Spline couplings are used in applications involving high torque; however, due to variations in teeth clearances, all teeth in spline couplings do not engage simultaneously, causing some of the teeth to carry a disproportionately large portion of the total load. Variations in tooth-to-tooth clearances mean the first pair of teeth to engage will carry more load and fail sooner. This has lead to an industry practice of designing splines around the criteria that only 25-50% of the teeth on a spline coupling will engage and carry the load, and the load is generally assumed to be uniformly distributed. This research on tooth engagement is part of an ongoing study sponsored by an industrial partner with the intent to more accurately describe and improve tooth engagement in spline couplings. Tooth engagement in involute spline couplings is difficult to predict due to the complex geometry and even more complex manufacturing processes. Although manufacturing is closely controlled, with precision tooling, engagement problems persist. Presented herein is a detailed study of an involute spline coupling and its associated errors. Mating internal and external involute splines have been analyzed in order to identify variation and error patterns associated with spline coupling assemblies. These error patterns aid in understanding the manufacturing processes and ways in which we can better understand and predict tooth engagement. Spline manufacturing processes were studied in an attempt to relate tooling and processing errors to the resultant error patterns observed in production couplings. Some correlation with tooth engagement measurements have been found, but significant differences remain unexplained. Tooth engagement measurements exhibited anomalous behavior, which raised questions about test apparatus and procedures. The main contributions of this work are: A process for analytically creating torque-deflection curves in any configuration using measurement data, confirmation of the analytical tooth engagement sequence model from measured variation data, a better understanding of the experimental results, how to design future experimental tests, and the importance of early quasi-simultaneous tooth engagement. Several valuable insights have resulted in a better understanding of the mechanics of tooth engagement and load-sharing among spline teeth. The progress made should encourage further study, which may lead to processes which are better understood and controlled, and to designs which are more robust to variation, with more predictable performance and improved load-carrying capacity.

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Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-05-15T12:36:32Z No. of bitstreams: 2 Dissertação - Cláudio Lourenço Araújo - 2018.pdf: 6612329 bytes, checksum: e33b28e2708d4315d41b176011d56ffe (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-05-15T15:09:39Z (GMT) No. of bitstreams: 2 Dissertação - Cláudio Lourenço Araújo - 2018.pdf: 6612329 bytes, checksum: e33b28e2708d4315d41b176011d56ffe (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-05-15T15:09:39Z (GMT). No. of bitstreams: 2 Dissertação - Cláudio Lourenço Araújo - 2018.pdf: 6612329 bytes, checksum: e33b28e2708d4315d41b176011d56ffe (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-05-07 / The objective of this work is to contribute to the teaching-learning process of planas curves, in high school as wellas in higher education. To achieve this goal, we present the concepts, de_nitions and studies of planas curves, addressing algebra and geometry through Geogebra Software. Using this tool, we will approach mechanically generated curves (roulettes) and discuss some concepts. The theme provides us with a re_ection on the use of Geogebra software as a facilitating tool in the teaching-learning process. The possibility of being able, on a single screen, to analyze the algebraic and geometric behavior of planas curves contributes to the construction of mathematical knowledge. To this end, we will conduct a brief discussion on the use of Geogebra Software in teaching. Then we will present the main concepts of _at curves such as parameterization, tangent vector, normal vector, Frenet system, arc length, reparametrization, curvature, evolute and involute. In the discussion of all these concepts, Geogebra is present, in order to assist in the discussion and to show the possibilities of its use. Finally, we discuss a proposed activity in the classroom. / O objetivo deste trabalho é contribuir para o processo de ensino-aprendizagem de curvas planas, tanto no ensino médio como no ensino superior. Para atingir tal objetivo, apresentamos os conceitos, definições e estudos das curvas planas abordando álgebra e geometria através do software Geogebra. Utilizando esta ferramenta, abordaremos as curvas geradas mecanicamente (roulettes) e discutiremos alguns conceitos. O tema nos proporciona uma reflexão do uso do software Geogebra como ferramenta facilitadora no processo de ensino-aprendizagem. A possibilidade de poder, em uma única tela, analisar o comportamento algébrico e geométrico das curvas planas contribui para a construção do conhecimento matemático. Com esta finalidade, iremos realizar uma breve discussão sobre o uso do Software Geogebra no ensino. Depois iremos apresentar os principais conceitos de Curvas Planas como a parametrização, vetor tangente, vetor normal, sistema de Frenet, comprimento de arco, reparametrização, curvatura, evoluta e involuta. Na discussão de todos estes conceitos, o Geogebra se faz presente, a fim de auxiliar na discussão e mostrar as possibilidades de seu uso. Por fim, discutiremos uma proposta de atividade em sala de aula.

