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DeCaires, Brian J. "Variation analysis of involute spline tooth contact /." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1176.pdf.
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De, Caires Brian J. "Variation Analysis of Involute Spline Tooth Contact." BYU ScholarsArchive, 2006. https://scholarsarchive.byu.edu/etd/375.
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The purpose of this thesis is to provide an in-depth understanding of tooth engagement in splined couplings based on variations in clearances between mating teeth. It is standard practice to assume that 25-50% of the total spline teeth in a coupling are engaged due to variations from manufacture. Based on the assumed number of teeth engaged, the load capability of a splined coupling is determined. However, due to the variations in tooth geometry from manufacuture, the number of teeth actually engaged is dependent on the applied load and the tooth errors. The variations result in sequential tooth engagement with increasing load. To date, little work has been done to model tooth engagement and the stresses resulting from unequal load sharing among engaged teeth. A Statistical Tooth Engagement Model (STEM) has been developed which allows designers to estimate tooth engagement and resulting stress based on a statistical representation of the tooth errors. STEM is validated with finite element models as well as some preliminary experimental tests. Parametric studies are performed to determine the effect and sensitivities of variations in tooth parameters and tooth errors.
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Vogel, Olaf [Verfasser]. "Gear-Tooth-Flank and Gear-Tooth-Contact Analysis for Hypoid Gears : An Application of Singularity Theory / Olaf Vogel." Aachen : Shaker, 2007. http://d-nb.info/1170528155/34.
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Yang, Feng. "Numerical analysis and three dimensional modelling of worm gearing with localised tooth contact." Thesis, University of Exeter, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302638.
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Vaidyanathan, Sathyanarayanan. "Application of plate and shell models in the loaded tooth contact analysis of bevel and hypoid gears." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1335540802.
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Adnan, Md Asif, and Ahmed Shehata. "Stress Analysis Validation for Gear Design." Thesis, Blekinge Tekniska Högskola, Institutionen för maskinteknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-16862.
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Gear stress analysis and understanding the effect of misalignment and microgeometry is important for gear designers and for those who work in gear maintenance. The misalignment can lead to the higher stress acting in one side of the gear tooth and the micro-geometry modification can improve the stress distribution in the gear teeth. In this research, a helical gear pair was modeled using three different software and tools; LDP, KISSsoft and Abaqus. Three different cases were modeled to study the effect of misalignment and microgeometry. Finally, the results from different tools were presented and discussed. It was observed that the tooth contact analysis software resulted in significantly higher stresses than the FE software. The results have been discussed to understand the differences in the cases obtained from the used tools. The results showed how bad is the effect of the misalignment on the gear mesh and the stress distribution and how the microgeometry modifications are used to compensate that effect.
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Kolivand, Mohsen. "DEVELOPMENT OF TOOTH CONTACT AND MECHANICAL EFFICIENCY MODELS FOR FACE-MILLED AND FACE-HOBBED HYPOID AND SPIRAL BEVEL GEARS." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1245266082.
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Song, Yongle. "Optimum design and 3D CAD/CAE simulation of spiroid and worm gears." Thesis, Nottingham Trent University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369311.
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Guyonneau, David. "Contribution à la détermination de surfaces conjuguées pour la transmission de puissance." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4134.
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Les travaux présentés à travers ce manuscrit s'inscrivent dans un contexte de recherches exploratoires sur l'optimisation des surfaces engrenantes. Après une étude approfondie de l'emploi des engrenages dans un environnement aéronautique, l'élaboration d'une nouvelle méthodologie de génération de profils de denture est proposée. Les travaux s'attachent à caractériser le comportement mécanique spécifique d'un montage d'engrenages dans les Boites de Transmission de Puissances (BTP) d'hélicoptère.Un outil informatique a été créé dans le module VBA (Visual Basic Application) d'Excel. Il permet de créer automatiquement des profils de denture conjugués et optimisés. Il a l'avantage de définir analytiquement plusieurs grandeurs physiques. L'outil a ainsi pour objectif de proposer des profils de denture optimisés selon plusieurs critères. Les « objectifs » retenus sont le rendement et la contrainte équivalente de Hertz au contact suivant le critère de Von Mises.Les travaux s'articulent autour de trois axes : - la reconstruction de profils conjugués de denture par une approche novatrice basée sur le « contact », - la construction de critères physiques (glissement, pression, contrainte, …), - la recherche de profils de denture optimaux en utilisant la simulation de Monte Carlo.Enfin, la perspective de rendre générique cette méthode afin qu'elle puisse générer n'importe quels types d'engrenage est envisagée en fin de manuscritThe work described in the present manuscript is part of exploratory researches dealing with gears meshing surfaces optimization. After a short study of gears used in an aeronautical environment, the development of an innovative tool for tooth profile design is defined. Then, the specific behavior of a gear mesh within a helicopter main gearbox (MGB) is evaluated.A VBA software has been coded under MS Excel to generate conjugated and optimized gear tooth profiles. It advantageously defines and uses several physical parameters with their analytical formulation. The software provides at the user optimized tooth profiles according to a couple of criteria. The two “objective” functions evaluated are the efficiency and the Hertz equivalent stress within the contact using the Von Mises criterion.The work has been focused on three aspects:- The design of conjugated tooth profiles by contact sharing,- The definition of the relevant physical parameters,- The optimization of tooth profiles using Monte Carlo SimulationEventually, a generic method to design gear profiles, taking into account any physical parameters related to a gear mesh, could be expected as a future of this thesis work
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Bruyère, Jérôme. "Contribution à l'optimisation de la conception des engrenages coniques à denture droite : analyse et synthèse de la géométrie et des tolérances." Phd thesis, Paris, ENSAM, 2006. http://pastel.archives-ouvertes.fr/pastel-00002262.
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La maîtrise accrue des matériaux et des procédés de forgeage permet aujourd'hui d'obtenir des engrenages coniques d'une qualité suffisante pour pouvoir les utiliser sans autre procédé de finition. Ce sont les pièces dites «net shape». Grâce à cette évolution technologique, il est nécessaire de d'optimiser la définition géométrique de ces engrenages en tenant compte des possibilités des procédés de forgeage, en particulier. Tout d'abord, la définition de la géométrie nominale des engrenages coniques à denture droite basée sur les propriétés géométriques et cinématiques du profil en développante de cercle sphérique est réétudiée et a abouti à une modélisation paramétrique des surfaces actives en intégrant un bombé longitudinal. Afin de garantir un certain niveau de qualité de l'engrènement, il est nécessaire de limiter les variations inhérentes au procédé de forgeage et aux ressources de fabrication, il s'agit de l'analyse et de la synthèse des tolérances. Cette analyse a nécessité une modélisation géométrique des engrenages incluant les écarts intrinsèques et les écarts de situation. L'analyse de l'impact de ces écarts sur l'erreur cinématique (Tooth Contact Analysis) repose sur la résolution d'un système d'équations non linéaires pour chaque position du pignon et d'un traitement de ces résultats; la difficulté de cette analyse est la grande sensibilité des résultats aux écarts. Cet outil «TCA» est le module principal de l'analyse des tolérances qui est réalisée de façon statistique par simulation de Monte Carlo. L'analyse des tolérances permet de valider une solution d'allocation de celles-ci mais ne permet pas son allocation automatique. Ainsi une approche de synthèse des tolérances a été validée, il s'agit de l'optimisation par algorithme génétique où la fonction objectif est de minimiser le ratio coût des tolérances sur la probabilité de respect des exigences. Cette analyse et cette synthèse ont été menées dans un premier temps sans charge, en considérant l'engrenage comme indéformable. Puis, la prise en compte des déformations est réalisée par la méthode des coefficients d'influences. Le problème de contact et de déformation globale de la denture sont découplés. Les coefficients d'influences de contact sont estimés par la méthode de Boussinesq et Cerruti. Les coefficients d'influence de flexion sont estimés par interpolation et méthode des éléments finis. Ce modèle permet l'analyse de l'engrènement sous charge mais les temps de calculs restent un handicap pour l'analyse des tolérances. Ces modèles de comportement pourront être affinés dans de futurs travaux et être le support de nouveaux modèles de spécification des engrenages, de suivi du processus de fabrication, d'une meilleure connaissance des interactions géométrie-mécanique-matériau, etc.
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Vondra, Róbert. "Deformačně napěťová analýza zubové spojky." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-432792.
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This thesis deals with the contact analysis study of crown gear couplings during the simulation of its working conditions. The toothed coupling transmits high torque, even when the input and output shafts are misaligned due to outside tooth shape. For this reason, it is necessary to design the gear shape correctly. The inherent use of toothed couplings results in a wide range of working speeds and load transfers. This can cause several problems, if the parameters are selected incorrectly. Among the most significant of these is the generation of vibrations during gear engagement, accompanied by noise and the excessive loading of components, such as shafts and bearings. It is not possible to completely reduce uneven running, even with knowledge of the latest trends in the field of gear development. For this reason, it is necessary to eliminate the paths where the vibrations can propagate during the design itself. Inefficient and costly experiments are often used to determine the correct shape of gear teeth. For this purpose, a computational approach to describe a contact pressure on the teeth of couplings at different misalignment and loads is proposed. The model helps to understand the composition of the contact pressure during the working mode of misalignment and its behaviour within the rotation of the gear coupling. The introductory part of thesis presents the current state of knowledge of gear couplings and a description of load distribution issues, regarding the angular misalignment, torque and friction. In the following chapter, three possible approaches to the problem are described - analytical, experimental and computational. The following work offers the introduction and creation of two different computational models, varying in different tooth shape on the hub and the sleeve. Each geometry was subjected to a different load moment, a misalignment of the hub, or the rotation of the gear coupling as a whole. The main monitored parameter was the course of contact pressure in each step, when changing the degree of misalignment or the rotation of the model. Finally, three main sets of contact pressure on the teeth are presented, in connection with the reduced pressure plotted on the toothed rings. There is derivation of results and mutual comparison of each load case. The computation approach in FEM program Ansys Workbench was used to solve the problem.
