标题: | 少齿数螺旋齿轮之齿形设计 Tooth Profile Design on the Helical Gear with Small Number of Teeth |
作者: | 陈建发 Chien-Fa Chen 蔡忠杓 Chung-Biau Tsay 机械工程学系 |
关键字: | 摆线;渐开线;螺旋齿轮;齿形设计;Cycloidal;Involute;Helical gear;Tooth profile design |
公开日期: | 2002 |
摘要: | 对于平行轴减速机构而言,要达到高减速比的要求,往往需要用数个齿轮做多段的排列组合而成,实务上常基于成本、齿轮数目和齿轮箱体积方面的考量,而无法使用多阶式减速之齿轮组设计,因此,必须考虑使用一阶式减速齿轮组以达到高减速比的目的。然而具高减速比的一阶式减速齿轮对,其中之一个齿轮的齿数必须非常少,也因为齿数少而使得齿轮之齿形会有过切现象产生。本研究系根据齿轮原理及基本微分几何的观念,探讨具少齿数之平行轴摆线螺旋齿轮与渐开线螺旋齿轮之齿形设计。 本研究使用具转子外形之摆线形齿轮做为少齿数摆线形螺旋齿轮之线形。此摆线形螺旋齿轮之主动齿轮其齿冠为圆弧形,齿根则是由一个同样具圆弧形齿冠之被动齿轮所创成而得。根据齿轮原理及齿轮创成机构推导少齿数摆线形螺旋齿轮之数学模式,对于齿轮之齿形的过切问题亦加以探讨。此外,根据齿形几何的分析,探讨齿冠与齿根间齿形之连续性。同时研究过切指标 对于齿形过切与连续性之影响。齿形特性分析的结果,能帮助齿轮设计者设计一个既不产生齿形过切且齿轮之齿形也连续的齿轮。本论文的研究结果不仅可用于少齿数摆线形螺旋齿轮,亦可做为鲁氏泵及由两个相同齿轮带动的螺旋压缩机之转子使用。 本研究亦推导修整型少齿数渐开线螺旋齿轮之数学模式,也依据所推导的齿轮齿形数学模式探讨其齿形之过切问题,再以齿形转位的方法减缓少齿数齿轮的齿根过切现象。其次根据基本几何观念,以圆弧线形来修整少齿数渐开线螺旋齿轮的齿根过切,因而可得到不具齿形过切的少齿数渐开线螺旋齿轮。本研究亦同时使用齿形转位切削与齿根修整的双重方法来改善齿根之过切,经与只使用齿形转位切削方法所获得之齿形比较后显示,本论文所提出之同时考量齿形转位切削与齿根圆弧修整的双重方法,将可以得到较好的结果。利用齿顶经修整后之小齿轮外形做为成型刨齿刀之外形,并考虑齿条刀创成小齿轮的转位切削,来创成与修整小齿轮相互啮合之修整大齿轮。分析之结果发现,此啮合齿轮对之中心距之改变量仅与成型刨齿刀创成大齿轮之转位系数有关。 最后,本论文发展了一套电脑模拟程式,并分别绘出所设计的少齿数摆线与渐开线螺旋齿轮之电脑模拟齿形。本研究之成果不仅可以做为少齿数摆线螺旋齿轮与渐开线螺旋齿轮之齿形设计之参考,亦可应用于具高减速比的一阶式减速摆线与渐开线螺旋齿轮的齿形设计,不但可以减少齿轮箱之体积、简化传动机构之构造并且可以使得齿轮组装更为容易,所需成本也较低。 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. |
URI: | http://140.113.39.130/cdrfb3/record/nctu/#NT910489067 http://hdl.handle.net/11536/70824 |
显示于类别: | Thesis |