G2 Continuity for Multiple Surfaces Fitting

Fitting 3D known data into sculptured surfaces has received extensive attention. However, most algorithms available are suitable only for an isolated surface. A part typically contains multiple surface regions that must be blended to a degree of continuity. The conventional approach based on blending, lofting, stitching, etc. cannot guarantee the quality of the surface near the jointed area. The purpose of this work is to present a surface-fitting algorithm for multiple sets of data, concentrating on G 2 continuity across the boundary of the fitted surfaces. The proposed surface-fitting algorithm essentially fits several sets of data simultaneously, and yields a B-spline surface for each set of data. The G 0 ,G 1 , and G 2 continuity conditions between B-spline surface patches were addressed. Based on these results, additional constraints were specified to achieve G 2 continuity across the surface boundary. A successful demonstration of the proposed strategy is provided also.     

Harmonic Fitting Approach for Plane Geometry Measurements

The paper proposes the harmonic fitting (HF) approach for the selection of the number of sampled points when measuring a plane geometry. HF is the spatial frequency correspondent of the least squares method (LSM) and it will be demonstrated that following HF, the estimated errors can be evaluated as a function of the number of sampled points with closed analytical formulae. This is the basis for the development of a parsimonious sampling for coordinate measuring machines (CMMs).     

基于B样条曲面的点云孔洞拟合填充

为了后续曲面重构的需要,针对有孔洞的点云数据,提出了一种孔洞拟合填充的自适应方法。由于孔洞与其周围离散点有一定的连续性,该算法首先从孔洞周围已有的点云数据中选取离散点,用新的参数化方法对得到的离散点参数化后,用最小二乘法进行自适应曲面拟合,对得到的拟合曲面通过迭代法逐步逼近优化,考虑曲率变化的影响在曲面上取点,实现了孔洞光滑填充。实例表明,改进的参数化方法使算法的复杂度减低,进一步迭代优化提高了曲面拟合精度,在面上取点时考虑了曲率变化,因此该方法可以应用于具有复杂曲面形状的点云中的孔洞填充。     

UG中桥接曲线参数的自动寻优方法研究

如何快速、精确、光滑地连接多个曲面块,是广泛存在于CAD建模工作中的一个难题。在UG平台上进行多曲面连接系统的二次开发过程中,需要由最小曲率半径值反求出桥接曲线(Bridge Curve)的两个参数。本文找出了桥接曲线的等效数学模型,并在此基础上确定出桥接曲线最小曲率半径与桥接参数之间的关系,给出了求解理论方程组。由于求解精确理论值非常困难,本文采用最优化方法对方程组进行了数值求解,并依据经验给出了桥接质量的评价标准。通过验证表明,该方法精度可满足工程实际需要。     

A New Parameterisation Method for NURBS Surface Interpolation

A new method is proposed for the parameterisation of data points in NURBS surface global interpolation. In this method, the parameter value at the maximum of each rational B-spline basis function is defined as the parameter value of the associated data point. Some advantages of this method in geometric modelling are: 1. It selects the knot vectors freely, regardless of the distribution of data points. 2. It is invariant under affine transformations of the data points. 3. It allows multiple data points.     

An Operation Planning System for Multi-Axis Milling of Sculptured Surfaces

Multi-axis milling of sculptured surfaces with cylindrical or toroidal cutters has many advantages compared to the use of three-axis milling with ball nose cutters. Surfaces to be machined are often of complex shape and characterised by convex, concave and saddle areas. Today, CAM-systems do not support the user in the selection of the different operations in order to finish the workpiece. This paper describes an operation planning system, which facilitates process planning for the multi-axis machining of sculptured surfaces. The core of the system is surface analysis, which divides the surfaces into regions, each characterised by a preferred milling direction and tool diameter. Further, for each region or set of regions, a drive surface is constructed that is used as the basis for the tool-path calculation. The drive surface approximates to the original workpiece as closely as possible, and the isoparametric lines which will be the tool-path feed direction lie in the preferred milling direction.     

五轴联动数控加工中的刀具轨迹控制算法

已有的五轴联动数控加工系统往往忽略刀轴矢量插补问题,只是简单地通过对线性轴进行插补、对旋转轴进行跟随的方式来实现刀具轨迹的控制,导致产生非线性误差和刀具碰撞与干涉等问题。为此,提出一种基于刀轴矢量插补的刀具轨迹控制算法。该算法采用大圆弧插补法对加工过程中的刀轴矢量进行控制,同时采用NURBS曲线拟合方法对控制过程中产生的中间点进行处理,并通过对拟合而成的NURBS曲线进行插补来实时计算各运动轴的位置。该算法不仅能够有效地提高五轴联动数控加工的精度,而且可以有效减小数据存储量。仿真和实际加工验证了算法的有效性和实用性,证明算法具有轨迹过渡平稳、非线性误差小的特点。     

A Two-Level Modelling Approach to Acquire Functional Design Knowledge in Mechanical Engineering Systems

Modelling as a means of knowledge acquisition has been proposed by some workers in artificial intelligence. In this paper the authors describe an approach using two-level knowledge modelling that employs the concepts of a functional model (extended FEBS model) and an object model to capture domain-specific functional design knowledge. The functional model serves as a basis for communication between domain experts and a knowledge engineer. The object model is used to bridge the gap between the functional model and an executable knowledge base. The approach is viewed as an important method for building a function-laden knowledge base that is useful for developing a knowledge-based functional design expert system. The proposed knowledge acquisition method is applied to an automatic assembly system for manufacturing electronic connectors to illustrate the general idea.     

