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.

An automatic grid generation approach over free-form surface for architectural design

An essential step for the realization of free-form surface structures is to create an efficient structural gird that satisfies not only the architectural aesthetics,but also the structural performance.Employing the main stress trajectories as the representation of force flows on a free-form surface,an automatic grid generation approach is proposed for the architectural design.The algorithm automatically plots the main stress trajectories on a 3D free-form surface,and adopts a modified advancing front meshing technique to generate the structural grid.Based on the proposed algorithm,an automatic grid generator named "St-Surmesh" is developed for the practical architectural design of free-form surface structure.The surface geometry of one of the Sun Valleys in Expo Axis for the Expo Shanghai 2010 is selected as a numerical example for validating the proposed approach.Comparative studies are performed to demonstrate how different structural grids affect the design of a free-form surface structure.

Parametric design of a part with free-form surfaces

3D solid models for parts with regular-form surfaces (PRFSs) are effectively generated using traditional parametric design techniques. A new model is obtained by changing some parameters defining the model. The parts with free-form surfaces (PFFSs), however, cannot be defined by several parameters. Usually they are defined by some geometric elements like profile curves. The traditional parametric design approaches have not easily dealt with the PFFSs. A method for generating a solid model and an engineering drawing for PFFSs is proposed in this paper: First, the new profiles are generated from input point data. Second, the profile information is extracted from the existing model. Last, the old profiles are replaced with the new profiles. This method can preserve the associative information of the existing model and automatically generate the drawing including views, dimen- sions, and annotations. The proposed method has been implemented using a commercial CAD/CAM system, Unigraphics, and API functions written in C-language, and were applied to the blades of a turbine generator. Some illustrative examples are pro- vided in order to show the effectiveness of the proposed method.

Study of the Contact Force in Free-form Surfaces Compliant EDM Polishing by Robot

With an elastic negative pole being driven by ultra so nic vibration and being moved along the surface of work-piece compliantly by ro bot, a new kind of effective EDM, the compliant EDM, cuts the electrically condu ctive materials away and polishes work-piece of free-form surface. The study o f the contact force between the end of polishing tool and the surface of work-p iece is the key for the compliant EDM to study its cutting mechanism and to make better use of it. This paper makes a model for the contact force and verifies i t by experiments and simulation based on the theory of elastic body kinetics and dynamic stress concentration. The research work shows that this contact force i s caused by both the electrical impulsion of EDM and the mechanical force of ult rasonic vibration, the discharge frequency of compliant EDM has a much more clos er connection with the vibration frequency of polishing tool rather than the fre quency of ultrasonic vibration.

ADAPTIVE MEASUREMENT METHOD BASED ON CHANGING-CURVATURE FOR UNKNOWN FREE-FORM SURFACE

Current measurement method for unknown free-form surface has low efficiency.To acquire given precision, a lot of null points are measured. Based on change surface curvature, anew measurement planning is put forward. Sample step is evaluated from the change curvature and thelocally-bounded character of extrapolating curve. Two coefficients, maximum error coefficient andlocal camber coefficient, are used to optimize sampling step. The first coefficient is computed toavoid sampling-point exceeding the measurement range and the second control sampling precision.Compared with the other methods, the proposed planning method can reduce the number of themeasuring-point efficiently for the given precision. Measuring point distributes adaptively by thechange surface curvature. The method can be applied to improve measurement efficiency and accuracy.

NEW VISUAL METHOD FOR FREE-FORM SURFACE RECONSTRUCTION

A new method is put forward combining computer vision with computer aidedgeometric design (CAGD) to resolve the problem of free-form surface reconstruction. The surface isfirst subdivided into N-sided Gregory patches, and a stereo algorithm is used to reconstruct theboundary curves. Then, the cross boundary tangent vectors are computed through reflectance analysis.At last, the whole surface can be reconstructed jointing these patches with G^1 continuity(tangentcontinuity). Examples on synthetic images are given.

Research on the Fault Monitoring System in Free-form Surface CNC Machining Based on Wavelet Analysis

Carrying out experiments and researches on tool bre ak age and undercut of work-piece of free-form surface by using wavelet analysis, both the fault features can be extracted in a special frequency segment of wave let decompose. According to the feature of transient fault, the author proposes for the first time the automatic determination technology of the threshold by us e of the adaptive filter characteristic of wavelet transform. Based on profound researches on steady fault feature, this dissertation makes an effective token o f steady fault feature by using wavelet energy method, and proposes the new idea to identify cut-in case and cut-out case, thereby successfully gives an uniqu e description quantitatively on the characterization of the variation of fault a nd cutting condition in the monitoring system.

Real-time accurate Free-Form Deformation in terms of triangular Bézier surfaces

We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessel- lation shader algorithms.

Tool-path planning for free-form surface high-speed high-resolution machining using torus cutter

In CNC machining, two essential components decide the accuracy and machining time for a sculptured surface: one is the step-size interval, the other is the tool-path interval. Due to the limitation of the conventional method for calculating the tool-path interval, it cannot satisfy the machining requirement for high-speed and high-resolution machining. Accordingly, for high-speed and high-resolution machining, the current study proposes a new tool-path interval algorithm, plus a variable step-size algorithm for NURBS. Furthermore, a new type cutter, which can improve the cutting efficiency, is investigated in the paper. The transversal equation of the torus cutter onto the flat plan is given in this paper. The tool-path interval is calculated with the transversal equation and the proposed algorithm. The illustrated example shows that the redundant tool paths can be reduced because an accurate tool-path interval could be calculated.

