Ride comfort evaluation for road vehicle based on rigid-flexible coupling multibody dynamics

In the present research two different whole vehicle multibody models are established respectively, including rigid and rigid-flexible coupling multibody vehicle models. The former is all composed by rigid bodies while in the later model, the flexible rear suspension is built based on the finite element method （FEM） and mode superposition method, in which the deformations of the components are considered. The ride simulations with different speeds are carried out on a 3D digitalized road, and the weighted root mean square （RMS） of accelerations on the seat surface,backrest and at the feet are calculated. The comparison between the responses of the rigid and rigid-flexible coupling multibody models shows that the flexibility of the vehicle parts significantly affects the accelerations at each position, and it is necessary to take the flexibility effects into account for the assessment of ride comfort. C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi： 10.1063/2.1301304]

Rigid-Flexible Coupling Dynamic Analysis of Sub-Launched Vehicle During the Vertical Tube-Exit Stage

During the launching stage,hydrodynamic pressure and adapters' reaction loads can influence the vehicle's rigid motion as well as cause its structural vibration,which is a typical rigid-flexible coupling dynamic problem. This paper presents a 2-D rigid-flexible coupling model to calculate the vehicle's dynamic responses in that period.The vehicle was equivalent to a flexure beam with axial deformation. Hybrid coordinate and modal superposition methods were used to describe its large rigid displacement and small deformation. By the second Lagrange equation,the vehicle centroid's displacements,rotational angle and modal coordinates were chosen as generalized coordinates and then the vehicle 's rigid-flexible coupling dynamic equations were obtained. By numerical simulation,the results of vehicle's motion parameters and transverse internal loads were acquired.The calculation results showed that differences of the vehicle's motion parameters between the rigid-flexible coupling model and the rigid body assumption are noticeable and the peak magnitude of the vehicle's transverse internal loads in the rigid-flexible coupling model is higher remarkably than that in the rigid body assumption.

A rigid-flexible coupling finite element model of coupler for analyzing train instability behavior during collision

Rail vehicles generate huge longitudinal impact loads in collisions.If unreasonable matching exists between the compressive strength of the intermediate coupler and the structural strength of the car body,the risk of car body structure damage and train derailment will increase.Herein,a four-stage rigid-flexible coupling finite element model of the coupler is established considering the coupler buckling load.The influence of the coupler buckling load on the train longitudinal-vertical-hori-zontal buckling behavior was studied,and the mechanism of the train horizontal buckling instability in train collisions was revealed.Analysis results show that an intermediate coupler should be designed to ensure that the actual buckling load is less than the compressive load when the car body structure begins to deform plastically.The actual buckling load of the coupler and the asymmetry of the structural strength of the car body in the lateral direction are two important influencing factors for the lateral buckling of a train collision.If the strength of the two sides of the car body structure in the lateral direction is asymmetrical,the deformation on the weaker side will be larger,and the end of the car body will begin to deflect under the action of the coupler force,which in turn causes the train to undergo sawtooth buckling.

Dynamic thermo-mechanical responses of road-soft ground system under vehicle load and daily temperature variation

A complete road-soft ground model is established in this paper to study the dynamic responses caused by vehicle loads and/or daily temperature variation.A dynamic thermo-elastic model is applied to capturing the behavior of the rigid pavement,the base course,and the subgrade,while the soft ground is characterized using a dynamic thermo-poroelastic model.Solutions to the road-soft ground system are derived in the Laplace-Hankel transform domain.The time domain solutions are obtained using an integration approach.The temperature,thermal stress,pore water pressure,and displacement responses caused by the vehicle load and the daily temperature variation are presented.Results show that obvious temperature change mainly exists within 0.3 m of the road when subjected to the daily temperature variation,whereas the stress responses can still be found in deeper places because of the thermal swelling/shrinkage deformation within the upper road structures.Moreover,it is important to consider the coupling effects of the vehicle load and the daily temperature variation when calculating the dynamic responses inside the road-soft ground system.

Multi-Body Dynamics Modeling of Heavy Goods Vehicle-Rail Interaction

Based on the principle of vehicle-track coupling dynamics, SIMPACK multi-body dynamics software is used to establish a C80 wagon line-coupled multi-body dynamics model with 73 degrees of freedom. And the reasonableness of the line-coupled dynamics model is verified by using the maximum residual acceleration, the nonlinear critical speed of the wagon. The experimental results show that the established vehicle line coupling dynamics model meets the requirements of vehicle line coupling dynamics modeling.

