In light of ignoring the effect of backlash on mesh stiffness in existing gear dynamic theory, a precise profile equation was established based on the generating processing principle. An improved potential energy method was proposed to calculate the mesh stiffness. The calculation result showed that when compared with the case of ignoring backlash, the mesh stiffness with backlash had an obvious decrease in a mesh cycle and the rate of decline had a trend of decreasing first and then increasing, so a stiffness coefficient was introduced to observe the effect of backlash. The Fourier series expansion was employed to fit the mesh stiffness rather than time-varying mesh stiffness, and the stiffness coefficient was fitted with the same method. The time-varying mesh stiffness was presented in terms of the piecewise function. The single degree of freedom model was employed, and the fourth order Runge–Kutta method was utilized to investigate the effect of backlash on the nonlinear dynamic characteristics with reference to the time history chart, phase diagram, Poincare map, and Fast Fourier Transformation (FFT) spectrogram. The numerical results revealed that the gear system primarily performs a non-harmonic-single-periodic motion. The partially enlarged views indicate that the system also exhibits small-amplitude and low-frequency motion. For different cases of backlash, the low-frequency motion sometimes shows excellent periodicity and stability and sometimes shows chaos. It is of practical guiding significance to know the mechanisms of some unusual noises as well as the design and manufacture of gear backlash.

The study performs a dynamic analysis of a microsegment gear system with respect to the time-varying stiffness, gear backlash, time-varying pressure angle, and comprehensive error. The period expansion method is proposed to construct a single-degree-of-freedom nonlinear dynamic model of a spur microsegment gear pair. To improve the accuracy of simulation results, the time-varying mesh stiffness and the time-varying pressure angle are expressed in terms of piecewise Fourier functions, respectively. The effect of mesh frequency, backlash, mesh damping, and input power on bifurcation, and chaos properties of the system are analyzed. The numerical results indicate that the system performs a chaotic motion after several frequency jumps as the mesh frequency increases. When the backlash increases, the frequency region of double-side impact and chaos tends to be decreased. The effect of mesh damping and input power on bifurcation characteristics is also investigated. The increase in mesh damping and input power can stabilize the system and avoid double-side impact. The results potentially present a useful source of reference for technicians and engineers for the dynamic design and vibration control of the aforementioned system with a nonconstant pressure angle.

When a submersible is sitting on a seabed, it could lose buoyancy because of the bottom-sitting adsorption effect. In this article, a numerical calculation model and experimental scheme for eliminating the bottom-sitting adsorption effect of under-sea equipment were established. An analysis of the hydrostatic pressure variation on a submersible’s bottom was carried out, and a submerged water jet which was based on the method of soil liquefaction was proposed to solve the problem of reducing hydrostatic pressure. It was shown that a water jet could liquefy soil to restore hydrostatic pressure on the submersible’s bottom, and there was an optimal jet velocity to form the largest liquefied soil thickness. A rectangular pulsed jet was the best way to liquefy soil in terms of efficiency and the liquefaction degree, which can be seen from the calculation of the two-dimensional two-phase flow. Through the calculation of the three-dimensional two-phase flow, it was found that the soil liquefaction developed from the periphery to the center, and a variation in jet liquefaction with the top wall constraint was obtained. Finally, an experiment was carried out to prove that a submerged water jet could eliminate the bottom-sitting adsorption effect of a submersible. The results showed that the submerged jet was an efficient way to liquefy soil, and a submersible could quickly recover hydrostatic pressure on the bottom and refloat up independently.