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Tooth Root Modeling Induced Variations of the Calculated Transmission Error

When it comes to gear dynamics, vibrations and acoustics, the gear transmission error is a reliable value to evaluate the system behavior. Many research projects have intensively investigated the different reasons for the occurrence of the transmission error (TE) and how to optimize or completely prevent it. State of knowledge is, that the TE depends on the micro and macro geometry of gears as well as on the load applied. In general, one differs between the static (STE) and the dynamic transmission error (DTE), whereby usually only the STE is part of a typical gear design process. The reason for that is the high complexity of influences on the DTE. In contrast to the STE, which primarily considers influences of tooth bending and hertzian pressure, the DTE also considers the inertias of the system. To determine the latter, you will have to solve equations of motion in time domain, e.g. using a multi-body system. For the validation of your results, you need to install high frequency sensors to collect data at high rotational speeds. The calculation of the STE of a gearpair uses a simplified model of tooth bending depending on the load applied. Research projects in the first place often investigate the general kinematic and load depending TE and the influence of tip relief on the STE. Some also consider variations of the root relief to reduce the bending of the tooth. This mainly influences the kinematic transmission error. Numeric or measured time functions are thereby evaluated from peak to peak to interpret the occurring amplitudes and mean values. The modifications of tip and root mentioned above are applied on the involute part of the tooth. It is unclear to what extent the manufacture of the tooth root area, which lies outside the involute, influences the tooth bending and thus the TE. Influencing variables are the specific bottom clearance and the fillet root radius. Many models use simplified approaches or completely neglect the fillet root radius, because the geometry generation is very complex and requires a complete manufacturing simulation/rolling simulation. This article therefore compares the static transmission error for a) a geometry generated using a complete manufacturing simulation, b) a geometry simplifying the tooth root area and c) a geometry completely ignoring the fillet root radius. It also investigates the influence of variations of the specific bottom clearance and the fillet root radius for a typical spur gear. The results will be interpreted to describe a minimum required geometry of the tooth root area and to adapt a simplified geometry to a geometry, similar to the manufacturing simulation. The article will furthermore discuss, if one can use simplified models in the design process, if the manufacturing process is not defined yet.

Document Details

ReferenceNWC23-0251-fullpaper
AuthorsSchulz. C Kieß. B Graness. H
LanguageEnglish
TypePaper
Date 16th May 2023
OrganisationsUniversity of Applied Sciences Regensburg (OTH Regensburg) TH Wildau
RegionGlobal

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