Flight Dynamic Analysis of Hypersonic Vehicle Considering Liquid-Solid Coupling

With the liquid propellant making up 60%—70% of the takeoff weight of the hypersonic vehicle,the dynamic load caused by great propellant sloshing interacts with the flexible structure of the aircraft.Therefore,the dynamic model displays characteristics of strong coupling with structure/control and nonlinearity.Based on the sloshing mass dynamic simplified as a spring-mass-damping model,a rigid-flexible-sloshing model is constructed.Moreover,the effect on the dynamic performance of the coupled model is analyzed with changing frequency and damping.The results show that propellant sloshing dynamics significantly affects the rigid body motion modes,especially flexible mode and short mode.The right half plane pole(RHP)moves far from the imaginary axis with the consumption of the propellant.The flexible mode attenuates with the increase of the sloshing damping,and the coupling becomes stronger when sloshing frequency is close to the short mode frequency or the flexible frequency of the beam.

Dynamic Simulation for Rigid-Flexible Coupling Model of Gear Transmission System Based on ADAMS

The influence of the flexible body for the motion of gear transmission system is analyzed and the foundation for a more accurate assessment of gear transmission system is established when it has battle damage faults. By using Pro / E software,the virtual prototype model of gear transmission system in the speed reducer is established,and the rigid model and rigid-flexible coupling model are simulated respectively in ADAMS to obtain the data of gear meshing force. It can be concluded that rigid-flexible coupling model can reflect the real motion better than rigid model by comparing the simulation data of two models.

COUPLING VIBRATION OF VEHICLE-BRIDGE SYSTEM

By applying the sinusoidal wave mode to simulate the rugged surface of bridge deck,accounting for vehicle-bridge interaction and using Euler-Bernoulli beam theory, a coupling vibration model of vehicle-bridge system was developed. The model was solved by mode analyzing method and Runge-Kutta method, and the dynamic response and the resonance curve of the bridge were obtained. It is found that there are two resonance regions, one represents the main resonance while the other the minor resonance, in the resonance curve. The influence due to the rugged surface, the vibration mode of bridge, and the interaction between vehicle and bridge on vibration of the system were discussed. Numerical results show that the influence due to these parameters is so significant that the effect of roughness of the bridge deck and the mode shape of the bridge can't be ignored and the vehicle velocity should be kept away from the critical speed of the vehicle.

Nonlinear dynamic analysis on rigid-flexible coupling system of an elastic beam

Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.

An analysis on a rigid-flexible coupling system of an oscillating massand a rotating disk

A mass-rod-disk system consisting of an oscillating mass attached to a rigid rotating disk by an elastic rod is designed to study rigid-flexible coupling mechanism.Suppose the rod is lightweight and has enough stiffness,the theorems of linear momentum and angular momentum are applied to the mass-rod-disk system based on the kinematic description of the system.With respect to two deflections of the mass and one angular velocity of the system,a group of nonlinear differential equations are established where the tangential inertial force,centrifugal force,Coriolis force as well as the moments of additional inertial forces take important effects on the dynamic response.For the sake of description,these three types of inertial forces mentioned before are referred to as additional inertial forces in this paper.The horizontal deflections of the mass and the angular velocity of the disk rotating about a fixed-axis are numerically solved for the prescribed external torque.The oscillating trajectory of the mass is deeply influenced by the additional inertial forces,meanwhile the dynamic fluctuations of the angular velocity and rotary inertia of the system are strongly affected by the mass oscillation.

A vertical coupling dynamic analysis method and engineering application of vehicle–track–substructure based on forced vibration

Purpose–This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.Design/methodology/approach–The track and substructure are decomposed into the rail subsystem and substructure subsystem,in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener.The rail is treated as a continuous beam with elastic discrete point supports,and spring-damping elements are used to simulate the constraints between rail and fastener.Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system,while the external load is used to deal with the reverse effect.The fastener failure is simulated with the methods that cancel the forced vibration transmission,namely take no account of the substructure–rail interaction at that position.Findings–The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method.Local fastener failure will slightly affect the vibration of substructure and carbody,but it will significantly intensify the vibration response between wheel and rail.The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value,respectively,under the train speed of 350 km$h
1.At the same time,the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%,respectively,from the normal value.Originality/value–This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.

