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 freeform surface model; secondly, apply freeform surface fitting method determine the geometry and topology properties of recovery 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~ 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 Gt continuity requirements in reverse engineering. This research converts the problem of topology recovery for consistent surface model to the problem of constructing G1 patches from a given curve network, and provides a new idea to model repairing study.

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.

NON-CONTACT MEASUREMENT SYSTEM OF FREEFORM SURFACE AND NURBS RECONSTRUCTION OF MEASUREMENT POINTS

Based on the development of the non-contact measurement system of free-formsurface, NURBS reconstruction of measurement points of freeform surface is effectively realized bymodifying the objective function and recursive procedure and calculating the optimum number ofcontrol points. The reconstruction precision is evaluated through Ja-cobi's transformation method.The feasibility of the measurement system and effectiveness of the reconstruction algorithm aboveare proved by experiment.

CNC NON-CONTACT MEASURING SYSTEM FOR FREEFORM SURFACE

Developing CNC measuring method on the base of coordinate machine can makethe best of the hardware resource of CNC system and realize the integration of CAD/CAM/CAT. Based onthe evenly spaced parallel planes scanning, a new adaptive digitizing approach for freeform surfacenamely arc length extrapolation is put forward. By this way, the digitizing approach can be addedto the CNC system, while the system's hardware and software are not changed.

Investigation of a dynamics-oriented engineering approach to ultraprecision machining of freeform surfaces and its implementation perspectives

In current precision and ultraprecision machining practice,the positioning and control of actuation systems,such as slideways and spindles,are heavily dependent on the use of linear or rotary encoders.However,positioning control is passive because of the lack of direct monitoring and control of the tool and workpiece positions in the dynamic machining process and also because it is assumed that the machining system is rigid and the cutting dynamics are stable.In ultraprecision machining of freeform surfaces using slow tool servo mode in particular,however,account must be taken of the machining dynamics and dynamic synchronization of the cutting tool and workpiece positioning.The important question also arises as to how ultraprecision machining systems can be designed and developed to work better in this application scenario.In this paper,an innovative dynamics-oriented engineering approach is presented for ultraprecision machining of freeform surfaces using slow tool servo mode.The approach is focused on seamless integration of multibody dynamics,cutting forces,and machining dynamics,while targeting the positioning and control of the tool–workpiece loop in the machining system.The positioning and motion control between the cutting tool and workpiece surface are further studied in the presence of interfacial interactions at the tool tip and workpiece surface.The interfacial cutting physics and dynamics are likely to be at the core of in-process monitoring applicable to ultraprecision machining systems.The approach is illustrated using a virtual machining system developed and supported with simulations and experimental trials.Furthermore,the paper provides further explorations and discussion on implementation perspectives of the approach,in combination with case studies,as well as discussing its fundamental and industrial implications.

Study on manufacturing freeform surface parts in micro EDM based on skin effect theory

Micro fabrication of freeform surface parts made of hard and brittle materials is always a tough job in micro machining field. This paper tries to fabricate freeform surface feature by using smooth surface of tool electrode after tool wear in micro EDM. According to the skin effect theory, the tool end shape in the stage of uniform wear can be changed by adjusting the frequency of discharge pulse. The electrical energy distributing rule of tool electrode section in RC circuit has been investigated under the influence of skin effect, and the law of spark location change has been summarized. The experimental studies demonstrate that different shapes of tool ends can be achieved by varying the pulse frequencies of discharge power supply. Additionally, a micro part of freeform surface feature with high precision and good surface quality has been successfully obtained by micro EDM through adopting the smooth surface after tool wear.

Tool path generation and optimization for freeform surface diamond turning based on an independently controlled fast tool servo

Diamond turning based on a fast tool servo(FTS)is widely used in freeform optics fabrication due to its high accuracy and machining efficiency.As a new trend,recently developed high-frequency and long-stroke FTS units are independently driven by a separate control system from the machine tool controller.However,the tool path generation strategy for the independently controlled FTS is far from complete.This study aims to establish methods for optimizing tool path for the independent control FTS to reduce form errors in a single step of machining.Different from the conventional integrated FTS control system,where control points are distributed in a spiral pattern,in this study,the tool path for the independent FTS controller is generated by the ring method and the mesh method,respectively.The machined surface profile is predicted by simulation and the parameters for the control point generation are optimized by minimizing the deviation between the predicted and the designed surfaces.To demonstrate the feasibility of the proposed tool path generation strategies,cutting tests of a two-dimensional sinewave and a micro-lens array were conducted and the results were compared.As a result,after tool path optimization,the peak-to-valley form error of the machined surface was reduced from 429 nm to 56 nm for the two-dimensional sinewave by using the ring method,and from 191 nm to 103 nm for the micro-lens array by using the mesh method,respectively.

