Bending-torsional-axial-pendular nonlinear dynamic modeling and frequency response analysis of a marine double-helical gear drive system considering backlash

The double-helical gear system was widely used in ship transmission. In order to study the influence of backlash on the nonlinear frequency response characteristics of marine double-helical gear system, according to the structural characteristics of double-helical gear transmission, considering the time-varying meshing stiffness, backlash, damping, comprehensive transmission error, external load excitation, and other factors, a three-dimensional bending-torsional-axial-pendular coupling nonlinear dynamic modeling and dynamic differential equation of 24-DOF double-helical gear transmission system were established. The Runge–Kutta numerical method was used to analyze the influence of backlash, time-varying meshing stiffness, damping, error and external load excitation on the amplitude frequency characteristics. The results show that the backlash can cause the runout of the double-helical gear system, and the system has first harmonic and second harmonic response. With the increase of backlash, the amplitude of the system increases and the jumping phenomenon remains unchanged. The amplitude frequency response of the system is stimulated by time-varying meshing stiffness and comprehensive transmission error, and restrained by damping and external load excitation. The vibration displacement amplitude of the system increases with the increase of vibration displacement and has little effect on the state change of the system. The vibration test of double-helical gear is carried out. The frequency response components obtained by numerical simulation are basically consistent with the experimental results, which proves the correctness of the theoretical calculation. It provides a technical basis for the study of vibration and noise reduction performance of double-helical gear.

Where is all the nonlinearity: flexible nonlinear modeling of behaviorally relevant neural dynamics using recurrent neural networks

Understanding the dynamical transformation of neural activity to behavior requires modeling this transformation while both dissecting its potential nonlinearities and dissociating and preserving its nonlinear behaviorally relevant neural dynamics, which remain unaddressed. We present RNN PSID, a nonlinear dynamic modeling method that enables flexible dissection of nonlinearities, dissociation and preferential learning of neural dynamics relevant to specific behaviors, and causal decoding. We first validate RNN PSID in simulations and then use it to investigate nonlinearities in monkey spiking and LFP activity across four tasks and different brain regions. Nonlinear RNN PSID successfully dissociated and preserved nonlinear behaviorally relevant dynamics, thus outperforming linear and non-preferential nonlinear learning methods in behavior decoding while reaching similar neural prediction. Strikingly, dissecting the nonlinearities with RNN PSID revealed that consistently across all tasks, summarizing the nonlinearity only in the mapping from the latent dynamics to behavior was largely sufficient for predicting behavior and neural activity. RNN PSID provides a novel tool to reveal new characteristics of nonlinear neural dynamics underlying behavior.

Nonlinear dynamic modeling and fluid–mechanism interaction analysis of reciprocating pump–pipeline system

The dynamic characteristics of reciprocating pump–pipeline system are directly affected by the fluid–mechanism dynamic interaction related to the slider-crank mechanism, valves and pipes conveying fluid. In this article, the fluid–mechanism interaction and nonlinearities involved in the kinetic of slider-crank mechanism, the motions of pump valves and the dynamic transmission in pipeline are explored for the nonlinear dynamic modeling of reciprocating pump–pipeline interaction systems. The nonlinear fluid–mechanism coupling model and corresponding analysis procedure are presented for investigating the system dynamic characteristics at all operating conditions. An experiment platform consisting of a simplex plunger reciprocating pump and suction and discharge pipes with a flow control valve is established to validate the proposed model. By the comparisons of pressure pulsations under multi-working conditions, the results obtained from the proposed model show good agreement with the test data. The dynamic characteristic of pump, as well as the effects of interaction and nonlinearity on the flow pulsation, are studied with the proposed model. It is found that nonlinear factors such as joint clearance and nonlinear spring stiffness are of great importance to the lag characteristics of pump valves and the pressure pulsation of pump–pipe system. The amplitudes of pressure pulsation increase with the decrease of control valve opening nonlinearly, and the effect of flow control valve becomes significant when the opening is less than 40%.