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Lagresle, Charly. "Analyse du processus d’usure abrasive et optimisation d’engrenage aéronautique." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEI113.
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Les organes de transmission de puissance par engrenages sont couramment utilisés dans de nombreux domaines, parmi lesquels celui de l'aéronautique. Le système étudié dans ces travaux de thèse est un réducteur d'hélicoptère. Son rôle est de transmettre la puissance générée par le turbomoteur à la boîte de transmission principale, tout en adaptant la vitesse de rotation au besoin de cette dernière. Pour maximiser la puissance massique des systèmes, les engrenages aéronautiques peuvent être dotés de voiles minces, réduisant la masse de l'ensemble, mais favorisant aussi leurs flexibilités. Très sollicités en termes de nombre de rotations et de conditions de fonctionnement, ces engrenages à voile mince du réducteur présentent un risque d’apparition de surpressions locales et sont d'autant plus susceptibles d’être soumis à un certain nombre d'avaries, telles que l'usure abrasive, le grippage ou encore le micro-écaillage. Le premier objectif de ces travaux de thèse est la compréhension et la simulation du processus d'usure abrasive sur les engrenages. Ce processus d'arrachement de matière sur le flanc des dentures est simulé par l'intermédiaire de la loi d'Archard adaptée aux contacts lubrifiés. Lors des différentes phases de vol (décollage, atterrissage, etc.), les conditions de fonctionnement évoluent et modifient les paramètres quasi-statiques de l’engrènement, la lubrification du système et par conséquent la quantité de matière arrachée. Afin de prendre en considération les évolutions des conditions de fonctionnement dans le processus d'usure, une méthodologie de cumul de l'usure a été adoptée et adaptée aux besoins de la simulation. Il est alors possible d'étudier la cinétique et l'intensité de l'usure sur les différentes phases de vol afin d'en déterminer les plus sévères. Le second objectif fait écho au premier. Après avoir cerné la problématique de l'usure, l'optimisation des paramètres quasi-statiques de l'engrenage à voile mince est mise en place. Cette optimisation, basée sur la recherche d'une micro-géométrie idéale, a pour vocation de réduire les causes potentielles de ces avaries, notamment les surpressions de contact ou le facteur de grippage d'Almen. Le problème étant qualifié de complexe, un algorithme MO-TRIBES d'optimisation multivariables et multicritères est déployé. De nombreux exemples d'optimisation sont proposés afin d'améliorer le comportement de cet engrenage à voile mince : réduction des fluctuations des signaux d'erreur de transmission sous-charge, des pressions maximales de contact, des facteurs de grippage, en simple et en multi-objectifs. Le choix des corrections de denture et de leur forme est aussi abordé. Finalement, grâce à ce module d'optimisation, il est possible de réduire l'arrachement de matière afin d'allonger la durée de vie de l'engrenagePowers transmissions are commonly used in many areas, including aeronautics. The studied system in this thesis is a helicopter gearbox. Its purpose is to transmit the power generated by the turbine engine to the main gearbox and to adapt the rotational speed of the input shaft. Aeronautical gears are light weight in order to maximize the power to weight ratio of the system. With thin rims, the mass of the system is reduced but its flexibility is increased. These types of gears, subjected to large number of revolutions and severe operating conditions, are more likely to be exposed to failures such as abrasive wear, scoring or micro-pitting. The first objective of this PhD thesis is the understanding and the simulation of the abrasive wear process for spur and helical gears. The material removal calculation is based on the well-known Archard equation, adapted to lubricated contacts. During the different phases of flight (take-off, landing, hover flight), the specific working conditions change. Consequently, the quasi-static gearing behaviour, the lubrication and therefore the quantity of wear need to be adapted. To this end, a new methodology is proposed to accumulate wear depths over several and different working conditions. This methodology makes it possible to analyze the kinetics and the intensity of the abrasive wear process and deduce the most severe phases of flight. The second goal echoes the first one. Following the identification of the problem of abrasive wear, a multi-objective optimization of the quasi-static behaviour of the thin rimmed gear is proposed. The goal of this optimization, based on the search of optimal tooth modifications, is to reduce potential sources of gear failures, in particular localized overpressures on tooth flanks or the Almen factor governing scuffing. Due to the complexity of the problem, a meta-heuristic multi-variable optimization algorithm (MO-TRIBES) is introduced. Multiple mono- and multi-objective gear optimization examples are provided in order to improve the quasi-static behaviour of the aeronautical gear : minimization of fluctuations of the transmission error under load, reduction of the maximal contact pressures, decrease of the scuffing risk factors. The ideal type of tooth modifications is discussed. Finally, by using the optimization module, the amount of wear is significantly reduced and a comfortable lifetime extension for the studied gear is provided
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Teixeira, Alexandre Carvalho. "Análise das tensões nos primeiros pré-molares superior e inferior, em contato, através do método de elementos finitos." Universidade do Estado do Rio de Janeiro, 2006. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=752.
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As lesões cervicais não cariosas foram, durante muito tempo, atribuídas à abrasão causada pela escovação dental, e/ou por processos erosivos. Teorias biomecânicas consideram a possibilidade de que concentrações de tensões na região cervical, causadas pela flexão de cúspides, poderiam contribuir, associadas a outros fatores clínicos, para o desenvolvimento dessas lesões chamadas de abfração O presente trabalho pretende através do método de elementos finitos, utilizando o programa ANSYS versão 8.1, analisar a distribuição de tensões na região cervical de modelos bidimensionais parametrizados dos primeiros prémolares superior e inferior quando estes são colocados em contatos cêntrico e excêntricos no plano frontal, sob uma carga de 1 N. Para simulação da diminuição da mobilidade do ligamento periodontal sob cargas de impacto, o valor real do seu módulo de elasticidade foi aumentado para o correspondente ao do osso esponjoso e ao do osso cortical. Os resultados permitiram concluir que, de uma maneira geral, nas posições excêntricas, os dentes se flexionam e tensões de tração ocorrem na região cervical oposta ao contato com valores compatíveis para formação das lesões. Na posição cêntrica, as tensões de tração se manifestam mais na região da fossa central de ambos os dentes e na cervical do pré-molar inferior. A simulação da diminuição da mobilidade dentaria sob cargas de impacto reduziu o valor das tensões de tração, em todas as regiões analisadas, na ordem de 33% para o pré-molar superior e 66% para o inferior, mas não alterou seu padrão de distribuição.Non carious cervical lesions were often attributed to toothbrush abrasion and/or erosive process. Biomechanical theories consider that stress concentration in the cervical area, caused by cuspal flexure, may contribue, associated to other clinical factors for the development of the lesion called abfraction. The aim of this finite element study, using the ANSYS version 8.1, is to analyze the stress distribution in the cervical region of superior and inferior premolars bidimensional models. Contacts in centric and eccentric positions were reproduced under a 1 N load. To simulate tooth mobility reduction under impact loads, the elastic modulus of the periodontal ligament was increased to reach the corresponding ones of the alveolar and cortical bone. The results showed that, in eccentric positions, teeth bend and tensile stress are generated at the cervical region opposed to the contact side, justifying the possibility to initiation of the lesion. In centric position, tensile stress occurred on both teeth at the central fossae and at the buccal cervical area of the inferior premolar. The simulation of tooth mobility reduction under impact loads diminished the tensile stress value, at all of the analyzed positions, in a rate of 33% and 66% respectively to superior and inferior premolars.
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Liu, Chih-Wei, and 劉誌偉. "Tooth Contact Analysis between Arbitrary Tooth Surfaces." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/58047553880429517235.
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碩士國立中正大學
機械工程所
93
This paper develops a tooth contact analysis between arbitrary tooth surfaces. The tooth surface of mating gears is mathematically modeled by the free form curves and surfaces of NURBS. The least rotation angle method with improved search method is developed to find out the contact points and the transmission error is calculated according to the contact point data. The separations near the contact point are used to find the contact area. The numerical results prove that the least rotation method could determine contact points on tooth edges and show the tooth contact situation precisely.
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Chung, Tsang Dong, and 鍾藏棟. "Tooth Contact Analysis of Face-Gears." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/94160850807899697256.
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博士國立臺灣大學
機械工程學研究所
87
A complex face-gear drive formed by a spur pinion and two face-gears is a torque split reducer. Due to the division greatly reduces the size and weight, the predicted payoff is greatly reduced weight and cost compared to conventional design which formed by two pairs of spiral bevel gears. It was usually applied in the helicopter transmission. A simple face-gear drive is formed by a pinion and a face-gear. Because of the pinion is a conventional spur (or helical) gear, transmission error is similar to that of the spiral bevel gear and contact pattern is also similar to that of the spiral bevel gear, face-gear is used much often in the recently years. In this paper, by using homogeneous coordinate system transformation method according to the space relationship between the gear and shaper coordinate systems, equation of the generated face-gear surface can be obtained. The effects of assembly errors of generated face-gear on the surface of the face-gear, and the effects of parameters of shaper such as module, tooth number and pressure angle on the undercutting and pointing phenomena during the cutting processes were also discussed. Several design charts were developed to avoid undercutting and pointing during the face-gear generation. The transmission of a simple face-gear drive were studied as well. By applying tooth contact analysis, homogeneous coordinate transformation method and meshing equation, the effects of parameters of face-gear and shaper and assembly errors of face-gear on transmission errors were also investigated. The face-gears can also applied to the hard face-gear harmonic drive, and transmission errors of the hard face-gear harmonic drive were analyzed.
