Search results for: geometric dimensioning and tolerances

Authors: Ragi Poyyara, V. Vivek, Ashish Khaparde

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The Product Development Process (PDP) in the technology group plays a very important role in the launch of any product. While a manufacturing process encourages the use of certain measures to reduce Health, Safety and Environmental (HSE) risks on the shop floor, the PDP concentrates on the use of Geometric Dimensioning and Tolerancing (GD&T) to develop a flawless design. Furthermore, PDP distributes and coordinates activities between different departments such as marketing, purchasing, and manufacturing. However, it is seldom realized that PDP makes a significant contribution to developing a product that reduces HSE risks by encouraging the Technology group to use effective GD&T. The GD&T is a precise communication tool that uses a set of symbols, rules, and definitions to mathematically define parts to be manufactured. It is a quality assurance method widely used in the oil and gas sector. Traditionally it is used to ensure the interchangeability of a part without affecting its form, fit, and function. Parts that do not meet these requirements are rejected during quality audits. This paper discusses how the Technology group integrates this quality assurance tool into the PDP and how the tool plays a major role in helping the HSE department in its goal towards eliminating HSE incidents. The PDP involves a thorough risk assessment and establishes a method to address those risks during the design stage. An illustration shows how GD&T helped reduce safety risks by ergonomically improving assembling operations. A brief discussion explains how tolerances provided on a part help prevent finger injury. This tool has equipped Technology to produce fixtures, which are used daily in operations as well as manufacturing. By applying GD&T to create good fits, HSE risks are mitigated for operating personnel. Both customers and service providers benefit from reduced safety risks.

Keywords: HSE risks, product development process, geometric dimensioning and tolerances, mechanical engineering

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Authors: M. Linek, P. Nita

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In the previous airfield construction industry, pavements made of reinforced concrete have been used very rarely; however, the necessity to use this type of pavements in an emergency situations justifies the need reference to this issue. The paper concerns the problem of airfield pavement dimensioning made of reinforced concrete and the evaluation of selected dimensioning methods of reinforced concrete slabs intended for airfield pavements. Analysis of slabs dimensioning, according to classical method of limit states has been performed and it has been compared to results obtained in case of methods complying with Eurocode 2 guidelines. Basis of an analysis was a concrete slab of class C35/45 with reinforcement, located in tension zone. Steel bars of 16.0 mm have been used as slab reinforcement. According to comparative analysis of obtained results, conclusions were reached regarding application legitimacy of the discussed methods and their design advantages.

Keywords: rainforced concrete, cement concrete, airport pavements, dimensioning

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Authors: Ridzuan Hussin, Mohd Zaihidee Arshad

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The creativity of earlier artists and sculptors in designing geometric is extraordinary provided with only a compass. Indeed, geometric in Islamic art and design are unique and have their own aesthetic values. In order to further understand geometric, self-learning with the approach of hands on would be appropriate. For this study, Islamic themed geometric designed and created, concerning only; i. The Square Repetition Unit and √2, ii. The Hexagonal Repetition Unit and √3 and iii. Double Hexagon. The aim of this research is to evaluate the creativity of Islamic geometric pattern artworks, through Fundamental Arts and Gestalt theory. Data was collected using specific tasks, and this research intends to identify the difference of Islamic geometric between 21 untitled selected geometric artworks (conventional design method), and 25 digital untitled geometric pattern artworks method. The evaluation of creativity, colors, layout, pattern and unity is known to be of utmost importance, although there are differences in the conventional or the digital approach.

Keywords: Islamic geometric design, Gestalt, fundamentals of art, patterns

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Authors: Hamed Afrasiab, Saeed Khodaygan

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Prediction of machining process capability in the design stage plays a key role to reach the precision design and manufacturing of mechanical products. Inaccuracies in machining process lead to errors in position and orientation of machined features on the part, and strongly affect the process capability in the final quality of the product. In this paper, an efficient systematic approach is given to investigate the machining errors to predict the manufacturing errors of the parts and capability prediction of corresponding machining processes. A mathematical formulation of fixture locators modeling is presented to establish the relationship between the part errors and the related sources. Based on this method, the final machining errors of the part can be accurately estimated by relating them to the combined dimensional and geometric tolerances of the workpiece – fixture system. This method is developed for uncertainty analysis based on the Worst Case and statistical approaches. The application of the presented method is illustrated through presenting an example and the computational results are compared with the Monte Carlo simulation results.

