Multibody System Dynamics最新文献

In multi-body systems, flexible components and couplings between them can be subject to large displacements and rotations. This contribution presents a general objective and geometrically exact node-to-node coupling element that pursues two innovations. Firstly, the coupling element represents a consistent extension to an existing nonlinear mechanical framework. The coupling element is intended to preserve its attributes of objectivity, path independence and adherence to the energy-conserving or energy-dissipative time integration method. Secondly, beside elasticity, inertia and damping properties are also considered. For this purpose, a director-based formulation is employed within a total Lagrangian description. The avoidance of an angle-based representation, along with the additive updating of state variables, results not only in path independence but also in the avoidance of cumulative errors during extended simulations. An objective deformation measure is chosen based on the Green–Lagrange strain tensor. The inertia forces are considered by an arbitrarily shaped continuum located at the centre of the coupled nodes. Damping is considered by using two different objective first-order dissipation functions, which further ensure energy conservation or dissipation. We successfully demonstrate the coupling element within the mechanical framework on using example applications. Firstly, the geometrically exact behaviour is shown compared to a linear deformation measure. Secondly, we numerically show the path independence of the formulation. The dynamic behaviour is demonstrated in a transient analysis of a damped structure. Finally, the modal analysis of a wind turbine shows the application of the coupling element to model the soil–structure interaction.

Shoulder muscle forces estimated via modelling are typically indirectly validated against measurements of glenohumeral joint reaction forces (GHJ-RF). This validation study benchmarks the outcomes of several muscle recruitment strategies against public GHJ-RF measurements. Public kinematics, electromyography, and GHJ-RF data from a selected male participant executing a 2.4 kg weight shoulder abduction task up to 92° GHJ elevation were obtained. The Delft Shoulder and Elbow Model was scaled to the participant. Muscle recruitment was solved by 1) minimising muscle activations squared (SO), 2) accounting for dynamic muscle properties (CMC) and 3) constraining muscle excitations to corresponding surface electromyography measurements (CEINMS). Moreover, the spectrum of admissible GHJ-RF in the model was determined via Markov-chain Monte Carlo stochastic sampling. The experimental GHJ-RF was compared to the resultant GHJ-RF of the different muscle recruitment strategies as well as the admissible stochastic range. From 21 to 40 degrees of humeral elevation, the experimental measurement of the GHJ-RF was outside the admissible range of the model (21 to 659% of body weight (%BW)). Joint force RMSE was between 21 (SO) and 24%BW (CEINMS). At high elevation angles, CMC (11%BW) and CEINMS (14%BW) performed better than SO (25%BW). A guide has been proposed to best select muscle recruitment strategies. At high elevation angles, CMC and CEINMS were the two most accurate methods in terms of predicted GHJ-RF. SO performed best at low elevation angles. In addition, stochastic muscle sampling highlighted the lack of consistency between the model and experimental data at low elevation angles.

Finding the stable static equilibrium position of multibody systems is a well-known problem. Dynamic relaxation methods are frequently utilized in engineering, however, they often require a significant amount of time. Alternatively, most commercial software employs the Newton–Raphson iterative method to solve a set of nonlinear equations to find the equilibrium position directly, in which the time derivatives of any quantity are set to zero. Nevertheless, this approach is highly dependent on initial conditions and can only find one equilibrium position for a specific initial condition, no matter how many degrees of freedom a system has. A path-following method is implemented in this paper to find the equilibrium position of the multibody system by using the reduced multibody system transfer matrix method to evaluate the acceleration functions and its Jacobian matrix, where the notion of direct differentiation is applied. The solution curves for changing generalized accelerations are then tracked using the arc-length method to obtain candidate equilibrium states if they vanish and identify the stable static equilibrium position. To demonstrate the effectiveness of the proposed method, numerical examples are presented, which provide a detailed overview of the complete computational flow.

