropy in different orientations and on different planes, which are consistent with the critical depths of cut well. Therefore, the material removal rate anisotropy of lapped surface layer can be analyzed by comparing the critical depths of cut on different crystallographic planes and in different orientations of the identical plane quantitatively.     

Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools

Parametric interpolation for Non-Uniform Rational B-Spline (NURBS) curve has become more important than ever before in the control of CNC machine tools. An effective NURBS interpolator not only can obtain accurate contour trajectories, but also have smooth dynamics performance. This paper proposes a numerically efficient NURBS interpolation scheme which consists of two stages namely preprocessing and interpolating. In the stage of pre-processing, the parameter interval is split into several blocks at breakpoints and an iterative numerical quadrature method is applied for each block. By means of the iterative quadrature method, the initial parameter intervals of each block are divided into several subintervals according to the arc length approximation error. Meanwhile, the curvature of each knot and the cubic polynomial coefficients of each subinterval are obtained. Then the critical points with large curvature of each block are found from the candidate points and the tolerated speed of each critical point is calculated according to the constraints of chord error and centripetal acceleration. Hence, the feedrate scheduling based on the S-shaped acceleration profile for each block can be preplanned via the approximate arc length of each subinterval, the tolerated speed of each critical point and kinematics characteristics such as acceleration/deceleration and jerk limits of the machine tools. In the stage of interpolating, the parameter of the next interpolation point can be calculated directly using the cumulative arc length and the cubic polynomial coefficients of each subinterval. Finally, a series of numerical simulations and real machining experiments are conducted, and the simulation and experimental results have showed the good performance of the proposed NURBS interpolator both in efficiency and accuracy.     

数控机床的轮廓误差的控制

本文在分析两轴数控系统轮廓误差的基础上,提出了基于神经元的自适应交叉耦合控制器。仿真结果表明,本文提出了轮廓误差控制方法可以有效地提高数控的系统的轮廓加工精度。     

数控机床进给滚珠丝杠的选择与计算

本文论述了数控机床进给用滚珠丝杠的选择与计算方法 。     

Effect of valency on material removal rate in electrochemical machining of aluminium

Material removal rate (MRR) of aluminium work piece has been obtained by electrochemical machining using NaCl electrolyte at different current densities and compared with the theoretical values. It has been observed that resistance of the electrolyte solution decrease sharply with increasing current densities. The over-voltage of the system initially increases and then attains a saturation value with increasing current densities. The material removal rate, determined experimentally, almost corresponds to theoretical value with Al³⁺ state. On the other hand, taking into account over-voltage, MRR comes out be 72%. It appears that removal of a fraction of aluminium occurs in Al⁺ which subsequently gets converted into Al³⁺ through a series chemical reactions. A mechanism of such chemical reactions is proposed.     

A wafer-scale material removal rate profile model for copper chemical mechanical planarization

Chemical mechanical polishing (CMP) models based on the Preston equation, which states that the material removal rate (MRR) is proportional to the product of the pressure and relative velocity, have focused on representing the average MRR as a function of the pressure and relative velocity. In this study, we tried to establish a semi-empirical CMP model, which can provide the MRR profile. The model is based on a modified form of the Preston equation and involves the use of a spatial parameter (Ω). The relative velocity distribution, normal contact stress distribution, and chemical reaction rate distribution are considered for obtaining the MRR profile in the copper CMP process. The results of the modeling and experimental analysis performed in this study facilitate process optimization and provide information that can contribute to the development of a wafer-scale CMP simulator.     

变轴数控机床的静刚度特性分析

刚度是变轴数控机床设计需要考虑的主要因素之一.文章以BKX-I型变轴数控机床为研究对象,利用矩阵结构分析法建立了变轴数控机床的静刚度计算模型.在此基础上,扼要地分析了BKX-Ⅰ型变轴数控机床静刚度在工作空间中的分布规律,并讨论了机床结构参数对刚度的影响情况.     

A new compensation method for geometry errors of five-axis machine tools

The present study aims to establish a new compensation method for geometry errors of five-axis machine tools. In the kinematic coordinate translation of five-axis machine tools, the tool orientation is determined by the motion position of machine rotation axes, whereas the tool tip position is determined by both machine linear axes and rotation axes together. Furthermore, as a nonlinear relationship exists between the workpiece coordinates and the machine axes coordinates, errors in the workpiece coordinate system are not directly related to those of the machine axes coordinate system. Consequently, the present study develops a new compensation method, the decouple method, for geometry errors of five-axis machine tools. The method proposed is based on a model that considers the tool orientation error only related to motion of machine rotation axes, and it further calculates the error compensations for rotation axes and linear axes separately, in contrast to the conventional method of calculating them simultaneously, i.e. determines the compensation of machine rotation axes first, and then calculates the compensation associated with the machine linear axes. Finally, the compensation mechanism is applied in the postprocessor of a CAM system and the effectiveness of error compensation is evaluated in real machine cutting using compensated NC code. In comparison with previous methods, the present compensation method has attributes of being simple, straightforward and without any singularity point in the model. The results indicate that the accuracy of positioning was improved by a factor of 8–10. Hence, the new compensation mechanism proposed in this study can effectively compensate geometry errors of five-axis machine tools.     

