Characterization of surface defects in fast tool servo machining of microlens array using a pattern recognition and analysis method

Microlens array (MLA) is a type of structured freeform surfaces which are widely used in advanced optical products. Fast tool servo (FTS) machining provides an indispensible solution for machining MLA with superior surface quality than traditional fabrication process for MLA. However, there are a lot of challenges in the characterization of the surface defects in FTS machining of MLA. This paper presents a pattern recognition and analysis method (PRAM) for the characterization of surface defects in FTS machining of MLA. The PRAM makes use of the Gabor filters to extract the features from the MLA. These features are used to train a Support Vector Machine (SVM) classifier for defects detection and analysis. To verify the method, a series of experiments have been conducted and the results show that the PRAM produces good accuracy of defects detection using different features and different classifiers. The successful development of PRAM throws some light on further study of surface characterization of other types of structure freeform surfaces.     

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。     

Topology recovery technique for complex freeform surface model after local geometry repair

Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations.Local geometry repair,such as cover holes or replace bad surfaces by adding new surface patches for dealing with inconsistencies among the confluent region,where multiple surfaces meet,is a common technique used in CAD model repair and reverse engineering.However,local geometry repair destroys the topology of original CAD model and increases the number of surface patches needed for freeform surface shape modeling.Consequently,a topology recovery technique dealing with complex freeform surface model after local geometry repair is proposed.Firstly,construct the curve network which determine the geometry and topology properties of recovery freeform surface model;secondly,apply freeform surface fitting method to create B-spline surface patches to recover the topology of trimmed ones.Corresponding to the two levels of enforcing boundary conditions on a B-spline surface,two solution schemes are presented respectively.In the first solution scheme,non-constrained B-spline surface fitting method is utilized to piecewise recover trimmed confluent surface patches and then employs global beautification technique to smoothly stitch the recovery surface patches.In the other solution scheme,constrained B-spline surface fitting technique based on discretization of boundary conditions is directly applied to recover topology of surface model after local geometry repair while achieving G 1 continuity simultaneously.The presented two different schemes are applied to the consistent surface model,which consists of five trimmed confluent surface patches and a local consistent surface patch,and a machine cover model,respectively.The application results show that our topology recovery technique meets shape-preserving and G 1 continuity requirements in reverse engineering.This research converts the problem of topology recovery for consistent surface model to the problem of constructing G 1 patches from a given curve network,and provides a new idea to model repairing study.     

A robust surface fitting and reconstruction algorithm for form characterization of ultra-precision freeform surfaces

Ultra-precision freeform surfaces are non-rotational symmetric surfaces possessing sub-micrometer form accuracy and nanometric surface finish. Although they can be fabricated accurately by ultra-precision machining technology, their surface quality is difficult to be characterized. Surface reconstruction is a vital task in the form characterization of ultra-precision freeform surfaces. This paper presents a robust surface fitting algorithm to reconstruct a high fidelity surface from measured discrete points while the surface smoothness can be ensured as well. A fitting threshold named confidence interval of fitting error is proposed to strike the balance between fitting accuracy and surface smoothness in the fitting process. The fitting algorithm is in two steps. In the first step, bidirectional sampling method is developed to extract a curve network from measured points cloud to construct an initial surface. In the second step, the fitting error of the initial surface is minimized to meet the prescribed fitting error threshold. A series of experimental work has been conducted and the results show that the proposed algorithm is able to provide effective means for increasing the accuracy in the form characterization of ultra-precision freeform surfaces.     

Grain mapping to freeform surface for machining using parameter-based incremental tracking method

This paper presents a novel method for mapping a texture for machining onto a freeform surface. When a grain texture designed on a 2D plane is projected onto a freeform surface simply, the texture is distorted along the curvature of the surface in the projection direction. Therefore, a method is required to suppress this distortion. The algorithm proposed in this paper rapidly generates a point cloud that represents a texture with less distortion on a simply connected parametric surface. Specifically, four equations that express local geometry constraints instead of conventional parameterization methods are presented to reduce the distortion between adjacent points on the point cloud. Solving these equations can generate grain textures on freeform surfaces. This paper examines two grain images mapped to two freeform surfaces that were prepared as case studies to demonstrate the effectiveness of the proposed method.     

