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    <title language="eng">Advanced calculation of the deflection of worm shafts with FEM</title>
    <abstract language="eng">Worm gears are gear units with a shaft angle of mostly 90°. They are used in a variety of industrial applications due to large gear ratios and high transmittable torques. The high sliding ratio in the tooth contact requires a hard/soft material combination that is insensitive to scuffing. Worm shafts usually are made of case-hardened steel and worm wheels of a copper-tin-bronze alloy. Since damage predominantly occurs at the wheel (pitting, wear, tooth fracture, etc.), a wide range of calculation methods for load capacity and service life were developed. Regarding the worm shaft, only the deflection is examined, because high displacements of the shaft shifts the contact pattern, which leads to transmission errors and may lead to increased wear. Common calculation methods, e.g. according to DIN 3996 and ISO/TS 14521 provide a good approximation of the deflection. However, simplifications are made in favour of the manageability of the calculation method. Geometric modifications on the worm such as reduced tooth thickness or different lead angles cannot be taken into account with common methods. In order to close this gap, a new approach was presented by Norgauer in 2021, however, significantly overestimating the stiffening effect of the gearing in some cases by neglecting the helical winding of the worm teeth. For efficiency-optimal design of minimally thin worm shafts, approaches that go beyond the deflection are also missing. Investigations by the authors on worm gears using the finite element method (FEM) show a deviation of the bending line of worm shafts from the common calculation methods. The FEM calculations simulate the tooth meshing under load by a driving torque on the shaft, whereas the standard calculations simplify the load distribution on the worm shaft as a radial force introduced at a point. In addition to the magnitude of the radial forces, the axial tooth force component was identified as an influence factor on the bending line since it causes a displacement of the maximum bending location. Especially for increasing diameter factors the displacement of the bearings under load must be taken into account since they may be in the same range as the deflection. Furthermore, the helical winding of the teeth around the shaft leads to an average stiffening effect of the gearing. The cross-section depends on the gear meshing position and causes a periodic fluctuation of the area moment of inertia and a wobbling motion of the shaft. The changing load distribution on several teeth causes a periodic change of the lever arms and an additional dependence of the deflection from the mesh position. An analytical calculation method for the deflection of worm shafts is proposed. It aims at the precise calculation of the spatial expression of the bending line, extends the commonly used simplified model and takes the newly identified factors into account. The bending lines in both radial directions are considered separately. The values of the new introduced factors are derived from the FEM results. Finally, the calculated bending lines are compared with the FEM results and verified.</abstract>
    <parentTitle language="eng">IOP Conference Series: Materials Science and Engineering</parentTitle>
    <identifier type="issn">1757-8981</identifier>
    <identifier type="doi">10.1088/1757-899X/1190/1/012006</identifier>
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    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Johannes Gründer</author>
    <author>Alexander Monz</author>
    <author>Philipp Norgauer</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Wormgears</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Load capacity</value>
    </subject>
    <collection role="institutes" number="">Fakultät Maschinenbau und Versorgungstechnik</collection>
    <collection role="institutes" number="">Institut für Chemie, Material- und Produktentwicklung</collection>
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    <issue>1</issue>
    <volume>89</volume>
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    <publishedDate>2025-08-18</publishedDate>
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    <title language="eng">Tooth root strength of worm gear shafts with concave and convex tooth profiles</title>
    <abstract language="eng">The load-bearing capacity of industrial worm gearboxes is primarily limited by failure of the worm wheel due to the soft bronze material. While worm gear boxes with higher strength wheel materials like cast iron or steel are most used in low-speed applications, the usage of these materials is generally increasing for a variety of applications. Therefore, the load limiting part of the gearbox is shifting towards the worm shaft, which is usually only designed against deflection. Fractures of worm teeth have been observed occasionally in the past, but only simplified approaches for the stress calculation—if any—are provided in worm gear standards. This paper therefore aims to further develop existing methods from the authors by investigating the influence of the tooth profile on the stress in the worm tooth root. A detailed analysis of the stress in the tooth root using the finite element method is provided. To determine the fracture behaviour due to static overload, two geometrically different worm gear shafts with concave and convex flank profiles taken from an industrial worm gearbox are investigated. A single tooth of the worm shaft is loaded by the means of a tensile test machine until a fracture occurs. The theoretical stresses are compared with the observed fractures.</abstract>
