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Spiral bevel gears tooth geometry based on tooth trace and contact ellipse theory

Die Radzahngeometrie von Spiralkegeln basierend auf Zahnkurve und Kontaktellipsentheorie

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Abstract

This paper presents a novel procedure for spiral bevel gear design without classical gear machine cutting parameters considerations; it is based on favorable conditions of contact and interference avoidance constraints. In the first step, the work is focused on the tooth trace mathematical model; it is built on the pitch cone surface with its normalized parameters. In the second step, tooth surface geometry is generated by a kinematic procedure using the calculated tooth trace. Design parameters are calculated to satisfy favorable conditions of meshing and contact using relationships between principal curvatures and directions of pinion and gear surfaces and Tooth Contact Analysis (TCA) algorithm. Calculated tooth surface is evaluated using two tools TCA and Finite Element Analysis (FEA); function of transmission errors obtained from TCA tool has the same parabolic form and magnitude as the convensional geometry; FEA gives a potential contact locus on the mean pich line of the drive teeth without edge contact or stress concentration zones.

Zusammenfassung

Dieses Papier stellt ein neuartiges Verfahren für das Design von Spiralkegelrädern vor, ohne die klassischen Schneidparameter von Zahnradmaschinen zu berücksichtigen. Es basiert auf günstigen Kontaktbedingungen und der Vermeidung von Interferenzen. Im ersten Schritt liegt der Fokus auf dem mathematischen Modell der Zahnkurve; es wird auf der Kegelkegeloberfläche mit ihren normalisierten Parametern aufgebaut. Im zweiten Schritt wird die Geometrie der Zahnfläche mithilfe eines kinematischen Verfahrens unter Verwendung der berechneten Zahnkurve erzeugt. Designparameter werden berechnet, um günstige Bedingungen für das Eingreifen und den Kontakt zu erfüllen, unter Verwendung von Beziehungen zwischen den Hauptkrümmungen und Richtungen der Ritzel- und Zahnradflächen sowie des Zahnkontaktanalysenalgorithmus (ZKA). Die berechnete Zahnfläche wird mithilfe von zwei Werkzeugen bewertet: ZKA und Finite-Elemente-Analyse (FEA). Die Funktion der Übertragungsfehler, die mit dem ZKA erhalten wurden, hat die gleiche parabolische Form und Größe wie die konventionelle Geometrie; FEA gibt einen potenziellen Kontaktort auf der mittleren Steigungslinie der Antriebszähne ohne Kantenkontakt oder Spannungskonzentrationszonen an.

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Authors and Affiliations

  1. Laboratoire Conception des Systèmes Mécaniques (LCSM), Ecole Militaire Polytechniques, 16111, Alger, Bordj el Bahri, Algeria

    Sadek Kobzili & Akram Riani

  2. Laboratoire de Recherche en Génie Mécanique et Matériaux (LRGMM), Académie Militaire de Cherchell Défunt Président Houari Boumédiene, 42067, Tipaza, Cherchell, Algeria

    Yacine Benabid

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  1. Sadek Kobzili
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  2. Yacine Benabid
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Correspondence to Yacine Benabid.

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Kobzili, S., Benabid, Y. & Riani, A. Spiral bevel gears tooth geometry based on tooth trace and contact ellipse theory. Forsch Ingenieurwes 88, 8 (2024). https://doi.org/10.1007/s10010-024-00729-3

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