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kuo, Yu-Li, and 郭育里. "Numerical Method for Tooth Contact Analysis." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/13868151991109918356.
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碩士國立成功大學
數學系應用數學碩博士班
96
In this paper, we introduce a numerical method to compute the kinematics of the contacting point of two plane teeth. Regard mesh of two plane teeth as point contact of two planar curves, then express the coordinates of planar curve by parametric curve and Rigid-Body Motion. Since two curves have the same coordinates and unit normal vector at the contacting point, the problem of the mesh of two planar curves is transformed into an ordinary differential equation by vector analysis. We have the solution to the equation by numerical method and computer calculation. After repeating the way of computing the solution to the equation, we have the contacting points. Simulate the mesh of a gear and a rack or the mesh of a gear and a gear by two planar circle curves. In the end, simulate the mesh of two plane teeth of shape of involutes which most used in the shape of plane gears.
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Wu, Yi-Chen, and 吳懿真. "Tooth Contact Analysis of Cycloidal Gears." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/84430108340102189158.
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碩士清雲科技大學
機械工程研究所
95
In this study, the mathematical models cycloidal gears are derived based on the theorem of gearing firstly. Then, the meshing model of cycloidal gear pair is set up and tooth contact analysis (TCA) is adopted to investigate the transmission errors with different design parameters and assembly conditions. Furthermore, the general-purpose FEA software, ABAQUS, was applied to evaluate the formation of bearing contacts and stress distribution on the tooth surfaces according to different design parameters. Results in this study not only verify the contact nature of cycloidal gear pairs, but also provide the bases for upcoming research on cycloidal gear pairs such as curvature analysis and sliding ratios.
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林居財. "Tooth Contact Analysis of Straight Bevel Bear." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/41992215563501394250.
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碩士國立中正大學
機械系
90
Straight bevel gear is applied to power transmission of the nonparallel axes, and suits the operation of low speed. It is convenient and applied widely. This paper help us getting the design size of straight bevel gear and trim the profile by the simulated machine tool. The mathematical model of the paper imitates the corresponding machine tool working mode, and contrasts the machine tool setting. It saves time and cost to design different straight bevel gears by the computer calculation. This paper help us handling the tooth contact analysis on computer for the purpose of cutting the suited gear we want.
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Huang, Chao-Jun, and 黃超俊. "The Tooth Contact Analysis of Silent Chains." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/58729636563989638626.
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碩士國立成功大學
機械工程學系碩博士班
91
In mechanical power transmission applications, two of the most popular chain drive types are the roller chain and the silent chain, both of which have been employed in industry for decades. Silent chains have many advantages. It is quieter and more efficient than roller chains. However, there are not many research reports of silent chains in literature. This thesis aims to investigate the kinematics of pin-jointed silent chains. Based upon conjugate theory, this thesis studies the motion analysis of silent chains. We analyze silent chains by using the techniques of tooth contact analysis with force equilibrium equations incorporated. First, we assume two fixed models of link with respect to the sprocket. Second, we establish four stages of the motion of a link, starting from tight chain span until it is fixed with respect to the sprocket. These four stages are conjugate contact stage, stationary contact stage, pulled suspension stage, and conjugate suspension stage. Finally, we change the curvature of the inner curve of the link to investigate the relationship between the curvature of links and the chain motion. Some animations of the engagement process are demonstrated to illustrate the results. In conclusion, we have proposed a systematic approach for analyzing the motion of silent chains. The results of this research can also be applied to mechanical system with multiple bodies in contact.
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Wang, Sheng-Feng, and 王勝鋒. "Tooth Contact Analysis of Internal conical Gear Pairs." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/15969544833986627261.
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碩士清雲科技大學
機械工程研究所
95
The gear is one of the most important mechanical elements used in the machinery transmission system. It is the main target to design and manufacture gears with low cost,low noise, light weight and high efficiency. Internal gear pairs are widely used in reduction gear systems for parallel axes gearing with high gear ratios and small space requirements. Internal gears are generally more efficient since the sliding velocity along the mating tooth surfaces is lower than that of an equivalent external gear pair. Due to the concave nature of the internal tooth profile and the thicker tooth base, the tooth strength of an internal gear is higher than that of an equivalent external gear. The conical internal gear pair investigated in this study is composed of a conical internal gear cut by shapers and a conical pinion cut by hobs. In addition to retain the advantages of the conventional internal gear pair, the backlash of a conical internal gear pair can be easily controlled by axial adjustments without affecting its center distance owing to its tapered tooth thickness. In this study,tooth contact analysis of conical internal gear pair is proceeded firstly.Then contact ellipse simulation of the conical internal gear pair have been performed based on the concept of differential geometry. The effects of design parameters on the dimensions of contact ellipses were studied as well. Meanwhile, an automatic mesh-generation program was developed to discretize the three-dimensional tooth model for finite element analysis (FEA) on the basis of the derived tooth geometry. Then, the general-purpose FEA software, ABAQUS, was applied to evaluate the formation of bearing contacts and stress distribution on the tooth surfaces. The results of the FEA and contact ellipse simulations can be verified mutually.
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Jin, Kai-Wei, and 金凱威. "Simulation of Gear Shaving with Tooth Profile Modification and the Tooth Contact Analysis." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/fvg9r8.
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碩士國立虎尾科技大學
機械與機電工程研究所
95
Gear shaving is the most important refinement method to manufacture the helical and spur gears by the CNC shaving machine. In this thesis, the rack cutter is used to generate a shaving cutter firstly, the shaving cutter is then used for the generation of gears. The rack cutter with modified profile proposed by Professor Litvin is used to derive the mathematical model of shaving cutter. The shaving process is then simulated according to the shaving machine to generate the gear tooth surface with double crowning. The TCA of two types of tooth surfaces, i.e., double crowning and crowning in longitudinal direction only, are investigated in this research. Taguchi method is used to find out the optimum combination of parameters in different conditions of assembly. The results of this thesis provide important informations for the study on the shaving machine and characteristics of gears. It also provides the reference for the stress analysis of shaved gears.
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Li, Wei-Ching, and 李韋慶. "Three-Dimensional Tooth Contact Analysis of Straight Bevel Gears." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/tzdf4a.
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碩士國立虎尾科技大學
機械設計工程研究所
100
The common gear dynamic contact analysis, its analysis time has grown, affects the following gear design and the processing flow. In order to reduce the gear contact analysis time, the present paper establishes a set of three dimensional straight bevel gear contact analysis mold train, by the rack cutter form, the penetration differential geometry and the meshing theory, constructs the straight bevel gear mathematical model, carries on the formula composition because of mathematical computation software Mathematica, obtains its computation the spot material to converge in PRO/E to construct the three-dimensional model, again converges the three-dimensional model HyperMesh to carry on the limited element model grid division, after completes the plan grid model to converge Workbench to carry on the material nature hypothesis, the contact pattern choice, the load hypothesis and the analysis control and so on, finally carries on the analysis solution operation by ANSYS, obtains the gear in the static contact load lower teeth surface contact stress. The present paper use gear contact model, is different with the general differential geometry computation, in the gear contact analysis can reflect contact of situation real gear, and before Workbench structure static analysis processes in the hypothesis to carry on the adjustment, may the short time complete the gear contact analysis, compared to general dynamic analysis larger reduction analysis time.
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Lo, Wei-Hsu, and 羅偉旭. "Mathematical Model and Tooth Contact Analysis of Spherical Gears." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/91615147475010356302.
Full textAbstract:
碩士國立交通大學
工學院碩士在職專班精密與自動化工程組
95
Spherical gears have been used for years, however, spherical gears generated by a hob cutter with circular-arc profiles have not found yet. Besides, there is no research on the tooth contact analysis of this type of spherical gears with tooth profile modification. Therefore, to establish the mathematical model of this type of gears and to investigate the contact characteristic of the gear pairs are most helpful to the applications of this tooth modified spherical gears. In this research, the tooth mathematical model of the spherical gears with modified tooth profiles, generated by a hob cutter with circular-arc profiles, is developed based on the theory of gearing and the spherical gear generation mechanism. A concept of applying the curvilinear-tooth rack cutter with circular-arc profiles to simulate the hobbing generation of a hob cutter with circular-arc profiles is proposed. Based on the developed tooth mathematical model of the modified spherical gear as well as the theory of gear meshing and the developed tooth contact analysis computer simulation programs, the tooth contact simulations, characteristic analysis and kinematical errors of the gear pairs under various assembly errors are performed and discussed.
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Liu, Po-Chun, and 劉柏村. "Synthesis and Tooth Contact Analysis of Spatial Involute Gears." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/37109163726093953764.
Full textAbstract:
碩士國立成功大學
機械工程學系專班
94
Planar involute gearing is popular for over a century because involute gears are easy to produce and, most importantly, insensitive to assembly errors. Nevertheless, to have this characteristic, the axes of planar involute gear pairs must be parallel. Philips proposed a new spatial involute gear in 2000, based on the idea of a slip track, which can be thought of as a spatial involute curve. Philips designed general spatial involute gears that can be used in skew-axis transmission applications. However, he defined the spatial involute gears based on geometric constructions only. In this thesis, we seek to build the mathematic models of an involute gear tooth surface and its conjugate surface. First, we use coordinate transformations to build the parametric equation of a spatial involute gear tooth surface. Second, we use conjugate theories to synthesize its conjugate tooth surface. Finally, we employ TCA technique to analyze spatial involute gearing and to demonstrate that it is insensitive to assembly errors. This thesis has built mathematical models of conjugate spatial involute gear pairs and conjugate rack-and-pinion systems. This research can serve as a foundation for further investigation of spatial involute gearing.
