Analysis of arbitrary tooth profiles of cylindrical gears using normal polar coordinates (Application to the generation of a gear tooth profile by a given tooth profile of rack cutter and its interference problem)

• Published in: Journal of Advanced Mechanical Design, Systems, and Manufacturing Vol. 18; no. 1; p. JAMDSM0004
• Main Authors: MURAYAMA, Yuya, KISHI, Satoshi, HENMI, Nobuhiko, YAMAZAKI, Hiroshi
• Format: Journal Article
• Language: English
• Published: Tokyo The Japan Society of Mechanical Engineers 2024; Japan Science and Technology Agency
• Subjects: Arbitrary tooth profile; Gear; Gear teeth; Inclination angle; Interference; Interference problem; Involute teeth; Normal polar coordinates; Path of contact; Polar coordinates; Straight lines
• ISSN: 1881-3054; 1881-3054
• DOI: 10.1299/jamdsm.2024jamdsm0004

Various coordinate systems have been used in tooth profile analysis for cylindrical gears. An effective approach to tooth profile expression using normal polar coordinates is proposed. In this expression, the intersection between the normal at any point on the tooth profile and the operating pitch circle is determined. Then the tooth profile is represented using the length of the normal from the point on the tooth profile to the intersection, inclination angle between the normal and the straight line connecting the center of gear, and coordinate value of the intersection. Using this expression method, the path of contact is represented in polar coordinates by the length of the normal and its inclination angle. The tooth profile of the gear generated is the shape obtained by transforming the path of contact using the coordinates of the points of intersection. By applying the normal polar coordinates to a gear with an arbitrary tooth profile, the analysis to obtain the tooth profile by generation can be handled relatively easily. This method also works effectively for the analysis of the interference problem on tooth profiles. The application of this method to the analysis of a specific non-involute tooth profile adopted in this paper showed that a range of profile shift without interference could be determined, and that the interference could be prevented by modifying the tooth profile of rack. Furthermore, the interference occurring in the middle of the non-involute tooth profile was the same type of interference as undercutting in involute gears.