Accurate evaluation of free-form surface profile error based on quasi particle swarm optimization algorithm and surface subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline(NURBS) for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system(DCS) and measurement coordinate system(MCS) for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization(QPSO) is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.     

Fabrication of 3D submicron to micro textured surfaces using backside patterned texturing (BPT)

This work presents a novel fabrication method for submicron to micro size textures on flat surfaces using the backside patterned texturing (BPT). The proposed method utilizes the pre-fabricated macro-features on the backside of work material, and thereafter the front side is face turned with a single point diamond tool to generate textured surfaces. Different from existing texturing methods, BPT produces textured surfaces from submicron to micro scale without any external gadgets such as vibration assisted machining or synchronized tool-spindle motion. The miniature feature arises on the diamond turned surface due to the induced residual stresses when the specimen is unleashed from the machine. To demonstrate the efficacy of the method, a series of machining experiments were conducted to fabricate various types of freeform surface textures like water-drop freeform, cylindrical freeform surfaces, etc. The fabrication methodology of different sizes of bumps with precisely controlled surface quality is illustrated. The texture profiles comprising the deformation height from hundreds of nanometer to few micrometers with mirror surface quality were successfully fabricated on the diamond machined surface. The experimental results suggest that the pre-fabricated pattern, workpiece thickness and machining condition play a critical role to determine the final shape and geometry of generated textures.     

Design of a Universal Fixture for Laser Scanning

In this paper, a universal fixture for 3D laser scanning is presented. In order to reconstruct the surface or CAD model from the scanned data of an existing part, it is necessary to integrate the point data from several views of an object into a common reference frame. When the registration is implemented with a feature-based method using tooling balls, the reference coordinate system is established by several common tooling balls from different point clouds. The laser scanner is often used to acquire the surface information of the part, but is limited in its measuring direction, which is fixed only along the z-axis. A universal fixture using several joints and an adjustable tooling ball holder is designed considering the convenience of the part set-up and the accuracy of the registration. The location of the tooling balls can be arranged to avoid the occlusion of the part and to minimise the registration error. The universal fixture was applied to a wrap-around part having freeform surfaces to demonstrate the effectiveness of the proposed design.     

CAD-DIRECTED INSPECTION PLANNING FOR FREEFORM SURFACE USING CONTACT PROBES

A methodology for CAD-directed measurement of freeform surface using a coordinate measuring machine equipped with a touch-trigger probe is presented,mainly including adaptive sampling of measurement points and registration of freeform surface.The proposed sampling method follows four steps: Freeform surface is fitted by bi-cubic B-spline; Curvedness measure of the surface is computed; Given a number of sampling points,an iterative algorithm is constructed for selecting a set of measurement points by employing the curvedness information; The measurement points is regularized for tradeoff between maximizing the measurement accuracy and minimizing the sampling time and cost.The aforesaid algorithm is demonstrated in term of a marine propeller blade.An offset surface registration method is presented to improve alignment accuracy of freeform objects,and Monte Carlo simulation is conducted to verify the effectiveness of the method.     

Prediction of surface reconstruction uncertainties for freeform surface inspection

A method is introduced to predict uncertainties of the B-spline freeform surfaces that are reconstructed from the measurement points for inspection of freeform surfaces. The uncertainties of a reconstructed B-spline surface are modeled by variances of coordinates of points on this freeform surface. Prediction of the uncertainty at any location on the reconstructed B-spline surface is carried out in two steps: (1) estimation of variances of the B-spline surface’s control points introduced by the surface reconstruction process, and (2) propagation of the variances from the control points to the points on the B-spline freeform surface. In this research, the variances of the control points of the reconstructed B-spline surface in all three directions are considered to improve the accuracy of uncertainty prediction in the regions with significant changes of geometric shapes. Both the errors and uncertainties at different locations on the reconstructed surface are considered in freeform surface inspection to compare the manufactured surface against the design surface and its tolerance. The developed method has been applied to two case studies to demonstrate its effectiveness.     