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FENG, ZHAN-HUA, and 馮展華. "TOOTH CONTACT ANALYSIS AND OPTIMIZATION OF SPIRAL BEVEL GEARS." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/53258147533130910739.
Full textAbstract:
博士國立交通大學
機械工程研究所
79
A mathematical model of the circular-cut spiral bevel gear set has been developed, and simulations of the gear manufacture and working conditions have also been investigated in this thesis. The research subjects are: (a) Constructing a general mathematical model to represent the geometry of the circular-cut spiral bevel gear tooth surfaces. The tooth surfaces of the spiral bevel gear are described by the simplified surface coordinates, and they are termed as the "soft" spiral bevel gear. (b) Developing a mathematical model to simulate the kinematical characteristics of the universal bevel gear roll tester. By employing the "imaginary" roll tester to imitate the working conditions of the "soft" spiral bevel gear set, and using the loaded tooth contact analysis (LTCA) techniques to evaluate the meshing conditions between the contacting tooth surfaces. (c) Applying the proposed mathematical model to simulate the existing Gleason spiral bevel gear cutting machines, and to study the relations between the Gleason machine settings and parameters of the mathematical model. (d) To create a kinematical optimization model for the spiral bevel gear set. The objects of the optimization are: (1) minimizing the rotational kinematic errors, (2)to discard the discontinuous teeth meshing, and (3) to move the contact pattern toward the center region of the tooth surfaces with a proper bias. (e) To investigate the undercutting conditions of the circular-cut spiral bevel gear. Deriving the equations for the limit of the generating tool setting, and the edge of regression on the generated gear tooth surface. The proposed mathematical models are the basis for the expert system of designing the spiral bevel gear set. The applications of the proposed mathematical model are illustrated by numerical examples and computer graphics. 根據齒輪原理及微分幾何，作者推導出圓切式蝸線傘齒輪之數學模式．此數學模式能 模擬現存之大部分圓切式蝸線傘齒輪創成機及測試機的特性，精確且迅速的得到齒面 幾何及齒輪對之運動特性．本論文包括： （１）建立圓切式蝸線傘齒輪之齒面數學模式，並以精簡之參數來描述齒面的幾何． 所推導之齒面數學模式可當作圓切式蝸線傘齒輪之檢驗標準． （２）根據萬用傘齒輪測試機（Universal bevel gear roll tester）之機構，發展 出圓切式蝸線傘齒輪之齒輪接觸分析的數學模式．利用此數學模式來模擬蝸線傘齒輪 對在負載下運轉的情形，同時得到齒面嚙合的齒印及剛體運動誤差． （３）運用所發展之數學模式來模擬格里森（Gleason ）公司之圓切式蝸線傘齒輪創 成機器，並將數學模式所用之參數轉換成實際加工時所用的機器設定．同時發展一系 列之圓切式蝸線傘齒輪電腦輔助設計軟體，只要將機器設定輸入電腦就可得到齒形之 電腦繪圖及齒輪對之運轉情形． （４）根據前所推導之數學模式及最佳化理論，發展出圓切式蝸線傘齒輪之最佳化模 式．以此模式可將運動誤差、間歇性之齒面接觸及齒印位置調整到最佳之折衷點． （５）根據微分幾何，證明圓切式蝸線傘齒輪之過切存在的條件，並據此條件找出避 免齒形過切之機器設定及進刀量的限制． 本文所發展之數學模式不僅可作為圓切式蝸線傘齒輪之檢驗標準，且可作為圓切式蝸 線傘齒輪設計製造之專家系統的基礎．文中並以許多例子來說明所發展之數學模式的 應用及其可靠度．
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Guo, Ren-jie, and 郭仁傑. "Loaded Tooth Contact Analysis of Gear Pairs with Tip Relief." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/48713490272482914105.
Full textAbstract:
碩士國立中央大學
機械工程學系
101
Involute gears have advantages such as simple manufacturing process, low sensitivity due to the center distance deviation, and high transmission efficiency etc., so it is widely applied in various power transmission equipments. However, vibration, noise, and even tooth surface damage will occurr during the gear mesh because of variation of mesh stiffness and tooth tip corner contact. Therefore, profile modification on gear teeth is a commonly method to reduce the violent change of loading on teeth and to avoid tooth contact on tip corners beyond the normal line of action. But the profile modification is equivalent to a special kind of tooth profile deviation, it is necessary to analyze the loaded tooth contact stress of the gear pairs with or without profile modification to understand the influence of different profile modification design on the performace of gear drives in practical application. The aim of this study is to analyze the influence of tip relief, a common profile modification method for involute spur gear, on tooth contact stress. This study includes (a) identification of occurrence of tooth tip corner contact and analysis of contact stress distribution of the involute spur gear pair without profile modification, and (b) the influence of different tip relief types on load sharing and contact stress distribution of involute spur gear pairs. At first in the thesis, occurrence of tooth tip corner contact of involute spur gear pairs without profile modification under different loads is identified based on the geometric relation of gear mesh. Then static load sharing and tooth contact stress distribution of spur gear pairs without and with different tip relives are analyzed by using stiffness method and influence coefficient method respectively. The types of tip relief discussed in the study include linear long and short tip relief, tip rounding, parabolic tip relief, etc. The results of the load sharing analysis show that linear tip relief and parabolic tip relief can improve problem of the violent load change, but tip rounding or other tip chamfer types can not improve it. According to the results of the loaded tooth contact analysis, non-Hertzian contact of tooth pairs occurs at the positions before the theoretical contact begin and after the theoretical contact end of the tooth pair without tip relief. The values of the corresponding contact stress are much larger than the value of normal contact. The maximum contact stress occurs at the position nearby theoretical contact begin and end position. The type of non-Hertzian contact can be avoided effectively by using the linear tip relief and the parabolic tip relief, but tip corner contact of tooth pair with tip rounding still occurrs. In addition, stress concentration can be also found at starting position of the tip relief, if the tip relief curve is not smooth. The analysis results show that the calculation modules for load sharing and loaded tooth contact analysis developed in this study are reliable and time-saving for calculattion, so they can be used for tip relief design and analysis efiiciently. Keywords: Tooth Tip Corner Contact, Tip Relief, Tip rounding, Load Sharing, Tooth Contact Stress
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Chan, Tzu-chiang, and 詹自強. "Geometric Design and Tooth Contact Analysis of Spiral Bevel Gear." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/31586473475226058110.
Full textAbstract:
碩士正修科技大學
機電工程研究所
96
In order to comprehend the tooth contact analysis and stress analysis of spiral bevel gear drives, this thesis derives the surface equation of spiral bevel gear based on the differential geometry and homogeneous coordinate transformation. Firstly, the generating surfaces of the head-cutter are formed by rotation of the blade. The derivation of the equations of the generated gear tooth surface is in accordance with the application of two equations: equation of the family of head-cutters surfaces and equation of meshing that have to be considered simultaneously. The surface and solid model are built through CAD/CAM software. The formation of bearing contact during the cycle of meshing and perform the stress analysis are investigated by application of finite element analysis (ANSYS). The design of finite element models and the settings of boundary conditions are automatized.
28
Gu, Ming-Lune, and 古鳴倫. "Tooth Contact Analysis of a Curvilinear Gear Set with Modification." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/15135278796346859012.
Full textAbstract:
碩士國立中央大學
機械工程研究所
99
Modified curvilinear gears can be generated by an imaginary rack-cutter with a circular-arc normal section. The tooth thickness of the modified curvilinear gears is larger in the central transverse section, and the left and right tooth surfaces are not symmetric. One of the tooth surfaces is concave and the other is convex. A modified curvilinear gear set has point contact and will not incur point contact under assembly errors. In this study, firstly the mathematical model of the imaginary rack cutter is developed. The mathematical model of the modified curvilinear gears was derived based on the imaginary rack cutter and the generation mechanism. Tooth contact analysis (TCA) of a modified curvilinear gear set was established to simulate the influences of design parameters and assembly errors on transmission errors. The contact ratio of the gear set was also calculated from the TCA results. The solid model of the gear set was established by computer aided design software, and finite element analysis (FEA) was performed to analyze the contact stress and root bending stress under different design parameters and different rotational angles. Finally, the modified curvilinear gears were manufactured by using a 5-Axes CNC Machining Center. Experiments of transmission errors and contact patterns were performed on a universal gear tester to verify the FEA results.
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Lin, Hung-Jeng, and 林宏政. "Simulation of Gear Shaving Machines and Gear Tooth Contact Analysis." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/2ah2hx.
Full textAbstract:
碩士國立虎尾科技大學
動力機械工程研究所
94
Gear shaving is commonly used for gear finishing process, due to it has higher efficiency and accuracy. When the gear pair having axis misalignment, crowning is popularly used for the gears making the contact point located at the middle region of the tooth face to keep off the phenomenon of edge contact. Besides introducing the basic concept of the gear shaving motion, this research also uses the theories of gearing and the differential geometry to derive the mathematical models of the shaved gear with crowning by considering the parameters adjustment of the gear shaving machine. This research compares the crowning method proposed by Professor Litvin and the crowning action generated by the shaving machine manufactured by a local company -HOTA. Considering the shaving motion of the two crowning methods, the mathematical models of the work gears are developed. The effects of the parameters of the shaving machine can thus be studied. Then, the tooth contact analysis (TCA), contact pattern analysis, and transmission error analysis are investigated when the work gears are meshing in theoretical condition or with the axis misalignment.