Keywords: process capability, machining error, dimensional and geometrical tolerances, uncertainty analysis

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Authors: Eric Mxolisi Mkhondo

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Geometrical deviations and interaction of mechanical parts influences the performance of miniature systems.These deviations tend to cause costly problems during assembly due to imperfections of components, which are invisible to a naked eye.They also tend to cause unsatisfactory performance during operation due to deformation cause by environmental conditions.One of the effective tools to manage the deviations and interaction of parts in the system is tolerance analysis.This is a quantitative tool for predicting the tolerance variations which are defined during the design process.Traditional tolerance analysis assumes that the assembly is static and the deviations come from the manufacturing discrepancies, overlooking the functionality of the whole system and deformation of parts due to effect of environmental conditions. This paper presents an integrated tolerance analysis approach for miniature system in operation.In this approach, a computer-aided design (CAD) model is developed from system’s specification.The CAD model is then used to specify the geometrical and dimensional tolerance limits (upper and lower limits) that vary component’s geometries and sizes while conforming to functional requirements.Worst-case tolerances are analyzed to determine the influenced of dimensional changes due to effects of operating temperatures.The method is used to evaluate the nominal conditions, and worse case conditions in maximum and minimum dimensions of assembled components.These three conditions will be evaluated under specific operating temperatures (-40°C,-18°C, 4°C, 26°C, 48°C, and 70°C). A case study on the mechanism of a zoom lens system is used to illustrate the effectiveness of the methodology.

Keywords: geometric dimensioning, tolerance analysis, worst-case analysis, zoom lens mechanism

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Authors: Ferdağ Çulhan, Emine Gaye Çontay

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Geometric thinking levels created by Van Hiele are used to determine students' progress in geometric thinking. Many studies have been conducted on geometric thinking levels and they have taken their place in teaching curricula over time. It is thought that geometric thinking levels, which have become so important in teaching, can be examined in depth. In order to make an in-depth analysis, it was decided that the most appropriate management was discourse analysis. In this study, the focus is on examining the geometric thinking levels of 8th grade students from a discursive point of view. Sfard (2008)'s "Commognitive" theory will be used to conduct discursive analysis. The "Global Van Hiele Questionnaire" created by Patkin (2014) and translated into Turkish for this research will be used in the research. The "Global Van Hiele Questionnaire" contains questions from the sub-learning domain of triangles and quadrilaterals, circles and geometric objects. It has a wider scope than many "Van Hiele Questionnaires". “Global Van Hiele Questionnaire” will be applied to 8th grade students. Then, the geometric thinking levels of the students will be determined and interviews will be held with two students from each of the 1st, 2nd and 3rd levels. The interviews will be recorded and the students' discourses will be examined. By evaluating the relations between the students' geometric thinking levels and their discourses, it will be examined how much their discourse reflects their level of thinking. In this way, it is thought that students' geometric thinking processes can be better understood.

Keywords: mathematical discourses, commognitive framework, geometric thinking levels, van hiele

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Authors: Chia-Hung Liao, Shih-Chieh Lin

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X-ray computed tomography (CT) technology has been used in the electronics industry as one of the non-destructive inspection tools for years. The key advantage of X-ray computed tomography technology superior to traditional optical inspection is the penetrating characteristics of X-rays can be used to detect defects in the interior of objects. The objective of this study is to find a way to estimate the system geometric deviation of X-ray CT equipment. Projection trajectories of the characteristic points of standard parts were tracked, and ways to calculate the deviation of various geometric parameters of the system will be proposed and evaluated. A simulation study will be conducted to first find out the effects of system geometric deviation on projected trajectories. Then ways to estimate geometric deviation with collected trajectories will be proposed and tested through simulations.

