Reducing instabilities of mesh stiffness variation in two-stage gear using phasing method
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JMST Advances https://doi.org/10.1007/s42791-020-00035-3
LETTERS
Reducing instabilities of mesh stiffness variation in two‑stage gear using phasing method S. H. Gawande1 · V. V. Palande1,2 Received: 2 November 2019 / Revised: 3 August 2020 / Accepted: 28 August 2020 © The Korean Society of Mechanical Engineers 2020
Abstract Mesh stiffness variation is a phenomenon that occurs in a mechanical system when there is a change in number of teeth within the system. This phenomenon leads to parametric instabilities and can cause gear systems to experience severe vibration. This paper investigates the effect of mesh stiffness parameters like mesh phasing and contact ratios, in reducing vibrations, when applied to two-stage gear train. Each gear pair is replaced by two gear pairs, each having half the width as that of primary gear pair. The present study has adopted a systematic approach to develop theoretical expressions for evaluation of instability regions that are created by the connections formed between stiffness variations present at the two meshes and four meshes of the primary gear pairs and replaced gear pairs, respectively. The paper has also studied primary instability, secondary instability and combined instability. Required mesh phasing to eliminate instability regions for four gear meshes was found numerically using MATLAB. It is observed that replaced four gear pairs with proper mesh phasing eliminate the instability regions of original two gear pairs of two stage gear train. Graphic abstract
Keywords Mesh stiffness · Instability · Two-stage gear · Method of phasing
1 Introduction * S. H. Gawande [email protected] Extended author information available on the last page of the article
Spur gears are used commonly in variety of industrial fields like automotive, marine and many other power transmission applications. Noise and vibration reduction is a key field of
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research in the applications of gears. Hence, in recent years, many studies addressed gear dynamics and techniques to reduce gear vibrations. The mesh stiffness variation of teeth during interlocking is a major source of internal excitation force and vibration. One of the techniques that have been widely studied for reducing the variation in mesh stiffnes is modification of the shape of tooth and contact ratio (CR) of the teeth. The causes of main variations in stiffness are changes in numbers of meshing pair, with the recommended number being between 1 and 2 for spur gears. It is not possible to avoid this variation completely because of the integer gear teeth numbers. Phase shift, which is basically defined as the offset between the points when the gear stages enter mesh, is an essential parameter in this study. Phase shift values belong to the closed set [0, 1]. Extereme values 0 and 1 mean a concurrent beginning of the two gear meshes. For a phase shift between 0 and 1, the gear meshes rotate with an offset. Cheon [1] studied a half width and half-pitch phasing method in single stage gears. There are two gears
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