The spiral bevel gear processed by face hobbing adopts the principle of indirect generation method to ensure that the large and small gear surfaces can mesh and drive according to the required transmission ratio. Therefore, in theory, the large and small gear surfaces have linear conjugate contact characteristics. However, the tooth surface with linear conjugate contact is prone to edge contact in the presence of machining and installation errors of spiral bevel gears. It is necessary to modify it properly to form local contact characteristics to adapt to these errors and the deformation of spiral bevel gear under load. The usual modification method is to tilt the cutter head axis towards the spiral bevel gear node at a certain angle on the premise of ensuring that the normal vector of the nodes of the large and small gear surfaces remains unchanged. At this time, the plane generating wheel becomes a conical generating wheel, and the generating wheel for processing the large and small wheels changes, so that the concave convex surfaces of the processed large and small wheels lose the linear conjugate contact characteristics and become a local contact with the tooth surface node as the midpoint of the contact area. Although this modification method is easy to realize, the position of the midpoint of the contact area on both sides of the concave convex can not be arbitrarily selected according to the load condition of the spiral bevel gear, and the contact characteristic parameters (contact area length coefficient, diagonal direction, transmission error) are not easy to control. Based on this problem, this paper proposes a cutting adjustment calculation method for spiral bevel gear face hobbing. This method can arbitrarily specify the position of contact reference point on both concave and convex surfaces, and accurately control the morphological parameters of contact area.
Firstly, according to the basic transmission parameters of spiral bevel gear pair, the pitch cone parameters of large and small wheels and the pitch cone parameters of production wheels are calculated on the basis of ensuring that the nodes meet the meshing conditions. The generating wheel pitch cone forms the gear cutting meshing pitch cone respectively in the large and small wheel pitch cone, so that the installation parameters of gear blank during large and small wheel processing can be determined. At the same time, according to the forming principle of forming wheel, the tooth surface equation of forming wheel can be calculated. According to the meshing principle of spiral bevel gear, the equation of large and small gear tooth surface can be solved by generating gear tooth surface equation and gear blank installation parameters. As the tooth surface without modification, at this time, the two should have the characteristics of wired contact.
In order to form local contact and control the contact characteristics of both concave and convex surfaces, firstly, the position of the contact reference point is specified on the shaft section of the gear tooth surface. Then the radial vector, normal vector and curvature parameters of the contact reference point on the gear tooth surface can be obtained according to the gear tooth surface equation and the specified contact reference point position. Under the condition of ensuring the installation parameters and transmission ratio of large and small wheels, according to the diameter vector and normal vector of the contact reference point on the gear tooth surface, the diameter vector and normal vector of the contact reference point on the gear tooth surface can be obtained from the meshing equation. At this time, the shape parameters of the contact area (length coefficient of the contact area, diagonal direction and transmission error) are given. According to the curvature of the contact reference point of the large gear tooth surface, the curvature parameters of the contact reference point of the small gear tooth surface can be obtained by the local contact synthesis method. The normal vector and curvature parameters of the contact reference point of the small wheel calculated above are compared with the parameters calculated by the tooth surface equation of the small wheel. If there will be deviation between the two, the tool inclination angle is introduced in the process of small wheel gear cutting, and the tool position, tool position angle, pressure angle of internal and external tools and blade curvature of small wheel machining are corrected, so as to correct the tooth surface shape of small wheel until the normal vector and curvature parameters meet the requirements. At this time, the machine tool adjustment parameters and tool parameters of the output large and small wheels are used for processing, which can ensure that the processed spiral bevel gear pair has predetermined contact characteristics. In the actual calculation process, because there are many constraint variables, but the adjustable independent variables are limited, and some adjustable independent variables have similar effects on the contact characteristic parameters, the normal vector and curvature parameters of the contact reference points on both concave and convex sides of the small wheel can not be fully guaranteed. The iteration of normal vector and curvature parameters can be carried out respectively. The inner layer iteratively adjusts the tool position, tool position angle and pressure angle of inner and outer tools to control the normal vector, and the outer layer iteratively controls the tool inclination and blade curvature to control the tooth surface curvature. The inner layer iteration needs to be solved strictly to ensure the accurate contact position. The outer layer iteration uses the optimization method to obtain the approximate solution and obtain the shape of the contact area which is similar to the expectation.