Multi-body System Dynamics Model Research Articles

Carbody swaying suppression for a high-speed rail vehicle by utilising active lateral suspension control

This study proposes the use of active lateral secondary suspension (ALS) to address low-frequency carbody swaying in high-speed rail vehicles under low wheel-rail conicity conditions. Field experiments reveal lateral acceleration exceeding 0.10 g at a dominant frequency of 1.4 Hz, with a Sperling index exceeding 3.0 during carbody swaying occurs. By integrating field-measured wheel/rail profiles and yaw damper parameters into a multibody dynamics model of vehicle system, the coupling between bogie hunting and carbody yaw and upper-center roll modes is identified as the root cause of swaying. Evaluating classic sky-hook ALS controls, damping control proves highly effective. Doubling the damping coefficient and blow-off force becomes essential when only half of the four actuators per vehicle are active. Stiffness control adjusts carbody suspension modal characteristics to prevent resonances with the bogie hunting mode, effectively suppressing swaying. In contrast, inerter control exhibits limited efficacy. Semi-active control, with optimised gain settings, can also alleviate swaying, with control system delay identified as a critical factor, suggesting a 100 ms limit for effective swaying suppression.

Noise analysis of interior structure under powertrain excitation

To accurately identify the structural noise problem caused by vibration in the cockpit, an experimental study was conducted on a certain type of SUV under uniform acceleration conditions. Based on the planning of the multi-body system dynamics model, a transfer path model with secondary contributions is constructed, and the load is identified using the single degree of freedom model and multi-frequency bandwidth model under the OPAX method based on this path. The results indicate that the second-order vibration of the powertrain is transmitted to the entire suspension system through the X direction of the right suspension. The second-order vibration of the suspension system is then transmitted to the Z direction of the right rear bolt of the subframe, causing the entire subframe vibration and ultimately reaching the target point. This structural path has the greatest impact on the interior noise of the vehicle. This path research method can more accurately determine the main excitation points that cause interior noise problems on a certain path and better understand the overall energy transfer characteristics along the transmission path.

Multibody Dynamics Modeling of a Continuous Rubber Track System. Part 2—Experimental Evaluation of Load Prediction

<div>Vehicles equipped with rubber track systems feature a high level of performance but are challenging to design due to the complex components involved and the large number of degrees of freedom, thus raising the need to develop validated numerical simulation tools.</div> <div>In this article, a multibody dynamics (MBD) model of a continuous rubber track system developed in Part 1 is compared with extensive experimental data to evaluate the model accuracy over a wide range of operating conditions (tractor speed and rear axle load). The experiment consists of crossing an instrumented bump-shaped obstacle with a tractor equipped with a pair of rubber track systems on the rear axle. Experimental responses are synchronized with simulation results using a cross-correlation approach.</div> <div>The vertical and longitudinal maximum forces predicted by the model, respectively, show average relative errors of 34% and 39% compared to experimental data (1–16 km/h). In both cases, the average relative error is lower for tractor speed from 1 to 7 km/h, namely 20% and 35%. The model and experimental amplitudes spectra of the force signals are compared using the coefficient of determination <i>r</i><sup>2</sup>. In the 1 to 7 km/h tractor speed range, the average vertical and longitudinal coefficients of determination are, respectively, 0.83 and 0.42. The coefficients, respectively, reduce to 0.27 and 0.14 for speeds over 7 km/h.</div> <div>In summary, the model can predict the maximum vertical and longitudinal forces in addition to the amplitude spectrum of those signals for operating conditions up to 7 km/h, regardless of the rear axle load, with accuracy acceptable for many applications, such as load case determination for preliminary structural design. Several factors affecting the accuracy of the model at higher tractor speed are identified for future work including suspension creeping, suspension compression characterization at high strain rates, and temperature dependence of material properties.</div>

The prediction of projectile-target intersection for moving tank based on adaptive robust constraint-following control and interval uncertainty analysis

To improve the hit probability of tank at high speed, a prediction method of projectile-target intersection based on adaptive robust constraint-following control and interval uncertainty analysis is proposed. The method proposed provides a novel way to predict the impact point of projectile for moving tank. First, bidirectional stability constraints and stability constraint-following error are constructed using the Udwadia-Kalaba theory, and an adaptive robust constraint-following controller is designed considering uncertainties. Second, the exterior ballistic ordinary differential equation with uncertainties is integrated into the controller, and the pointing control of stability system is extended to the impact-point control of projectile. Third, based on the interval uncertainty analysis method combining Chebyshev polynomial expansion and affine arithmetic, a prediction method of projectile-target intersection is proposed. Finally, the co-simulation experiment is performed by establishing the multi-body system dynamic model of tank and mathematical model of control system. The results demonstrate that the prediction method of projectile-target intersection based on uncertainty analysis can effectively decrease the uncertainties of system, improve the prediction accuracy, and increase the hit probability. The adaptive robust constraint-following control can effectively restrain the uncertainties caused by road excitation and model error.

