Optimal five-axis tool path generation algorithm based on double scalar fields for freeform surfaces

In order to generate efficient tool path with given precision requirements, scallop height should be kept under a given limit, while the tool path should be as short as possible to reduce machining time. Traditional methods generate CC curves one by one, which makes the final tool path far from being globally optimal. This paper presents an optimal tool path generation model for a ball-end tool which strives to globally optimize a tool path with various objectives and constraints. Two scalar functions are constructed over the part surface to represent the path intervals and the feedrate (with directions). Using the finite element method (FEM), the tool path length minimization model and the machining time minimization model are solved numerically. The proposed method is also suitable for tool path generation on mesh surfaces. Simulation results show that the generated tool path can be direction parallel or contour parallel with different boundary conditions. Compared to most of the conventional tool path generation methods, the proposed method is able to generate more effective tool paths due to the global optimization strategy.     

基于面形斜率的光学自由曲面表征

对光学自由曲面设计的关键问题——光学自由曲面的表征模型进行了研究。在传统高斯径向基模型的基础上,通过改善基函数的分布特性以及基于面形斜率调整基函数的形状因子,建立了基于面形斜率的高斯径向基表征模型。利用建立的模型、传统径向基模型和Zernike多项式模型拟合了不同类型的自由曲面,并进行了分析比较。结果证实了文中提出的模型较传统径向基模型的面形拟合精度提高了1~2个数量级,具有较强的面形表征能力。应用该模型进行了离轴三反系统的设计,结果显示设计的三反系统的全视场平均调制传递函数(MTF)达到80%以上。与传统面形表征模型相比,该模型的应用提高了系统的像差平衡能力,改善了系统的成像质量。综合分析表明,该模型适用于表征具有显著非对称性的、面形矢高带有显著局域性变化的自由曲面,有望应用于具有大离轴量和大视场的光学系统设计中。     

采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响

鉴于自由曲面模型的面形拟合精度在自由曲面表征以及面形初始结构选取等研究中的重要性,本文针对基于面形斜率的高斯径向基表征模型,研究了不同的采样点分布类型对该模型面形拟合精度的影响。采用不同采样点分布拟合离轴二次曲面和带凸起的抛物面,结果表明采用均匀随机分布的采样点有利于实现高精度的面形拟合,且达到一定的拟合精度后,采样点的数目对拟合精度的影响有限。以离轴三反系统为设计实例,对比了由不同采样方式生成初始面形后系统的像质优化结果。结果显示,采用均匀随机型采样方式得到的初始面形进行系统优化,最终全视场平均调制传递函数(MTF)可以达到0.72以上,远高于由边缘集中采样方式生成初始面形后系统像质的优化结果,从而印证了理论研究结果。     

Triangulated surface flattening based on the physical shell model

Journal of Mechanical Science and Technology - Triangulated surface flattening plays an important role in the surface shape design of a complex product, such as a vehicle, a train and an air plane....     

Tool path generation by offsetting curves on polyhedral surfaces based on mesh flattening

Polyhedral surfaces are used as representation model for CAM and process planning purposes because of its simplicity for data exchange and geometric computation. However, there are few tool path planning strategies for such surfaces but isoplanar method. This paper presents a contour offset approach to tool path generation for three-axis ball-end milling of polyhedral surfaces, based on a novel method for offsetting curves on polyhedral surfaces. One of its salient features is to reduce the task of removing complex interfering of offsets from 3D physical surfaces to 2D plane by flattening mesh surfaces and avoid costly 3D Boolean set operations and relatively expensive distance calculation. Moreover, in practical implement, the procedures of calculating offset points and removing interfering loops are merged and carried out simultaneously results in an efficient tool path generation method. Empirical examples illustrate the feasibility of the proposed method.     

Diamond shaping of blazed gratings on freeform surfaces

The study of spectral signatures of various elements has been enabled with the ability to diffract light using optical gratings, coupled with the ability to control light using lenses and mirrors. As technological devices seek to become more compact while maintaining or increasing operational efficiency, integration of functions becomes necessary to reduce the overall component count. However, due to the lack of axial flexibility, integrated microstructures on complex forms have shown to be challenging to manufacture. Thus, the need for fabrication techniques to be able to produce such microstructures on non-planar surfaces arises. The Continuous Rotating Freeform Shaping (CRFS) algorithm proposed in this paper utilizes the axial flexibility and precision of Ultra-Precision Machining (UPM) to directly fabricate optical quality blazed gratings on complex profiles which can directly be used as mirrors or molds. The developed algorithm not only maintains the tool along the primary profile of the optical surface, but also the rake angle of the tool at every point along the surface for a constant cutting mechanism. This is coupled with a rotation of the tool to maintain the blazed angle across the surface, optimizing the surface for the efficiency of the grating for a specific wavelength. In this paper, the developed algorithm is presented with experimental verifications of the generation of blazed gratings on a high curvature spherical surface and a freeform tri-axial ellipsoidal surface, followed by the corresponding analysis.     