Keywords: geometric calibration, X-ray computed tomography, trajectory tracing, reconstruction optimization

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Authors: Nima Valibeig, Haniyeh Mohammadi, Neda Sadat Abdelahi

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Persian domes follow different forms depending on the materials used to construct and other factors. One of the factors that shape the form of a dome is the geometric proportion used in the drawing and construction of the dome. Some commonly used proportions are revealed by analysing the shapes and geometric ratio of the monuments’ domes. The proportions are achieved by the proficiency of the skilled architects of the buildings. These proportions can be used to reconstruct damaged parts of the historical monuments. Most of the research on domes is about the historical or stability features of domes, and less attention is made to the geometric system in domes. Therefore, in this study, we study the explicit and implicit geometric proportions in Iranian dome structures for the first time. The study is done based on a literature review and field survey. This research reveals that the permanent geometric rules are perfectly used in the design and construction of the prominent domes.

Keywords: geometry in architecture, architectural proportions, prominent domes, iranian golden ratio, geometric proportion

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Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

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Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

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Authors: Kai Warsoenke, Maik Mackiewicz

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To achieve a high quality of assembled car body structures, tolerancing is used to ensure a geometric accuracy of the single car body parts. There are two main techniques to determine the required tolerances. The first is tolerance analysis which describes the influence of individually tolerated input values on a required target value. Second is tolerance synthesis to determine the location of individual tolerances to achieve a target value. Both techniques are based on classical statistical methods, which assume certain probability distributions. To ensure competitiveness in both saturated and dynamic markets, production processes in vehicle manufacturing must be flexible and efficient. The dimensional specifications selected for the individual body components and the resulting assemblies have a major influence of the quality of the process. For example, in the manufacturing of forming tools as operating equipment or in the higher level of car body assembly. As part of the metrological process monitoring, manufactured individual parts and assemblies are recorded and the measurement results are stored in databases. They serve as information for the temporary adjustment of the production processes and are interpreted by experts in order to derive suitable adjustments measures. In the production of forming tools, this means that time-consuming and costly changes of the tool surface have to be made, while in the body shop, uncertainties that are difficult to control result in cost-intensive rework. The stored measurement results are not used to intelligently design tolerances in future processes or to support temporary decisions based on real-world geometric data. They offer potential to extend the tolerancing methods through data analysis and machine learning models. The purpose of this paper is to examine real-world measurement data from individual car body components, as well as assemblies, in order to develop an approach for using the data in short-term actions and future projects. For this reason, the measurement data will be analyzed descriptively in the first step in order to characterize their behavior and to determine possible correlations. In the following, a database is created that is suitable for developing machine learning models. The objective is to create an intelligent way to determine the position and number of measurement points as well as the local tolerance range. For this a number of different model types are compared and evaluated. The models with the best result are used to optimize equally distributed measuring points on unknown car body part geometries and to assign tolerance ranges to them. The current results of this investigation are still in progress. However, there are areas of the car body parts which behave more sensitively compared to the overall part and indicate that intelligent tolerancing is useful here in order to design and control preceding and succeeding processes more efficiently.

Keywords: automotive production, machine learning, process optimization, smart tolerancing

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Authors: Nicolas Peyret, Sylvain Courtois, Gaël Chevallier

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This article outlines the development of the Project Based Learning (PBL) at the level of a last year’s Bachelor’s Degree. This form of pedagogy has for objective to allow a better involving of the students from the beginning of the module. The theoretical contributions are introduced during the project to solving a technological problem. The module in question is the module of mechanical dimensioning method of Supméca a French engineering school. This school issues a Master’s Degree. While the teaching methods used in primary and secondary education are frequently renewed in France at the instigation of teachers and inspectors, higher education remains relatively traditional in its practices. Recently, some colleagues have felt the need to put the application back at the heart of their theoretical teaching. This need is induced by the difficulty of covering all the knowledge deductively before its application. It is therefore tempting to make the students 'learn by doing', even if it doesn’t cover some parts of the theoretical knowledge. The other argument that supports this type of learning is the lack of motivation the students have for the magisterial courses. The role-play allowed scenarios favoring interaction between students and teachers… However, this pedagogical form known as 'pedagogy by project' is difficult to apply in the first years of university studies because of the low level of autonomy and individual responsibility that the students have. The question of what the student actually learns from the initial program as well as the evaluation of the competences acquired by the students in this type of pedagogy also remains an open problem. Thus we propose to add to the pedagogy by project format a regressive part of interventionism by the teacher based on pedagogy by example. This pedagogical scenario is based on the cognitive load theory and Bruner's constructivist theory. It has been built by relying on the six points of the encouragement process defined by Bruner, with a concrete objective, to allow the students to go beyond the basic skills of dimensioning and allow them to acquire the more global skills of engineering. The implementation of project-based teaching coupled with pedagogy by example makes it possible to compensate for the lack of experience and autonomy of first-year students, while at the same time involving them strongly in the first few minutes of the module. In this project, students have been confronted with the real dimensioning problems and are able to understand the links and influences between parameter variations and dimensioning, an objective that we did not reach in classical teaching. It is this form of pedagogy which allows to accelerate the mastery of basic skills and so spend more time on the engineer skills namely the convergence of each dimensioning in order to obtain a validated mechanism. A self-evaluation of the project skills acquired by the students will also be presented.

