Modeling and dynamic analysis of spiral bevel gear coupled system of intermediate and tail gearboxes in a helicopter

Abstract

The coupled dynamic model of the intermediate and tail gearboxes’ spiral bevel gear-oblique tail shaft-laminated membrane coupling was established by employing the hybrid modeling method of finite element and lumped mass. Among them, the dynamic equation of the shaft was constructed by Timoshenko beam; spiral bevel gears were derived theoretically by the lumped-mass method, where the effects of time-varying meshing stiffness, transmission error, external imbalance excitation and the like were considered simultaneously; laminated membrane coupling was simplified to a lumped parameter model, in which the stiffness was obtained by the finite element simulation and experiment. On this basis, the laminated membrane coupling and effects of several important parameters, including the unbalance value, tail rotor excitation, oblique tail shaft’s length and transmission error amplitude, on the system’s dynamic characteristics were discussed. The results showed that the influences of laminated membrane coupling and transmission error amplitude on the coupled system’s vibration response were prominent, which should be taken into consideration in the dynamic model. Due to the bending-torsional coupled effect, the lateral vibration caused by gear eccentricity would enlarge the oblique tail shaft’s torsional vibration; similarly, the tail rotor’s torsional excitation also varies the lateral vibration of the oblique tail shaft. The coupled effect between the eccentricity of gear pairs mainly hit the torsional vibration. Also, as the oblique tail shaft’s length increased, the torsional vibration of the oblique tail shaft tended to diminish while the axis orbit became larger. The research provides theoretical support for the design of the helicopter tail transmission system.

The inter‐history iteration method for seismic response analysis of seismically isolated structures and its secondary development based on ABAQUS

“…The steps for modeling the SISs using MATLAB are listed below. [55][56][57] (a) The structure is discretized based on the local coordinate system, and the element stiffness matrix Κ e , element mass matrix M e , and external excitation matrix P e are determined. When building the plane frame model, the beams are assumed to be Euler-Bernoulli beams, in which the shear deformation is not considered.…”

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“…As shown in Figure 5 is the jth bearing-housing element, one end node of the bearinghousing element is at the midpoint of the bearing, and the other end node is at the housing node, that is, at the center hole of the bearing seat. The bearing stiffness matrix K j b can be expressed as equation (9). Most of the coupled stiffness of bearings is very small, and the calculation equation only retains the main stiffness k xx , k yy , k zz , k uxux , k uyuy .…”

“…Papers by Walha et al, 6 Raclot and Velex, 7 and Shen et al 8 studied the two-stage spur gear system, and found the coupled vibration effect. Zhu et al 9 established the coupled dynamics model of the middle and tail gearboxes of the helicopter. They found that the diaphragm coupling has a significant effect on the vibration response of the coupling system.…”

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“…5 As shown in Figure 1, the TDSS of an armed helicopter is composed of horizontal tail drive system, intermediate gearbox, oblique tail shaft system, tail gearbox, etc. 6,7 The horizontal tail drive shaft system (HTDSS) is the longest part of the TDSS and is the most likely to be shot by a bullet. When performing military missions, the tail drive shaft (TDS) extends from the fuselage to the tail rotor, which is particularly exposed during hovering.…”