The spirac method is usually used to process the transmission ratio i12 ≥ 3 or the taper angle of large wheels δ2. For Cycloid Bevel gear or hypoid gear pair with an angle ≥ 60 °, the gear tooth profile is close to a straight line. When processing, the large wheel adopts the continuous dividing non generating cut in method, and the small wheel adopts the dual method, which has a higher production efficiency than the Oricon knife tilt full generating method. This chapter studies the calculation methods of the geometric parameter design, tooth cutting adjustment and tooth surface contact analysis of Cycloid Bevel Gears and hypoid gears, and deduces the calculation formulas of tooth surface and its normal vector equation, characteristic parameters such as pressure angle and helix angle at the reference point, and curvature parameters.
The blank design method of Cycloid Bevel Gear and hypoid gear and the machining principle of spirac method are studied, and the mathematical model is established, which provides a theoretical basis for the practical application and further research of the method. The main contents include:
(1) Based on the meshing theory based on the reference point, according to the relative position and relative motion of the two gears and the position of the given reference point, the geometric parameter relationship of Cycloid Bevel Gear and hypoid gear is given, the wheel return parameters are calculated, and the calculation formula of crown wheel parameters is given with reference to the forming principle of “hypothetical production wheel”, It provides a theoretical basis for the machining design of gear pairs;
(2) According to the kinematic relationship between the cutter, machine tool and workpiece during gear cutting, the mathematical model of the cutter inclination and semi evolution gear cutting adjustment of Cycloid Bevel Gear and hypoid gear pair is established, and the gear tooth surface, small wheel generating surface and their normal vector equations are derived, as well as the calculation formulas of the characteristic parameters at the reference point – helix angle, pressure angle and curvature parameters;
(3) The matching two gears are installed according to the working position, the meshing process of the tooth surface is simulated, and the calculation formulas of the tooth surface contact trace and instantaneous contact rounding are derived. Taking a pair of cycloid hypoid gear pairs as an example, the calculation and TCA analysis are carried out. According to the results, the contact quality and kinematic characteristics of the two gear surfaces of the gear pair are analyzed by TCA.