Analysis of critical time delay in active lateral suspension systems for high-speed trains
In the actuation process of active suspension systems for high-speed trains,the phenomenon of time delay is inevitable,which to some extent restricts the performance of these systems.This paper aims to investigate the impact of time delay in secondary lat-eral active suspension systems on the dynamic performance of vehicles.Firstly,a simplified 1/4 vehicle lateral model with two degrees of freedom(DOF)was established,and the theoretical calculation formula for critical time delays was derived.Next,a full-DOF dynam-ics model of high-speed trains was developed,and a control module was built in Simulink for co-simulation.A first-order low-pass filter was subsequently used to simulate the amplitude attenuation and phase lag characteristics of actual control forces.Furthermore,the influ-ence laws of various strategies on time delays were explored,including modal sky-hook and PID control methods.Simulation results show that as time delays increase,the modal sky-hook control strategy leads to rapid deterioration in carbody vibrations and a rapid rise in the lateral Sperling index beyond 2.0.In contrast,the PID semi-active control brings about minimal increases in the lateral Sperling in-dex.Time delays within 50 ms under both strategies don't cause severe deterioration in the vibrations of the bogie frames.When consid-ering the Sperling index as the criterion for critical time delays,most control strategies other than PID control strategy resulted in de-creased critical time delays with increasing train speeds.This paper presents a systematic investigation into the issue of time delays,offer-ing guidance for the design and optimization of active suspension systems for high-speed trains.