Influence of vehicle-road coupled vibration on tire adhesion based on nonlinear foundation

The influence of pavement vibration on tire adhesion is of great significance to the structure design of vehicle and pavement.The adhesion between tire and road is the key to studying vehicle dynamics,and the precise description of tire adhesion affects the accuracy of dynamic vehicle responses.However,in most models,only road roughness is considered,and the pavement vibration caused by vehicle-road interaction is ignored.In this paper,a vehicle is simplified as a spring-mass-damper oscillator,and the vehicle-pavement system is modeled as a vehicle moving along an Euler-Bernoulli beam with finite length on a nonlinear foundation.The road roughness is considered as a sine wave,and the shear stress is ignored on the pavement.According to the contact form between tire and road,the LuGre tire model is established to calculate the tire adhesion force.The Galerkin method is used to simplify the partial differential equations of beam vibration into finite ordinary differential equations.A product-to-sum formula and a Dirac delt function are used to deal with the nonlinear term caused by the nonlinear foundation,which realizes the fast and accurate calculation of super-high dimensional nonlinear ordinary differential equations.In addition,the dynamic responses between the coupled system and the traditional uncoupled system are compared with each other.The obtained results provide an important theoretical basis for research on the influence of vehicle-road coupled vibration on tire adhesion.

Dynamic model of vertical vehicle-subgrade coupled system under secondary suspension

As it is known, track transportation can be divided into track system above and track system below. While the train is moving, the parts above and below are interacted and influenced. Therefore, in fact, the problem of track transportation is the match between the vehicle and the raihvay line system. In this paper, on a basis of dynamic analysis of the vehicle-subgrade model of vertical coupled system under primary suspension, utilizing track maintenance standard and simulating track irregularity excitation, the dynamic interaction of vehicle-track-subgrade system is researched in theory and dynamic model of the vertical vehicle-track-subgrade coupled system under secondary suspension is established by compatibility condition of deformation. Even this model considers the actual structure of a vehicle, also considers vibration characteristic of the substructure of track including subgrade and foundation. All these work want to be benefit for understanding and design about the dynamic characters of subgrade in high speed railway.

Experimental investigation on vibration characteristics of the medium-low-speed maglev vehicle-turnout coupled system

The steel turnout is one of the key components in the medium–low-speed maglev line system.However,the vehicle under active control is prone to vehicle–turnout coupled vibration,and thus,it is necessary to identify the vibration characteristics of this coupled system through field tests.To this end,dynamic performance tests were conducted on a vehicle–turnout coupled system in a medium–low-speed maglev test line.Firstly,the dynamic response data of the coupled system under various operating conditions were obtained.Then,the natural vibration characteristics of the turnout were analysed using the free attenuation method and the finite element method,indicating a good agreement between the simulation results and the measured results;the acceleration response characteristics of the coupled system were analysed in detail,and the ride quality of the vehicle was assessed by Sperling index.Finally,the frequency distribution characteristics of the coupled system were discussed.All these test results could provide references for model validation and optimized design of medium–low-speed maglev transport systems.

A Study of Dynamic Analysis Method for the Rigid-Flexible Coupled Bar Linkage System

In order to present a dynamic analysis method for the rigid-flexible coupled bar linkage system(RFCBLS),the flexible element motion equation was gotten by Lagrange Equation and the rigid element motion equation was gotten based on rigid constraint conditions.The multi-body system(MBS) is a complex mechanism and its components have quite different rigidities.If it is considered as a rigid MBS(RMBS) to do its dynamic analysis,elastic deformation's ignorance will lead to inaccurate analysis.If it is considered as a flexible MBS(FMBS) to establish,analyze,and solve the model,quite large system equations make it difficult to solve.The better method is as follows:the complex mechanism system is regarded as a rigid-flexible coupled system(RFCS) to make dynamic characteristic of rigid components be equivalent,system equation is established by FMBS' way,and system equation dimensions are reduced by transition matrices' introduction.A dynamic analysis method for rigid element and flexible element coupling was presented based on the FMBS.The analyzed crank slide-block mechanism results show that the dynamic analysis method for RFCBLS is quick and convenient.

