scholarly journals Computer Synthesis Approaches of Hyperboloid Gear Drives with Linear Contact

2014 ◽  
Vol 44 (3) ◽  
pp. 3-20 ◽  
Author(s):  
Valentin Abadjiev ◽  
Haruhisa Kawasaki
Keyword(s):  
Mathematical Models ◽  
Contact Point ◽  
Optimal Solution ◽  
Computer Programs ◽  
Strength Analysis ◽  
Computer Design ◽  
Scientific Support ◽  
High Reduction ◽  
The Creation ◽  
Gear Drives

Abstract The computer design has improved forming different type software for scientific researches in the field of gearing theory as well as performing an adequate scientific support of the gear drives manufacture. Here are attached computer programs that are based on mathematical models as a result of scientific researches. The modern gear transmissions require the construction of new mathematical approaches to their geometric, technological and strength analysis. The process of optimization, synthesis and design is based on adequate iteration procedures to find out an optimal solution by varying definite parameters. The study is dedicated to accepted methodology in the creation of soft- ware for the synthesis of a class high reduction hyperboloid gears - Spiroid and Helicon ones (Spiroid and Helicon are trademarks registered by the Illinois Tool Works, Chicago, Ill). The developed basic computer products belong to software, based on original mathematical models. They are based on the two mathematical models for the synthesis: “upon a pitch contact point” and “upon a mesh region”. Computer programs are worked out on the basis of the described mathematical models, and the relations between them are shown. The application of the shown approaches to the synthesis of commented gear drives is illustrated.

scholarly journals One Approach to the Synthesis, Design and Manufacture of Hyperboloid Gear Sets With Face Mating Gears. Part 1: Basic Theoretical and Cad Experience

2016 ◽  
Vol 46 (2) ◽  
pp. 3-26 ◽  
Author(s):  
Valentin Abadjiev ◽  
Emilia Abadjieva
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Models ◽  
Contact Point ◽  
Computer Programs ◽  
Tooth Contact ◽  
Synthesis Design ◽  
Gear Drives ◽  
Design And Manufacture ◽  
Special Case

Abstract Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid and Helicon gear drives. The classical gear drives of this type are the Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion possesses threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three types transmis- sions with face mating gears and a conic pinion are titled Spiroid and all three types transmissions with face mating gears and a cylindrical pinion are titled Helicon. Principles of the mathematical modelling of tooth contact synthesis are discussed in this study. The presented research shows that the synthesis is realized by application of two mathematical models: pitch contact point and mesh region models. Two approaches for synthesis of the gear drives in accordance with Olivier’s principles are illustrated. The algorithms and computer programs for optimization synthesis and design of the studied hyperboloid gear drives are presented.

scholarly journals MODIFYING MATHEMATICAL MODELS FOR CALCULATING OPERATIONAL CHARACTERISTICS OF DIESEL ENGINES BURNING RME BIOFUELS / MATEMATINIŲ MODELIŲ PRITAIKYMAS DYZELIŲ, DIRBANČIŲ RME BIODEGALAIS, DARBO PROCESUI IR EKSPLOATACINIAMS RODIKLIAMS SKAIČIUOTI / ДОРАБОТКА МАТЕМАТИЧЕСКИХ МОДЕЛЕЙ РАСЧЕТА ПОКАЗАТЕЛЕЙ РАБОТЫ ДИЗЕЛЯ НА БИОДИЗЕЛИНАХ РРМЭ

Transport ◽  
2011 ◽  
Vol 26 (1) ◽  
pp. 50-60 ◽  
Author(s):  
Sergejus Lebedevas ◽  
Galina Lebedeva ◽  
Kristina Bereišienė
Keyword(s):  
Diesel Engine ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Diesel Engines ◽  
Fuel Injection ◽  
Internal Heat ◽  
Computer Programs ◽  
Toxic Substances ◽  
Load Range ◽  
Operational Characteristics