基于FreeForm的CAD模型细节添加与修改

分析了FreeForm造型的特点及优势,并针对FreeForm在造型过程中的细节添加与修改功能进行了详细论述,将传统CAD建模与触觉交互造型有机结合起来,提出了一种基于FreeForm的CAD模型细节添加与修改方法,并给出了应用实例.     

A weighted least square based data fusion method for precision measurement of freeform surfaces

The trend towards product miniaturisation and multi-functionality constitutes a driving force for the application of complex surfaces in many fields such as advanced optics. The precision measurement of these surfaces should be carried out at multiple scales, of which process commonly involves several datasets obtained from different sensors. This paper presents a weighted least square based multi-sensor data fusion method for such measurement. The method starts from unifying the coordinate frames of the measured datasets using an intrinsic feature based surface registration method. B-spline surface is used to fit linear surface model to each identified overlapping area of the registered datasets, respectively. By forming a common basis function, the fitted surface models and the corresponding residuals are then combined to construct a weighted least square based data fusion system which is used to generate a fused surface model. An analysis of the uncertainty propagation in data fusion process is also given. Both computer simulation and actual measurement on various freeform surfaces are conducted to verify the validity of proposed method. The results indicate that the proposed method is capable of fusing multi-sensor measured datasets with notable reduction of the measurement uncertainty.     

Measurement of nonrigid freeform surfaces by coordinate measuring machine

Nonrigid part could be subjected to significant distortion after the removal of manufacturing forces. This condition, known as free-state variation, is principally due to weight and flexibility of the part and the release of internal stresses resulting from fabrication. The present work deals with the inspection of freeform surfaces belonging to nonrigid parts. A manufactured aeronautic component, named Mid Cowling, is considered as case study. The design of an appropriate fixture equipment will be firstly presented: it enables both to simulate the mating part interface and to locate the part in coordinate measuring machines working volume. Then, a method for evaluation of a freeform surface with respect to the nominal one will be presented. This evaluation is based on Euclidean distance between actual and nominal surfaces. Finally, an analysis of the part deformation presented in order to evaluate the measurement process in terms of interaction of the measurement system with the inspected part will be proposed. The adopted method, based on a finite element analysis, was proposed in order to evaluate the interaction, due to the measuring force, between the touch probe and the inspected surface and thus its effect on the measurement result.     

Path planning of multi-patched freeform surfaces for laser scanning

In this paper, a new method for scanning a complex surface model with multiple patches is proposed. In scanning of freeform-shaped models, it is difficult to generate a measuring plan by human intuition due to the complexity of the part. The developed method calculates the number of scans, scan direction, and scan path for a stripe-type laser scanner. The user can designate the surface patches that need to be scanned. In generating the scan plan, surface information is first extracted from the CAD model automatically. Other information such as, design knowledge, functionality and machine parameters are provided interactively. Based on this information, the original surface model is sampled in the u, v parameter domain and the sampled points are grouped using the view angle of the laser scanner. The scan direction is determined by calculating the global mean vector of the sampled points that belong to a group. The range of the view angle can be varied to enhance the quality of captured point data. The optical scan paths for each scan direction are calculated by projecting the sampled points onto a 2D plane. The optical constraints are also verified to guarantee the generated scan plan.     

基于光学自由曲面的离轴三反光学系统

为了研制长焦距大视场离轴三反空间光学系统,描述了自由曲面光学数理模型,设计了基于自由曲面的离轴三反光学系统.针对焦距为4500 mm,成像视场角为11°,系统总长与焦距的比值为1/3的光学系统,对比分析了传统离轴三反光学系统和次镜为自由曲面的离轴三反光学系统的关键性能.在提出的光学系统中次镜采用自由曲面设计,提升了光学...     