Coupled Dynamic Analysis of a Bottom-Fixed Elastic Platform with Wave Energy Converters in Random Waves

A Wavestar-type Wave Energy Converter (WEC) on an elastic foundation structure was investigated using an author-developed coupled dynamic analysis computer program. The program included an elastic foundation structure composed of beam elements, a multi-body dynamics model of the entire system, a hydrodynamics model of the dual-buoy, and fully coupled dynamics considering the interaction between the structure and WECs. The selected WEC models a heaving-point-absorber (HPA), one of the oscillating body systems which causes rotational motions of a connecting rod attached to the foundation structure. A rotational-damper-type hydraulic power take-off (PTO) system on the foundation structure produced electricity. The bottom-fixed foundation structure was modeled by three-dimensional beam elements, and the entire system, including HPA, was analyzed by multi-body dynamics. Random wave data at Buan, a nearshore region of Korea, collected by the Korea Meteorological Administration (KMA), was used as a demonstration study using the developed computer programs. Through the case study, the displacement and stress of the foundation structure were increased significantly by the dynamic coupling effects with the WECs, which underscores that the coupled dynamic analysis is essential for a reliable performance evaluation and the design of such a system.

Unsteady Aerodynamic Characteristics of a High-Speed Train Induced by the Sudden Change of Windbreak Wall Structure: A Case Study of the Xinjiang Railway

Under strong winds, the effect of sudden windbreak transition (WT) on high-speed trains is severe, leading to a deterioration of train aerodynamics and sudden yawing motion of the car body. To address these problems, based on a high-speed train and the specific geometric conditions derived from Xinjiang railway, first, the impact of a WT on the train and reasons for sudden changes in aerodynamic forces were determined by flow structural analysis. Furthermore, based on a multibody system dynamic model, the dynamic responses to WT were analysed. The results show that the impacts of WT were the strongest on the head car. WT had a strong effect on the train due to the unreasonable structural shape and the insufficient height of the windbreak in the transition region. This led to a strong push effect on the train; subsequently, the train’s dynamic characteristics deteriorated.

Research on the Mechanical Mechanism of the Shuffle Problem of Electric Vehicles and the Sensitivity to Clearances

In order to address the shuffle problem of the electric powertrain system that occurs at the moment of torque reversing, a multibody dynamics model of the powertrain system, with the measured motor torque applied as the input loading, has been established to analyze the generating mechanism of the rotating speed ripple of the drive system which is regarded the root of shuffle. The influence on speed ripple from cumulative gap size and motor torque has been investigated. The model was validated by showing good agreement between the simulated speed response and the measured data. Perturbance on each backlash was performed in the simulation to reveal the sensitivity of the speed ripple on the size of the backlash. Much higher speed-to-gap sensitivities have been observed for the low-speed engagement pairs than the high-speed engagement pairs, indicating that compressing the backlashes of the former could achieve more NVH (noise, vibration, harshness, i.e., NVH) performance improvement.

The Influence of Aerodynamic Loads on Carbody Low-Frequency Hunting of High-Speed Trains

Low-frequency hunting problems of high-speed railway vehicles frequently occur due to the complex operating environment and degradation of wheel–rail contact conditions, which significantly affect the running safety and ride comfort of high-speed trains (HSTs). This paper presents a numerical investigation of the influence of aerodynamic loads on the carbody low-frequency hunting behaviors of HST. Considering the effect of aerodynamic loads, a multi-body system dynamics model for a HST train is formulated and applied to reproduce the carbody low-frequency hunting behavior. The influence of aerodynamic loads and wheel–rail contact conditions on the nonlinear stability of HST is analyzed. The range of aerodynamic coefficients of different aerodynamic loads which can stimulate the low-frequency hunting behavior of HST is proposed. The results show that the aerodynamic loads have a prominent effect on the nonlinear stability of HSTs. The low-frequency hunting motion of the HST tail car can be motivated by the lift airflow generated during service operation with a high traveling speed. The running stability of HSTs is more easily influenced by the aerodynamic loads when wheels are reprofiled.