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.

The Construction Technology of Freeform Surface Spatial Bending-Torsion Steel Structure

Taking the construction project of the National Cybersecurity Talents and Innovation Base as an example,this paper studies the construction technology of freeform surface spatial bending-torsion steel structure based on structural design model transformation,including the parametric modeling of deepening design model,computer-aided bending and torsion frame production,flexible docking in the bending-torsion combination unit,and welding stress deformation,in hope to provide reference for similar projects in the future.

Constructing G^2 Continuous Curve on Freeform Surface with Normal Projection

This article presents a new method for G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surfaee with prescribed tangent direction and curvature vector, respectively, at every point. First, a G2 continuous curve is constructed in three-dimensional space. Then the curve is projected normally onto the given surface. The desired interpolation curve is just the projection curve, which can be obtained by numerieally solving the initialvalue problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit ease. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface. Numerical experiments demonstrate that it is effective and potentially useful in numerical control （NC） machining, path planning for robotic fibre placement, patterns design on surface and other industrial and research fields.

Viewpoint Planning for Freeform Surface Inspection Using Plane Structured Light Scanners

This paper proposes an automatic model-based viewpoint planning method, which can achieve high precision and high efficiency for freeform surfaces inspection using plane structured light scanners. The surface model is utilized in stereolithography format, which is widely used as an industrial standard. The proposed method consists of 4 steps： topology reconstruction, mesh refinement, scan direction determination and viewpoint generation. In the first step, the topology structure of the surface model is reconstructed according to a designed data structure, based on which a neighborhood search algorithm is developed. In the second step, big facets in the surface model are segmented into several small ones, which are suitable for viewpoint planning. In the third step, an initial scan region of a viewpoint is grouped by the neighborhood search algorithm combining with total area and normal vector restrictions. Accordingly, the scan direction is determined by the normal vectors of facets in the initial scan region. In the fourth step, the position, the orientation, and the final scan region of the viewpoint are determined by 4 scan constraints, i.e., field of view, working distance range, view angle and overlap. Experimental results verify the effectiveness and advantages of the proposed method.

Model-based adaptive non-null interferometry for freeform surface metrology

A model-based adaptive non-null interferometry （MANI） is proposed for steep optical freeform surfaces in situ testing. The deformable mirror （DM） affording the flexible compensation is monitored with the beam in the interferometer by a wavefront sensor. The residual wavefront aberration in the non-null interferogram is eliminated by the multi-configuration ray tracing algorithm based on the system model, especially the DM surface model. The final figure error can be extracted together with the surface misalignment aberration correction. Experiments proving the feasibility of the MANI are shown.

Ray targeting for optimizing smooth freeform surfaces for LED non-rotational illumination

We propose an effective optimization method for generating smooth freeform surfaces for light-emitting diode(LED)non-rotational illumination based on ray targeting.This method begins with a starting design and goes through two optimization steps.An initial estimate is determined using a partial differential equation(PDE)method and a variable separation mapping.In the first optimization step the merit function is developed with ray targeting to ensure the shape of the illumination pattern.The purpose of the second optimization is to further improve the optical performance by constructing the merit function with uniformity and efficiency.Smooth freeform reflective and refractive surfaces,which can produce a uniform rectangular illumination without rotational symmetry,are designed using this method.The results show that uniform rectangular illumination is achieved and that smooth freeform surfaces are obtained.With ray targeting,the design efficiency can be significantly enhanced,and excellent optical performance can be achieved.

Off-axis three-mirror reflective zoom system based on freeform surface

A reflective optical system is not affected by chromatic aberration, so it has a wide range of applications. Based on the design theory of reflective zoom system with three mirrors, this paper presents the simulation, optimiza- tion, and image quality evaluation of the traditional off- axis three-mirror zoom system and freeform off-axis three- mirror reflective zoom system.. In these systems, the optical design was aided by software CODEV. Through the analysis of aberrations and structural performance for the traditional aspherical off-axis three-mirror system, the freeform surface was introduced to the tertiary mirror to improve the balance capacity for optical aberrations. This off-axis three-mirror reflective zoom system based on freeform surface could provide technical reference to the study of such systems.

Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review

Driven by the ever increasing demand in function integration,more and more next generation high value-added products,such as head-up displays,solar concentrators and intra-ocular-lens,etc.,are designed to possess freeform(i.e.,non-rotational symmetric)surfaces.The toolpath,composed of high density of short linear and circular segments,is generally used in computer numerical control(CNC)systems to machine those products.However,the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration,which will decrease the machining efficiency and product surface finish.Driven by the ever-increasing need for high-speed high-precision machining of those products,many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry,aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods.This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications.The advantages and disadvantages of these approaches are discussed.Possible future research directions are also offered.

Design of a hyper-numerical-aperture deep ultraviolet lithography objective with freeform surfaces

We have proposed and developed a design method of a freeform surfaces （FFSs） based hyper-numerical-aperture deep ultraviolet （DUV） projection objective （PO） with low aberration. With an aspheric initial configuration, lens-form parameters were used to determine the best position to remove elements and insert FFSs. The designed FFSs PO reduced two elements without increasing the total thickness of the glass materials. Compared with aspheric initial configuration, the wavefront error of the FFSs PO decreased from 0.006λ to 0.005λ, the distortion reduced from 1 to 0.5 nm, and the aspheric departure decreased from 1.7 to 1.35 mm. The results show that the design method of the FFSs PO is efficient and has improved the imaging performance of PO. The design method of FFSs PO provides potential solutions for DUV lithography with low aberrations at 10–5 nm nodes.

Surface form inspection with contact coordinate measurement:a review

Parts with high-quality freeform surfaces have been widely used in industries,which require strict quality control during the manufacturing process.Among all the industrial inspection methods,contact measurement with coordinate measuring machines or computer numerical control machine tool is a fundamental technique due to its high accuracy,robustness,and universality.In this paper,the existing research in the contact measurement field is systematically reviewed.First,different configurations of the measuring machines are introduced in detail,which may have influence on the corresponding sampling and inspection path generation criteria.Then,the entire inspection pipeline is divided into two stages,namely the pre-inspection and post-inspection stages.The typical methods of each sub-stage are systematically overviewed and classified,including sampling,accessibility analysis,inspection path generation,probe tip radius compensation,surface reconstruction,and uncertainty analysis.Apart from those classical research,the applications of the emerging deep learning technique in some specific tasks of measurement are introduced.Furthermore,some potential and promising trends are provided for future investigation.

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.

Efficient cutting path planning for a non-spherical tool based on an iso-scallop height distance field

Iso-scallop height machining means,when machining a freeform surface,the scallop height between any two neighboring tool paths on the surface will be a constant(i.e.,the given threshold),which is preferable among various freeform surface machining strategies due to its high machining efficiency as well as better machine tool’s dynamics.However,all the existing iso-scallop height path planning methods pertain to only the ball-end or flat-end types of tools.In recent years,the non-spherical cutting tool has become more and more popular,especially for five-axis machining of complex freeform surfaces,majorly owing to its non-constant curvature which can be utilized to adaptively fit the tool to the surface to both avoid the local gouging and enlarge the cutting width.However,there have been no reported works on iso-scallop height five-axis tool path generation for a non-spherical tool,and,in this paper,we present one.Specifically,we first define and construct two fields on the surface to be machined-the collision-free tool orientation field(vector)and the iso-scallop height distance field(scalar).The iso-lines of the scalar field and their associated tool orientation field vectors then naturally serve as potential iso-scallop height five-axis tool paths,and we present a propagation-based algorithm to construct the desired tool path from the iso-lines.The computer simulation and physical cutting experiments confirm that everywhere on the surface,except maybe near the saddle curves of the scalar filed,the scallop height is exactly the given thresh-old.By adding the saddle curves as extra tool paths,the final machined surface then is assured of the required scallop height requirement.

Automatic recognition of intersecting features of freeform sheet metal parts

This paper presents an approach for recognizing both isolated and intersecting geometric features of freeform surface models of parts,for the purpose of automating the process planning of sheet metal forming.The developed methodology has three major steps:subdivision of B-spline surfaces,detection of protrusions and depressions,and recognition of geometric features for sheet metal forming domain.The input geometry data format of the part is based on an IGES CAD surface model represented in the form of trimmed B-spline surfaces.Each surface is classified or subdivided into different curvature regions with the aid of curvature property surfaces obtained by using symbolic computation of B-spline surfaces.Those regions satisfying a particular geometry and topology relation are recognized as protrusion and depression(DP) shapes.The DP shapes are then classified into different geometric features using a rule-based approach.A verified feasibility study of the developed method is also presented.