自由曲面加工中NURBS曲线的插补实现

针对复杂型面零件的高精度曲面加工,传统上应用直线、圆弧和螺旋线等插补。由于曲面轮廓离散成大量微段直线或圆弧来加工,这不仅使编程复杂、代码量膨胀,而且不可避免地带来逼近误差,影响零件的加工精度、表面粗糙度和生产效率。提出一种NURBS曲线的实时插补算法,它基于NURBS曲线的参数表示法来求出优化的曲线参数,实现了NURBS曲线高速、高精度加工的插补控制。试验的结果表明,这种插补方法是有效的。     

An efficient methodology for the structural synthesis of geared kinematic chains

Through the use of acyclic graphs, an efficient methodology has been developed for the synthesis of the kinematic structure of geared kinematic chains with any number of links. First, a systematic approach is proposed for the enumeration of N-vertex acyclic graphs. For each N-vertex acyclic graph, all the N-vertex geared graphs are generated by adding (N — F — 1) geared edges to the acyclic graphs, eliminating geared graphs which violate the fundamental rules, and non-isomorphic geared graphs are obtained by comparing the structural codes. Finally, the catalog of the graphs of one-degree-of-freedom (DOF) geared kinematic chains with N links are synthesized from the catalog of acyclic graphs with N vertices. As a result, the structural synthesis of one-DOF geared kinematic chains with up to eight links has been successfully constructed.     

A framework for non-contact measurement and analysis of NURBS surfaces

The paper presents an implementation of a methodology for reliable and feasible dimensional measurement of engineering components containing free-form surfaces. Two main requirements had to be satisfied. First, a large number of points had to be accurately measured. Secondly, the set of corresponding points on the nominal model had to be computed within a reasonable time. The first aspect was satisfied by adopting a non-contact measurement technique based on laser triangulation. High accuracy was achieved through software prealignment for precise component localisation and through appropriate measurement planning, both based on the CAD model. Determination of the corresponding nominal points was solved by best-fitting. Significant speed improvements were achieved through an implementation of the iterative closest point algorithm, based on a dual representation of the surface. The nominal surface is defined using NURBS entities and its approximation is determined as a polyhedral mesh. A sampling criterion for complex surfaces was derived and implemented, producing encouraging results. Validity of the proposed approach is supported by experiments and by simulation studies involving real engineering components.     

A new approach to generating arc length parameterized NURBS tool paths for efficient three-axis machining of smooth, accurate sculptured surfaces

With the development of a new function of computer numerical control controllers, nonuniform rational B-spline (NURBS) interpolation, NURBS tool path generation for sculptured surface machining is under extensive research. The common procedures of the current NURBS tool path planning methods are as follows: first, to find a group of cutter contact points on a sculptured surface; second, to calculate their corresponding cutter locations (CLs); then, to fit a NURBS tool path to the CLs within a prescribed tolerance; and finally, to inspect the tool path for possible gouge by the tool and delete the invalid path segments, if any. However, the NURBS tool path has the following problems: (a) although it passes through the discrete CLs of the theoretical CL path, the deviation along the two paths could be larger than the tolerance; (b) its parameter is not the arc length of the path; and (c) it is difficult to detect gouge along the NURBS path and to remove the invalid segments from it. Consequently, NURBS tool paths generated with the current methods of commercial computer-aided design/computer-aided manufacturing (CAD/CAM) software cannot be used to make smooth and accurate surfaces. To address these problems, this work proposes a new approach to generating arc length parameterized NURBS tool paths with high accuracy in terms of the theoretical CL paths and without gouge and interference. Two practical examples in this work clearly demonstrate the feasibility of this approach and the advantages of the generated NURBS tool paths. Therefore, this approach can be implemented into the CAD/CAM software to promote NURBS machining in industry.     