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.

With energy demands at an all time high, mechanical power systems are under great scrutiny. Substantial efforts are being made throughout the world to reduce energy use in common mechanical systems such as the internal combustion engine and transmission system. Eliminating or reducing efficiency losses in the transmission is a potential source of improving the efficiency of the system. To do so, various alternative types of transmissions are being investigated. At Brigham Young University, development of a Positively Engaged Continuously Variable Transmission (PECVT) is progressing. In addition to the efficiency increases that would occur as a result of operating the engine at a more constant speed, a PECVT type transmission may reduce efficiency losses that occur in a standard transmission by eliminating the disengagement of involute gear sets to change gear ratios of the transmission. For a PECVT, this is done by maintaining engagement of the input and output members of the transmission, while changing the gear ratio. Both of these types of losses are major contributing factors to the overall efficiency of the transmission and engine system, thus a PECVT is of great interest. The investigation for developing a feasible PECVT began with the identification of a behavioral issue identified in all known PECVT embodiments. This behavioral issue, known as the Non-Integer-Tooth-Problem (NITP), is due to the geometry of an involute gear and prevents specific gear ratios from being achieved. The research effort presented in this thesis returns to the conceptual design of a PECVT to address involutometry along with the NITP. A design tool entitled the Line-of-Action Model is developed which assists in quantifying how a conceptual solution can address the NITP using involutometry principles. As a result of the Line-of-Action Model, the Hybrid Involute Profile was discovered. Due to the simplicity of The Hybrid Involute Profile, it has proven to be an elegant solution to the NITP. Validation of the Hybrid Involute Profile concept was conducted to ensure that this concept satisfies the objectives and requirements of a PECVT and solves the NITP. The validation was completed using two case studies and a theoretical analysis. As a result of the validation, the Hybrid Involute Profile is declared a conceptual principal solution to the NITP. Fulfillment of the PECVT objectives, requirements list and elimination of the NITP by the Hybrid Involute Profile is also demonstrated. With the Hybrid Involute Profile as the conceptual principle solution, the development of a commercially viable PECVT is believed to be attainable.

This master's thesis deals with the design of FEM model of gear pair with an intention to find out how stiffness changes during meshing. It firstly describes the necessary knowledge needed to analyse the problem, like the geometry of an involute tooth and evaluation of meshing stiffness. Followed by a description of work procedures from the creation of models through settings of mesh, contacts and analysis to evaluating of results.

This thesis deals with a design of new dot-wheels gearing. These wheels serve for closing of paper covers of tea bags. First of all the suggested spare options of the gearing shape are compared with the original. On the basis of the comparison results the gearing is solved as a substandard kind of involute gearing. The involute gearing is designed by the method of generalized parameters. For the gearing design the program GEARING – symetrical profile version 1.5. was used. Consequently this program was adapted for the case of the change of the instrument shape by the user. The kind of wheels material was designed. Further the way of wheels production for single-piece and batch production was also designed. At the end the economic evaluation of the wheels production with newly designed profile was done.