Effects of fundamental factors on coupled vibration of wind-rail vehicle-bridge system for long-span cable-stayed bridge

In a wind-vehicle-bridge(WVB) system,there are various interactions among wind,vehicle and bridge.The mechanism for coupling vibration of wind-vehicle-bridge systems is explored to demonstrate the effects of fundamental factors,such as mean wind,fluctuating wind,buffeting,rail irregularities,light rail vehicle vibration and bridge stiffness.A long cable-stayed bridge which carries light rail traffic is regarded as a numerical example.Firstly,a finite element model is built for the long cable-stayed bridge.The deck can generally be idealized as three-dimensional spine beam while cables are modeled as truss elements.Vehicles are modeled as mass-spring-damper systems.Rail irregularities and wind fluctuation are simulated in time domain by spectrum representation method.Then,aerodynamic loads on vehicle and bridge deck are measured by section model wind tunnel tests.Eight vertical and torsional flutter derivatives of bridge deck are identified by weighting ensemble least-square method.Finally,dynamic responses of the WVB system are analyzed in a series of cases.The results show that the accelerations of the vehicle are excited by the fluctuating wind and the track irregularity to a great extent.The transverse forces of wheel axles mainly depend on the track irregularity.The displacements of the bridge are predominantly determined by the mean wind and restricted by its stiffness.And the accelerations of the bridge are enlarged after adding the fluctuating wind.

Numerical simulation of aircraft arresting process with an efficient full-scale rigid-flexible coupling dynamic model

The arresting process of carrier-based aircraft is widely recognized as a challenging task,characterized by the highest accident rate among all carrier-based aircraft operations.Dynamic simulation plays a crucial role in assessing the intricate responses of the arresting process,favoring the design of carrier-based aircraft.An efficient and accurate rigid-flexible coupling model for analyzing the dynamic response of the arresting process is proposed.By combining the dynamic characteristics of airframe,landing gear,arresting hook and arresting gear system,the rigid-flexible coupling dynamic model is established to reflect the relative motion of the coupling parts and arresting load.The dynamic model is verified through simulations of landing gear landing drops and by comparing the arresting simulation results with corresponding data in the US military standard.Additionally,simulations of the arresting process under different off-center distance and aircraft yaw angle are conducted to obtain the dynamic response of the aircraft during the arresting process.The result indicates that the rigid-flexible coupling dynamic model proposed is effective for analyzing the arresting dynamics response of carrier-based aircraft.The axial force of the arresting cable on both sides of the hook engagement point,pitch and yaw angle of aircraft are inconsistent under yaw and off-center arresting.The analysis method and obtained results provide valuable references for assessing the dynamic responses of carrier-based aircraft during arresting process and offer valuable in-sights in the design of carrier-based aircraft.

Numerical analysis of dynamic response of vehicle–bridge coupled system on long-span continuous girder bridge

To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.

MODEL OF CENTRIFUGAL EFFECT AND ATTITUDEMANEUVER STABILITY OF A COUPLEDRIGID-FLEXIBLE SYSTEM

The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field', and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.

Distribution characteristics and influencing factors of the frequency-domain response of a vehicle–track vertical coupled system

Employing theory on vehicle-track coupled dynamics, the equation of motion of a vehicle-track vertical coupled system was established by combining frequency analysis and symplectic mathematics. The frequency response of the vehicle-track vertical coupled system was calculated under the excitation of the German low-interfer- ence spectrum, and the effects of the vehicle speed, vehicle suspension parameters, and track support parameters on the frequency response of the coupled system were studied. Results show that, under the excitation of the German low- interference spectrum, the vertical vibration of the car body is mainly concentrated in the low-frequency band, while that of the bogie has a wide frequency distribution, being strong from several Hertz to dozens of Hertz. The vertical vibrations of the wheel-rail force, wheelset, and track structure mainly occur at a frequency of dozens of Hertz. In general, the vertical vibration of the vehicle-track coupled system increases with vehicle speed, and the vertical vibrations of the car body and bogie obviously shift to higher frequency. Increasing the vehicle suspension stiffness increases the low- frequency vibrations of the vehicle system and track struc- ture. With an increase in vehicle suspension damping, the low-frequency vibrations of the car body and bogie and the vibrations of the wheel-rail vertical force and track structure decrease at 50-80 Hz, while the mid-frequency and high- frequency vibrations of the car body and bogie increase. Similarly, an increase in track stiffness amplifies the vertical vibrations of the wheel-rail force and track structure, while an increase in track damping effectively reduces the vertical vibrations of the wheel-rail vertical force and track structure.