    <parentTitle language="eng">Forschung im Ingenieurwesen</parentTitle>
    <identifier type="issn">0015-7899</identifier>
    <identifier type="doi">10.1007/s10010-025-00868-1</identifier>
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While worm gear boxes with higher strength wheel materials like cast iron or steel are most used in low-speed applications, the usage of these materials is generally increasing for a\u00a0variety of applications. Therefore, the load limiting part of the gearbox is shifting towards the worm shaft, which is usually only designed against deflection. Fractures of worm teeth have been observed occasionally in the past, but only simplified approaches for the stress calculation\u2014if any\u2014are provided in worm gear standards. This paper therefore aims to further develop existing methods from the authors by investigating the influence of the tooth profile on the stress in the worm tooth root. A\u00a0detailed analysis of the stress in the tooth root using the finite element method is provided. To determine the fracture behaviour due to static overload, two geometrically different worm gear shafts with concave and convex flank profiles taken from an industrial worm gearbox are investigated. A\u00a0single tooth of the worm shaft is loaded by the means of a\u00a0tensile test machine until a\u00a0fracture occurs. 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    <author>Johannes Gründer</author>
    <author>Alexander Monz</author>
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    <title language="deu">Additive Verzahnung</title>
    <abstract language="deu">Das Vorhaben untersucht die grundsätzliche Eignung additiver Fertigungsverfahren zur Herstellung von Laufverzahnungen mit verschleißbedingtem Einlauf der Oberflächen – konkret: Schneckenverzahnun-&#13;
gen. Forschungsziel ist die Herstellung einer Praxisverzahnung in ausreichend guter Verzahnungsqualität, die Inbetriebnahme eines geeigneten Getriebeprüfstandes sowie die Durchführung von stichpunktartigen Laufversuchen. Zentrales Ergebnis ist eine vergleichende Gegenüberstellung der Leistungsfähigkeit einer additiv gefertigten Laufverzahnung (Stahlschnecke/Kunststoffrad) mit einer klassisch spanend hergestellten Verzahnung (Stahlschnecke/Bronzerad). Zunächst werden Schneckenräder mit der Verzahnungsgeometrie eines Referenz-Getriebes aus der Praxis mittels verschiedener, am Ohm-CMP zur Verfügung stehenden additiven Fertigungsverfahren aus unterschiedlichen gängigen Materialien hergestellt. Der Einfluss des in der additiven Fertigung üblichen schichtweisen Aufbaus der Schneckenräder auf die Reibung im Zahnkontakt wird für Trockenlauf untersucht. Auf dieser Basis steht eine Methode zur Vorausberechnung der eingebrachten Reibleistung auf den Zahnflanken zur Verfügung, um darauf aufbauend die Möglichkeit gezielter Mikro-Modifikationen auf den Zahnflanken zur Reduktion der im Betrieb entstehenden Temperatur zu geben. Das Reibverhalten der zur Verfügung stehenden Werkstoffe aus der additiven Fertigung bei Materialpaarung mit Einsatzstahl wird an einem Scheibe–Stift-Tribometer unter Trockenlauf sowie bei Schmierung mit zwei Schmierfetten aus der Praxis untersucht. Die Stifte werden für die Versuche additiv hergestellt, die Scheibe besteht aus 16MnCr5. In den Versuchen werden Kraft und Gleitgeschwindigkeit variiert, um zusätzlich eine Abhängigkeit vom&#13;
Belastungszustand zu ermitteln. Bei den Versuchsergebnissen zeigt sich für alle untersuchten Werkstoffe das günstigste Verhalten bezüglich des Reibkoeffizienten für das Material Nylon12 sowohl im Trockenlauf als auch im geschmierten Zustand. Im Rahmen des Projektes wird ein Schnecken-&#13;
getriebeprüfstand für kleine Achsabstände aufgebaut. Die Belastung an der Abtriebswelle des Schneckenrades erfolgt sinusförmig, angetrieben wird an der Schneckenwelle mit einem Elektromotor durch Vorgabe der Drehzahl. Die Verzahnungen laufen in einem Getriebegehäuse aus der Praxis. Die bereits vorhandene Schneckenwelle aus 16MnCr5 wird für die Versuche verwendet, die Schneckenräder werden additiv aus Nylon12 hergestellt und in den Versuchen ausgetauscht. Der Reibungszustand wird indirekt über die im Betrieb nahe des Zahneingriffs entstehende Wärme charakterisiert. Die Versuchsdauer für jede Material-, Schmierstoff- und Lastkombination beträgt fünf Stunden. Geringere Beharrungstemperaturen werden als günstigerer Reibungszustand mit geringerer Reibung, höhere Temperaturen als höhere Reibung im Zahnkontakt interpretiert. Die Temperaturen im Getriebe werden im laufenden Betrieb kontinuierlich gemessen. Schließlich wird das Betriebsverhalten mit Schneckenrad aus Bronze mit dem Schneckenrad aus Nylon12 bei verschiedenen Fetten und Betriebszuständen gegenübergestellt.&#13;
An einem Schneckenrad aus Nylon12 beim Betrieb im Trockenlauf ist während des Versuchs ein Schaden am Schneckenrad durch Abscheren der Zähne entstanden. Dieser Schaden wird auf die starke Temperaturentwicklung wegen der hohen Reibung im Trockenlauf zurückgeführt.</abstract>
    <parentTitle language="deu">Vorlaufforschung / Schriftenreihe der Georg-Simon-Ohm-Hochschule, Nürnberg (2023)</parentTitle>
    <subTitle language="deu">Additive Fertigung von Schneckenverzahnungen zur lastoptimalen Geometrieauslegung</subTitle>
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