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Title: Study on an Internal Gear with Asymmetric Involute Teeth
Authors: Yang, Shyue-Cheng
Contributors: 車輛科技研究所
Keywords: Asymmetric involute-teeth;Double envelope
Date: 2007-08
Issue Date: 2014-01-15T04:19:24Z
Publisher: Elsevier
Abstract: In this paper, a double envelope concept is used to determine the basic profile of an internal gear with asymmetric involute teeth including driving and driven gears. The teeth of the proposed gear are asymmetric involute teeth. Based on this concept, a mathematical model of the meshing principles of a driven gear meshed with a driving gear is presented. Here, two gear types are illustrated. One is a spur gear and the other is a helical gear.
The double envelope concept is used to determine the driven gear of an internal gear. Based on this concept, the required driving gear can be obtained by the envelope to a one-parameter family of a rack cutter surface. The obtained envelope becomes the generating surface. Then, the driven gear is the envelope for the family of the generating surfaces (driving gear). Through the proposed method, the profile of an internal gear with asymmetric involute teeth can be easily obtained.
Using the developed mathematical models and the tooth contact analysis, the kinematic errors are investigated according to the obtained geometric modeling of the designed gear meshing when assembly errors are present. The influence of misalignment on the kinematic errors has been investigated. A comparison of the helical tooth and spur tooth shows that the internal gear with a helical tooth is superior to the internal gear with a spur tooth. Moreover, some results of change of shifting coefficient of internal gear in kinematic errors are studied. The goal of the current study is to investigate von-Mises stress in the proposed internal gear. A structural load is assumed to act on an internal spur gear and an internal helical gear.
The rack cutter is shown for design and manufacturing of a driving gear. As an example, the internal gear with a gear ratio of 4:5 was presented. Using rapid prototyping and manufacturing technology, an internal gear with asymmetric involute tooth, a driving gear and a driven gear were manufactured.
The rapid prototyping primitives provide an actual full-size physical model that can be analyzed and used for further development. Results from these mathematical models should have applications in the design of internal gear mechanism.
Relation: Mechanism and Machine Theory, 42(8): 977-994
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