Shape Optimization of a Camoid Follower Surface

2008 ◽  
Author(s):  
Karim A. Aguib ◽  
Keith A. Hekman ◽  
Ashraf O. Nassef
Keyword(s):  
Genetic Algorithms ◽  
Shape Optimization ◽  
Three Dimensional ◽  
Characteristic Surface ◽  
Design Constraints ◽  
B Splines ◽  
Surface Interpolation ◽  
Specific Objective ◽  
Interpolation Technique ◽  
Real Coded Genetic Algorithms

Camoids are three dimensional cams that can produce more complex follower output than plain disc cams. A camoid follower motion is described by a surface rather than a curve. The camoid profile can be directly synthesized once the follower surface is fully described. To define a camoid follower motion surface it is required that the surface pass by all predefined constraints. Constraints can be follower position, velocity and acceleration. These design constraints are scattered all along the camoid follower surface. Hence a fitting technique is needed to satisfy these constraints which include position and its derivatives (velocity and acceleration). Furthermore if the fitting function can be of a parametric nature, then it would be possible to optimize the follower surface to obtain better performance according to a specific objective. Previous research has established a method to fit camoid follower surface positions, but did not tackle the satisfaction of derivative constraints. This paper presents a method for defining a camoid follower characteristic surface B-Splines on two steps first synthesizing the sectional cam curves then using a surface interpolation technique to generate the follower characteristic surface. The fitting technique is parametric in nature which allows for its optimization. Real coded Genetic algorithms are used to optimize the parameters of the surface to meet a specified objective function. A demonstration problem to illustrate the suggested methodology is presented.

A Hybrid Genetic-Direct Search Algorithm for the Shape Optimization of Solid C-Frame Cross-Sections

2000 ◽  
Author(s):  
Ashraf O. Nassef ◽  
Hesham A. Hegazi ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithms ◽  
Shape Optimization ◽  
Cross Section ◽  
Random Search ◽  
Direct Search ◽  
Search Method ◽  
Optimization Techniques ◽  
Hybrid Optimization ◽  
The Cross ◽  
Real Coded Genetic Algorithms

Abstract The hybridization of different optimization methods have been used to find the optimum solution of design problems. While random search techniques, such as genetic algorithms and simulated annealing, have a high probability of achieving global optimality, they usually arrive at a near optimal solution due to their random nature. On the other hand direct search methods are efficient optimization techniques but linger in local minima if the objective function is multi-modal. This paper presents the optimization of C-frame cross-section using a hybrid optimization algorithm. Real coded genetic algorithms are used as a random search method, while Nelder-Mead is used as a direct search method, where the result of the genetic algorithm search is used as the starting point of direct search. Traditionally, the cross-section of C-frame belonged to a set of primitive shapes, which included I, T, trapezoidal, circular and rectangular sections. The cross-sectional shape is represented by a non-uniform rational B-Splines (NURBS) in order to give it a kind of shape flexibility. The results showed that the use of Nelder-Mead with Real coded Genetic Algorithms has been very significant in improving the optimum shape of a solid C-frame cross-section subjected to a combined tension and bending stresses. The hybrid optimization method could be extended to more complex shape optimization problems.

Accuracy and Fitting-Time Minimization in the Reverse Engineering of Prismatic Features

1999 ◽  
Author(s):  
Ashraf O. Nassef ◽  
Ayman M. Ashraf ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithms ◽  
Reverse Engineering ◽  
Three Dimensional ◽  
Direct Search ◽  
Search Method ◽  
Direct Search Method ◽  
Simplex Search ◽  
Time Minimization ◽  
Engineering Models ◽  
Real Coded Genetic Algorithms

Abstract In many years of industry, it is desirable to create geometric models of existing objects for which no such models are available. Reverse engineering transforms real parts into engineering models and concepts. This paper presents an approach for fitting three-dimensional prismatic features using real-coded genetic algorithms. The approach is compared with the Nelder Meade Simplex search method as a variant of the traditional direct search method. The results show the superiority of the real-coded genetic algorithms over the traditional direct search method with respect to accuracy. The paper also concerns with the minimization of the fitting time through minimizing the number of objective function evaluations. This is done by optimizing the genetic algorithms parameters such as the number of times for which the various cross-overs and mutations should be applied.