30
Kosasih, Leo, and 劉權慶. "The Tooth Contact Analysis of Rocker-Pin Jointed Silent Chains." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/46602349424608750685.
Full textAbstract:
碩士國立成功大學
機械工程學系碩博士班
92
Two of the most popular chain drives in power transmission applications are roller chains and silent chains. Silent chains are mostly used for higher speed and higher load requirements. In addition, silent chains are quieter and more efficient than roller chains. However, research reports on silent chains in literature are limited. Two types of silent chains are used in industry: round pin jointed and rocker-pin jointed silent chains. This thesis explores the tooth contact analysis of rocker-pin jointed silent chains. Simplified models of silent chains are established based on some assumptions, ignoring the effects of wear and tolerance. Based upon conjugate theory, the motion analysis of silent chains has been studied. Silent chains are analyzed by using the techniques of tooth contact analysis with geometric constraints and force constraints incorporated. For silent chains with internal contacts, two cases are investigated: at most one link in contact and at most two links in contact. Five phases have been identified throughout the analysis: tight span phase, conjugate-contact phase, stationary phase, suspended phase, and fixed phase. The stationary phase only occurs at round pin types with at most one links in contact. For silent chains with external contacts, the conjugate-contact stage doesn’t exist, since the link plates are fixed as soon as they are in contact with the sprocket. In addition, the real fixed position of the link plates and the chordal actions of silent chains are investigated. The real fixed position of the rocker-pin link plate is found to be later than that of the round pin link plate. The chordal actions of rocker-pin silent chains are smaller than those of round pin silent chains. Furthermore, the relationship between the rocker-pin size and the chordal action is also studied. This thesis purposes a systematic approach for analyzing the motion of silent chains, and the result of this research can also be applied to mechanical system with multiple bodies in contact.
31
Chang, Chi-Kang, and 張岐康. "Mathematical Model and Tooth Contact Analysis of Straight Bevel gears." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/61430296128657877670.
Full textAbstract:
碩士國立交通大學
機械工程系
87
MATHEMATICAL MODEL AND TOOTH CONTACT ANALYSIS OF STRAIGHT BEVEL GEARS Student：Chi-Kang Chang Advisor：Chung-Biau Tsay Institute of Mechanical Engineering National Chaio Tung University ABSTRACT Straight bevel gears are widely used for power transmissions between the intersected shafts. However, only a few of technical literatures related to straight bevel gears can be found. In this thesis, a mathematical model of the straight bevel gear with octoid form has been developed based on the theory of gearing and the concept of differential geometry. The developed mathematical model can be used to simulate the gear manufacture and meshing conditions of the gear set. The tooth undercutting , tooth contact analysis, profile shifting, and kinematic errors have also been investigated. The research subjects are: (a) Development of a general mathematical model to represent the geometry of the straight bevel gear tooth surfaces with the octoid form. The tooth surfaces of straight bevel gear are described by the simplified surface coordinates, and they are termed as the "soft" straight bevel gears. The developed mathematical model can be used to the surface inspection as the standard gear tooth surface profile. (b) Based on the theory of tooth contact analysis, a tooth contact analysis computer simulation program has been developed. According to the developed computer program is used to simulate the kinematic errors of the gear train and to investigate the bearing contact of straight bevel gear. (c) Constructing a mathematical model for the profile-shifted straight bevel gears, and comparing the differences between the ordinary profile and shifted profile. Relations between the tooth surface parameters and its tooth thickness and tooth height have also been investigated. (d) Investigation on the necessary and sufficient conditions for undercutting of the straight bevel gear with octoid form. Machine-tool settings for tooth non-undercutting are also investigated according to the developed tooth undercutting conditions. The relationship between the undercutting and the coefficient of the profile shifting are also studied. The proposed mathematical model of straight bevel gears is the basis for the inspection, finite element analysis and expert system development of straight bevel gears. The applications and correctness of the proposed mathematical model are illustrated by some numerical examples, tables and computer graphs. Those investigations and results shown in this thesis are most helpful to engineers in the design and manufacture of straight bevel gears with octoid form.
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Ye, Siang-Yu, and 葉湘羭. "Loaded Tooth Contact Analysis of Planetary Gear Sets with Flank Modification." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/8vfd67.
Full textAbstract:
博士國立中央大學
機械工程學系
104
Compared with the parallel axis gear drive, the planetary gear drive, as a power-split mechanism, has the advantages of high power density, coaxial input and output shaft, as well as compact design. Therefore, it is widely applied in various transmissions. But in actual operation, the time-variant mesh stiffness as well as manufacturing and assembly errors will cause the uneven load sharing among multiple planet gears and the jump in variation of contact stress and shared load of contact tooth pairs of the planetary gear set. On the other hand, the deformation of the components in the planetary gear set will also result in uneven load distribution on the tooth flanks. The effective solution in the practice is to apply flank modification to enhance the load capacity and also to improve transmission performance. But the loaded contact characteristics of the drive have to be simulated in advance, so as to proceed suitable flank modification. The goal of the dissertation is thus to propose a loaded tooth contact analysis model for planetary gear drives, so as to simulate and analyze the contact characteristics of the engaged teeth under the real condition. The equations of the three-dimensional modified flanks, manufactured by profile grinding, are at first derived in the dissertation. Considering the flank modification and the errors, a tooth contact analysis model (TCA) is developed for calculating the variables of the contact points. The transmission errors, the backlashes and the clearances in the planetary gear sets can be analyzed accordingly. The errors, involved in the TCA model, include the tooth thickness error of the planets, the position errors of the pin-hole, the eccentric errors of the carrier, the sun gear and the planet gears, as well as the angular misalignments of the planet pin. The proposed loaded tooth contact analysis (LTCA) model for planetary gear sets, is based on the influence coefficient method, and involves the influences of the deformation of the teeth, the carrier, the sun gear and the planet pins. The topological conditions of the contact teeth calculated by the TCA model are also involved in the analysis, so as to simulate the Hertzian and Non-Hertzian tooth contact and to analyze the influences of the various manufacturing/assembly errors on the loaded tooth contact. In order to verify the reliability of the proposed LTCA model, the analyzed results are compared with the finite element method (FEM). The results include the contact stress on the tooth flank along the face-width and the load sharing among each planet gear with the non-floating and floating sun gear. The comparative results show the same trend of contact stress and the difference with less than 10%. This indicates the model is in a good agreement with FEM. A planetary gear set used in the practice is analyzed by the proposed TCA and LTCA model. The variation of the transmission errors and the backlashes of the planetary gear set is analyzed by applying the developed TCA approach, considering various cases with and without flank modification and errors. The variation of shared loads, contact stress and loaded transmission errors stress during gear meshing, as well as the contact pattern and stress distribution on each engaged tooth flank are analyzed by using the LTCA model. The non-Hertzian contact stresses of tip corner edge contact due to deformation and the face-end edge contact due to misalignment of the planet pin are also simulated. The influence of the errors on the load sharing among planets and the trajectory of the floating sun gear are also analyzed in the dissertation. The analysis results show that tip corner contact occurs more likely in the planet-annulus gear pairs than sun-planet gear pairs. The contact stress on the flanks of planet-annulus gear pairs distributes more uneven due to the stiffness of the carrier. The stress distributions of the engaged tooth pairs are even and symmetric after flank modification. On the other hand, the eccentric error of the carrier has a larger influence on the load sharing among planet gear and loaded transmission errors. The proposed LTCA model for planetary gear sets in the dissertation can simulate effectively and efficiently contact characteristics of engaged teeth with or without loading during gear meshing. The results can provide good evidence for designing flank modification of a planetary gear set. It can serve as the model for evaluating the influence of the manufacturing/assembly accuracy on loaded or unloaded transmission errors, backlash, as well as load sharing among planet gears.
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Wu, Fu-Chuan, and 吳福傳. "TOOTH CONTACT ANALYSIS OF STRAIGHT BEVEL GEAR PAIR WITH CROWNING TEETH." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/4aed2j.
Full textAbstract:
碩士國立臺灣科技大學
機械工程系
105
The mathematical models for tooth contact analysis (TCA) of a gear pair have been well derived in the literature. TCA includes evaluation of contact path, angle transmission error, and elliptical contact pattern. The existing method is systematic, efficient, and commonly applied in gear industry. However, it has a drawback in unstable solution when the edge contact happens. Normal vectors of tooth surfaces of the pinion and gear at the edge point do not collinear that leads to a divergence in solving nonlinear equations. In addition, an ellipse is adopted to approach the contact pattern according to curvatures of two tooth surfaces. The deviations of contact pattern get larger while their curvatures change greatly. The paper therefore develops a new mathematical model of TCA. Here, the optimization method of Golden ratio is adopted to directly determine the contact points. The proposed method avoids divergences in solving equations due to avoidance of involving the condition of same normal vectors between the mapped tooth surfaces. Moreover, a searching method for the boundary of contact pattern is applied to find the real contact pattern. The paper also establishes the mathematical models of straight bevel gears, cylindrical gears and spiral bevel gears with double crowning tooth surfaces. Their tooth surfaces are based on a spherical involute, standard involute and face-milled surfaces, respectively. Two methods, the existing and proposed methods, are adopted for evaluating the tooth contact analyses of gear pairs. The results confirm the correctness of the proposed mathematical models.