Investigation of the spark cycle on material removal rate in wire electrical discharge machining of advanced materials

The development of new, advanced engineering materials and the need for precise and flexible prototypes and low-volume production have made the wire electrical discharge machining (EDM) an important manufacturing process to meet such demands. This research investigates the effect of spark on-time duration and spark on-time ratio, two important EDM process parameters, on the material removal rate (MRR) and surface integrity of four types of advanced material: porous metal foams, metal bond diamond grinding wheels, sintered Nd-Fe-B magnets, and carbon–carbon bipolar plates. An experimental procedure was developed. During the wire EDM, five types of constraints on the MRR due to short circuit, wire breakage, machine slide speed limit, and spark on-time upper and lower limits are identified. An envelope of feasible EDM process parameters is generated for each work-material. Applications of such a process envelope to select process parameters for maximum MRR and for machining of micro features are discussed. Results of Scanning Electron Microscopy (SEM) analysis of surface integrity are presented.     

On the mechanism and mechanics of material removal in ultrasonic machining

Precision abrasive machining processes such as ultrasonic machining are commonly employed to machine glasses, single crystals and ceramic materials for various industrial applications. Until now, precision machining of hard and brittle materials are poorly investigated from the fundamental and applied point of views. Taking into account the major technological importance of this subject to the production of functional and structural components used in high performance systems, it is often desired to estimate the machining rate for productivity while maintaining the desired surface integrity. The success of this approach, however, requires not only the fundamental understanding of the material removal on the microstructural scale but also the relationship between the machining characteristics and material removal rate in ultrasonic machining. In this study, the ultrasonic machining of glass was investigated with respect to mechanism of material removal and material removal rate (with basic machining parameters) with a mild steel tool using boron carbide abrasive in water as slurry. The analysis indicates that the material removal was primarily due to the micro-brittle fracture caused on the surface of the workpiece. For micro-brittle fracture mode, the relationship for the material removal rate, considering direct impact of abrasive grains on the workpiece, based on a simple fracture mechanics analysis has been established. The effect of machining conditions on material removal rate has been discussed. This research provides valuable insights into the material removal mechanism and the dependence of material removal rate on machining conditions and mechanical properties of workpiece material in ultrasonic machining.     

数控机床用伺服系统性能测试装置的研究

介绍了国家“九五”重点科技攻关成果“数控机床用伺服系统性能测试装置”的基本构成、主要功能与特点以及对国外某公司全数字交流伺服系统（1．3kW)的部分测试结果。     

Modeling of material removal rate in electric discharge grinding process

The mechanism of material removal in electric discharge grinding (EDG) is very complex due to interdependence of mechanical and thermal energies responsible for material removal. Therefore, on the basis of conceived process physics for material removal, an attempt has been made to predict the material removal rate (MRR). The proposed mathematical model is based on the fundamental principles of material removal in electric discharge machining (EDM) and conventional grinding processes. The inter-dependence of the thermal and mechanical phenomena has been realized by scanning electron microscopy (SEM) characterization of the samples machined at different processing conditions. The key input process parameters like pulse on time, pulse current, gap voltage, duty cycle, pulse off time, frequency, depth of cut, wheel speed and table speed are co-related with MRR for three distinct idealized processing conditions. The constant showing the extent of interdependence of two phenomena were evaluated by experimental data. The obtained expressions of MRR have been validated for processing conditions other than those used for obtaining constants. It was found that the discharge energy plays prominent role in material removal. The percentage difference in experimental findings and theoretical predictions was found to be less than 3%.     

Verification and evaluation method for volumetric and positional errors of CNC machine tools

This paper provides a testing device and an automatic sampling technique for fast checking of volumetric errors of CNC machine tools. With the proposed automatic sampling technique, the verification work is carried out automatically and reliably. Furthermore, the analyzed result obtained via the traditional least-squares method is not the minimum zone solution, and may overestimate the volumetric error. Thus, genetic algorithms (GAs) are employed to obtain the minimum zone solution in this paper. Experimental test results show that the proposed method is superior to the least-squares method.     

A new method of optimising material removal rate using EDM with copper–tungsten electrodes

Electrical discharge machining (EDM) is widely used in the production of dies. This paper describes an investigation into the optimisation of the process which uses the effect of carbon which has migrated from the dielectric to tungsten–copper electrodes. This work has led to the development of a two-stage EDM machining process where different EDM settings are used for the two stages of the process giving a significantly improved material removal rate for a given tool wear ratio.     

高精度棱体成形车刀的CAD/CAM系统

研究了高精度棱体成形车刀优化设计的数学模型,介绍了用VB语言开发的高精度棱体成形车刀的CAD/CAM子系统的构成及其主要模块的功能.该系统可由工件零件图直接生成加工该工件的高精度圆体成形车刀的零件图及刀具廓形的数控线切割加工程序,同时还能通过仿真检验所设计的刀具廓形及其加工程序代码的正确性.     

Modeling of material removal rate and surface roughness in finishing of bevel gears by electrochemical honing process

This paper describes mathematical modeling of material removal rate (MRR) and surface roughness of the bevel gears finished by the electro-chemical honing (ECH) process. Since, ECH hybridizes electrochemical dissolution (ECD) and mechanical honing therefore, contribution of ECD in MRR and surface roughness has been modeled using Faraday's law of electrolysis while contribution of mechanical honing has been modeled considering material removal as a phenomenon of uniform wear and using Archard's wear model. Formulations are also proposed for computing the surface area, required by these two models, along the inter-electrode gap (IEG) based on the geometry of the straight bevel gear tooth surfaces. The developed models were experimentally validated using an indigenously developed experimental setup for finishing of bevel gears by ECH based on an envisaged novel concept of twin complementary cathode gears. An aqueous solution containing 25% NaCl + 75% NaNO₃ was used as the electrolyte. The predicted values of MRR and surface roughness have shown close agreement with the experimental values. The experimental results, SEM images and bearing area curve have shown appreciable improvement in the surface roughness and surface integrity ensuring better operating performance of the gears finished by ECH within an optimized finishing time of 2 min.