Purpose -The purpose of this paper is to present the use of a CAD system for the analysis of meshing of spiral bevel gears. Design/methodology/approach -The TCA computer programs are based on a purely mathematical model and require to get the numerical solution of a set of nonlinear equations. There are situations that the programs fail to obtain the proper solution. In such cases, geometrical gear models defined in CAD environment prove to be a good choice. This paper describes a tool for analyzing tooth contact and transmission errors of spiral bevel gear sets with tooth flanks represented as CAD free-form surfaces. Findings -A new method has been proposed to keep those surfaces in continuous contact in the whole range of meshing of a mating tooth pair. During meshing, the points of contact as well as the corresponding angles of rotation of both the pinion and the ring gear are recorded. Thus, the tooth contact path as well as the motion transmission error graph is determined. Then, the contact pattern that is formed by a set of instantaneous contact ellipses is designated. Practical implications -The TCA results are essential for the assessment of the gear set quality in the early stages of the process of its development. Originality/value -All the results presented in graphical form are very illustrative and easy to interpret.
Purpose
This paper aims to present a comparison of numerical methods for determining the contact pattern of Gleason-type bevel gears. The mathematical model of tooth contact analysis and the finite element method were taken into consideration. Conclusions have been drawn regarding the usefulness of the considered methods and the compatibility of results. The object of the analysis was a bevel gear characterised by an 18:43 gear ratio and arc tooth line, and manufactured according to the spiral generated modified-roll method.
Design/methodology/approach
The mathematical model of tooth contact analysis consists of both the mathematical model of tooth generating and the mathematical model of operating gear set. The first model is used to generate tooth flanks of the pinion and the ring gear in the form of grids of points. Then, such tooth surfaces are used for the tooth contact analysis performed with the other model. It corresponds to the no-load gear meshing condition. The finite element method model was built on the basis of the same tooth flanks obtained with the former model. The commercial finite element method software Abaqus was used to perform two instances of the contact analysis: a very light load, corresponding to the former no-load condition, and the operating load condition. The results obtained using the two models, in the form of the contact pattern for no-load condition, were compared. The effect of heavy load on contact pattern position, shape and size was shown and discussed.
Findings
The mathematical models correctly reproduce the shape, position and size of the contact pattern; thus, they can be reliably used to assess the quality of the bevel gear at the early stage of its design.
Practical implications
Determination of the correct geometry of the flank surfaces of the gear and pinion teeth through the observation of contact pattern is a fundamental step in designing of a new aircraft bevel gear.
Originality/value
A possibility of the independent use of the mathematical analysis of the contact pattern has been shown, which, thanks to the compatibility of the results, does not have to be verified experimentally.
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