Durch die zunehmende technologische Entwicklung des Getriebe-, Gelenkwellen-, Werkzeugmaschinen-, Kraftfahrzeug-, sowie Landmaschinenbaus steigen die zu übertragenden Leistungen und Drehmomente enorm. Dies führt zu einem wachsenden Bedarf an formschlüssigen Profilwellenverbindungen und deren erhöhter Lebensdauer und Genauigkeit. Hierbei bilden die Zahnwellenverbindungen (ZWVen) mit Evolventenflanken nach DIN 5480 /N1/ den Regelfall für eine Vielzahl der Anwendung. Abhängig von Festigkeitsüberlegungen, Herstellungsverfahren und Platzbedarf treten in der Praxis nahezu ausschließlich die folgenden zwei Grundtypen auf. Es handelt sich dabei zum Ersten um die Zahnwelle (ZW) mit freiem Auslauf.Die zweite Geometrievariante ist die Zahnwelle mit gebundenem Auslauf, die eine nach DIN 471 /N2/ genormte Sicherungsringnut (SRN) enthalten kann. Zahnwellenverbindungen dienen zur Übertragung großer, wechselnder und stoßartiger Drehmomente ohne zusätzliches Verbindungselement durch die Profilierung der Welle und Nabe. Axiale Verschiebbarkeit unter Last, Profilverschiebungsmöglichkeit, einfache Montage und Demontage sowie die Herstellung mit hochleistungsfähigen umformenden und spanenden Massenfertigungsverfahren, die die Herstellungskosten verhältnismäßig niedrig halten, sind technisch bedeutsame Eigenschaften, die zum ansteigenden Einsatz von ZWVen führen (z.B. /N1/, /Vil84/, /Koh86/ und /Wes96/). Starke Kerbwirkung und erhebliche Überdimensionierung benachbarter Gestaltungszonen sind die wesentlichen Schwachpunkte der Profilverbindungen. Eine große Anzahl (ca. 80 %) von Ausfällen im Maschinenbau ist auf Schäden an Achsen und Wellen infolge konstruktiv bedingter Kerben zurückzuführen (z.B. /N3/ und /Hai89/). Speziell im Bereich der hochbeanspruchten Profilwellen-Verbindungen kommt es auf Grund der starken Querschnittsveränderungen und der häufig angewandten Ausläufe und Formelemente, z. B. Zahn- und Keilwellen zu Kerbwirkungen, die erhebliche örtliche Spannungskonzentrationen sowohl im Zahnfußbereich und Zahnlückenauslauf als auch im Bereich der Verbindung selbst verursachen. Diese Beanspruchungskonzentrationen sind fast in der Hälfte aller Zahnwellenbrüche die häufigste Ursache für Dauerbrüche (Ermüdungs- bzw. Schwingungsbrüche) und für Schäden (bleibende Verformung, Anriss, Gewaltbruch) infolge Maximalbelastung. Hier trifft die Lastüberhöhung am Welle-Nabe-Verbindungsrand mit dem Steifigkeitssprung des Verzahnungsendes auf der Welle zusammen /Die93/. Die erwähnten Schadensfälle belegen, dass der heutige Kenntnisstand über eine beanspruchungsgerechte Auslegung von Zahnwellen noch recht lückenhaft ist. Deshalb sind neue Erkenntnisse über Form- bzw. Kerbwirkungszahlen bei Einzel- und Mehrfachkerben von scharf und weniger scharf gekerbten Zahnwellen mit Auslauf für eine treffsichere Festigkeitsberechnung erforderlich und stellen damit die Hauptschwerpunkte dieser Arbeit dar. Das vorliegende Forschungsprojekt, welches sich erstmals mit der Ermittlung der Beanspruchungen in torsions-, und biegebelasteten Zahnwellen mit freiem und gebundenem Auslauf befasst, wurde im Rahmen der Forschungsvereinigung für Antriebstechnik e.V. (FVA) unter der Nummer T 467 und dem Forschungsthema „ Ermittlung der Kerbwirkung bei Profilwellen für die praktische Getriebeberechnung von Zahnwellen“ initiiert und untersucht.

In der Praxis weisen Wellen und Achsen häufig komplex gestaltete oder überlagerte Kerbformen (Mehrfachkerben) auf, die von normativen Methoden zur Berechnung der Ermüdungsfestigkeit nicht erfasst sind. Die vorliegende Arbeit widmet sich daher der Zusammenführung von Kerbspannungsergebnissen einer Finite-Elemente-Analyse mit dem genormten Ermüdungsfestigkeitsnachweis nach DIN 743. Dazu erfolgt die Ableitung einer neuen, spannungsmechanisch begründeten Berechnungsmethode zur Integration von örtlich mehrachsigen Spannungszuständen in den nennspannungsbasierten Tragfähigkeitsnachweis. Die grundlegende Vorgehensweise der Norm wird nicht verändert. Sensitivitätsanalysen an einem Anwendungsbeispiel liefern zentrale Aussagen zur Relevanz verschiedener festigkeitsbeeinflussender Effekte bei Mehrfachkerben. Die Ergebnisse münden in einer anwendungsbereiten und ganzheitlichen Berechnungsanleitung für die Ermüdungsfestigkeitsberechnung von Bauteilen mit Mehrfachkerben in Anlehnung an DIN 743. Der zweite Teil der Arbeit wendet die erarbeitete Methode auf eine in der Konstruktionspraxis immer wiederkehrende Mehrfachkerbe, die Zahnwellenverbindung mit freiem Zahnauslauf, an. Als Ergebnis einer umfangreichen Parameterstudie liegen dem Anwender Berechnungsfaktoren zur Erfassung der Kerbwirkung für Zahnwellenverbindungen nach DIN 5480 in Abhängigkeit von zahlreichen geometrischen Einflussparametern vor. Abschließend werden die entwickelten Berechnungsmethode im Allgemeinen und die ermittelten normspezifischen Kennwerte für Zahnwellenverbindungen im Speziellen an vorhandenen experimentellen Stichversuchen aus der Literatur gespiegelt.