The article considers and solves the problems of adapting the mathematical models, used in calculating operational characteristics of diesel engines burning mineral diesel oil, to engines converted to RME biofuels. The analysis of mathematical models of calculating the main technical and economic characteristics of diesel engines as well as the parameters of the in-cylinder process and the concentration of toxic substances in the exhaust gases is performed. The need for adjusting the calculation algorithms is also demonstrated. The computer programs based on single-zone thermodynamic models are used in the research. The programs of mathematical modelling are modified, i.e. supplemented with the algorithm for calculating energy characteristics of the combustion products (e.g. specific heat capacity, internal heat, the lower calorific value, etc.). Based on the computer programs, modified for examining diesel engines burning biofuels, the computer-aided mathematical modelling experiment is carried out. The results of modelling are compared with the data obtained in testing the diesel engine 1A41. The mathematical modelling performed demonstrates the accuracy acceptable for solving practical problems: the difference between the obtained calculation results and diesel engine testing data for the load range of (1.0÷0.5) Pi nom does not exceed ± 5÷7%. Higher accuracy of modelling the characteristics of diesel engines, operating in the low- and medium-load modes, may be accounted for by the adjustment of the algorithm for calculating the induction period and the on-set phase of fuel injection. Santrauka Publikacijoje pateikti dyzelio darbo proceso ir eksploatacinių rodiklių skaičiavimo matematinių modelių tobulinimo rezultatai, siekiant matematinius modelius pritaikyti dyzeliui dirbant riebiųjų rūgščių metilesterių, taip pat RME, biodegalais. Atlikta skaičiavimo algoritmų analizė ir pagrįsti pagrindiniai jų tobulinimo aspektai. Sukurtas kompiuterinis programinis modelis, skirtas darbinio kūno dyzelio cilindre energiniams parametrams skaičiuoti (specifinei šilumai, vidinei energijai), dyzeliui dirbant plačiąja elementinės cheminės sudėties biodegalų gama. Atliktas 1A41 dyzelio techninių ir ekonominių bei ekologinių rodiklių modeliavimas kompiuteriu, naudojant patobulintus matematinius modelius. Parodytas gautų rezultatų, pakankamų praktiniams uždaviniams spręsti, tikslumas: dyzeliui dirbant artimos nominaliosios apkrovos režimais (1,0÷0,5) Pi nom skirtumas tarp skaičiavimo ir dyzelio motorinių tyrimų rezultatų neviršija ±5÷7%. Dyzeliui dirbant mažos apkrovos režimu, matematinio modeliavimo rezultatų adekvatumo didinimas susijęs su kuro įpurškimo fazės bei savaiminio užsiliepsnojimo indukcijos periodo skaičiavimo algoritmo tobulinimu. Резюме Рассмотрены и решены задачи адаптации математических моделей расчета показателей дизеля при переводе их работы с минерального дизелина на биодизелины метилового эфира рапсового масла (МЭРМ). Выполнен анализ и дано обоснование направлений доработки расчетных алгоритмов ряда однозонных термодинамических математических моделей, используемых в практике исследования эксплуатационных показателей, параметров индикаторного процесса и эмиссии токсичных компонентов в выхлопных газах дизелей. В форме программного модуля составлен алгоритм расчета энергетических параметров рабочего тела в цилиндре (удельной теплоемкости, теплоты сгорания, внутренней энергии) для топлив с широким элементарным химическим составом. С использованием доработанных компьютерных программ выполнен широкий расчетный эксперимент и сопоставлены его результаты с данными моторных стендовых испытаний одноцилиндрового отсека дизеля 1А41. Показана приемлемая для решения практических задач точность математического моделирования: для нагрузочных режимов (1÷0,5) Pmi расхождения расчетных и экспериментальных значений параметров работы дизеля не превышают ±5÷7%. Повышение качества моделирования показателей дизеля на режимах средних и малых нагрузок связано с уточнением алгоритма расчета периода индукции и фазы начала видимого горения топлива в цилиндре.

Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
Normal Vector ◽  
Optimization Criteria ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The optimal solution is found using a two-step approach: first finding the description of the entire solution space for the contact force distribution for a statically stable stance under friction constraints, and then choosing an optimal solution in this solution space which maximizes the objectives given by the chosen optimization criteria. An incremental strategy of opening up the friction cones is developed to produce the optimal solution which is defined as the one whose foot contact force vector is closest to the surface normal vector for robustness against slipping. The procedure is aided by using the “force space graph” which indicates where this solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point for the case when one foot is more critical than the other. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

A Method for Constructing Standard Involute Gear Tooth Profile

2018 ◽  
Author(s):  
Edward E. Osakue ◽  
Lucky Anetor
Keyword(s):  
Gear Tooth ◽  
Contact Point ◽  
Contact Angles ◽  
Tooth Profile ◽  
Computer Design ◽  
Solid Models ◽  
Module Size ◽  
Involute Gears ◽  
Base Circle ◽  
Involute Curve

A simple but accurate combined computationaland graphical method for creating drawings and solid models of standard involute gears is presented. The method is predicated on the fact that the gear tooth angle at the base circle is fixed for a gear of specified module or size. As the contact point moves along the involute curve from the base circle point through the pitch point to the addendum circle point; the involute and gear tooth contact angles change continuously but their sum is fixed at the value it was at the base circle. This allows the coordinates of points on the involute curve to be generated analytically without employing the roll angle as current available methods. The generated data can be implemented in any computer design drafting (CDD) package platform to create an accurate gear tooth profile. The computations are done with Microsoft Excel which generates the graphical data for the gear tooth profile that are used in the CDD package. The required inputs to the Excel spreadsheet are the gear module size, the pressure angle, the number of teeth and the radial number of steps. A gearset example is considered and created with this method. The solid model of the example gearset in mesh and 2D drawing of the pinion are presented.

