# Double helix cutting principle of spiral bevel gear

Driven by the goal of high speed and high efficiency, foreign advanced countries have long eliminated the traditional “five knife method” which is still widely used in China, and turned to the more advanced tooth cutting technology with high efficiency and dry cutting characteristics – double helix method (for machining Gleason shrinkage teeth). “Double helix method” means that the large and small wheels use one cutter head to cut both sides of the tooth groove at the same time, also known as “two cutter method or whole process method”. The large wheel can be processed by forming method or generating method, and the small wheel can be processed by screw method. Compared with the “five tool method”, the double helix method has the following characteristics: high machining efficiency, low production cost, good consistency of geometric accuracy of spiral bevel gears in the same batch, high strength of spiral bevel gears, high-speed dry cutting, etc.

The double helix method was proposed and applied in practice by Gleason company of the United States. Gleason’s technology is completely blocked, and its specific calculation of adjustment card and gear cutting theory are not disclosed to the public. At present, there are few studies on the principle of double helical cutting for spiral bevel gears. China’s Taiwan scholar TSAY and others built a general mathematical model of spiral bevel gear cutting with double helix method. Ignacio et al. [4] studied the conversion relationship between a specific machine tool adjustment parameter and the nominal machine tool adjustment parameter based on the double helix method, and adjusted the contact area of spiral bevel gear pair by using the tool with parabolic profile; According to Gleason’s technical data, Wang Zhe and others took the large wheel generation method and the small wheel double helix method as the research object, and deduced the machine tool adjustment parameters of this method. At present, there are few detailed and complete research reports on the principle and machining technology of double helix gear cutting.

(1) Taking the forming method of large wheel as the research object, the mathematical model of full process method is established. The detailed calculation process of machine tool adjustment parameters is deduced from two different calculation methods of small wheel tooth surface curvature parameters. Based on the actual small wheel root vertebral angle, the geometric parameters of gear blank are corrected and calculated.

(2) A new method of tooth surface mismatch design is proposed, which greatly simplifies the calculation and achieves the same design effect.

(3) Taking a hypoid gear pair as an example, the machine tool adjustment parameters, tooth surface contact analysis and calculation, tooth cutting and rolling inspection tests are carried out. The simulation design results are basically consistent with the rolling inspection results, so as to verify the effectiveness of this method.

(4) The whole process method design software of spiral bevel gear is developed, which lays a theoretical and technical foundation for the wide popularization of the whole process method in China.

Based on the meshing principle of spiral bevel gear, taking the concave midpoint, convex midpoint and tooth top midpoint of large wheel as three reference points, the tooth cutting mathematical model of semi developed double helix method (forming method for large wheel and double helix method for small wheel) is established, and the adjustment parameters of machine tool using this method are deduced; A new tooth contact analysis (TCA) method is proposed. It provides a theoretical basis for the realization of double helix machining technology.

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