Fatigue Strength Detection Method for Crankshaft of Vehicle Internal Combustion Engine Based on Dynamics

To accurately determine the load boundary conditions required for the finite element calculation of crankshaft fatigue strength, a dynamic-based fatigue strength detection method for the crankshaft of the automotive internal combustion engine is proposed. Taking a certain type of automotive internal combustion engine as the research object, the multi-body system dynamics model of crank-connecting rod mechanism is established and the dynamic load spectrum of a crankshaft in a working cycle of the internal combustion engine is obtained through dynamic simulation analysis. The load boundary conditions of crankshaft finite element analysis are obtained and the finite element model which can simulate the contact state between crankshaft and bearing is established. The crankshaft fatigue strength is based on the dynamic load spectrum. Degree detection provides load boundary, the fillet sub-model is constructed and the stress distribution of the fillet sub-model under 12-unit displacement loads is obtained by calculating the stress field. The working fatigue safety factor of the crankshaft under dynamic stress is calculated. The analysis results show that the detection error of the proposed method is less than 5% under different noise intensities and the average energy consumption is lower than that of the comparative detection methods, which are 251.37 J and 617.37 J respectively and shows that the proposed method has strong anti-interference and low energy consumption.

Modeling of lubricated translational joints in rigid-partially flexible multibody systems and its application in two-stroke marine diesel engines

In this paper, a new tribodynamic model for the translational joints with clearance is proposed by coupling the mixed lubrication model and the rigid-flexible multibody system dynamic model. The lubrication behavior is described by the average Reynolds equation and the Greenwood-Tripp asperity contact theory. Under a unified framework of the absolute nodal coordinate formulation (ANCF), motion equations of the rigid-flexible multibody system are established. The assembled equations of tribodynamic model are solved by a stable and effective algorithm. An application example of a two-stroke marine diesel engine is then used to study the tribological and dynamic behaviors of the crosshead-guide translational joint with clearance. The results show that considering the elastic deformation of components will lead to more intense secondary motion and smaller local clearance, resulting in an oil film pressure distribution with great difference from the rigid body modeling.

Dynamic Analysis of Flexible Wind Turbine Tower by a Transfer Matrix Method

To generate more power, wind turbine rotors are growing in size and consequently, wind turbine tower are becoming increasingly taller and more flexible. As a result, fluid–structure interaction (FSI) of the flexible tower caused by strong wind is a very important phenomenon, and tower vibration must be carefully considered. In this paper, the physical model of the wind turbine tower is simplified appropriately, and then a multi-body dynamics model of wind turbine tower system is established based on Transfer Matrix Method of Multibody System (MSTMM). Compared with the data from finite element model (FEM) and field tests, the simulation results show that the model has a good accuracy. By coupling the mode shapes with two degrees of freedom (2-DOF) wake oscillator model, the dynamic responses of the flexible tower are computed. The influence of various foundation stiffness and top mass on tower vibration is studied systematically using this model. The results indicate that different boundary conditions can affect the maximum amplitude and displacement along the axis of the tower. This work provides a reference for dynamic modeling and simulation of high-rise flexible structure, and the prediction of the maximum amplitude of the tower vibration, which can be used for aeroelastic control purpose.

Numerical solution explore of rigid flexible coupling multi-body system dynamic model

This paper analyzes and discusses the problems related to the numerical solution of the rigid flexible coupling multibody system dynamic model. In order to solve the problems of high frequency oscillation and large calculation amount in the solution of the rigid ordinary differential equations, it tries to improve the explicit Runge Kutta method, and applies the Gill method to solve the dynamic differential equations. And confirmed by a case study: In the process of numerical solution of rigid-flexible coupling multi-body system dynamics model, the improved GILL method has small truncation error, fast integration speed and small computation amount. It can provide important basis for the subsequent algorithm improvement and optimization, which deserves the attention of the professional.