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。     

Three-dimensional surface profile measurement of a cylindrical surface using a multi-beam angle sensor

To investigate the application of the multi-beam angle sensor (MBAS) to high-precision optical aspheric and freeform surfaces, which are critical components in optical systems, we present a method of using an MBAS to reconstruct an aspheric surface from angle data. The MBAS is based on a multi-autocollimator system with a microlens array, which can split the beam into several spots and can convert centroid detection of the light intensity into an angle measurement. The MBAS is designed to address the curvature-range problem via a circumferential scan better than other methods and automatically eliminates the tilt error caused by rotation of a workpiece. Using a tracking technique, the MBAS can automatically determine focal spot positions from the centroid measurement of the light intensity. This is directly related to the accuracy of the angular difference measurement. The experimental results confirm the feasibility of using an MBAS for 3D surface profile measurements of cylindrical surfaces.     

基于实物的一种自由曲面逆向工程方法

提出一种基于实物的自由曲面逆向工程方法,利用投影栅相位法和ObjectARX开发工具,可在AutoCAD环境下自动建立三维曲面模型,方便地实现自由曲面的反求,并可直接实现与其他CAD软件的数据交换.     

Nanofinishing of freeform surfaces (knee joint implant) by rotational-magnetorheological abrasive flow finishing (R-MRAFF) process

Freeform complex surfaces have become an inevitable part of many devices to perform specific functions. Some of these components require nanolevel surface roughness value to meet the desired requirements in their applications. Finishing of freeform surfaces to nanometer surface roughness value is always difficult for any process. Rotational-magnetorheological abrasive flow finishing (R-MRAFF) process has been applied so far for finishing internal surfaces of relatively simple geometry. In this work, an attempt has been made to improve external topography of freeform surfaces using this process. Large hydrodynamic pressure coupled with magnetic fluid is the principal idea behind these experiments. A smooth mirror like finished surface is achieved with improved finishing rate (nanometer/min) by controlling two motions (axial and rotational) simultaneously on stainless steel workpiece similar to knee joint implant. Magnetorheological polishing fluid with different mesh sizes of abrasive particles and at different extrusion pressures is used to reduce final surface roughness value, to increase uniformity of surface finish on the freeform surface and to enhance finishing rate. Surface roughness ranging from 35 to 78 nm is achieved at various locations as compared to larger variation in Ra value obtained in the earlier research work.     

Repeated surface registration for on-line use

We consider the problem of matching sets of 3D points from a measured surface to the surface of a corresponding computer-aided design (CAD) object. The problem arises in the production line where the shape of the produced items is to be compared on-line with its pre-described shape. The involved registration problem is solved using the iterative closest point (ICP) method. In order to make it suitable for on-line use, i.e., make it fast, we pre-process the surface representation of the CAD object. A data structure for this purpose is proposed and named Distance Varying Grid tree. It is based on a regular grid that encloses points sampled from the CAD surfaces. Additional finer grids are added to the vertices in the grid that are close to the sampled points. The structure is efficient since it utilizes that the sampled points are distributed on surfaces, and it provides fast identification of the sampled point that is closest to a measured point. A local linear approximation of the surface is used for improving the accuracy. Experiments are done on items produced for the body of a car. The experiments show that it is possible to reach good accuracy in the registration and decreasing the computational time by a factor 700 compared with using the common kd-tree structure.     

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.     

自由曲面工件多点连续成形方法

为了实现自由曲面工件的高效率、低成本制造,分析与比较常用的柔性成形方法;从成形过程的连续性考虑,将柔性成形分为分段成形与连续成形;从变形区大小考虑,又划分为点成形、面成形与线成形等不同类型。比较不同成形方式的优点与缺点,指出自由曲面工件的高质量、高效率成形是亟待解决的技术难题。提出基于连续线成形方法的自由曲面工件高效、柔性成形思路;并提出采用多点调整式柔性辊的多点连续成形技术方案;探讨多点连续成形技术的基本原理、关键技术及主要特点。运用具有多个控制点的挠性轴设计出可弯曲、可调整的柔性辊,开发出多点卷板成形试验装置。多种三维曲面板类件的连续成形试验结果表明,多点连续成形技术能够解决自由曲面工件的高效加工难题。     

EQUIVALENT NORMAL CURVATURE APPROACH MILLING MODEL OF MACHINING FREEFORM SURFACES

A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.