A Calculation Approach to Complete Profile of Noncircular Gear Teeth
In this paper, the authors propose a practical approach for calculating the complete tooth profile of a noncircular gear based on the fundamental laws of plane gearing and the offset theory of planar curve, together with all details contained in algorithm
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Abstract In this paper, the authors propose a practical approach for calculating the complete tooth profile of a noncircular gear based on the fundamental laws of plane gearing and the offset theory of planar curve, together with all details contained in algorithm and numerical solution process. The algorithm not only has a simpler construction and higher calculation efficiency than other published approaches but also no special limitation imposed upon the types of the gear to be dealt with. The approach is explained referring to a machining model using a rack cutter with straight tooth profile to machine the gears; however, it is also applicable to other machining models such as employing a pinion cutter if performing some minor modifications in the algorithm. The effectiveness of the approach is illustrated through a practical example of design and manufacturing for a pair of noncircular gears. Keywords Noncircular gear • Complete tooth profile • Plane gearing • Offset curve
1 Introduction As a variable transmission ratio mechanism, noncircular gears have early been researched [1]. However, the difficulties in manufacturing significantly restrict the applications. In most of practical utilizations up to now, elliptical gears are employed since the tooth profile machining is relatively easy.
H. Qiu (*) Department of Mechanical Engineering, Kyushu Sangyo University, Fukuoka 813-8503, Japan e-mail: [email protected] G. Deng Department of Mechanical Systems Engineering, University of Miyazaki, Miyazaki, Japan W. Wang (ed.), Mechatronics and Automatic Control Systems, Lecture Notes in Electrical Engineering 237, DOI 10.1007/978-3-319-01273-5_3, © Springer International Publishing Switzerland 2014
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H. Qiu and G. Deng
With the advances of NC machining technology, in recent years, the circumstance of noncircular gear manufacture is being improved [2]. Thus, in addition to elliptical gears, the noncircular gear transmissions with more general characteristics attract the attentions of researchers and engineers again. Many new applications of noncircular gears have been reported, for example, a planetary gear train built in high performance bicycle [3], a mechanical hinge with variable stiffness applicable to robot [4], a ratio variation system to transmit power and motion continuously [5], and so on. As an unfortunate fact, however, nowadays only a few makers deal with the noncircular gear manufacturing. Different from circular gears, the tooth profile of a noncircular gear is generated based on the tooth cutting method, the gear pitch curve type and the cutter tooth profile, and thus it is possible that every tooth has a profile distinct from the others. Most of the published analysis approaches provide a calculation method on the profile belong to the working part, in general, but does not deal with the profile of the root fillet, tip and bottom land of the gear tooth [2, 6]. Only a few published calculation models carry out the whole profile of gear teeth but almost limited to elliptical gears, and the
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