Nonplanar slicing and path generation methods for robotic additive manufacturing

Additive manufacturing (AM, generally called 3D printing) has attracted great research interests due to its ability to build complex shapes. It transforms design files to functional products through slicing and material accumulation. Typically, the planar slicing strategy is used in AM to convert CAD model into accumulating layers. However, when building overhang structures and curved parts, it often needs support structures and generates a large number of planar layers, which lead to the fact that it spends more time in manufacturing. To reduce the need for support structures and decrease the number of layers, this paper presents two nonplanar slicing approaches: a decomposition-based curved surface slicing strategy and a transformation-based cylinder surface slicing method. The former is implemented based on STEP models and the latter is capable of slicing mesh models. The feasibility of the proposed methods are validated by printing two parts with a robotic fused deposition modelling system.     

A quick deviation zone fitting in coordinate metrology of NURBS surfaces using principle component analysis

Evaluation of the tolerance zone using discrete measured points plays a critical role in today’s manufacturing, metrology, and many industrial applications. The deviation zone is typically evaluated using a fitting method that locates an ideal desired geometry corresponding to a set of measured points while a function of the Euclidean distances of the measured points to the ideal surface becomes minimum. This paper presents a quick and reliable algorithm called Dynamic Principle Component Alignment (DPCA) for fitting complex surfaces to the coordinate metrology measured points using the information that is dynamically generated by Principal Component Analysis (PCA) of the measurement data and the corresponding fitted geometry. The developed algorithm efficiently eliminates the necessity for applying commonly used optimization methods for the fitting (localization) process, which decreases the computational cost and uncertainty of the evaluation process. Moreover, DPCA is very reliable and practical in coordinate metrology with large data sets in processes such as laser scanning and other optical methods. The results show that the proposed methodology more accurately finds fitting parameters in comparison with the other commonly used methods while the computational cost is considerably reduced.     

An adaptive off-line NURBS interpolator for CNC machining

As a key technique in CNC machining, nonuniform rational B-spline (NURBS) interpolator has been proposed to overcome the drawbacks caused by linear and circular interpolator, such as large data size, velocity discontinuity, shocks or variations in mechanical systems, and low machining efficiency. To improve machining quality and efficiency, an adaptive off-line interpolator was developed for NURBS curves in this paper. Both the chord accuracy and the acceleration/deceleration capability of machine tool are considered in the algorithm. There are four modules in the algorithm, adaptive feed rate adjustment, acceleration/deceleration disposal, feed rate modification, and S-type velocity generation. The acceleration/deceleration around the sharp corners is carefully calculated by those modules. A case study was provided to evaluate the feasibility of the interpolator.     

非均匀有理B样条曲面五轴加工数控指令的构建与处理

为了将非均匀有理B样条曲面的几何信息和工艺信息完整地传输到计算机数字控制系统中,提出了一种新的非均匀有理B样条曲面,直接插补G指令与加工信息的传输和处理机制.解决了传统的非均匀有理B样条曲面加工方法中将曲面离散成曲线时,丢失待加工曲面与刀具接触点的法向信息和刀具轨迹切向信息的问题,有助于在计算机数字控制中实现在线三维刀具补偿和智能控制.仿真结果证实了这种方法的有效性和准确性.     

An algorithm of NURBS surface fitting for reverse engineering

Reverse engineering is an approach for constructing a CAD model from a physical part through dimensional measurement and a surface model. Different from conventional methods, this paper develops a new algorithm by which a desired fitted surface is obtained with less computation. Let selected m×n measured points be control points to construct B-spline or NURBS surface, then modify this constructed surface by using all the measured points and least squares minimization. A new algorithm for parameterization for measured points is also presented in this paper. The effectiveness and efficiency of these proposed algorithms are demonstrated.     

