Hong-Tzong Yau

Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery

Methodologies for planning motion trajectory of parametric interpolation such as non-uniform rational B-spline (NURBS) curves have been proposed in the past. However, most of the algorithms were developed based on the constraints of feedrate, acceleration/deceleration (acc/dec), jerk, and chord errors. The errors caused by servo dynamics were rarely included in the design process. This paper proposes an integrated look-ahead dynamics-based (ILD) algorithm which considers geometric and servo errors simultaneously. The ILD consists of three different modules: a sharp corner detection module, a jerk-limited module, and a dynamics module. The sharp corner detection module identifies sharp corners of a curve and then divides the curve into small segments. The jerk-limited module plans the feedrate profile of each segment according to the constraints of feedrate, acc/dec, jerk, and chord errors. To ensure that the contour errors are bounded within the specified value, the dynamics module further modifies the feedrate profile based on the derived contour error equation. Simulations and experiments are performed to validate the ILD algorithm. It is shown that the ILD approach improves tracking and contour accuracies significantly compared to adaptive-feedrate and curvature-feedrate algorithms.

Real-time NURBS interpolation using FPGA for high speed motion control

Modern motion control adopts NURBS (Non-Uniform Rational B-Spline) interpolation for the purpose of achieving high-speed and high-accuracy performance. However, in conventional control architectures, the computation of the basis functions of a NURBS curve is very time-consuming due to serial computing constraints. In this paper, a novel FPGA (Field Programmable Gate Array) based motion controller utilizing its high-speed parallel computing power is proposed to realize the Cox-de Boor algorithm for second and higher degrees NURBS interpolation. The motion control algorithm is also embedded in the FPGA chip to implement real-time control and NURBS interpolation simultaneously for multi-axis servo systems. The proposed FPGA-based motion controller is capable of performing the Cox-de Boor algorithm and the IIR (Infinite Impulse Response) control algorithm in about 46 clock cycles, as compared to the 1303 clock cycles by the traditional approach. Numerical simulations and experimental tests using an X-Y table verify the outstanding computation performance of the FPGA-based motion controller. The result indicates that shorter sampling time (10 @ms) can be achieved for NURBS interpolation which is highly critical to the success of high-speed and high-accuracy motion control.

A Delaunay-based region-growing approach to surface reconstruction from unorganized points

This paper presents a Delaunay-based region-growing (DBRG) surface reconstruction algorithm that holds the advantages of both Delaunay-based and region-growing approaches. The proposed DBRG algorithm takes a set of unorganized sample points from the boundary surface of a three-dimensional object and produces an orientable manifold triangulated model with a correct geometry and topology that is faithful to the original object. Compared with the traditional Delaunay-based approach, the DBRG algorithm requires only one-pass Delaunay computation and needs no Voronoi information because it improves the non-trivial triangle extraction by using a region-growing technique. Compared with the traditional region-growing methods, the proposed DBRG algorithm makes the surface reconstruction more systematic and robust because it inherits the structural characteristics of the Delaunay triangulation, which nicely complements the absence of geometric information in a set of unorganized points. The proposed DBRG algorithm is capable of handling surfaces with complex topology, boundaries, and even non-uniform sample points. Experimental results show that it is highly efficient compared with other existing algorithms.

Reverse engineering of engine intake ports by digitization and surface approximation

Abstract This paper describes a research development for the design of engine intake ports using reverse engineering techniques. The background is typical of many automotive applications where digitization and reverse engineering become necessary when the design is subject to changes during production or testing. After careful analysis of the problem, CMM contact measurement was selected to digitize the complex intake ports. Part segmentation and semi-automatic scanning were applied to the digitization process. For the purpose of data reduction and surface approximation, a new approach to the fitting of rational B-splines was developed. This is because rational B-splines have more flexibility and can approximate complex geometry more accurately than traditional Bezier or B-splines. Furthermore, skinning—a cross-sectional design technique—was utilized to construct the surface to reduce the computation cost. Surface merging was also implemented to maintain the surface boundary continuity. Finally, the enclosed surface volume is produced and can be transferred to commercial CAD/CAM systems through IGES translation. Examples with complex intake ports were described to validate the approach.

Extension of surface reconstruction algorithm to the global stitching and repairing of STL models

In the design of complex parts involving free-form or sculptured surfaces, the design is usually represented by a B-rep model. But in production involving rapid prototyping (RP) or solid machining, the B-rep model is often converted to the popular STL model. Due to defects such as topological and geometric errors in the B-rep model, the resulting STL model may contain gaps, overlaps, and inconsistent orientations. This paper presents the extension of a surface reconstruction algorithm to the global stitching of STL models for RP and solid machining applications. The model to be stitched may come from the digitization of physical objects by 3D laser scanners, or the triangulation of trimmed surfaces of a B-rep model. Systematic procedures have been developed for each of these two different but equally important cases. The result shows that the proposed method can robustly and effectively solve the global stitching problem for very complex STL models.

