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A multibody model for riderless bicycle dynamics considering tire characteristics is presented. A riderless bicycle is regarded as a multibody system consisting of four rigid bodies: rear wheel, frame, front fork, and front wheel. Every two bodies are connected with a revolute joint. The mass center coordinates and Euler angles of the rigid bodies are used as the generalized coordinates to describe their positions and orientations. The system equations of motion are obtained using Lagrange equations of the first kind. Due to the existence of the three revolute constraints and the use of dependent generalized coordinates, the Lagrange multipliers are employed to account for revolute reaction forces. As for the contact between the wheel and the ground, many studies regarded the wheel as a rigid body with a knife edge, which lead to the nonholonomic constraints between the wheel and the ground.

To study the torque distribution of track and tire in the wheel-track hybrid drive vehicle driving along the shoreline, an analysis model of wheel-track hybrid drive vehicle was established by using multi-body dynamics (MBD), discrete element (DEM), and shoreline pavement construction methods. The vehicle speed, acceleration, torque, vertical load, sinkage, slip, and other indicators when the vehicle passes the shoal at different wheel speed of rotation are analyzed. The relationships between wheel speed of rotation and slip, sinkage and slip, and vertical load and driving moment were studied, and the laws that the sinkage of tires and tracks is positively related to their slippage and the driving moment of wheels and tracks is positively related to their vertical load were obtained.

Many vehicles have been equipped with air springs as elastic elements to get better performance in comfort, but absorbers may not work in an optimal state due to the variation of suspension stiffness. While the function of semi-active suspension is to enable the absorber damping to be adjusted according to different road roughness levels and to coordinate between comfort and handling. To solve the problem of matching the damping coefficient of variable stiffness suspensions represented by air springs, this paper proposed a method for calculating the optimal damping ratio of a semi-active suspension system in real-time with sprung mass acceleration and dynamic tire load to establish the objective function and suspension dynamic deflection as the constraint to reflect the unification of comfort and handling.

The rubber bushing is the key component to suppress vibration in the suspension system, an accurate constitutive model of rubber bushing should capture the amplitude and frequency dependency. Based on the lumped parameter model, three types of rubber bushing models are applied and compared, including the common Kelvin-Voigt model. To evaluate the model parameter and suitable frequency range, the quasi-static and dynamic tests have been performed. Comparing with the testing result, the fractional Kelvin-Voigt model combined with Berg’s friction has the minimum relative error of dynamic stiffness on the whole. Finally, two examples of chassis bushing under different loading conditions are presented. The rubber force and deflection are analyzed in both the time domain and the frequency domain, and the results show the difference of stiffness and hysteresis loop relative to frequency.

The vehicle ride comfort behavior is closely associated with the vibration isolation system such as the primary suspension system, the engine mounting system, the cab suspension system and the seat suspension system. Air spring is widely used in the cab suspension system for its low vibration transmissibility, variable spring rate and inexpensive automatic leveling. The mathematical model of the air spring is presented. The amplitude and frequency dependency of the air spring's stiffness characteristic is highlighted. The air spring dynamic model is validated by comparing the results of the experiment and the simulation. The co-simulation method of ADAMS and AMESim is applied to integrate the air spring mathematical model into the cab multi-body dynamic model. The simulation and ride comfort test results under random excitation are compared.

The ride comfort of the commercial vehicle is mainly affected by several vibration isolation systems such as the primary suspension system, engine mounting system and the cab mounting system. A rigid-flexible coupling model for the truck was built and analyzed in multi-body environment (ADAMS). The method applying the excitation on the wheels center and the engine mountings in time domain was presented. The variables' effects on the ride performance were studied by design of experiment (DOE). The optimal design was obtained by the co-simulation of the ADAMS/View, iSIGHT and Matlab. It was found that the vertical root mean square (RMS) acceleration and frequency-weighted RMS acceleration on the seat track were reduced about 17% and 11% respectively at different speeds relative to baseline according to ISO 2631-1.

