Modelling of Spur Gear Contact Using Adaptive Mesh
Lahtivirta, Juuso (2015)
2015
Konetekniikan koulutusohjelma
Teknisten tieteiden tiedekunta - Faculty of Engineering Sciences
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Hyväksymispäivämäärä
2015-08-12
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tty-201507291451
https://urn.fi/URN:NBN:fi:tty-201507291451
Tiivistelmä
The gear drive is a critical part of a power transmission system. Modelling and simulating of the gear pair takes important role as a part of the design process to estimate the stresses, deformations and damage risks in various operating conditions. Finite element method (FEM) is typically used for these calculations. However, localized gear pair contact moves along the line of action arising need for very dense mesh over the whole gear flanks. The challenge is to reduce the number of elements so that the accuracy is preserved.
In this study an effective parameterized model for the analysis of stresses in gear contact and gear root was developed. The main idea and feature of the contact model was to use a local adaptive finite element (FE) mesh, which moves with the point of contact along the line of action. This enabled a dense FE mesh around the contact point and a sparse FE mesh elsewhere, which resulted in a faster model with reasonable accuracy. The adaptive FE mesh, rotation of gear pair and the accurate surface profile was created in Matlab environment to obtain a good control of the flank profile and meshing parameters. These were integrated with commercial finite element method (FEM) to calculate the deformations and stress distributions. An accurate surface profile of the gear tooth flank was created by simulating the gear manufacturing i.e. the hobbing process. The parameterization of the model was important because needed mesh density is case dependent. Tooth dimensions and loading affect to the selection of the FE mesh parameters.
The developed FE mesh approach was validated successfully against analytical Hertzian theory using 2D cylinder cylinder model. The size of the dense part of the FE mesh, mesh density, and element shape (element distortion) were systematically studied with 2D and 3D cylinder cylinder models and the proper mesh parameters were concluded. The spur gear model was compared to the results of gear standard ISO 6336 and the commercial gear calculation software. Contact points including one teeth pair engagement along the line of action were calculated. The maximum contact pressure and tooth root stresses corresponded relatively well to each other with maximum differences of 1–7%. The deeper analysis of these differences was not in the primary scope of this study.
In this study an effective parameterized model for the analysis of stresses in gear contact and gear root was developed. The main idea and feature of the contact model was to use a local adaptive finite element (FE) mesh, which moves with the point of contact along the line of action. This enabled a dense FE mesh around the contact point and a sparse FE mesh elsewhere, which resulted in a faster model with reasonable accuracy. The adaptive FE mesh, rotation of gear pair and the accurate surface profile was created in Matlab environment to obtain a good control of the flank profile and meshing parameters. These were integrated with commercial finite element method (FEM) to calculate the deformations and stress distributions. An accurate surface profile of the gear tooth flank was created by simulating the gear manufacturing i.e. the hobbing process. The parameterization of the model was important because needed mesh density is case dependent. Tooth dimensions and loading affect to the selection of the FE mesh parameters.
The developed FE mesh approach was validated successfully against analytical Hertzian theory using 2D cylinder cylinder model. The size of the dense part of the FE mesh, mesh density, and element shape (element distortion) were systematically studied with 2D and 3D cylinder cylinder models and the proper mesh parameters were concluded. The spur gear model was compared to the results of gear standard ISO 6336 and the commercial gear calculation software. Contact points including one teeth pair engagement along the line of action were calculated. The maximum contact pressure and tooth root stresses corresponded relatively well to each other with maximum differences of 1–7%. The deeper analysis of these differences was not in the primary scope of this study.