In this paper, a mathematical foundation for the generation of the hub paths for external involute and double helical gears was presented. The solution of the interpolation equations for the hub path generation are derived from the previous paper by Wittling et al. . The equations are validated through similarity comparison with FE results in case of a symptom-free meshing. Furthermore, the influence of the involute form and tooth number to shape errors in relation to form clearance cF and extremal value g is considered. The curvature of the involute and double helical hub paths under condition of an excessive form clearance is investigated. It is shown that a small form clearance cF allows a decoupling of the deflections of the hub and shaft. In contrast thereto, an extended form clearance with cFcFmin, the influence of the eccentric motion of the tip circle cannot be neglected.
For helical gear geometries with a constant pitch n1, a method for the modification of the involute root form is presented in this paper. For meshing with gear meshes known to be affected by non-dynamic imbalance, the inertia moment of the helix L' of the modified gear is calculated and the results are sent to teeth that should be split in order to erase the influence of the non-dynamic imbalance on the mesh geometry. Finally, the effects of an increase of the pitch by differential active twist and the effects of a modified hub path using a symplectic equation are considered.
For spline teeth and hubs of helical gears, the introduction of the DIN 3960 concept by the splined connection allows the calculation of the modified spline pitch with respect to the profile diameter. Simultaneously, the teeth and hubs are deformed in the plane normal to the lank of engagement in order to simplify the tooth deflection analysis. d2c66b5586