Mathematical Models of the Ocurved Spring Tubes Surfaces

2019 ◽  
Vol 16 (11) ◽  
pp. 4554-4559 ◽  
Author(s):  
Valeriya Leonidovna Vorontsova ◽  
Alfiya Gizzetdinovna Bagoutdinova ◽  
Almaz Fernandovich Gilemzianov
Keyword(s):  
Heat Exchange ◽  
Mathematical Models ◽  
Heat Exchangers ◽  
Coil Spring ◽  
Compact Heat Exchangers ◽  
Curved Channels ◽  
Exchange Processes ◽  
Heat Exchange Surface ◽  
The Creation ◽  
Exchange Surface

One of the ways to intensify heat exchange processes is the creation of compact heat exchangers with a developed heat exchange surface. It is known that coil-type channels provide a developed heat exchange surface and belong to one of the most efficient and technological designs of heat exchange elements. In this regard, the authors proposed a small-size heat exchanger of the “pipe in pipe” type with an internal coil spring-twisted channel, and the authors of the proposed article developed mathematical models describing the heat-exchange surfaces of pipes of complex configurations, including coil spring-coiled channels. The equations of heat transfer surfaces are written in vector-parametric form based on the fundamental principles of analytical and differential geometry. In order to verify the adequacy and visualization of the written equations, surfaces were constructed using the Matlab application software package. The proposed mathematical models can be used in computer simulation of hydrodynamic processes during the flow of liquid media in curved channels, which will allow to explore and further optimize their internal geometry by changing the parameters of the equations. This work is a continuation of research on the creation of efficient heat exchangers.

The Optimization Design of Wind Turbine Gearbox Based on Improved Genetic Algorithm and Feasibility Analysis

2014 ◽  
Vol 889-890 ◽  
pp. 107-112
Author(s):  
Ji Ming Tian ◽  
Xin Tan
Keyword(s):  
Genetic Algorithm ◽  
Wind Turbine ◽  
Optimization Design ◽  
Optimal Solution ◽  
Optimization Method ◽  
Strength Analysis ◽  
Improved Genetic Algorithm ◽  
Global Optimal Solution ◽  
Wind Turbine Gearbox ◽  
Global Optimal

The design of the gearbox must ensure the simplest structure and the lightest weight under the premise of meeting the reliability and life expectancy. According to the requirement of wind turbine, an improved method combined dynamic penalty function with pseudo-parallel genetic algorithm is used to optimize gearbox. It takes the minimum volumes as object functions. It is showed that the ability to search the global optimal solution of improved genetic algorithm and less number of iterations. The global optimal solution is worked out quickly. The size parameters are optimized, as much as the driving stability and efficiency. To verify the feasibility of improved genetic algorithm, ring gear of the gearbox is analyzed. Static strength analysis shows that the optimization method is reasonable and effective.

Identifying Real Stiffness Properties of Structural Elements of Adapted Finite-Element Models of Buildings and Structures - Part 1: Problem Setting

2014 ◽  
Vol 670-671 ◽  
pp. 732-735 ◽  
Author(s):  
Pavel I. Novikov
Keyword(s):  
Finite Element ◽  
Mathematical Models ◽  
Dynamic Characteristics ◽  
Finite Element Models ◽  
Structural Elements ◽  
Reliable Analysis ◽  
Adaptive Procedures ◽  
Stiffness Properties ◽  
The Creation ◽  
Problem Setting

The distinctive paper is devoted to problem of identification the dynamic characteristics of mathematical models based on the measured dynamic characteristics of real constructions. It is describes a problem of discrepancy of measured and modeling eigen pairs. It is shown that the problem is systemic. The creation and verification processes of mathematical (finite element) models used in the design constructions need some work and adjustments. For a reliable analysis of the construction ways are suggested to overcome the identified gaps using adaptive procedures.

scholarly journals MODEL MATEMATIKA SEDERHANA REDAMAN GETARAN PADA SAYAP PESAWAT TERBANG

2016 ◽  
Vol 8 (1) ◽  
pp. 8
Author(s):  
Rukmono Budi Utomo
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Aircraft Engine ◽  
Aircraft Wing ◽  
Wing Vibration ◽  
The Creation

We have known that when the plane encountered turbulence or in a hard landing, the aircraft engine will swing to dampen vibrations of the aircraft wing. Thus, based on rights, this research is investigating and constructing mathematical model of aircraft wing vibration. In this research, we described not only the creation of mathematical models, but also the analysis of the model and its interpretation.

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