2) Computational Nonlinear Vibration Analysis of Gear Pairs Using a Three-Dimensional Model: This work investigates the nonlinear vibration of gear pairs, where the nonlinearity is due to portions of gear teeth contact lines losing contact (partial contact loss). The gears are modeled as rigid bodies that admit motion in six degrees of freedom. A network of distributed stiffnesses models the nonlinear gear contact, shown in Figure 6. The distributed stiffness scheme is obtained by discretizing the kinematic contact lines into segments, each with the possibility of losing contact. Whether these segments are actually in contact or not is determined by the gear deflections and tooth modifications. The modeling is verified with finite element analysis and experimental measurements from the literature. The combination of a translational and a tilting spring is proven to be identical to the distributed stiffness model. This equivalent representation of the mesh identifies a nonlinear tilting mesh stiffness that accompanies the well-known translational gear mesh stiffness typically modeled by a single spring. The effect of varying lead modification magnitude is shown in Figure 7. Modal analysis reveals a mesh tilting vibration mode where this spring dominates, in addition to the mesh deflection vibration mode. Computational dynamic analysis of a helical gear pair near the natural frequencies of the mesh tilting and deflection modes exhibit nonlinear vibrations. Both cases involve nonlinearity due to partial contact loss where only part of a nominal contact line loses contact at an instant. The consequence is a distorted dynamic contact pattern in comparison with the static contact pattern, shown in Figure 8. The vibrations are nonlinear (Figure 9).  Figure 6. Gear mesh model using distributed springs across the facewidth.  Figure 7. Effect of circular lead modification on translational mesh stiffness. This is a helical gear pair.
 Figure 8(b). Dynamic contact pattern  Figure 9. Dynamic response of a helical gear pair. |
Figure 8(a). Static contact pattern.