Keywords: Bruner's constructivist theory, mechanisms dimensioning, pedagogy by example, problem based learning

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Authors: H. Ghodbane, A. A. Taleb, O. Kraa

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This paper presents geometric design of induction heating system. The objective of this design is to improve the temperature distribution in the load. The study of such a device requires the use of models or modeling representation, physical, mathematical, and numerical. This modeling is the basis of the understanding, the design, and optimization of these systems. The optimization technique is to find values of variables that maximize or minimize the objective function.

Keywords: optimization, modeling, geometric design system, temperature increase

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Authors: Yan Lyu, Yiqun Pan, Zhizhong Huang

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In the design stage of a new building, the energy model of this building is often required for the analysis of the performance on energy efficiency. In practice, a certain degree of geometric simplification should be done in the establishment of building energy models, since the detailed geometric features of a real building are hard to be described perfectly in most energy simulation engine, such as ESP-r, eQuest or EnergyPlus. Actually, the detailed description is not necessary when the result with extremely high accuracy is not demanded. Therefore, this paper analyzed the relationship between the error of the simulation result from building energy models and the geometric simplification of the models. Finally, the following two parameters are selected as the indices to characterize the geometric feature of in building energy simulation: the southward projected area and total side surface area of the building, Based on the parameterization method, the simplification from an arbitrary column building to a typical shape (a cuboid) building can be made for energy modeling. The result in this study indicates that this simplification would only lead to the error that is less than 7% for those buildings with the ratio of southward projection length to total perimeter of the bottom of 0.25~0.35, which can cover most situations.

Keywords: building energy model, simulation, geometric simplification, design, regression

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Authors: Boris Melnikov, Ye Zhang, Dmitrii Chaikovskii

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This study explores the pseudo-geometric version of the extensively researched Traveling Salesman Problem (TSP), proposing a novel generalization of existing algorithms which are traditionally confined to the geometric version. By adapting the "onion husk" method and introducing auxiliary algorithms, this research fills a notable gap in the existing literature. Through computational experiments using randomly generated data, several metrics were analyzed to validate the proposed approach's efficacy. Preliminary results align with expected outcomes, indicating a promising advancement in TSP solutions.

Keywords: optimization problems, traveling salesman problem, heuristic algorithms, “onion husk” algorithm, pseudo-geometric version

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Authors: Narendra Akhadkar, Philippe Delcambre

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In power protection and control products, assembly process variations due to the individual parts manufactured from single or multi-cavity tooling is a major problem. The dimensional and geometrical variations on the individual parts, in the form of manufacturing tolerances and assembly tolerances, are sources of clearance in the kinematic joints, polarization effect in the joints, and tolerance stack-up. All these variations adversely affect the quality of product, functionality, cost, and time-to-market. Variation simulation analysis may be used in the early product design stage to predict such uncertainties. Usually, variations exist in both manufacturing processes and materials. In the tolerance analysis, the effect of the dimensional and geometrical variations of the individual parts on the functional characteristics (conditions) of the final assembled products are studied. A functional characteristic of the product may be affected by a set of interrelated dimensions (functional parameters) that usually form a geometrical closure in a 3D chain. In power protection and control products, the prerequisite is: when a fault occurs in the electrical network, the product must respond quickly to react and break the circuit to clear the fault. Usually, the response time is in milliseconds. Any failure in clearing the fault may result in severe damage to the equipment or network, and human safety is at stake. In this article, we have investigated two important functional characteristics that are associated with the robust performance of the product. It is demonstrated that the experimental data obtained at the Schneider Electric Laboratory prove the very good prediction capabilities of the variation simulation performed using CETOL (tolerance analysis software) in an industrial context. Especially, this study allows design engineers to better understand the critical parts in the product that needs to be manufactured with good, capable tolerances. On the contrary, some parts are not critical for the functional characteristics (conditions) of the product and may lead to some reduction of the manufacturing cost, ensuring robust performance. The capable tolerancing is one of the most important aspects in product and manufacturing process design. In the case of miniature circuit breaker (MCB), the product's quality and its robustness are mainly impacted by two aspects: (1) allocation of design tolerances between the components of a mechanical assembly and (2) manufacturing tolerances in the intermediate machining steps of component fabrication.