A new approach to z-level contour machining of triangulated surface models using fillet endmills

Precision z-level contour machining is important for various computer-aided manufacturing (CAM) applications such as pocket machining and high-speed machining (HSM). This paper presents a new z-level contour tool-path generation algorithm for NC machining of triangulated surface models. Traditional approaches of z-level machining rely on the creation of accurate CL (cutter location) surfaces by surface offsetting or high-density z-map generation, which is computationally expensive and memory demanding. In contrast, this paper presents a novel approach to the generation of CL data directly from the section polygon of a triangulated surface model. For each polygon vertex of the contour, the offset direction is determined by the normal to the edge, while the offset distance is not fixed but is determined from the cutter shape and the part surface. An interference-free tool-path computation algorithm using fillet endmills is developed. Since there is no need to create a complete CL surface or high-density z-map grids, this proposed method is highly efficient and more flexible, and can be directly applied to triangulated surfaces either tessellated from CAD models, or reconstructed from 3D scanned data for reverse engineering (RE) applications.

Development of command-based iterative learning control algorithm with consideration of friction, disturbance, and noise effects

In this brief, a command-based iterative learning control (ILC) architecture is proposed to compensate for friction effect and to reduce tracking error caused by servo lag. In contrast to a feedback-feedforward control structure, the proposed methodology utilizes the learning algorithm that updates the input commands based on the tracking errors from the previous machining process. The effects of noise accumulations from each learning process of the ILC are analyzed by formulating the equivalent error dynamic and updated command equations, and the P-type ILC with a zero-phase filter is applied to alleviate noise and disturbance effects. It is shown that, for tracking a circle, the quadrant protrusions caused by friction can be reduced substantially by the updated command containing a concave shape located at the crossing of the zero velocity. Finally, analytical simulation and experimental results demonstrate that the command-based ILC algorithm can enhance the tracking performance significantly.

A Reverse Engineering Approach to Generating Interference-Free Tool Paths in Three-Axis Machining from Scanned Data of Physical Models

An NC tool path is usually generated by sweeping parametric surfaces of a CAD model. In modern design, freeform or sculptured surfaces are increasingly popular for representing complex geometry for aesthetic or functional purposes. Traditionally, a prototype is realised by machining the workpiece using the NC codes generated from a CAD model. The machined part can then be compared with the CAD model by measurement using a coordinate measuring machine. In this paper, a reverse engineering approach to generating interference-free tool paths in three-axis machining from the scanned data from physical models is presented. There are two steps in this procedure. First, a physical model is scanned by a 3D digitiser, and multiple data sets of the complex model are obtained. A surface registration algorithm is proposed to align and integrate those data to construct a complete 3D data set. A shortest-distance method is used to determine the connecting sequence of the neighbouring points between two adjacent scan lines, such that the scanned data are converted into triangular polygons. Tool paths are then generated from the tessellated surfaces. Using the Z-map method, interference-free cutter-location data are calculated, relative to the vertex, edges, and planes of the triangles. The algorithms for tool-path generation are usually different for cutters of different geometries. Some algorithms found in the literature require complex numerical calculations and are time consuming. In this paper, an efficient algorithm is developed to calculate interference-free cutter-location data by easy geometric reasoning without complex computation. This robust method is suitable for generally used cutters such as ball, flat, and filleted end mills, and the time taken to obtain full tool paths of compound surfaces is short. Some real applications are presented to validate the proposed approach.

Uncertainty analysis in geometric best fit

In computing geometric tolerances using point data from a coordinate measuring machine (CMM), a best fit process is needed to match the measurement data to the substitute geometry. Since the measurement data does not precisely conform to the substitute geometry, the best fit result always contains uncertainties resulting from surface deviations, different point locations, and various sample size. Because the best fit uncertainties reduce accuracy of the evaluated tolerances, it is important to estimate and control the best fit uncertainties. In this paper, a theoretical model is presented to predict the uncertainty zones of the best fit parameters. Supported by simulations and experiments, the proposed model is proved to be effective in determining the best fit uncertainties. To explore factors that affect uncertainty variations, relationships between geometric variables and uncertainties are investigated. Then, to understand the effect of point location on the best fit uncertainty, an optimization scheme which minimizes the total uncertainties is used to find the best measurement locations. Simulations also show that the best fit uncertainty is inversely proportional to the squared root of the number of measurement points. This result can be used to estimate the CMM sample size that can control the best fit uncertainty under specified tolerances.

Reverse engineering of complex geometry using rational B-splines

Rational B-splines have become the new standard for representing free-form curves and surfaces. This paper presents a method for approximating rational B-splines using digitised data. Instead of using the classical optimisation approach to solve the multivariable nonlinear equations, a new method based on iterations of least-squares solutions and single variable mimimisation is developed. This is made possible by modifying the original objective function to avoid the rational format. Simulation of fitting a 90° arc shows that the algorithm can produce accurate solutions close to nominal values. The efficiency of the algorithm also makes it possible to apply the method to day-to-day reverse engineering problems using rational B-splines.