| Summary: | 博士 === 國立交通大學 === 機械工程系 === 91 === In order to obtain a gear reduction box with high gear ratio, usually it needs more than two gears for multi-stage assembly. Based on the considerations of the cost, the total number of gears and the volume of a gearbox, the use of multi-stage gears to obtain a reduction gear set with high gear ratio is not allowable. Instead, an one-stage reduction gear set should be considered and one of the gears must be extremely small. However, tooth undercutting on the generated gear may occur when the gear has a small number of teeth. This thesis investigates the tooth-profile design on both the helical cycloidal and involute gear sets with small number of teeth for parallel axes, based on the gear theory and the concept of differential geometry.
In this research, a cycloidal gear with rotor profiles is used for the tooth profile of helical cycloidal gears with small number of teeth. The addendum profile of the driving gear of cycloidal helicoids is a circular arc, and the dedendum profile of the driving gear is generated by the addendum of the driven gear tooth-profile that is also a circular arc. A complete mathematical model of the cycloidal helicoid is developed, and tooth undercutting of the generated gear is investigated. Moreover, the tooth profile continuity between the addendum and dedendum of the gear is also investigated according to the geometric analysis. The influences of the undercutting index on tooth undercutting and profile continuity are studied. The characteristic analysis results are most helpful to the designers for avoiding the tooth undercutting and keeping the continuity of tooth profile. The results of this research can be applied not only to cycloidal helicoids with a small number of teeth but also to screw compressors and Root’s Blowers that rotors are driven by two equal gears mounted on the shafts of the rotors.
The mathematical model of the modified helical involute gear with small number of teeth is developed based on the tooth-profile shifting method and basic geometry modification. Tooth-profile undercutting of this type of gears with small number of teeth is examined by using the developed mathematical model and the tooth-profile shifting method. Furthermore, an alternative method for lessening the tooth-profile undercutting is also presented by considering a modification of the basic fillet geometry using a modified rack cutter. A third method, combining the aforementioned two methods for the design of helical gears with small number of teeth, is also proposed to yield a gear set without tooth undercutting. The mating gear with tooth-profile shifting is generated using the pinion as a shaper. The tip fillet and root fillet are modified and a clearance between the pinion and the mating gear is also included in the design. Analysis result indicates that the change of gear set center distance depends only on the tooth-profile shifting of the mating gear. Results of this research can be used in designing spur and helical gear sets with small number of teeth.
Finally, computer simulation programs are developed and computer graphs are also displayed for both the helical involute and cycloidal gear sets with small number of teeth. The results of this research can be used not only to the tooth design of cycloidal and involute gears with small number of teeth, but also to the design of a gearbox with one-stage high gear ratio gear pairs. Consequently, the total volume of the gearbox can be reduced, the structure of the gear transmission mechanism can also be simplified, the gear assembly made easier and the cost is lower.
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