The Basics of Spiral Bevel Gears1 Gearing Principles Cylindrical and Straight Bevel GearsThe purpose of gears is to transmit motion and torque from one shaft to another, That transmission normally has to occur with a constant ratio, the lowest possible disturbances derived from a straight rack with straight tooth profile. A particular gear, rolling in the rack with constant center distance to the rack, requires involute flank surfaces. A shaping tool with the shape of rack can machine a gear with a perfect involute flank form. Figure 1 shows a cylindrical gear rolling in a rack. In the case of a single index face milling method, the tooth lead function is circular, as the blade in the cutter performs a circular motion, while the generating gear rests in a fixed angular position.The tooth profiling between the cutter and the generating gear does not require any rotation of the generating gear. The virtual generating gear is formed by the cutter head in a non-generating process. In Figure 3, the rotating blades in the cutter head can be understood to represent one tooth of the generating gear.As explained earlier, the generating gear is the bevel gear equivalent of the straight rack for generating a cylindrical gear tooth. The pinion slot produced in that way has two defects. First, the profile will not allow rolling between pinion and generating gear (compare to the rack and cylindrical gear tooth in Figure 1). Second, the pinion slot does not have the proper depth along the face width. As soon as the teeth have a spiral angle and the slot inclines to an angle on an axial plane, the teeth wind around the work gear body. In a fixed angular position, just the heel section, for example, is cut to the proper depth.The roll motion rotates the virtual generating gear and the work gear with the proper ratio while they are engaged (similar to the linear motion of the rack, Figure 1, in conjunction with the gear rotation).That procedure was for machining one slot. To machine the next slot, the cutter withdraws, and the work indexes one pitch. The spiral angle is the inclination angle of the curved tooth tangent to the radius vector from the intersection point of pinion and gear axis (see Figure 4). Because of the curved shape of the tooth length, different points along the lace width have different spiral angles. The nominal spiral angle of the spiral bevel gear or pinion is the angle measured from the center of the tooth.It is possible to use a bevel generating gear that is identical to tile ring gear. File pinion is in that case generated by rolling with the bevel generating gear, and the gear is manufactured simply by plunging the cutter to full depth without rolling (non-generated form cutting).A straight tooth bevel gear set has contact lines that are parallel to the pitch line(Figure 5, top). The first contact between a generating gear tooth and a pinion tooth starts, for example, in the root and moves during the rotation of the two mating members along the path of contact straight up to the top. The contact lines represent the momentary contact between the two flanks in mesh.With a spiral bevel gear set the contact lines are inclined relative to the pitch line orientation. Unlike the contact lines of the straight bevel gear set, the contact lines of the spiral bevel gear set have different lengths. The bottom of figure 5 shows the movement of the contact from heel top to toe root. The very short contact length increases from the beginning of the roll towards the center of the face width and reduces as the roll approaches the exit at the toe end.The contact lines between pinion and generating gear are identical to the contact lines between cutter blades and pinion flanks.2 Single Index Process- Face MillingIn a single index process, just one slot is cut at a time. For the non-generated member only, the cutter rotates and is fed into the work gear to the full depth. After reaching the full depth, the cutter withdraws and the work indexes one pitch to the next desired slot position (Figure 6, right side). The process repeats until all slots have been machined. The resulting flank lead function is a circular arc.Machining a generated member is done by plunging at the heel roll position first. After plunging, the roll motion begins, and generating of the flanks from heel to toe occurs. The flank lead function for a face milled, generated gear is a circular arc that is wound around a conical surface.The manufacturing .of a face milled bevel gear pair is possible in a five-cut process or in a completing process. The five-cut process consists of the following five independent operations: 1. Gear roughing (alternate roughing blades), 2. Gear finishing (alternate finishing blades), 3. Pinion roughing (alternate roughing blades), 4. Pinion finishing convex (inner blades only), and 5. Pinion finishing concave (outer blades only).A completing process uses two