The mesh stiffness of gear pairs used in aerospace applications, such as geared turbofan, has a vital influence on vibration and noise. To compensate for the deficiencies of the conventional method that does not consider slice coupling and structure coupling simultaneously, a comprehensive mathematical model for computing the mesh stiffness of helical gears is established. In this novel model, the effect of structure coupling and slice coupling between neighboring sliced gears are considered. The effect of the axial component of meshing force is also taken into account simultaneously. The results obtained by the comprehensive model are consistent with the finite element method and it proves that the novel mathematical model is sound. The influences of the helical angle and addendum modification coefficient on mesh stiffness are studied. The results show that the mesh stiffness of helical gears would be decreased in multiteeth regions caused by structure coupling. With or without consideration of the axial component, the relative mean values of mesh stiffness become larger with an increasing helical angle. The fluctuation value of mesh stiffness decreases when a positive addendum modification coefficient is adopted. The addendum modification also changes the phase of mesh stiffness. This study is helpful for a vibration analysis of gear transmission systems.

This study presents a novel electromagnetic variable stiffness isolator that achieves bidirectional stiffness regulation, which means that the isolator experiences a reduced stiffness when the applied current is positive and an increased stiffness when the opposite current is applied. In addition, the stiffness variations are equal for two currents with the same magnitude but opposite polarities. The proposed isolator can not only ensure the vibration isolation performance in working frequency zone that is relatively far from the natural frequency, but also can realize high-damping-like effect for shock response attenuation, without introducing any additional damping components that may complicate the system. The bidirectional stiffness regulation was realized by combining mechanical springs with hybrid magnets (permanent magnets and coil windings). Variation in the overall stiffness of the proposed isolator occurred when the current was continuously adjusted. A prototype of the isolator was designed, fabricated and then tested with a round displacement step shock at the base. The theoretical analysis revealed that this device could be utilized as an active vibration isolator through certain control strategies. The experimental results proved the effectiveness of the proposed mechanism in shock isolation and revealed that it outperforms the conventional isolator in suppressing the residual vibration.