Multibody System Dynamics最新文献

This paper further develops the Udwadia–Kalaba-approach-based view for the study of the controller design of underactuated systems. A challenge issue of the controller design for such complex systems is to implement an effective control input due to the non-full-rank feature of the control force configuration space. It becomes more difficult especially for the situation in which the control constraints are, in general, incompatible with the modeling constraints. In this paper, the modeling constraints are further divided into the natural and underactuated constraints, which can well capture the proper physical descriptions of underactuated systems. The control input that minimizes the control error and cost function can be derived by matrix operations, and then an additional constraint will be designed fully to address the incompatibility between the modeling and control constraints. This allowed us to develop an approach with precise effectiveness, high stability, and good robustness, which is applicable for various typical cases of complex underactuated systems. Finally, several representative numerical examples, including the fixed-point stabilization and trajectory tracking of a mobile robot, and the trajectory tracking of a hovercraft, are presented to demonstrate the proposed method.

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.