Keywords: geometrical variation, product robustness, tolerance analysis, variation simulation

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Authors: Han Ding, Wang Xiaoliang, Duan Dengping

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During the process of airship design, the layout and the geometric shape of the hull and fins are crucial to the motion characteristics of the airship. In this paper, we obtained the quantification motion sensitivity of the airship to geometric parameters through turning circles and horizontal/vertical zigzag maneuvers by the parameterization of airship shape and building the dynamic model using Lagrangian approach and MATLAB Simulink program. In the dynamics simulation program, the affection of geometric parameters to the mass, center of gravity, moments of inertia, product of inertia, added mass and the aerodynamic forces and moments have been considered.

Keywords: airship, Lagrangian approach, turning circles, horizontal/vertical zigzag maneuvers

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Authors: Xavier Lorang, Ahmadali Tahmasebimoradi, Chetra Mang, Sylvain Girard

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The additive manufacturing processes (e.g. selective laser melting) allow us to produce lattice structures which have less weight, higher impact absorption capacity, and better thermal exchange property compared to the classical structures. Unfortunately, geometric imperfections (defects) in the lattice structures are by-products results of the manufacturing process. These imperfections decrease the lifetime and the strength of the lattice structures and alternate their mechanical responses. The objective of the paper is to present a simulation strategy which allows us to take into account the effect of the geometric imperfections on the mechanical response of the lattice structure. In the first part, an identification method of geometric imperfection parameters of the lattice structure based on point clouds is presented. These point clouds are based on tomography measurements. The point clouds are fed into the platform LATANA (LATtice ANAlysis) developed by IRT-SystemX to characterize the geometric imperfections. This is done by projecting the point clouds of each microbeam along the beam axis onto a 2D surface. Then, by fitting an ellipse to the 2D projections of the points, the geometric imperfections are characterized by introducing three parameters of an ellipse; semi-major/minor axes and angle of rotation. With regard to the calculated parameters of the microbeam geometric imperfections, a statistical analysis is carried out to determine a probability density law based on a statistical hypothesis. The microbeam samples are randomly drawn from the density law and are used to generate lattice structures. In the second part, a finite element model for the lattice structure with the simplified geometric imperfections (ellipse parameters) is presented. This numerical model is used to simulate the generated lattice structures. The propagation of the uncertainties of geometric imperfections is shown through the distribution of the computed mechanical responses of the lattice structures.

Keywords: additive manufacturing, finite element model, geometric imperfections, lattice structures, propagation of uncertainty