Tool selection and collision-free in 5-axis numerical control machining of free-form surfaces

The methodology of 5-axis cutter selection to avert collision for free-form surface machining by flat-end cutters is presented. The combination of different cutters is adopt aiming at short machining time and high precision. The optimal small cutter is determined based on the geometric information of the points where a cutter most probably collide with the machined surface. Several larger cutters are selected to machine the surface in order to find the interference-free area. The difference of machining time for this area between the optimal small cutter and the large cutters is calculated. The functional relationship between the machining time and the radius of a cutter is established, by which the optimal number of cutters is obtained. The combination of cutters, which possesses the minimum overall machining time, is selected as the optimal cutter sizes. A case study has demonstrated the validity of the proposed methodology and algorithms.

A Computer Vision Method for 3D Reconstruction of Curves-Marked Free-Form Surfaces

Visual method is now broadly used in reverse engineering for 3D reconstruction. The traditional computer vision methods are feature-based, i.e., they require that the objects must reveal features owing to geometry or textures. For textureless free-form surfaces, dense feature points are added artificially. In this paper, a new method is put forward combining computer vision with CAGD. The surface is subdivided into N-side Gregory patches using marked curves, and a stereo algorithm is used to reconstruct the curves. Then, the cross boundary tangent vector is computed through reflectance analysis. At last, the whole surface can be reconstructed by jointing these patches with 1Gcontinuity.

A Real-time NURBS Surface Interpolator for 5-axis Surface Machining

A real-time non-uniform rational B-spline （NURBS） surface interpolator is proposed and 5-axis machining method with a flat-end cutter is discussed. With the Taylor expansion and the coordinate transformation, the algorithms of NURBS interpolation, cutter effective machining radius, cutter offsetting and.inverse kinematics are deduced and implemented, respectively. Different from the conventional free-form surface machining, the proposed interpolator can real-time generate the motion commands of computer numerical control （CNC） machines with CC feedrate, rather than that of CL. An example part surface is demonstrated and the results of simulation show that the proposed method can be applied in actual 5-axis surface machining.

Path,feedrate and trajectory planning for free-form surface machining:A state-of-the-art review

Nowadays,free-form surfaces have been widely used in various industrial fields.They are usually machined by CNC machine tools,but recently have also begun to be manufactured by industrial robotic arm manipulators,thanks to low cost,large operation reaching space and high machining flexibility of robot.So far,various methodologies have been proposed to improve efficiency and quality of free-form surface machining,thus this paper aims at providing a state-ofthe-art review on research advances in free-form surface machining.In this review,tool path generation,feedrate scheduling in Cartesian space and trajectory planning in joint space are focused for both CNC machining and robot machining,and their research statues,existing difficulties and key issues are discussed in detail.Finally,the feasible routes,breakthrough points and future development trend are also expounded.

TOOL ORIENTATION PLANNING FOR FIVE-AXIS CNC MACHINING OF OPEN FREE-FORM SURFACES

For the geometry characteristics of open free-form surfaces,it is hard to consider global interference during the planning of feasible domains.Therefore,the optimal kinematic orientation of tool axis will no longer be confined to the boundary of feasible domains.In this paper,according to the principle demanding that the tool should be fitted to a surface as close as possible and relevant processing parameters,a feasible domain of tool orientation for each cutter contact is planned in the local feed coordinates system.Then,these feasible domains of the tool orientation are transformed into the same coordinates system of the machine tool by the inverse kinematics transformation.The linear equations based feasible domain method and Rosen gradient projection algorithm are used to improve the optimization process in precision and efficiency of the algorithm.It constructs the variation of tool orientation optimization model and ensures the smoothness of tool orientation globally.Simulation and analysis of examples show that the proposed method has good kinematics performance and greatly improves the efficiency.

Automatic surface localization by defining weighted-iteration distance function and Lyapunov-test statistic

Automatic localization,aligning the measured points with the design model,is a basic task in free-form surface inspection.The main difficulty of current localization algorithms is how to define effective distance function and localization reliability index.This paper proposes a new method of calculating motion parameters and evaluating localization reliability.First,improved modified coefficient is defined and applied to weighted-iteration distance function,which better approximates the point-to-surface closest distance.It can control the contribution ratios of different measured points by considering the curvature feature and iterative residual.Second,the mapping relationship between localization error and geometric error is analyzed,from which a Lyapunov-test statistic is derived to define a frame-independence index.Then,the determination of localization reliability changes into a supposition examination problem.This can avoid rejecting correct motion parameters,which exists in the traditional judgment of absolute root-mean-square distance.In addition,two test experiments are implemented to demonstrate the proposed localization algorithm.

Solving the input data in error correc-tion of optical fabrication by finite Fourier coefficient algorithm

A free-form lens (FFL) is a special surface that is difficult to be fabricated. FFL are usually fabricated by computer-controlled optical surfacing (CCOS) technique. During CCOS, the material removal amount is determined by the unit removal function (URF) convoluting with the input data――the dwell time. When the removal amount and the URF are known, how to solve the input data involves the special algorithm――deconvolution. Usually, the input data are solved by virtue of low pass filter or iterative methods. However, an approximation solution would destroy the machining stability nec-essary to perform precisely CCOS. In this paper, to solve the input data, a new method that is based on the finite Fourier coefficient is put forward. It can give a continuous and accurate solution for fabricating choice. Several parameters are simulated, which influ-ence the process of CCOS, and evaluating on the effect of the method is also carried out. Experimental results verify that this method is suitable for guiding the manufacturing of high precision FFL.