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Mathematical model and worm wheel tooth working surfaces of the ZN-type hourglass worm gear set. (English) Zbl 1178.70016

Summary: The hourglass worm gear set is composed of a ZN-type hourglass worm generated by straight-edged blade cutters and a ZN-type hourglass worm wheel generated by worm-type hourglass hob cutters. Mathematical model of the ZN-type hourglass worm gear set is derived based on its generation mechanism and the theory of gearing. According to the developed mathematical model of the gear set, computer graphs of the ZN-type hourglass worm and worm wheel are presented. The tooth working surface, boundary lines and contact lines of the ZN-type hourglass worm gear set under different lead angles, pressure angles and modules are investigated and compared with those of the ZA-type hourglass worm gear set.

MSC:

70B15 Kinematics of mechanisms and robots
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References:

[1] Maki, M.; Sakai, T.: A study on hourglass worm gearing with developable tooth surfaces, Journal of mechanical design 100, 451-459 (1978)
[2] Ishida, K.: Theoretical and experimental investigation of a new plane toothed wheel and its enveloping hourglass worm, Journal of mechanical design 100, 460-469 (1978)
[3] Maki, M.; Sakai, T.: A study on hourglass worm gearing with contact slide-roll ratio, Journal of mechanical design 101, 274-280 (1979)
[4] Winter, H.; Wilkesmann, H.: Calculation of cylindrical worm gear drives of different tooth profiles, Journal of mechanical design 103, 73-82 (1981)
[5] Simon, V.: Grinding wheel profile for hob relief grinding, Journal of mechanical design 104, 731-742 (1982)
[6] Simon, V.: Computer aided manufacture of high precision hob, International journal of machine tools and manufacture 28, No. 4, 443-452 (1988)
[7] V. Simon, Double enveloping worm gear drive with smooth gear tooth surface, in: Proceedings, International Conference on Gearing, Zhengzhou, 1988, pp. 191 – 194.
[8] V. Simon, A new type of ground double enveloping worm gear drive, in: Proceedings, 1989 ASME Fifth International Power Transmissions and Gearing Conference, Chicago, 1989, pp. 281 – 288.
[9] Simon, V., EHD lubrication of double enveloping worm gears, in: Proceedings, Japan International Tribology Conference, Nagoya, 1990, pp. 1527 – 1532.
[10] Simon, V.: Load distribution in double enveloping worm gears, ASME journal of mechanical design 115, 496-501 (1993)
[11] H. Gunbara, S. Shimachi, T. Kobayashi, H. Kawada, A study on hourglass-worm gearings designed to concentrate surfaces normals: design for worm gearings with large lead angle, in: Proceedings of 6th International Power Transmission and Gearing Conference, Scottsdale, 1992, pp. 153 – 159.
[12] Fang, H. S.; Tsay, C. B.: Mathematical model and bearing contacts of the ZN-type worm gear sets cut by oversize hob cutters, Mechanism and machine theory 35, No. 12, 1689-1708 (2000) · Zbl 1140.70395 · doi:10.1016/S0094-114X(00)00024-0
[13] Janninck, W. L.: Contact surface topology of worm gear teeth, Gear technology, 31-47 (1988)
[14] Litvin, F. L.: Gear geometry and applied theory, (1994) · Zbl 1079.70507
[15] Litvin, F. L.; Fuentes, A.: Gear geometry and applied theory, (2004) · Zbl 1079.70507
[16] Shi, W.; Qin, D.; Xu, W.: Meshing control of the double-enveloping worm gearing under the conditions of existing the errors and the load, Mechanism and machine theory 39, 61-74 (2004) · Zbl 1143.70367 · doi:10.1016/S0094-114X(03)00104-6
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