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Authors: M. Aouimeur

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The environmental risks of a dam and particularly the security in the Valley downstream of it,, is a very complex problem. Integrated management and risk-sharing become more and more indispensable. The definition of "vulnerability “concept can provide assistance to controlling the efficiency of protective measures and the characterization of each valley relatively to the floods's risk. Security can be enhanced through the integrated land management. The social sciences may be associated to the operational systems of civil protection, in particular warning networks. The passage of extreme floods in the site of the dam causes the rupture of this structure and important damages downstream the dam. The river bed could be damaged by erosion if it is not well protected. Also, we may encounter some scouring and flooding problems in the downstream area of the dam. Therefore, the protection of the dam is crucial. It must have an energy dissipator in a specific place. The basin of dissipation plays a very important role for the security of the dam and the protection of the environment against floods downstream the dam. It allows to dissipate the potential energy created by the dam with the passage of the extreme flood on the weir and regularize in a natural manner and with more security the discharge or elevation of the water plan on the crest of the weir, also it permits to reduce the speed of the flow downstream the dam, in order to obtain an identical speed to the river bed. The problem of the dimensioning of a classic dissipation basin is in the determination of the necessary parameters for the dimensioning of this structure. This communication presents a simple graphical method, that is fast and complete, and a methodology which determines the main features of the hydraulic jump, necessary parameters for sizing the classic dissipation basin. This graphical method takes into account the constraints imposed by the reality of the terrain or the practice such as the one related to the topography of the site, the preservation of the environment equilibrium and the technical and economic side.This methodology is to impose the loss of head DH dissipated by the hydraulic jump as a hypothesis (free design) to determine all the others parameters of classical dissipation basin. We can impose the loss of head DH dissipated by the hydraulic jump that is equal to a selected value or to a certain percentage of the upstream total head created by the dam. With the parameter DH+ =(DH/k),(k: critical depth),the elaborate graphical representation allows to find the other parameters, the multiplication of these parameters by k gives the main characteristics of the hydraulic jump, necessary parameters for the dimensioning of classic dissipation basin.This solution is often preferred for sizing the dissipation basins of small concrete dams. The results verification and their comparison to practical data, confirm the validity and reliability of the elaborate graphical method.

Keywords: dimensioning, energy dissipation basin, hydraulic jump, protection of the environment

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Authors: Benjamin Leiby, Darryl Ahner

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This study demonstrates an alternative stochastic imputation approach for large datasets when preferred commercial packages struggle to iterate due to numerical problems. A large country conflict dataset motivates the search to impute missing values well over a common threshold of 20% missingness. The methodology capitalizes on correlation while using model residuals to provide the uncertainty in estimating unknown values. Examination of the methodology provides insight toward choosing linear or nonlinear modeling terms. Static tolerances common in most packages are replaced with tailorable tolerances that exploit residuals to fit each data element. The methodology evaluation includes observing computation time, model fit, and the comparison of known values to replaced values created through imputation. Overall, the country conflict dataset illustrates promise with modeling first-order interactions while presenting a need for further refinement that mimics predictive mean matching.

Keywords: correlation, country conflict, imputation, stochastic regression

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Authors: A. Afroogh, R. Ramazani Omali, N. Hafezi Moghaddas, A. Nohegar

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Burkh anticline is located in Southeast of Zagros fold-thrust belt in the Fars Province. Geometric analyses of the anticline have been carried out to estimate the closure of the Dehram Group in order to evaluate its potential for gas reservoirs. Geometric analyses of the Burkh anticline indicate that the fold geometry is rather similar to that of the detachment folds. Based on the data from the geometric analysis, seven structural cross section the anticlines are drawn and using the cross sections, a structural contour for Dehram Group is constructed. The calculated values for the anticline closure prohibits this structure as it is not an appropriate host to gas reservoirs.

Keywords: Burkh anticline, Zagros fold-thrust belt, geometric analyses, vertical and horizontal closure, Dehram group

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Authors: Mark Schudeleit, Christian Sieg, Ferit Küçükay

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This publication focuses on the limits and potentials of 48V hybrid systems, which are especially due to the cost advantages an attractive alternative, compared to established high volt-age HEVs and thus will gain relevant market shares in the future. Firstly, at market overview is given which shows the current known 48V hybrid concepts and demonstrators. These topologies will be analyzed and evaluated regarding the system power and the battery capacity as well as their implemented hybrid functions. The potential in fuel savings and CO2 reduction is calculated followed by the customer-relevant dimensioning of the electric motor and the battery. For both measured data of the real customer operation is used. Subsequently, the CO2 saving potentials of the customer-oriented dimensioned powertrain will be presented for the NEDC and the customer operation. With a comparison of the newly defined drivetrain with existing 48V systems the question can be answered whether current systems are dimensioned optimally for the customer operation or just for legislated driving cycles.