34
Huang, Chorng-Shiann, and 黃重憲. "On the Surface Design, Tooth Contact Analysis, and Optimum Design of Cycloidal Drives with Modified Tooth Profiles." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/03317185194236448182.
Full textAbstract:
碩士國立成功大學
機械工程學系碩博士班
94
Cycloidal drives are used in many machinery. They have some advantages, such as larger range of speed ratio, more compact, lighter weight, higher capacity, and higher efficiency, etc. The main purpose of this study is to investigate the characteristics of the drives with modified tooth profiles and to determine the optimum amounts of tooth modifications such that they have better characteristics. Based on the theory of conjugate surfaces, a general model for the profile design of the cycloidal wheel without or with various tooth modifications is developed. Then, the model for the tooth contact analysis is evolved. Consequently, subjected to the required lubricant thickness and the tolerance for the assembly and manufacture errors, an optimization technique is applied to determine the amounts of tooth modifications such that the instantaneous velocity ratio error and the transmission error can be minimized. Examples are included to verify the correctness of the models developed and to demonstrate the characteristics of the drives. The models developed should be an aid for designing the cycloidal drives with better performance, and they are also useful for the development of other gear mechanisms.
35
Chang, Ling-Chiao, and 張甯喬. "Loaded Tooth Contact Analysis of Cycloid Planetary Gear Drives With Tooth Number Difference of Two Considering Bearing Stiffness." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/vgy36c.
Full textAbstract:
碩士國立中央大學
機械工程學系
106
Because the loads acting on the contact tooth pairs and the cranks of the cycloid planetary gear drives with tooth number difference (abbr. TND) of one are very large, and the contact ratio is reduced with flank modification, the load capicity cannot be enhanced effectively. Therefore the design concept by using TND of two is proposed in the study to give a possibility to improve the loaded contact characteristics. The cycloid disk with TND of two can be regarded as combination of two sam base cycloid profile rotated against each other with an pitch angle. Therefore the analysis model of the cycloid planetary gear reducers with TND of two can be expaned from the model with TND of one. With reguarding odd and even numbered tooth pairs, the gear meshing analysis and the loaded tooth contact analysis (LTCA) model of the cycloid profile with TND of two can be established based on the developed mathematic model and the related analysis models of the cycloid profile with TND of one. The LTCA approach in the study is based on the influence coefficient method with consideration of bearing stiffness. In this parper, the influences of the design parameters, i.e., the pin raidus and the eccentricity, on the loaded contact characterisitcs, such as the flank profile, the contact ratio, the shared loads and the contact stresses. Based on the analysis results, appropriate design parameters are determined for the following analysis: (1) the effect of the bearing stiffness of the loaded tooth contact characteristics, and (2) comparative analysis with the conventional drives with TND of one on the loaded contact charateristics. The results from the influence analysis of parameters show that the cycloid drive with TND of two having smaller pins and a larger eccentricity owns a larger contact ratio and reduced shared loads. The eccentricity affects the variation of the load sharing stronger than the pin radius, not only because of the tooth profile, but also because of the transmission angle. A larger eccentricity can lower the shared load and the contact stress, but smaller pins reduce shared load and increase larger contact stress sightly. The influence of the bearing stiffness, as the results show, causes the contact of the tooth pairs occuring earlier than the condtion without considering the bearing stiffness, because of additional displacements with three degrees of freedom. The maximum load sharing is enlarged because the displacement is closer to the front part of tooth pair due to the transmission angle. Moreover, the variation of the shared load on flank with considersing bearing stiffness performs in cyclic jumping type, but the period duration is reduced as a half due to the change of odd and even numbered tooth pair change. Even so the condition of bearing stiffness is not impact on the bearing load. The comparative analysis results with TND of one show that the maximum sharing load in the case of TND of two can be reduced 35% relative to TND of one, and is distributed more soomthly. On the other hand, the maximum contact stress for TND of two can be enlarged 25% with respect to TND of one. But the contact stress for TND of two still remains at the end of contact, and the contact stress concentration occurs due to the edge effect of the tip corner. Furthmore, the radial bearing load in the case of TND of two can reduce 50% relative to the case of TND of one. But the lowered radial force is still much smaller than the circumferential force. The radial bearing force reduce just 5% relative to TND of one. From the analysis results of this paper, the cycliod planetary gear drives with TND of two can effectively increase the contact ratio and reduce the maximum load sharing and the maximum contact stress. However, it can not efficiently reduce the bearing load on the crankshaft.
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Chen, Yei-ling, and 陳羿伶. "Study on the Tooth Contact Analysis of Worm & Worm Wheel Set." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/30354579628906557018.
Full textAbstract:
碩士國立中正大學
機械工程所
98
Nowadays, worm wheels are mainly manufactured by the hobbing process in the practical gear production instead of the fly cutting since its superior cutting ability. However, a worm hob is a slotting worm-shaped cutter and has the same tooth profiles with the worm mating with the manufactured worm wheel. Hence, there exits higher assembly sensitivity between a pair of worm gears and the tooth corrections are often used to increase the assembly tolerance. These may cause higher production time and cost. This thesis mainly establised a procedure to simulate the manufaturing process and the tooth contact of a pair of worm gears. First, the worm wheel is generated by using the pre-defined worm hob which is set up on the hobbing machine. Then, the obtained worm wheel is used to generated the conjugated worm. Finally, the contact position between this pair of worm gears can be corrected by adujsting the worm parameters. Following this proposed procedure, the pair of worm gears can contact at the right position, improve the operating characteristics and allow the common assembly errors.
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Wang, Zhi-Gen, and 王志根. "Tooth Contact Analysis of A Helical Gear Set with Linear Tip Relief." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/74940238512106197155.
Full textAbstract:
碩士國立中央大學
光機電工程研究所
104
The purpose of this study is to analyze the meshing characteristics of a single-stage helical gear speed reducer. The mathematical model of a helical gear pair with linear tip relief, lead crowning and profile shift was developed based on the theory of gearing and differential geometry. The transmission errors and contact patterns were calculated by tooth contact analysis. The effects of assembly errors on the contact stress and contact patterns were also investigated and discussed. An auto-mesh-generation computer program was developed based on the mathematical model. Finite element analysis and a commercial machine design package were used in the loaded tooth contact analysis. Based on the standards of tip relief and suggestions of commercial machine design package, an improved design was attained. In the dynamic simulation aspect, the dynamic model of a modified helical gear pair was developed. Based on the results of loaded tooth contact analysis, including the static transmission errors and meshing stiffness, the dynamic transmission errors (DTE) and vibration signals were solved by using Runge-Kutta method. Furthermore, the energy level of meshing frequencies and average energy of DTEs were evaluated by Fast Fourier Transform (FFT) and Root Mean Square (RMS) method. The results from original design and improved design were compared and discussed. The simulation results show that the improved design can reduce the amount of vibration.
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Chu, Kuo-chen, and 朱國禎. "Tooth Contact Analysis for Helical Gear of the Differential Applied to Electrical Vehicle." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/26393822334723718794.
Full textAbstract:
碩士正修科技大學
機電工程研究所
97
A differential is a device that allows a difference in velocity between two wheels. One of the applications is in the final drive mechanisms of electrical vehicles. When a four-wheeled vehicle turns, the wheels on the outside of the turn must travel farther than the inside wheels due to their different turning radii. The helical gears drives used as the reduction mechanism in the differential of electrical vehicle. Helical gears that transform rotation between parallel axes in opposite directions are in external meshing. In order to verify the design parameters of helical gears, in this thesis the equations of tooth surfaces and stress analysis are implemented. Based on the conjugate surface theory, homogeneous coordinate transformation and differential geometry, the equations of tooth surfaces of the involute helical gears are derived and the meshing of mating helical gears is analysed. The principal curvatures and the principal directions of the tooth surface both are evaluated. The bending and contact stress of contacting surfaces are calculated through the AGMA standard and the finite element method. The derivation of CAD model in the FEM is based on application of the equations of tooth surfaces.
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Wu, Jun-Long, and 吳俊龍. "Mathematical Model and Tooth Contact Analysis of Helipoid Gears Cut by Shaper Cutters." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/97223337732667518952.
Full textAbstract:
碩士國立交通大學
機械工程系
90
Crossed-axis helical gears and hypoid gears are two common types of crossed-axis power transmission devices. Hypoid gears offer a high load capability and a high contact ratio, and are used for rear-axle transmission in automobiles. However, hypoid gears should be manufactured by special machines with various machine-tool settings due to complex tooth surface geometries. A hypoid gear set can obtain good contact patterns and contact locations only with appropriate machine-tool settings. Accordingly, the manufacture of hypoid gear sets requires experienced and well-trained engineers. Therefore, the production and maintenance costs of a hypoid gear are relatively high. The manufacture of helical gears, however, requires only easily operated and conventional machines, and the production cost is lower. However, the load capability and the contact ratio are also lower. A new type of gear, named the helipoid gear, is proposed herein by Nagata, eminent professor of Nippon Instittude of Technology, in an attempt to achieve a better balance between gear performance and manufacturing cost than that of hypoid and crossed-axis helical gears. Helipoid gears are designed to exhibit the advantages of both hypoid and helical gears ─ higher load capability and contact ratio than those of a helical gear, and a lower manufacturing cost than that of a hypoid gear. A helipoid gear, like a helical gear, can be produced by two conventional gear manufacturing methods, hobbing and shaping methods. Thus, the manufacturing cost of the helipoid gear is similar to that of the helical gear and far less than that of the hypoid gear. In this paper, based on the theory of gearing the mathematical model for helipoid gears cut by a shaper cutter is developed. According to this mathematical model and the tooth contact analysis technique, transmission errors of the helipoid gear set are investigated. Furthermore, the gear set contact pattern is simulated by applying the contact surface topology method and the stress analysis software developed by applying the finite element method is also adopted for the tooth contact stress analysis. Besides, the relationships among the tooth numbers of the shaper cutter, helical angles and contact patterns and transmission errors are also investigated.
