Flender/Flender Gear Units/Bevel-helical gear unit B4
surfaces are called conjugate when they have line contact. Gears are termed conjugate when their tooth anks have line contact

in every meshingposition. Contact then extends over the entire tooth ank. If the tooth prole on cylindrical gears is an

involute, change in center distance does not alter tooth contact as the involute is self-equidistant curve (see Fig. 3.. small

change in the parallel alignment of the gear axis will, however, cause the anks to touch onlyat one edge of

the tooth.3.3 Tooth Contact Analysis 7 Unlike cylindrical gears, bevel gears possess tooth proles that change contin- uously along the face width. The tooth prole is not an involute, and displacement in the direction of the tooth depth leads to different meshing conditions. The transmitted torque causes deections in the housing, the gear bodies and the teeth, thereby yielding different relative positions of the pinion and wheel for each load case. In order to ensure acceptable tooth contact under all operating conditions, bevel gears are never made with perfectly conjugate tooth anks. The required insensitivity to relative displacements of the tooth anks is achieved by superimposing crowning by which the tooth anks deviate from their exactly conjugate form. Section 3.4is devoted to the effects of relative displacements between the meshing pinion and wheel. The necessary fundamentals of tooth ank design and the mechanisms that inuence the tooth shape are presented in the following sections. In designing bevel gears, distinction is drawn between the macro- and micro geometries. The macro geometry includes all the typical gear variables, such as number of teeth, face width, pitch diameter, hypoid offset, tooth depth, prole shift, spiral and pressure angles and tool radius. Only the coefcients of orders zero and one are needed to calculate the basic manufacturing kinematics (see Sect. 3.2.3 ). The higher order coefcients affect mainly the micro geometry, causing only insignicant changes to