Keywords: 48V hybrid systems, market comparison, requirements and potentials in customer operation, customer-oriented dimensioning, CO2 savings

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Authors: Steven D. P Moore

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A novel method referred to asKýklos(Ky) dimensional geometry is proposed as an entity specific core geometric dimensional measurement system. Ky geometric measures can constructscaled multi-dimensionalmodels using regular and irregular sets in IRn. This entity specific-derived geometric measurement system shares similar fractal methods in which a ‘fractal transformation operator’ is applied to a set S to produce a union of N copies. The Kýklos’ inputs use 1D geometry as a core measure. One-dimensional inputs include the radius interval of a circle/sphere or the semiminor/semimajor axes intervals of an ellipse or spheroid. These geometric inputs have finite values that can be measured by SI distance units. The outputs for each interval are divided and subdivided 1D subcomponents with a union equal to the interval geometry/length. Setting a limit of subdivision iterations creates a finite value for each 1Dsubcomponent. The uniqueness of this method is captured by allowing the simplest 1D inputs to define entity specific subclass geometric core measurements that can also be used to derive length measures. Current methodologies for celestial based measurement of time, as defined within SI units, fits within this methodology, thus combining spatial and temporal features into geometric core measures. The novel Ky method discussed here offers geometric measures to construct scaled multi-dimensional structures, even models. Ky classes proposed for consideration include celestial even subatomic. The application of this offers incredible possibilities, for example, geometric architecture that can represent scaled celestial models that incorporates planets (spheroids) and celestial motion (elliptical orbits).

Keywords: Kyklos, geometry, measurement, celestial, dimension

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Authors: Maamar Fatouma

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Mirror optical performance can experience varying levels of stress and tolerances, which can have a notable impact on optical parametric systems. to ensure proper optical figure and position of mirror mounting within design tolerances, it is crucial to have a robust support structure in place for optical systems. The optical figure tolerance determines the allowable deviation from the ideal form of the mirror and the position tolerance determines the location and orientations of the optical axis of the optical systems. A variety of factors influence the optical figure of the mirror. Included are self-weight (Deflection), excitation from temperature change, temperature gradients and dimensional instability. This study employs an analytical approach and finite element method to examine the effects of stress resulting from mirror mounting on the wavefront passing through the mirror. The combined effect of tolerance and deflection on mirror performance is represented by an error budget. Numerical mirror mounting is presented to illustrate the space application of performance techniques.

Keywords: opto-mechanical, bonded optic, tolerance, self-weight distortion, Rayleigh criteria

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: B. Touati, A. Saad, B. Lips, A. Abdenbi, M. Mokhtari.

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The purpose of this study is an application of experiment design method for dimensioning of a solar drying system. NIMROD software was used to build up the matrix of experiments and to analyze the results. The software has the advantages of being easy to use and consists of a forced way, with some choices about the number and range of variation of the parameters, and the desired polynomial shape. The first design of experiments performed concern the drying with constant input characteristics of the hot air in the dryer and a second design of experiments in which the drying chamber is coupled with a solar collector. The first design of experiments allows us to study the influence of various parameters and get the studied answers in a polynomial form. The correspondence between the polynomial thus determined, and the model results were good. The results of the polynomials of the second design of experiments and those of the model are worse than the results in the case of drying with constant input conditions. This is due to the strong link between all the input parameters, especially, the surface of the sensor and the drying chamber, and the mass of the product.

Keywords: solar drying, experiment design method, NIMROD, mint leaves

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Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava

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This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

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Authors: Peter Akayuure

Abstract:

Geometry is considered an important strand in mathematics due to its wide-ranging utilitarian value and because it serves as a building block for understanding other aspects of undergraduate mathematics, including algebra and calculus. Matters regarding students’ geometric thinking have therefore long been pursued by mathematics researchers and educators globally via different theoretical lenses, curriculum reform efforts, and innovative instructional practices. However, so far, studies remain inconclusive about the instructional platforms that effectively promote geometric thinking. At the University of Education, Winneba, an undergraduate geometry course was designed and delivered on UEW Learning Management System (LMS) using Moodle platform. This study utilizes van Hiele’s theoretical lens to examine the entry and exit’s geometric thinking behaviours of prospective teachers who took the undergraduate geometry course in the LMS platform. The study was a descriptive survey that involved an intact class of 280 first-year students enrolled to pursue a bachelor's in mathematics education at the university. The van Hiele’s Geometric thinking test was used to assess participants’ entry and exit behaviours, while semi-structured interviews were used to obtain data for triangulation. Data were analysed descriptively and displayed in tables and charts. An Independent t-test was used to test for significant differences in geometric thinking behaviours between those who entered the university with a diploma certificate and with senior high certificate. The results show that on entry, more than 70% of the prospective teachers operated within the visualization level of van Hiele’s geometric thinking. Less than 20% reached analysis and abstraction levels, and no participant reached deduction and rigor levels. On exit, participants’ geometric thinking levels increased markedly across levels, but the difference from entry was not significant and might have occurred by chance. The geometric thinking behaviours of those enrolled with diploma certificates did not differ significant from those enrolled directly from senior high school. The study recommends that the design principles and delivery of undergraduate geometry course via LMS should be structured and tackled using van Hiele’s geometric thinking levels to serve as means of bridging the existing learning gaps of undergraduate students.