Constrained deformation of freeform surfaces using surface features for interactive design

There is an increasing demand in conceptual design for more intuitive methods for creating and modifying freeform curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters but also on the user's specified constraints and shapes. This paper presents a new surface representation model for freeform surface deformation representation. The model is a combination of two functions: a displacement function and a function for representing an existing NURBS surface called a parent surface. Based on the surface model, the authors develop several novel deformation methods which are named SingleDef (Single-point constraint based deformation method), MultiDef (Multiple-points constraints based deformation method), CurDef (Curve constraints based deformation method) and FeatDef (Feature constraint based deformation method). The techniques for freeform surface deformation allow conceptual designers to modify a parent surface by directly applying point constraints, curve constraint or a surface constraint to the parent surface. The deformation methods are implemented in an experimental CAD system. The results show that designers can easily and intuitively control the surface shape.     

Any-degrees-of-freedom (anyDOF) registration for the characterization of freeform surfaces

This paper presents an any-degrees-of-freedom (anyDOF) registration method for the characterization of freeform surfaces. The method attempts to fill the research gap regarding traditional surface registration methods which are normally dedicated to solving the global optimization problem with all DOF but they lack flexibility. The proposed anyDOF method is capable of registering surfaces with any specified combination of DOF. This is particularly useful when some of the DOF are known to be unchanged according to the a priori knowledge. The anyDOF surface registration method is regarded as a typical optimization problem of finding the minimum distance from target surface to the reference surface, with constraints of the unwanted DOF. The problem is solved by the Levenberg-Marquardt method. Simulated experiments for a two-dimensional (2D) profile and a three-dimensional (3D) surface were undertaken, together with three measurement experiments including a fluid-jet polished surface, a bonnet polished surface and a diamond machined freeform surface. Experimental results show that the anyDOF registration method is highly flexible in the characterization of freeform surfaces.     

An accurate surface error optimization for five-axis machining of freeform surfaces

This paper presents an accurate surface error interpolation algorithm for five-axis machining of freeform surfaces. One of the most important steps in the interpolation process is to calculate the next cutter contact (CC) point according to the present one. In this paper, the next CC point is calculated by an accurate chord evaluation method. This method is developed based on the cutting simulation process, which can be vividly described as firstly planting dense grasses on the tool path curve and then cutting them when the tool moves by. The left lengths of the grasses either positive or negative are considered to be the machining error. The method is accurate also because the tool geometry and the tool orientation changes during five-axis machining are taken into consideration. With this method, the chord errors between CC points are controlled uniform along the tool path. The proposed interpolation algorithm is compared with the commercial CAM systems like PowerMILL and UG. The results show that the proposed algorithm can significantly reduce the number of cutter locations meanwhile confine the chord error. A real cutting experiment is implemented, and the result indicates its promising value in industrial applications.     

光学自由曲面快速刀具伺服车削误差的补偿

受各种误差因素以及周期性变化的切削力的影响,快速刀具伺服金刚石车削技术往往难以用一次车削获得满足光学性能要求的自由曲面。本文提出了一种利用线性差动传感器(LVDT)实现高精度接触式自由曲面在位测量的方法。该方法结合两自由度快速刀具伺服系统,实现了基于快速刀具伺服(FTS)的自由曲面车削加工的误差补偿。试验结果表明,该技术将自由曲面的加工精度提高了20%,表面粗糙度降低18.1%,解决了FTS系统与机床运动的同步问题,可补偿机床xyz三向运动误差,可用于自由曲面加工误差的修正。该方法还可用于不对称幅度较大的曲面或硬脆性材料的加工等,故促进了高精度光学自由曲面的推广应用。     

Novel hybrid robot and its processes for precision polishing of freeform surfaces

Freeform surfaces have important applications in various industrial fields. However, achieving a high level surface finish on freeform surfaces using polishing is always a challenging task. Hybrid robots are promising alternatives to conventional computer numerical control (CNC) machines and industrial robots for ultra-precision machining. Herein, we present a novel custom-built hybrid robot for freeform polishing. After the laboratory prototype was successfully developed, its automation for a specific freeform surface was a major obstacle preventing its application. This critical issue was addressed by presenting a process to deal with tedious robot programming. Random tool path planning was performed in the task space, and hybrid robot motion planning was conducted in the joint space. By integrating the process flows, a robot programming toolkit was developed to directly output the control program for a specific robot controller. An illustrative example with a freeform surface is provided to verify the functionality of the developed hybrid robot and the proposed control processes, and the corresponding experimental results verify their effectiveness.     

Fast tool servo diamond turning of optical freeform surfaces for rear-view mirrors

The International Journal of Advanced Manufacturing Technology - Optical freeform surfaces have been applied in optoelectronic systems more and more widely, but it is difficult to fabricate this...