Evaluation of Methods for Calculating Effects of Tip Relief on Transmission Error, Noise and Stress in Loaded Spur Gears


The connection between transmission error and noise and vibration during operation has long been established. Calculation methods have developed to describe the influence such that it is possible to evaluate the relative effect of applying a specific modification at the design stage. The calculations can allow the designer to minimize the excitation from the gear pair engagement at a specific load. This paper explains the theory behind transmission error and the reasoning behind the method of applying the modifications through mapping the surface profiles and deducing the load sharing. It can be used to explain the results of later experimental validation on various types of tip relief in low contact ratio (LCR) gears, from very long to very short. The paper will also demonstrate that though the effects of modification in any specific case can be modeled with some certainty, the same modifying strategy can not be applied universally but must consider the required operating conditions. It illustrates that the effect of tip relief on transmission error and load sharing is not a black art but can be fully explained by applying existing theory.
A study of high contact ratio (HCR) gears will be presented to demonstrate why it is often necessary to apply different amounts and extents of tip relief in such designs, and how these modifications affect load sharing and highest point of tooth loading. Specific attention will be paid to the phenomenon of extended contact, where if no modification or insufficient tip relief is applied, contact does not stop at the end of active profile but continues beyond this point as the gear rotates resulting in contact on the tip. This effectively increases contact ratio and has implications for the tooth load and in particular how this may affect the loading position, highest point of single tooth contact (HPSTC), which is relevant to both ISO and AGMA standard rating. The paper will consider 3 methods commonly employed in the industry; a simple 2D mapping procedure carried out on graph paper, a 3D linear tooth stiffness computation method, and a 3D finite element analysis (FEA) calculation. The paper will demonstrate that though in some cases these methods can produce similar results, albeit with varying degrees of accuracy, further examples will be presented which demonstrate behavior which can only be detected using some of the more complex analysis methods. The commercial viability of implementing a better quality models against the time constraints in the development process will be discussed and conclusions drawn.
ISBN: 978-1-55589-985-1 Pages: 15 Author: D. Palmer and M. Fish
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