40
Rung, Bi-Jang, and 榮必彰. "A Study on the Tooth Contact Analysis of Gear Sets with Skew Axes." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/21612052064372413569.
Full textAbstract:
碩士國立中山大學
機械與機電工程學系研究所
91
ABSTRACT Presently, many industrial applications of gear sets with skew axes, especially worm gear and hypoid gear, are most widely used. The main content of this thesis is to construct the contact analysis model of the line-contacted type tooth profile of gear sets with skew axes with assembly error. The influence of geometrical parameters of skew-axes gear to the transmission error is analyzed. The complex method for optimization is implemented to select the better skew-axes gear parameters with the best performance in transmission error with assembly error. To prove the presented analysis model, the optimized gear parameters are utilized to construct the solid model for analyzing the contact properties by using computer simulation program.
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Tseng, Rui-Tang, and 曾瑞堂. "Mathematical Model and Tooth Contact Analysis of Cylindrical gears with curvilinear shaped Teeth." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/05175957977530219036.
Full textAbstract:
碩士國立交通大學
機械工程系
87
ABSREACT The contact type of helical gears with parallel axes or spur gears is line contact, and the kinematic errors are sensitive to the gear axial misalignment. The gear set exists axial misalignments, the tooth edge contact will be occurred and this results in stress concentration, vibration and noise. The manufacture of cylindrical gears with curvilinear shaped teeth has been proposed by Liu in 1988. The advantages of curvilinear toothed gears are higher bearing and contacting strength, lower noise, better lubrication condition and no axial thrust forces. In this paper, the mathematical model of curvilinear toothed gears has developed based on the generation mechanism with an imaginary rack-cutter of circular-arc tooth profile. The tooth surface of curvilinear toothed gears can be displayed by using computer graphics and the developed computer simulation program. The right-side and left-side tooth surfaces of curvilinear toothed gears are different and the tooth thickness of central section is larger than those of other sections. According to the developed gear tooth mathematical model, location of the singular point or singular line on tooth surfaces can be obtained by applying the concept of differential geometry and numerical method, i.e. the undercutting of curvilinear toothed gears can be analyzed. In this study, the profile-shifted generation has been also investigated. The undercutting of curvilinear toothed gears can be avoided by using a positive profile-shifted modification during the gear set generation process. The tooth contact analysis technology has been utilized to the investigation on kinematic errors, contact ratios and contact patterns of the gear set under ideal and error assembly conditions. Since the contact type of the curvilinear toothed gear proposed in this paper is point contact, the gear set is not as sensitive to the gear axial misalignments, and the kinematic errors are quite small. The tooth edge contact can be avoided because the contact paths on gear tooth surfaces are located near the central section of face width. The contact ratio of point contact type curvilinear toothed gears is similar to that of spur gears. The contact pattern of curvilinear toothed gears can be obtained by applying the contact surface topology method. It is found that the contact point of the mating tooth surfaces may not be the center of contact ellipses, and the most important design parameter which influences the dimensions of gear contact ellipses is the nominal radius of face mill cutter.
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Wu, Cheng-Yang, and 吳承洋. "Mathematical modeling and tooth contact analysis of gear pairs based on line-arc racks." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/846sp4.
Full textAbstract:
碩士國立彰化師範大學
車輛科技研究所
107
In this study, the mathematical geometry concept is used to first by design the virtual straight-arc rack tool Mathematic equation, through the software of Mathermatica, we can build two virtual straight-arc rack tool geometry models, and the modification virtual straight-arc rack tool geometry models. Turning now set the relationship of coordinate system between the virtual rack tool and the gear pair, use the homogeneous coordinate transformation matrix equation, which can summarize the modification family of curved family equations before and after the virtual rack tool. In term of gear geometry and relative speed method, obtain the virtual rack tool and the gear pair meshing condition. Substituting the meshing condition to the modification family of curved family equations before and after the virtual straight-arc rack tool, find the mathematical model of gear pair before and after modification. Since has demonstrated the mathematical model of gear pair before and after modification, will now move on to assembly error cases, by tooth contact analysis, can present the result of the motion error of the gear pair under various installation error cases before and after the modification and the contact situation will marked the contact point to the gear, simulate the contact tooth print to observe the contact situation. Compare the two result by ANSYS Workbentch, turning now the distribution of the contact tooth marks and stress of the gear teeth before and after the gear shaping are under load.
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黃俊諭. "Mathematical Model and Tooth Contact Analysis of Helical Gears Generated by Modified Shaving Cutters." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/29726567553823824801.
Full textAbstract:
碩士國立交通大學
機械工程系所
94
In general, most of helical gears are generated by a CNC machine with Hob cutters. Many scholars have proceeded some studies on generation methods for helical gears that were generated by Hob cutters and then performed the tooth contact analysis of the generated gear pair. In this study, an imaginary rack-cutter is adopted to simulate a grinding wheel to generate a shaving cutter. The shaving cutter is then used for the helical gear generation to simulate the precision cutting of the gear. Shaving is a gear finishing process after gear hobbing process. The modified shaving cutter and the helical gear rotate with crossed axes in 3-dimentioanl space.In this study, the geometry of a modified shaving cutter was constructed at first, and the mathematical model of the helical gear shaved with plunge shaving by a modified shaving cutter was also developed. According to this mathematical model and tooth contact analysis, the gear surface deviation and kinematical error of the generated helical gear pair are investigated. The modified shaving cutter was modified with crowning modification along the lead direction and profile modification. The profile of the modified shaving cutter has crowned tooth modification and is composed of an involute curve and a circular-arc curve. The kinematical error curve of helical gear pair generated by modified shaving cutters approximates to a parabolic curve.
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Lee, Che-Yang, and 李哲仰. "Tooth contact analysis of modified spherical involute bevel gears considering the shaft deflection and errors." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/8frrgp.
Full textAbstract:
碩士國立中央大學
機械工程學系
105
The aim of the thesis is to develop a loaded tooth contact analysis model for powder metallurgy straight toothed bevel gears, in order to explore the tooth contact characteristics of the bevel gear pair under real working condition. In the research, the spherical involute and profile shifting are used for construction of the tooth profile. Because of the shaft deformation due to cantilever supporting of the bevel gears, the load distribution on the contact tooth is not uniform. On the other hand, the influences of errors of PM bevel gears on the tooth contact should be also reduced, Therefore, a double-crowning flank modification, i.e., lead crowning and profile crowning, is introduced in the research. The tooth contact analysis (TCA) is established based on the geometrical property of spherical involute. The influence of different assembly and eccentric errors on the contact positions and transmission errors of the bevel gear pairs were thus analyzed. The results show that the contact position along the facewidth of the tooth pair due to the offset error is the most sensitive, the next one is due to the mounting distance errors of the gear and the pinion. The shaft angle error only affects the location along tooth profile with the same facewidth. The curve of transmission error (TE) in the ideal case is parabolic; those in the case with errors are also parabolic. With larger mounting distance errors of the gear and the pinion, the TE curves become discontinuous. The TE curve due to the eccentric error is a regular curve with combination of the sinusoidal and the parabolic curve. Test bevel gears were also manufactured for measurement of transmission error to confirm the accuracy of the analysis model. The loaded tooth contact analysis (LTCA) is conducted with aid of a numerical approach based on the influence coefficient method. The LTCA model involves the influences of the deformations of teeth and shafts as well as the errors. The analysis approach can not only simulate the distribution of the tooth contact stress, the shape of the contact patterns, but also the load sharing and loaded transmission errors. The analysis results show that the position with maximum value of the contact stress is shifted near the heel due to the shaft deflection. The contact stresses at the begin and end of contact are zero due to profile crowning modification. With the increased torque, the average values of the loaded transmission error (LTE) increase. In the case of discontinuous variation of transmission errors, the jump will also increase with the increased torque.
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Chiu, Yu-Ting, and 邱鈺婷. "Profile-Shifted Transmission Design and Loaded Tooth Contact Analysis of Intersecting Helical Conical Gear Pairs." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/kvkxw2.