A Heuristic State–Space Approach to the Functional Design of Mechanical Systems

This paper presents a knowledge-based approach for automating the functional design of mechanical systems. By using our proposed automated functional reasoning strategy, which is based on a heuristic search method, a set of physical behaviours can be reasoned out automatically from the desired functions. The interconnection of these behaviours is possible when the functional outputs of one are compatible to the corresponding functional requirements of the next one. Though the design space for behavioural configuration is very large, by defining its heuristic evaluation function as a fuzzy multicriteria decision-making (FMCDM) problem, the proposed heuristic search method can lead to a near optimum design solution in a reasonable time. A case study for the automated functional design of an automatic assembly system is given to illustrate the operation of the proposed heuristic search method, and to show its effectiveness in functional reasoning and optimizing the final design.     

A Surface Based Approach for Constant Scallop HeightTool-Path Generation

The machining of sculptured surfaces such as moulds and dies in 3-axis milling relies on the chordal deviation, the scallop height parameter and the planning strategy. The choice of these parameters must ensure that manufacturing surfaces respect the geometrical specifications. The current strategies for machining, consist primarily in driving the tool in parallel planes which generates a tightening of the tool paths. A constant scallop height planning strategy has been developed to avoid this tightening. In this paper, we present a new method of constant scallop height tool-path generation based on the concept of the machining surface. The concept of the machining surface is developed and its use to generate constant scallop height tool paths is described. The approach is compared with existing methods in terms of precision and in particular its aptitude to treat curvature discontinuities.     

基于仿射算术和区间运算的直线与NURBS曲线/曲面求交

针对直线与参数空间NURBS曲线、直线与NURBS曲面求交问题,提出了一种改进的基于仿射算术和区间运算的直线与NURBS曲线/曲面求交的有效方法。该方法将基于边曲率或面曲率的子域分解方法应用到求交算法中,快速定位预迭代区间,减少不必要的迭代求交判断。与传统区间迭代算法相比,该求交算法为超线性收敛的快速迭代算法,在一定程度上解决了传统区间运算的“保守性”。另外,该方法放宽了对初始区间的要求,减少迭代次数,提高了迭代算法效率。通过计算区间算子判断给定直线与NURBS曲线/曲面有无交点和存在交点时的交点数目,保证了求解交点精度,为解决直线与曲线/曲面多交点判断及内外环或内外域判断等问题提供了有利条件。数值算例验证了该方法的有效性、计算精度和效率。     

Optimising Tool Positioning for End-Mill Machining of Free-Form Surfaces on 5-Axis Machines for both Semi-Finishing and Finishing

End-milling of free-form surfaces on 5-axis NC machine tools is a complex problem which has been studied by a large number of research scientists. When end-milling non-convex surfaces there is a risk of interference between the tool and the surface. Using a 5-axis NC machine tool enables the tool to be oriented in any spatial direction to access a given point. This means interference can be avoided and the position of the tool can be optimised so as to minimise residual material. Here, a new method is presented for tool positioning in end-milling of free-form surfaces based on evaluating the interference for a set of test points distributed around the circumference of the tip of the tool. Distinction is made between the cases of semi-finishing and finishing which can be performed using a large diameter flat-end tool and a toroidal tool, respectively. Further, all developments are implemented for interactive use in a CAD/CAM software environment.     

Error Compensation for Three-Dimensional Line Laser Scanning Data

In this paper, the problem of compensation of 3D line laser scanning data for improved inspection accuracy is addressed. This problem is important, as a 3D line laser scanner is about one order less accurate than a touch probe. The approach taken is to compensate through error characterisation. In other words, a software compensation is performed, instead of a hardware compensation, which is probably more expensive. To do so, the errors associated with a 3D line laser scanning system are first characterised. With error characterisation, an empirical formula is obtained relating the errors to the influencing factors including the projected angle and the scan depth. This empirical formula is used to compensate for the digitised surface data obtained by the corresponding laser scanning system. The results show that the proposed approach effectively improves inspection accuracy.     

气动元件等温流动近似流量公式的探讨

本文考虑了可压缩气体的特点,对伯努利方程作了修正,在此基础上推导出了可压缩气体等温流动下的近似流量公式。在近似情况下,所推导出的公式与常用的简易流量公式是一致的。本文在理论上证明了流量特性曲线在亚声速区近似一椭圆曲线。推导出了可压缩气体直接排入大气中的近似流量公式,它与雍塞流公式一致。本文还推导出了不可压缩气体近似流量公式,研究表明,在亚声速区,流量与压力比近于一个抛物线关系。