Multibody System Dynamics最新文献

We investigate how well a physics-based simulator can replicate a real wheel loader performing bucket filling in a pile of soil. The comparison is made using field-test time series of the vehicle motion and actuation forces, loaded mass, and total work. The vehicle was modeled as a rigid multibody system with frictional contacts, driveline, and linear actuators. For the soil, we tested discrete-element models of different resolutions, with and without multiscale acceleration. The spatiotemporal resolution ranged between 50–400 mm and 2–500 ms, and the computational speed was between 1/10,000 to 5 times faster than real time. The simulation-to-reality gap was found to be around 10% and exhibited a weak dependence on the level of fidelity, e.g., compatible with real-time simulation. Furthermore, the sensitivity of an optimized force-feedback controller under transfer between different simulation domains was investigated. The domain bias was observed to cause a performance reduction of 5% despite the domain gap being about 15%.

To alleviate the locking problem in the ANCF beam elements, sufficient transverse gradient vectors are incorporated in the cross section to enrich the distribution of transverse strain along the cross section of the beam. Building upon this novel concept, this paper utilizes Pascal trigonometric polynomial to determine the position interpolation field of beam elements, and the distribution of transverse gradient vectors along the beam section is clarified through the collocation of boundary points and Chebyshev interpolation nodes, and then a series of locking-free beam models, based on the absolute nodal coordinate formulation, are developed. Additionally, it reveals the inherent mechanical mechanism of higher-order beam models in alleviating locking through strict mathematical analysis. Furthermore, to demonstrate the effectiveness of the new elements, six numerical simulation examples are designed, namely, three static examples and three dynamic examples, which involve small deformation statics, large deformation statics, small-scale elastic deformation, large-scale elastic deformation problems. Finally, the simulation results of the first four order beam models, Patel–Shabana model, and ECM approach are compared and analyzed in detail. The results indicate that the proposed higher-order beam models have high accuracy and can effectively eliminate the unnecessary influence caused by locking in complex mechanical problems, involving statics and dynamics problems.

Mechanical systems with singular and/or configuration-dependent mass matrix can pose difficulties to Hamiltonian formulations, which are the standard choice for the design of energy-momentum conserving time integrators. In this work, we derive a structure-preserving time integrator for constrained mechanical systems based on a mixed variational approach. Livens’ principle (or sometimes called Hamilton–Pontryagin principle) features independent velocity and momentum quantities and circumvents the need to invert the mass matrix. In particular, we take up the description of rigid body rotations using unit quaternions. Using Livens’ principle, a new and comparatively easy approach to the simulation of these problems is presented. The equations of motion are approximated by using (partitioned) midpoint discrete gradients, thus generating a new energy-momentum conserving integration scheme for mechanical systems with singular and/or configuration-dependent mass matrix. The derived method is second-order accurate and algorithmically preserves a generalized energy function as well as the holonomic constraints and momentum maps corresponding to symmetries of the system. We study the numerical performance of the newly devised scheme in representative examples for multibody and rigid body dynamics.

Explicit Runge–Kutta methods are the gold standard of time-integration methods for nonstiff problems in system dynamics since they combine a small numerical effort per time step with high accuracy, error control, and straightforward implementation. For the analysis of beam dynamics, we couple them with a local coordinates approach in a Lie group setting to address large rotations. Stiff shear forces and inextensibility conditions are enforced by internal constraints in a coarse-grid discretization of a geometrically exact beam model. The resulting nonstiff constrained systems are handled by a half-explicit approach that relies on the constraints at velocity level and avoids all kinds of Newton–Raphson iteration. We construct half-explicit Runge–Kutta Lie group methods of order up to five that are equipped with an adaptive step-size strategy using embedded Runge–Kutta pairs for error estimation. The methods are tested successfully for a roll-up maneuver of a flexible beam and for the classical flying-spaghetti benchmark.

In this paper, a novel method for computing the nonlinear dynamics of highly flexible slender structures in three dimensions (3D) is proposed. It is the extension to 3D of a previous work restricted to inplane (2D) deformations. It is based on the geometrically exact beam model, which is discretized with a finite-element method and solved entirely in the frequency domain with a harmonic balance method (HBM) coupled to an asymptotic numerical method (ANM) for continuation of periodic solutions. An important consideration is the parametrization of the rotations of the beam’s cross sections, much more demanding than in the 2D case. Here, the rotations are parametrized with quaternions, with the advantage of leading naturally to polynomial nonlinearities in the model, well suited for applying the ANM. Because of the HBM–ANM framework, this numerical strategy is capable of computing both the frequency response of the structure under periodic oscillations and its nonlinear modes (namely its backbone curves and deformed shapes in free conservative oscillations). To illustrate and validate this strategy, it is used to solve two 3D deformations test cases of the literature: a cantilever beam and a clamped–clamped beam subjected to one-to-one (1:1) internal resonance between two companion bending modes in the case of a nearly square cross section.

This paper describes the development of a computational model for the rope–sheave contact interaction in reeving systems when the ropes are modeled with an arbitrary Lagrangian–Eulerian approach. This discretization approach has been developed in previous publications as a general and systematic method for the modeling and simulation of reeving systems. However, the rope–sheave contact model was avoided assuming the no-slip contact condition. The contact model developed in this paper introduces specialized ALE-ANCF-cubic rope contact elements that are used to discretize the rope segment winded at the sheave. The contact is modeled using a set of virtual discrete bristles attached to material points in the mid-line of the rope in one end and in contact with the sheave in the other end. Therefore, a second Lagrangian mesh, apart of the ALE mesh used to discretize the rope, is used to define the fixed ends of the bristles. The kinematics and dynamics used to calculate the normal and tangential contact forces are described in detail. The contact model is 3D and can be used to analyze the contact with a sheave groove with arbitrary shape. The tangential contact force model can be used to describe stick and slip contact conditions and, to improve the simulation performance of the model, an LuGre regularization tangential contact force model is used. The rope-sheave contact model is used to analyze the behavior of a simple elevator system. The numerical results show that the static rope-sheave contact interaction agrees well with an analytical solution of the problem. Finally, the same elevator system is analyzed dynamically for a cabin ride of 8 meters with a steady velocity of 1 m/s. Results show that the normal and tangential contact forces during the steady velocity period are not so different from the static solution, but very different from the classical Creep Theory and Firbank’s Theory.

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.