Full textAbstract:
碩士國立中央大學
機械工程學系
106
Helical conical involute gear as a special type of cylindrical involute gear is not only easily manufactured, but also is able to apply for various spatial gear pair with any cylindrical involute gear. Conical involute gears are often used in the application of the drives with a small shaft angle because of low sensitivity to assembly error, and the controllable backlash by adjusting the axial position of the conical gear. However, the intersecting helical conical gear has high contact stress due to point contact. Consequently, the surface durability cannot be increased for heavy power transmission. The concept of profile-shifted transmission is at first applied for geometrical design, in order to locate the contact point on the middle of tooth width. The contact stress on flanks can be therefore reduced due to increasing the radius of curvature on contact position. On the other hand, a mathematical model for the tooth surface of the conical gears is established considering the actual manufacturing condition. The tooth surfaces of the helical conical gear are generated by using the grinding worm, which is formed by a dressing conical disc with straight line. Comparing the calculated tooth surface from this model with the theoretical involute flank, the profile error is very small. Because the tooth contact condition of gear pairs influences the performance of the transmission and the contact stress, tooth contact analysis (TCA) model under unloaded condition and loaded tooth contact analysis (LTCA) model are established in the paper one after another. Based on the properties of involute gearing, the spatial relations with two axes of the gear tooth surfaces and the common contact normal line are established in order to simplify the calculation. The locus of contact points and the transmission error of the gear pair which are influenced by the error of the offset, shaft angle, axial mounting and eccentric errors are compared for design with standard and profile-shifted transmission respectively. From the results, the locus of contact points of the gear pair with profile-shifted transmission is close to the heel of the conical gear and indeed as expected locates on the middle of the tooth width. Among the various errors, the shaft angle error has the largest influence on the performances, and the axial mounting error has the less influence. The eccentric error causes the transmission error to perform as a sinus curve. The locus of contact points of the gear pair manufactured by continuous gear grinding has little difference from that of the gear pair with theoretical involute surface. LTCA model in the study is based on the influence coefficient method with considering the deformation of Hertzian contact, tooth bending deflection, shaft bending and shaft torsion. The corresponding contact patterns, the contact stress distribution and the angular displacement due to deformation of the engaged teeth can be simulated. The result of LTCA for the working flank on right side of gears with right hand helix angle (with respect to the conical gear) and that for the left flank of gears with left hand helix angle are the same, vice versa. Considering the conical gear with right hand helix angle, the tooth contact on right flank side is better than on left flank side because the concentrated stress on the edge occurs easily on the left flank. The contact stress of the gear drives with profile-shifted transmission is better than with the standard design because the contact patterns is close to the heel and the contact stress is reduced. And the same condition is also valid for the loaded transmission error where the peak-to-peak value with profile-shifted transmission is smaller. It can be verified from the analysis result that the proposed approach for profile-shifted transmission, tooth contact analysis and load tooth contact analysis in this thesis is indeed an efficient design tool for helical conical gear drives with intersecting axes to increase the tooth surface durability.
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Chen, Shin-Hung, and 陳信宏. "Mathematical Model and Tooth Contact Analysis of Helipoid Gears Cut by Helical Type Shaving Cutters." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/d5w6q5.
Full textAbstract:
碩士國立交通大學
機械工程系所
92
Crossed-axis helical gears and hypoid gears are two common types of crossed-axis power transmission devices. Hypoid gears offer a high load capability and a high contact ratio, and are widely used for rear-axle transmission in automobiles. However, hypoid gears should be manufactured by special machines with various machine-tool settings due to complex tooth surface geometries. Accordingly, the manufacture of hypoid gear sets requires experienced and well-trained engineers. Therefore, the production and maintenance costs of a hypoid gear are relatively high. The manufacture of helical gears, however, requires only easily operated and conventional machines, and the production cost is relatively lower. However, the load capability and the contact ratio are also lower. A new type of gear, named the helipoid gear, is conceptually proposed by Nagata, eminent professor of Nippon Instittude of Technology, in an attempt to achieve a better balance between gear performance and manufacturing cost than that of hypoid and crossed-axis helical gears. Helipoid gears are designed to exhibit the advantages of both hypoid and helical gears ─ higher load capability and contact ratio than those of a helical gear, and a lower manufacturing cost than that of a hypoid gear. In this research, a mathematical model for the helipoid gears cut by the helical type shaving cutters is developed based on the theory of gearing and the technique of computer aided design. According to this mathematical model and the tooth contact analysis technique, transmission errors of the helipoid gear set are investigated. Besides, the relationships among the tooth numbers and the helical angles of the helical type shaving cutter, the tooth surface deviations and tooth contact conditions are also investigated.
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Hsu, Ting-Hsiang, and 徐鼎翔. "Contact Force Analysis and Finite Element Simulation of the Cycloidal Speed Reducer with Modified Tooth Profile." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/42zv3e.
Full textAbstract:
碩士國立臺灣大學
機械工程學研究所
104
The cycloidal speed reducer has been widely used in precision machinery. Compared with the traditional planetary gear speed reducer, the cycloidal speed reducer has larger torque density, less backlash, smaller noise, higher efficiency and stable dynamic contact force. This paper presents the force analysis of the cycloidal speed reducer. First, the model of the force analysis for the reducer in three different types were established and the calculation of force reaction between the cycloidal disc and the contact pins was introduced. Then, a procedure of the analysis using finite element method was developed and simulation of the force reaction was performed. In the end, comparisons of the theoretical results and the finite element simulation were presented. It is anticipated that this procedure may help improve the design of the cycloidal speed reducer.
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Lin, Wen-Han, and 林文翰. "Tooth Contact Analysis of Helical Gear Pair with Double Involute and Double Circular Arc Ladder-shaped Teeth." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/40532519086341594025.
Full textAbstract:
碩士國立交通大學
機械工程系
89
The new trend of the gear design is to provide the gear teeth with surfaces being in contact at every instant at a point but not at a line to reduce the gear sensitivity to gear axial misalignments. By applying the mismatch of pinion-gear tooth surfaces, the tooth contact becomes a point contact instead of a line contact. The bearing contact is located at the middle region of the gear tooth surfaces and thus edge contact can be avoided. Unlike the generation of conventional involute helical gears, two imaginary rack cutters, instead of one, are applied for the generation of the proposed helical gear pair in this thesis. Since the profile of the proposed gear is in a ladder-shaped, the tooth thickness of the dedendum is larger than that of the conventional involute helical gears. This enables the gear set to obtain a two-zone of meshing instead of only one-zone of meshing existing in the conventional involute helical gears, and thus the gear has higher gear strength as well. The transmission error caused by gear axial misalignments is the main source of gear noise and vibration. Reduction of gear noise and vibration can be achieved by applying a predesigned function of transmission errors of a parabolic type. Such a predesigned parabolic function can absorb a discrete linear function of transmission errors caused by gear axial misalignments. Computerized simulations on gear meshing and contact of the designed gears demonstrate that the proposed design method for gear modifications produce a pair of gears with a parabolic transmission error function when axial misalignments are present. For the manufacture of the gear, the new relation between the rotational motions of the gear and cutting tool is nonlinear. This can be accomplished by the application of a computer numerical controlled (CNC) machine. For the pinion, a conventional manufacturing machine can be used for manufacturing since the relation between the rotational motion of the pinion and the cutting tool is linear. The contact of gear surfaces is spread over an elliptical area under the load due to the elasticity of the gear tooth surfaces. In this study, the dimensions and orientation of the instantaneous contact ellipse will be determined by applying the method of surface topology and method of gear curvature analysis. The latter one requires the determination of principal curvatures and directions of the contacting pinion-gear tooth surfaces, which can be obtain from the generation process of gears by rack cutters.
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Ye, Tai-hong, and 葉泰宏. "Surface Design, Curvature Analysis, Ranges of Design Parameters for Avoiding Undercutting and Tooth Contact Analysis of Convex and Concave Beveloid Gears." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/90307427010750193058.
Full textAbstract:
碩士國立成功大學
機械工程學系碩博士班
95
The main advantage of using beveloid gears to transmit the power between parallel axes, is that their backlash is adjustable by shifting the gear along its rotating shaft. Thus their applications have been found in various machines, such as speed reducers, transmissions, and other devices. Due to their geometry, they can be used to transmit the power between parallel, intersected, or crossed axes. Using a pair of convex beveloid gears on parallel axes, the edge contact induced by axial misalignments may be avoided. If the axes are non-parallel, concave beveloid gears can be used to reduce the contact stress. The main goals of this research are to propose a generating mechanism to manufacture convex and concave beveloid gears with higher efficiency, and to investigate the characteristics of these gears. A mechanism of using a hob tracing with a circular arc, to generate convex and concave beveloid gears, is proposed. Based on theory of gearing, the models for the surface design, curvature analysis, tooth contact analysis, and contact ellipse analysis of the gear are developed. Consequently, the methodology to determine the ranges of design parameters for avoiding undercutting of the gear is proposed. Examples are included to demonstrate characteristics of the gears, and to verify the correctness of the developed models in this study. According to the results, using a pair of convex or concave beveloid gears to transmit the power between two axes, their angular speed ratio is a constant as the specified one, even there are axis misalignments; and their loci of contact are straight line-segments. It is believed that the results are valuable in both of the academic field and industrial applications
50
Wu, Yi-Cheng, and 吳一正. "Mathematical Model and Tooth Contact Analysis of Gears with Curvilinear-Teeth Generated by a Disk-Type Circular-Arc Cutter." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/54524957553297362371.
Full textAbstract:
碩士國立交通大學
機械工程系所
94
The circular-arc curvilinear-tooth gear, which has curvilinear trace with circular-arc profile, is generated by a circular-arc disk-type cutter. Gears with curvilinear traces ensure that the gear pair is operated in a point contact condition, which is different from the line contact type of a helical gear pair or spur gear pair. The point contact condition can not only avoid the tooth edge contact, decreases the kinematical errors and vibro-acoustic due to axial misalignments, but also increases the bearing strength of the contact gears. Moreover, a gear pair with curvilinear-tooth traces operates without axial thrust force. The helical gears with circular-arc profile are used for transmitting with high load circumstance, because their loading capacity and lubricity are better than those of conventional helical gears. However, the circular-arc helical gear pair is quite sensitive to the central distance assembly errors. This study adopts the rack cutter with circular-arc profile to modify the profile of involute-type curvilinear-tooth gear pair. The gear surface is generated by an imaginary circular-arc rack cutter with a curvilinear trace. According to theory of gearing, a mathematical model of the gears with circular-arc profile and curvilinear-tooth trace is developed. The undercutting of the gears can be avoided by a positive profile-shifted modification during the gear set generation process. The tooth contact analysis technique is utilized to the investigation on kinematical errors, contact ratios and contact patterns of the gear set under axial misalignments.