Frequency veering is a phenomenon that occurs during modal parameter changes and is closely related to the response characteristics of the system. First, by taking a system with simple DOFs as the research object, the variations in the modal damping ratio and mode shape in the process of frequency veering are analysed, and a criterion for identifying this phenomenon is preliminarily proposed. Then, to explore the modal changes in complex vehicle systems with multiple DOFs, an adaptive modal continuous tracking algorithm based on a local search algorithm is proposed that takes the Euclidean closeness between complex mode shapes as an index. Frequency veering is analysed with the established vehicle system dynamics model (Model I) and reproduced through the SIMPACK model (Model II) for multibody dynamics simulation. The perturbation method is used to analyse the mechanism by which the vehicle system eigenvectors are prone to mutations during frequency veering, and the abnormal changes in the mode shapes during this process are further verified. In addition, two quantitative indices for identifying frequency veering phenomena are proposed based on the modal assurance criterion and mode shape similarity. Finally, the mapping relationship between the frequency veering and vehicle system response is explored. The results indicate that before and after frequency veering, the mode shapes interchange, and in the frequency veering zone, the damping-hopping phenomenon occurs, resulting in a significant decrease in system stability. Corresponding to the phenomena of modal damping ratios and mode shapes, the motion morphology of the vehicle system is clearly observable. Moreover, the response at the DOFs of the car body and bogie are obviously enhanced; these responses are also manifested in the increasing vibrations of the car body and bogie and the deterioration of the vehicle ride quality.

Train derailments may have catastrophic consequences, and therefore suitable measures should be designed and installed at specific safety-relevant sites to mitigate their effects. Mitigation measures, such as guard rails and containment walls, aim at restraining the motion of the derailed vehicle using suitable derailment containment devices. However, the design and structural sizing of these devices is challenging as the quantification of the loads caused by the impact with the vehicle is complex.

The aim of this paper is to extend previous work from the same authors aimed at defining a non-linear multi-body model for the simulation in time-domain of the post-derailment behaviour of a railway vehicle and the impact on a derailment containment wall. The extension presented in this paper is concerned with the model of the interaction of the derailed vehicle with the sleepers and with the ballast. To this aim, an algorithm is introduced to manage the different possible contact conditions the wheels of the vehicle may undergo during the derailment process: contact with the rail, with the sleepers and with the ballast. Then, a model of the impact between the derailed wheels and the sleepers is introduced, and a terramechanic model defining the forces acting on the wheels sinking in the ballast is established. The effect of the accurate modelling of forces exchanged by the derailed wheels with the sleepers and the ballast is quantified for a relevant derailment scenario and shown to be highly relevant to the estimation of the impact loads applied to the containment structure.

In recent times, many industrial applications have demanded innovative energy-efficient solutions. One of the main causes of energy loss is due to friction between body surfaces in contact. A great amount of research has been aimed at understanding the friction mechanisms to allow for its reliable prediction during multibody simulation. In the 1950s and 1960s, many experimental studies were carried out, leading to the coefficient of friction formulas for lubricated surfaces under a combination of sliding and rolling relative motion. The formulas have been mainly derived by the mathematical fitting of results obtained from experimental measurements on rolling disks and different load, lubricating and kinematic conditions. The purpose of this paper is twofold: on the one hand, it reviews semi-empirical formulas for computing the friction coefficient in lubricated contact under various operating conditions; on the other hand, it implements and compares contact force models coupled with the metal-metal lubricated empirical friction formulas in a multibody dynamics simulation environment. Implementing empirical formulas is straightforward and computationally efficient, but one can evaluate the performance of these models in characterizing the dynamics of the lubricated joint. For this purpose, a multibody simulation of a Scotch yoke and a Whitworth quick return mechanisms with a nonideal prismatic joint are conducted. The existence of clearance causes the dynamic behavior of the system to be different from the ideal joint. The difference between each friction coefficient model is emphasized by simulation output and computation time.