An iterative feedrate optimization method for real-time NURBS interpolator

Non-uniform rational B-spline (NURBS) interpolator has been widely used in modern manufacturing systems to machine arbitrary geometries with great relief of the data flow bottleneck and feedrate fluctuation. However, in practice, real-time feedrate does not always meet the computer numerical control (CNC) command exactly subject to the system dynamics. To solve this problem, we present a real-time NURBS interpolator with feedrate optimization for CNC machining tools in this work. The parametric curve is first approximated with the Adams–Bashforth method which provides uniform feedrate in each sampling period in the interpolation process. And then, a feedback scheme is introduced to adjust the feedrate in real time so as to guarantee a specified deviation between the measured and the desired feedrate. The convergence condition for this closed-loop algorithm is presented and analyzed. Simulation and real experiments on an X–Y table are employed to verify its feasibility. And the comparisons with traditional interpolators based on Taylor's expansion are also provided to demonstrate its improvement in accuracy.     

Blank optimization for sheet metal forming using multi-step finite element simulations

The present study aims to determine the optimum blank shape design for deep drawing of arbitrary shaped cups with a uniform trim allowance at the flange, i.e., cups without ears. The earing, or non-uniform flange, is caused by non-uniform material flow and planar anisotropy in the sheet. In this research, a new method for optimum blank shape design using finite element analysis is proposed. The deformation process is first divided into multiple steps. A shape error metric is defined to measure the amount of earing and to compare the deformed shape and target shape set for each stage of the analysis. This error metric is then used to decide whether the blank needs to be modified. The blank geometry change is based on material flow. The cycle is repeated until the converged results are achieved. This iterative design process leads to optimal blank shape. To test the proposed method, three examples of cup drawing are presented. In every case converged results are achieved after a few iterations. The proposed systematic method for optimal blank design is found to be very effective in the deep drawing process and can be further applied to other sheet metal forming applications such as stamping processes.     

基于预估误差补偿的NURBS曲线插补算法

针对传统NURBS曲线插补算法计算量大、耗时多的问题,提出基于预估误差补偿的NURBS曲线预估-校正插补算法。该算法能够以简单的线性运算代替复杂的求导运算,有效降低了计算的复杂度,提高了计算效率。并能根据曲线曲率变化趋势对预估参数值进行补偿,使预估参数值更接近实际值。为了解决传统校正公式收敛速度慢的问题,提出基于割线法的校正公式。该校正公式为超线性收敛,有效减少了迭代计算的次数。仿真结果表明:该算法的计算量小,可操作性强,稳定性好,可靠性高。能够对插补产生的速度波动进行有效控制,满足实时插补的要求。     

An accurate adaptive parametric curve interpolator for NURBS curve interpolation

In this paper, an adaptive parametric curve interpolator with a real-time look-ahead function is developed for non-uniform rational B-spline curves (NURBS) interpolation, which considers the maximum acceleration/deceleration of the machine tool. In the proposed interpolator, both constant feedrate and high accuracy are achieved while the inconsistency of feedrate is reduced dramatically as well. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, a look-ahead function is introduced to detect and adjust the feedrate adaptively. Two cases were respectively studied to evaluate the feasibility of the developed interpolator: one is for feedrate sensitive arc corner; the other is for feedrate sensitive sharp corner.     

Pneumatic non-contact topography characterization of finish-ground surfaces using multivariate projection methods

This paper reports on the application of multivariate analysis methods for the non-contact topography assessment of finish-ground surfaces of roughness in the range of 0.1-0.8 μm Ra. The roughness information is extracted from the frequency spectrum of the back pressure signal acquired using a pneumatic gauge as the surface traverses past the nozzle. Principal components analysis is demonstrated to be effective in the unsupervised classification of lapped and ground surfaces of an identical nominal roughness of 0.1 μm Ra, even under conditions that the corresponding frequency spectra are contaminated with noise and affected by vibration. Projection to latent structures analyses are further shown to be capable of discriminating cylindrical ground surfaces based on along-the-lay measurements from a rotating component, and formulating multivariate regression models appropriate for process monitoring.     