The suspension system of a heavy truck's driver seat plays an important role to reduce the vibrations transmitted to the seat occupant from the cab floor. Air-spring is widely used in the seat suspension system, for the reason that its spring rate is variable and it can make the seat suspension system keep constant ‘tuned’ frequency compared to the conventional coil spring. In this paper, vibration differential equation of air-spring system with auxiliary volume is derived, according to the theory of thermodynamic, hydrodynamics. The deformation-load static characteristic curves of air-spring is obtained, by using a numerical solution method. Then, the ADAMS model of the heavy truck's driver seat suspension system is built up, based on the structure of the seat and parameters of the air-spring and the shock-absorber. At last, the model is validated by comparing the simulation results and the test results, considering the seat acceleration PSD and RMS value.

This paper describes a simplified model to identify sprung mass using golden section method, the model treats the unsprung mass vertical acceleration as input and the sprung mass vertical acceleration as output, which can avoid the nonlinear influence of trye. Unsprung mass can be also calculated by axle load and the identified sprung mass. This study carries out road test on the vehicle ride comfort and takes a scheme that the group of 20 km/h is used to identify sprung mass and the group of 80 km/h is used to verify the identification result. The similarity of the results from the simulation and experiments performed are, for the sprung mass, 98.59%. A conclusion can be drawn that the simple method to measure the sprung mass in the suspension systems in used vehicles, such as the vehicle shown here, is useful, simple and has sufficient precision.

Vehicle systems often operate with some degree of uncertainty. This study applies the Chebyshev interval method to model vehicle dynamic systems operating in the presence of interval parameters. A full vehicle model is used as the numerical model and the methodology is illustrated on the steering wheel angle pulse input test. In the numerical simulation, suspension stiffness coefficients and suspension damping coefficients are chosen as interval parameters and lateral acceleration and yaw rate are chosen to capture vehicle dynamic characteristics. System responses in time domain are validated against Monte Carlo simulations and against the scanning approach. Results indicate that the Chebyshev interval method is more efficient than Monte Carlo simulations. The results of scanning method are similar to the ones obtained with the Chebyshev interval method.

There are many uncertain parameters in shock absorbers, which are induced by the manufacturing error, the wear of components and the aging of materials in real vehicle environment. These uncertainties often cause some deterioration of vehicle performance. To optimize the ride characteristic of a vehicle when the shock absorber includes uncertain parameters, the robust design method is used. In this paper, a Twin Tube shock absorber fluid system model has established on the multi-domain modeling environment. This model not only includes the commonly used parameters of the shock absorber but also takes into account the structure parameters of various valves in the shock absorber, which is more detailed and accurate than those models in the past literature. The robust design of the shock absorber parameters is successfully approached using the co-simulation technique, and the ride comfort performance of the vehicle is also improved.

As is known to all, there are some contradictions between the handling and ride performance during the design process of vehicles. Sometimes owing to serious collisions of each criterion in the high-dimensional solution space, the common method to deal with the contradiction is to transform into a single target according to weights of each objective, which may not obtain a desired result. A multi-criteria approach is therefore adopted to optimize both properties and the result of a multi-criteria design is not a unique one but a series of balanced solutions. This paper is focused on the robust design of a simplified vehicle model in terms of not only ride comfort but also handling and stability using a multi-objective evolutionary algorithm (MOEA) method. Using the proposed method, the conflicting performance requirements can be better traded off. One of the most important indexes to characterize the vertical ride comfort is the acceleration of the sprung mass.

To solve the dynamic response problem that contains uncertain parameters needs, the stochastic differential equations needs to be calculated. Interval analysis has been widely used to solve engineering problems which contain many uncertain parameters usually. But the numerical solution method for stochastic differential equations based on the interval analysis method was seldom investigated. In this study a new numerical interval method for the stochastic differential equations based on the Euler's method is presented, which can be used to solve the linear system effectively and efficiently. The probabilistic and interval dynamics analysis of a two-degree-of-freedom bike car model with uncertain parameters are presented.