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Circular arc tooth line cylindrical gear is a kind of cylindrical gear with convex and concave curve teeth which is processed by spiral bevel gear milling machine. The tooth line of this kind of gear is circular arc, and has the characteristics of symmetry about the central section of tooth width. The mathematical model of circular arc tooth profile circular arc tooth line cylindrical gear is established according to spiral bevel gear milling principle, and the 3 D solid model of double-arc tooth profile gear and quadruple-arc tooth profile gear is established according to the gear mathematical model. Finally, the contact stress analysis of the gear is carried out by using the finite element analysis software, and the static contact stress are obtained, the contact stress of quadruple-arc tooth profile gear is about 80% of the double-arc tooth profile gear. The research results can provide a theoretical basis for the design and application of circular arc tooth profile circular arc tooth line cylindrical gear.

The quadruple arc spiral bevel gear is a new type of gear with quadruple arc tooth profile applied to the spiral bevel gear. The three-dimensional model is built in Solid Works based on the tooth surface equation of spiral bevel gear with circular arc tooth profile. The static finite element analysis is carried out by using a pair of teeth based on Abaqus. Compared with the double arc spiral bevel gear,it is concluded that the load capacity of quadruple arc spiral bevel gear is 30% higher than that of double arc spiral bevel gear.

The quadruple-arc spiral bevel gear is a new type of spiral bevel gear which is obtained by apply the quadruple-arc tooth on the bevel gear. The meshing points of quadruple-arc spiral bevel gear are increased compare with double-arc spiral bevel gear,and the carry capacity is also increased. The mesh line figure is obtained by analyzing the cutting process of quadruple-arc spiral bevel gear,the multi-meshing points coefficient and multi-meshing teeth coefficient are calculated. The basis of calculation for the strength calculation and dimensions design of quadruple-arc spiral bevel gear is provided.

The contact stress in different meshing point is not the same of double circular arc gear due to its different teeth numbers,tooth width and tooth bending deformation. A meshing point contact force mathematical model of double circular arc gear is established,the gear tooth bend stiffness is calculated according to mechanics of materials and the theory of elasticity. The numerical example is calculated to obtain the contact force in different meshing point of double circular arc gear of different tooth number,modulus and contact ratio.The basis for the tooth profile modification and improving the gear load capacity of double circular arc gear is provided by the research result.