Keywords: geometric thinking, van Hiele’s, UEW learning management system, undergraduate geometry

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Authors: A. Rifa’i, Y. Takeshita, M. Komatsu

Abstract:

After Yogyakarta earthquake in 2006, the main problem that occurred in the first yard of Prambanan Temple is ponding area that occurred after rainfall. Soil characterization needs to be determined by conducting several processes, especially permeability coefficient (k) in both saturated and unsaturated conditions to solve this problem. More accurate and efficient field testing procedure is required to obtain permeability data that present the field condition. One of the field permeability test equipment is Constant Discharge procedure to determine the permeability coefficient. Necessary adjustments of the Constant Discharge procedure are needed to be determined especially the value of geometric factor (F) to improve the corresponding value of permeability coefficient. The value of k will be correlated with the value of volumetric water content (θ) of an unsaturated condition until saturated condition. The principle procedure of Constant Discharge model provides a constant flow in permeameter tube that flows into the ground until the water level in the tube becomes constant. Constant water level in the tube is highly dependent on the tube dimension. Every tube dimension has a shape factor called the geometric factor that affects the result of the test. Geometric factor value is defined as the characteristic of shape and radius of the tube. This research has modified the geometric factor parameters by using empty material tube method so that the geometric factor will change. Saturation level is monitored by using soil moisture sensor. The field test results were compared with the results of laboratory tests to validate the results of the test. Field and laboratory test results of empty tube material method have an average difference of 3.33 x 10^-4 cm/sec. The test results showed that modified geometric factor provides more accurate data. The improved methods of constant discharge procedure provide more relevant results.

Keywords: constant discharge, geometric factor, permeability coefficient, unsaturated soils

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Authors: Maatoug Hassine, Mourad Hrizi

Abstract:

In this paper, we consider a geometric inverse source problem for the heat equation with Dirichlet and Neumann boundary data. We will reconstruct the exact form of the unknown source term from additional boundary conditions. Our motivation is to detect the location, the size and the shape of source support. We present a one-shot algorithm based on the Kohn-Vogelius formulation and the topological gradient method. The geometric inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a source function. Then, we present a non-iterative numerical method for the geometric reconstruction of the source term with unknown support using a level curve of the topological gradient. Finally, we give several examples to show the viability of our presented method.

Keywords: geometric inverse source problem, heat equation, topological optimization, topological sensitivity, Kohn-Vogelius formulation

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Authors: Zuraidasahana Zulkarnain, Mohd Shafry Mohd Rahim, Nor Anita Fairos Ismail, Mohd Azhar M. Arsad

Abstract:

Handwritten signature is accepted widely as a biometric characteristic for personal authentication. The use of appropriate features plays an important role in determining accuracy of signature verification; therefore, this paper presents a feature based on the geometrical concept. To achieve the aim, triangle attributes are exploited to design a new feature since the triangle possesses orientation, angle and transformation that would improve accuracy. The proposed feature uses triangulation geometric set comprising of sides, angles and perimeter of a triangle which is derived from the center of gravity of a signature image. For classification purpose, Euclidean classifier along with Voting-based classifier is used to verify the tendency of forgery signature. This classification process is experimented using triangular geometric feature and selected global features. Based on an experiment that was validated using Grupo de Senales 960 (GPDS-960) signature database, the proposed triangular geometric feature achieves a lower Average Error Rates (AER) value with a percentage of 34% as compared to 43% of the selected global feature. As a conclusion, the proposed triangular geometric feature proves to be a more reliable feature for accurate signature verification.

Keywords: biometrics, euclidean classifier, features extraction, offline signature verification, voting-based classifier

Procedia PDF Downloads 344