Gear machining usually has direct generating method and indirect generating method. The direct generation method is to make the cutting surface of the tool the same as a tooth surface, and then use it to process the matched gear under the transmission condition of the gear pair, such as turbine machining, the cutting surface of the turbine hob is made the same as the tooth surface of the worm. The indirect generation method is to make a pair of cutting surfaces that coincide with two tooth surfaces at the same time, and then develop into two common reel surfaces in the gear pair, such as machining cylindrical gears with hob. When the gear is machined by the above two methods, it is only necessary to determine the relative position and transmission ratio between the tool and the workpiece.
When machining spiral bevel gears and hypoid gears, in order to process the root surface while developing the tooth surface, the tip plane of the cutter head should be tangent to the root cone of the workpiece, that is, the axis of the cutter head should be perpendicular to the root cone. Assembling the machined big wheel and small wheel together and drawing their cutterhead (figure 1), we can see that the axes of the two cutterheads cannot be parallel at all. That is to say, we can neither process the cutterhead cutting surface of the small wheel as the tooth surface of the big wheel, but also use the direct generating method to process the small wheel, nor can we use the indirect generating method to process the cutting surface of the large wheel cutter head and the cutting surface of the small wheel cutter head. In this way, the gear pair machined according to figure 1 cannot engage correctly in theory. Therefore, spiral bevel gears and hypoid gears can not be machined by direct generating method like other gears, but must be cut by “local conjugation principle”.
The so-called local conjugation principle is to calculate the small gear tooth surface which is completely shared with the large gear tooth surface by using the gear meshing principle according to the large gear tooth surface machined by the generating method or forming method. Although this kind of small gear tooth surface exists in theory, it can not be machined on the gear milling machine. At this time, you can select a little M on the tooth surface of the small gear, and then gently scrape off the tooth surface around M, and the farther away from the M point, the more you shovel more. Modify the theoretical tooth surface into an actual tooth surface that is tangent to the ideal tooth surface at M point and can be machined by the milling machine (figure 2) meshing this actual tooth surface with the large gear tooth surface, the contact area is no longer covered with the whole tooth surface but forms a local contact area with M point as the center.
The local conjugate gear pair can just overcome a major disadvantage of complete conjugation: if the installation position is wrong, the contact area will only move near the midpoint without concentrating the load on the edge of the gear teeth. Practice has proved that the application effect of this kind of gear pair is much better than that of completely conjugated gear pair. Local conjugation principle is an advanced method in modern gear machining.