Shape Optimization of NURBS Modeled 3D C-Frames Using Hybrid Genetic Algorithm

2002 ◽  
Author(s):  
Hesham A. Hegazi ◽  
Ashraf O. Nassef ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Shape Optimization ◽  
Cross Sections ◽  
Beam Theory ◽  
Direct Search ◽  
Search Method ◽  
Optimum Shape ◽  
Curved Beam ◽  
Real Coded Genetic Algorithms

The present paper introduces a new methodology for designing machine element shapes. The element is represented using non-uniform rational B-Spline (NURBS) in order to give it a form of shape flexibility. A special form of genetic algorithms known as real-coded genetic algorithms is used to conduct the search for the design objectives. Shape optimization of 3D C-frames are used as an application of the proposed methodology. The design parameters of these frames include the dimensions of their cross-sections, which should be chosen to withstand the applied loads and minimize the element’s overall weight. In a further development, the hybridization of different optimization methods has been used to find the optimum shape of the element. Real coded genetic algorithm is used as a random search method, while Nelder-Mead is used as a direct search method, where the result of the genetic algorithm search is used as the starting point of direct search. The results showed that the use of Nelder-Mead with Real coded Genetic Algorithms has been very significant in improving the optimum shape of a solid 3D C-frames subjected to a combined tension and bending stresses. The hybrid optimization method could be extended to more complex shape optimization problems. For the purpose of analysis, curved beam theory is applied on local cross-sections on the NURBS surface. A finite elements analysis was conducted on SDRC-IDEAS for verifying the results obtained using the curved beam theory.

scholarly journals Modeling of a Microscale Surface Using NURBS Technique

Coatings ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 775
Author(s):  
Jeongki Jang ◽  
Kyungmok Kim
Keyword(s):  
3D Model ◽  
Three Dimensional ◽  
Surface Profile ◽  
Surface Model ◽  
Nurbs Surface ◽  
Profile Data ◽  
B Spline ◽  
Surface Interpolation ◽  
Interpolation Technique

This article describes microscale surface modeling using the Non-Uniform Rational B-Spline (NURBS) surface interpolation technique. A three-dimensional surface model was generated on the basis of measured surface profile data. To validate this model, three brass specimens having different roughness values were used. Direct comparison between measured profiles and the curves modeled with NURBS was employed. It was identified that the proposed method allows the generation of microscale models similar to actual surfaces. Finally, a method to extract the Bearing Area Curve (BAC) from a 3D model was detailed. The proposed modeling will be useful for the characterization of bearing capacity of the surface and for contact analysis.

New approach to constrained shape optimization using genetic algorithms

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 51-61 ◽  
Author(s):  
M. C. Sharatchandra ◽  
Mihir Sen ◽  
Mohamed Gad-el-Hak
Keyword(s):  
Genetic Algorithms ◽  
Shape Optimization ◽  
New Approach

Three-Dimensional Computerized Anthropometry of the Nose: Landmark Representation Compared to Surface Analysis

2007 ◽  
Vol 44 (3) ◽  
pp. 278-285 ◽  
Author(s):  
Virgilio F. Ferrario ◽  
Fabrizio Mian ◽  
Redento Peretta ◽  
Riccardo Rosati ◽  
Chiarella Sforza
Keyword(s):  
Three Dimensional ◽  
Digital Data ◽  
Limits Of Agreement ◽  
B Splines ◽  
Surface Areas ◽  
Using Data ◽  
Difference Volume ◽  
T Values ◽  
Plaster Models ◽  
Plaster Casts

Objective: To compare three-dimensional nasal measurements directly made on subjects to those made on plaster casts, and nasal dimensions obtained with a surface-based approach to values obtained with a landmark representation. Methods: Soft-tissue nasal landmarks were directly digitized on 20 healthy adults. Stone casts of their noses were digitized and mathematically reconstructed using nonuniform rational B-splines (NURBS) curves. Linear distances, angles, volumes and surface areas were computed using facial landmarks and NURBS-reconstructed models (surface-based approach). Results: Measurements on the stone casts were somewhat smaller than values obtained directly from subjects (differences between −0.05 and −1.58 mm). Dahlberg's statistic ranged between 0.73 and 1.47 mm. Significant (p < .05) t values were found for 4 of 15 measurements. The surface-based approach gave values 3.5 (volumes) and 2.1 (surface area) times larger than those computed with the landmark-based method. The two values were significantly related (volume, r = 0.881; surface, r = 0.924; p < .001), the resulting equations estimated actual values well (mean difference, volume −0.01 mm3, SD 1.47, area 0.05 cm2, SD 1.44); limits of agreement between −2.89 and 2.87 mm3 (volume); −2.88 and 2.78 cm2 (area). Conclusions: Considering the characteristics of the two methods, and for practical purposes, nasal distances and angles obtained on plaster models were comparable to digital data obtained directly from subjects. Surface areas and volumes were best obtained using a surface-based approach, but could be estimated using data provided by the landmark representation.

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