Modeling and simulation of point contact multibody system dynamics based on the 2D LuGre friction model

The main purpose of this paper is to present a modeling method and algorithm for point contact non-smooth multibody system based on the 2D LuGre friction model. Firstly, parameter identification of the LuGre friction model is discussed. The identification method for micro-damping coefficient is given by analyzing the influence of it on the stiffness of the dynamic equations and the oscillation of the solution. The bristles stiffness coefficient is determined by comparing with the simulation results of the Coulomb dry friction model. The effectivity of the parameter identification method is verified by a numerical simulating example. Secondly, the dynamic model and algorithm of point contact multibody system with the 2D LuGre friction model are derived by using Lagranges equation of the first kind and Baumgartes stabilization method. Compared with the Coulomb dry friction model, the modeling method presented in this study can also describe the stick-slip motion very well, and greatly simplifies the numerical algorithm. Finally, the modeling method and algorithm are applied to the wheel mechanisms with single-point contact and multi-point contact, and the stick-slip motions of the systems are analyzed.

Effect of Variable Wheelset Steering Stiffness and Yaw Damper Damping on Hunting Stability

Due to the track curvature and irregularities difference, a high-speed dedicated railway vehicle running on a high-speed railway cannot achieve a good dynamics performance when it is operated on an existing railway for conventional low-speed railway vehicle. Then an adaptive bogie which can adjust its suspension parameters, like the steering stiffness of wheelset and the damping of yaw damper, is regarded as a solution to make the high-speed train be operated on an existing railways. In this investigation, a highly nonlinear dynamics model of the adaptive bogie vehicle multi-body system is built to study the effects of wheelset steering stiffness and yaw damper damping on the vehicle dynamics. Both a straight track passing and curved tracks negotiating scenarios are considered to examine the expected range of stiffness and damping when the bogie was operated those two kinds of railways. It shows that reducing the steering stiffness of wheelset leads to a significant decrease in the critical speed of vehicle, and the critical speed of vehicle decreases significantly when the yaw damper damping is less than 500 kN⋅s/m. In case of wheel wear, the smaller the wheelset steering stiffness or the yaw damper damping is, the lower the critical speed of vehicle is. Through the analysis, the limit values of wheelset steering stiffness and yaw damper damping are proposed. When the adaptive bogie vehicle operates on the existing track, the lower limit values of wheelset steering stiffness and yaw damper damping are 12 MN/m and 200 kN⋅s/m respectively.

Effect of Wheelset Steering Stiffness Difference on the Dynamics Performance of a High-speed Railway Vehicle

In order to study the influence of steering difference of wheelsets among one bogie on the dynamics performance of vehicle, a highly nonlinear dynamics model of the high-speed railway vehicle multi-body system is built. In numerical simulations, the combined condition of taking the upper and lower limits of the steering stiffness of wheelset is investigated, respectively. It shows that the effect of wheelset steering stiffness on the dynamic performance is not significant. Its influence on the lateral vibration of bogie frame, hunting stability of vehicle, operation safety when negotiating curved tracks and wheel wear is generally within 5%. Its influence on the maximum lateral and vertical acceleration of carbody is generally within 10% and the influence range of specific cases is within 20%. For all the numerical cases, the vehicle dynamics indexes all meet the required limit.

Theoretical modeling and numerical solution methods for flexible multibody system dynamics

Flexible multibody system dynamics (MSD) is one of the hot spots and difficulties in modern mechanics. It provides a powerful theoretical tool and technical support for dynamic performance evaluation and optimization design of a large number of complex systems in many engineering fields, such as machinery, aviation, aerospace, weapon, robot and biological engineering. How to find an efficient accurate dynamics modeling method and its stable reliable numerical solving algorithm are the two core problems of flexible MSD. In this paper, the research status of modeling methods of flexible MSD in recent years is summarized first, including the selection of reference frames, the flexible body’s kinematics descriptions, the deductions of dynamics equation, the model reduction techniques and the modeling methods of the contact/collision, uncertainty and multi-field coupling problems. Then, numerical solution technologies and their latest developments of flexible MSD are discussed in detail. Finally, the future research directions of modeling and numerical computation of flexible MSD are briefly prospected.