An evaluation of methods for preparing easily damaged cuticular surfaces of plants for scanning electron microscopy

Techniques were tested to ascertain the best method for preparing the surfaces of delicate plant cuticles for microscopic examination at magnifications not exceeding 10,000. Using scanning electron microscopy, comparative examinations were made of cuticles of fresh material, ambient dried, freeze dried, critical point dried, and frozen material kept at low temperature. Micrographs were compared with material examined using light microscopy which acted as a control at low magnification. Cuticles of the leaves of runner bean, Coleus and the petals of Nicotiana, showed best surface preservation and least wrinkling when frozen, held at low temperature, and examined on a cryostage.     

An improved feedrate scheduling method for NURBS interpolation in five-axis machining

Five-axis machining plays an important role in manufacturing by dint of its high efficiency and accuracy. While two rotation axes benefit the flexibility of machining, it also brings limitations and challenges. In order to further balance machining precision and efficiency, an improved feedrate scheduling method is presented considering geometric error and kinematic constraints for the Non Uniform Rational B-Spline (NURBS) interpolation in five-axis machining. A simplification method is proposed to calculate the geometric error which describes the deviation between the ideal tool path and the real tool path induced by the non-linear movement. A linear relation between geometric error and feedrate is built to limit the feedrate. The constraints determined by single axis kinematic performance and tangential kinematic performance are also considered. Under these constraints, a constrained feedrate profile is determined. Aiming to get more constant feedrate in the difficult-to-machine areas, this work proposes a scheduling method which combines morphological filtering and S-shape acceleration/deceleration (acc/dec) mode. Simulations and experiments are performed to compare the proposed feedrate scheduling method with two previous feedrate scheduling method and the results prove that the proposed feedrate scheduling method is reliable and effective.     

An adaptive slicing algorithm and data format for functionally graded material objects

Rapid prototyping technology makes the manufacturing of functionally graded material (FGM) objects possible. The FGM production process requires concurrent applications of digital design and manufacturing methods. For this reason, it is imperative to construct and capture information and other critical data regarding the geometry and materials about FGM objects for use in the manufacturing process. This paper proposes a simplex-clear data format for modeling FGM objects. This proposed data format captures both the geometry and material information of an FGM object. It also presents a finite element-based slicing algorithm which slices the FGM object into layers and captures each layer’s information for rapid prototyping manufacturing of the object. An example is given at the end of the paper to validate the data format and demonstrate the adaptive slicing algorithm.     

Note: An adhesion measurement setup for bioinspired fibrillar surfaces using flat probes

Current adhesion measurement setups designed for experiments on bioinspired fibrillar surfaces, either commercial or constructed in-house, do not allow adhesion measurements with in situ visualization, high resolution, high force range, and controlled alignment at the same time. In this paper a new adhesion tester is presented, which enables contact experiments with controlled tilt angle (accuracy of ±0.02°). This allows the use of flat probes and thus greatly simplifies the determination of experimental parameters such as pull-off strength or Young's modulus. The deflection of a double-clamped glass beam is measured by laser interferometry with an accuracy of ±60 nm, which yields a precise force measurement over three orders of magnitude force range without changing the glass beam. Contact formation and detachment events can be visualized in situ. The current adhesion tester is designed for force measurements in the range of 1 μN to 1 N and fills the gap between macroscopic tests and atomic force microscopy measurements.     

An efficient CFD-based method for aircraft icing simulation using a reduced order model

In-flight icing is a critical technical issue for aircraft safety and, in particular, the droplet impingement areas on aircraft surfaces must be investigated for anti-/de-icing devices. As a step toward the prediction of droplet impingement on aircraft, an Eulerian-based droplet impingement code that provides collection efficiency for air flows around an airfoil containing water droplets is developed. A computational fluid dynamics (CFD) solver was also developed to solve the clean airflow. Then, a proper orthogonal decomposition (POD) method, a reduced order model (ROM), that optimally captures the energy content from a large multi-dimensional data set is utilized to efficiently predict the collection efficiency and ice accretion shapes on an airfoil following the mean volume diameter, liquid water contents and angle of attacks. As a result it is shown that the collection efficiency and ice shapes were in good agreement with the simulated and predicted results.