Effect of pre-tensioned loads to vibration at the ladder tip in raising and lowering processes on a turntable ladder

A turntable ladder is an indispensable vehicle in fire and rescue work. Vibration on the top of the ladder is considerable when the ladder set is maximally extended. It induces the discomfort and unsafety for beings in the rescue cage. Aiming at the reduction of the vibration, in this study, one additional steel wire rope is assumedly added into each handrail of the ladder set. The steel wire ropes are suggested to be pre-tensioned before the turntable ladder works. This study is based on an available ladder set structure which includes three ladder sections with different area moments of inertia. Additionally, a ladder structure model is established as a multibody system dynamic model. The changes of kinetic parameters in the raising and lowering processes of the ladder set are investigated. The obtained results can be the fundamentals for modeling, experiments and applications of turntable ladders.

Modular design and analysis of the x-by-wire center point steering independent suspension for in-wheel electric vehicle

In this article, a new design scheme of x-by-wire steering suspension system is proposed, which aims to solve the adaptation problem of the traditional steering system, suspension system, and the electric wheel. It meets the requirement of four-wheel independent steering function with large scale. The design keeps wheel steering center axis to coincide with the virtual wheel kingpin, thereby realizing the application of the center point steering independent suspension system in electric wheels. In addition, modular design is adopted to reduce the coupling between the system and the car body, thereby realizing the generalization of the front and rear steering suspension system, and it also decreases the number of components. Furthermore, the theoretical analysis and parameter design of the self-aligning torque of the suspension are carried out. The multi-body dynamics model of system is established, and the performance is simulated in both time domain and frequency domain. The comparison test shows that the center point steering independent suspension has higher feasibility. Finally, a prototype of the system is developed, which provides a new idea for the designing of chassis for electric vehicles.

Multi-objective optimization of vibration characteristics of steering systems based on GA-BP neural networks

Currently, multi-objective optimization of steering systems has seldom been reported, and this paper adopted GA-BPNN algorithm to optimize the top two order frequencies of steering systems. Firstly, this paper established the multi-body dynamics model of the steering system and obtained the random road spectrum of 4 wheels through mathematical model. Results showed that random road spectrums at different wheels were not totally the same and the position and size of peak values were also different. Therefore, the road spectrum of a wheel could not be used to replace the road spectrum of all wheels in multi-body dynamics simulation model. Otherwise, computational results would have a big error. Then, vibration accelerations of the steering wheel at different positions were extracted through the multi-body dynamics model of steering system. Results showed that there were two obvious peak values on the curve of vibration acceleration, and peak frequencies were 48.6 Hz and 65.1 Hz. The finite element model of steering system was established to compute the vibration acceleration, and it was compared with the experimental result. Relative error was controlled within 5 %. It indicated that the finite element model in this paper was reliable. In addition, the computational two order modal frequencies were completely the same with the peak frequencies of vibration acceleration, which proved that the peak values of vibration acceleration were totally caused by the top two order modals. Finally, GA-BPNN algorithm was proposed to optimize the structural thickness of key parts on the steering system, and the optimized result was then compared with that of BPNN and PSO-BPNN. Results showed that the optimization efficiency and result of GA-BPNN were obviously superior to those of other algorithms in the process of optimization and iteration. The optimized parameters were reapplied to the computational model of this paper. Vibration accelerations of the steering system at many positions were extracted to compare with those of the original result. Peak frequencies were significantly improved. In addition, vibration accelerations at most frequency points of the whole frequency band were significantly improved.

A new numerical method for planar multibody system with mixed lubricated revolute joint

A new method for modeling and analysis of planar multibody systems with lubricated revolute joints is presented. This method is established by coupling the lubrication model of lubricated revolute clearance joint with the dynamics model of multibody system. The lubrication model is solved by the Finite Element Method, while the multibody dynamics equations are established by Lagrange's method. In order to take into account the effects of the surfaces roughness on the hydrodynamic lubrication when the oil film between the mating surfaces has a very small thickness, the average Reynolds equation is adopted. The hydrodynamic forces built up by the lubricant fluid are evaluated from the knowledge of the system variables and then included into the dynamics equations of the multibody system. In the end, the proposed approach is applied to the piston–connecting rod–crank system in a four-stoke gasoline engine with lubricated clearance joint at the big end of the connecting rod. The clearance size and lubricant viscosity are investigated so as to reveal their influences on both the dynamics and lubrication performances. From the main obtained results, it can be concluded that the use of lubricant at mechanism joints is an effective way to ensure better performance. Within a given range, the cases with smaller clearance or higher lubricant viscosity are conducive to maintaining the stability of the motion of mechanism, and will decrease the friction power loss.