Multibody System Dynamics最新文献

Existing models of vibration transmission through the seated human body are primarily two-dimensional, focusing on the mid-sagittal plane and in-plane excitation. However, these models have limitations when the human body is subjected to vibrations in the mid-coronal plane. Three-dimensional (3D) human models have been primarily developed for impact analysis. Recently, we showed that such a 3D active human model can also predict vibration transmission. However, existing 3D body models suffer from excessive computational time requirements due to their complexity. To effectively analyze motion comfort, this research presents a 3D computationally efficient human model (EHM), running faster than real-time, with scope for real-time vehicle and seat motion control to enhance comfort. The EHM is developed by considering various combinations of body segments and joint degrees of freedom, interacting with multibody (MB) and finite element (FE) seat compliance models. Postural stabilization parameters are estimated using an optimization process based on experimental frequency-dependent gain responses for different postures (erect/slouched) and backrest support (low/high) conditions. The model combines two postural control mechanisms: 1) joint angle control capturing reflexive and intrinsic stabilization for each degree of freedom with PID controllers, including integration to eliminate drift, and 2) head-in-space control minimizing 3D head rotation. Interaction with a compliant seat was modeled using deformable finite elements and multibody contact models. Results showed the importance of modeling both compressive and shear deformation of the seat and the human body. Traditional stick-slip multibody contact failed to reproduce seat-to-human vibration transmission. Combining efficient body modeling principles, innovative postural adaptation techniques, and advanced seat contact strategies, this study lays a robust foundation for predicting and optimizing motion comfort.

The inertial properties of an object (mass, center of gravity, and inertia tensor) are fundamental parameters that considerably affect the accuracy of motion control and simulation results. Therefore, an accurate identification of inertial properties is crucial. All inertial properties of individual links modeled with multiple links cannot be identified via link motion, interjoint torque, or external force data because they are redundant to the multibody dynamics model. The minimum dynamic parameters necessary to represent the multibody dynamics model have been defined and identified. These dynamic parameters are obtained by combining the geometric parameters and inertial properties of the counterpart elements and are called the minimal set of inertial parameters (MSIP). Conventional identification methods use a set of measured link motions and ground reaction forces. MSIP for a sagittal plane can be identified from motions such as the walking motion of human bodies. However, applying these methods to three-dimensional identification is challenging. The primary difficulty lies in the large number of parameters involved, making it challenging to find motions that appropriately excite all MSIP in three dimensions to be identified. In this study, a new method for identifying the MSIP of a multibody system is developed by expanding and applying the identification method based on free vibration measurements, which is the identification method for the inertial properties of a single body. This method shows that MSIP for three dimensions can be identified theoretically and experimentally with high accuracy via considerably simple motion measurements.

This research proposes a novel approach for the residual modeling of inverse dynamics employed to control a real robotic device. Specifically, we use techniques based on linear regression for residual modeling while a nominal model is discovered by physics-informed neural networks such as the Lagrangian Neural Network and the Feedforward Neural Network. We introduce an efficient online learning mechanism for the residual models that utilizes rank-one updates based on the Sherman–Morrison formula. This enables faster adaptation and updates to effects not captured by the neural networks. While the time complexity of updating the model is comparable to other successful learning methods, the method excels in prediction complexity, which depends solely on the model dimension. We propose two online learning strategies: a weighted approach that gradually diminishes the influence of past measurements on the model, and a windowed approach that sharply excludes the oldest data from impacting the model. We explore the relationship between these strategies, offering recommendations for parameter selection and practical application. Special attention is given to optimizing the computation time of the weighted approach when recomputation techniques are implemented, which results in comparable or even lower execution times of the weighted controller than the windowed one. Additionally, we assess other methods, such as the Woodbury identity, QR decomposition, and Cholesky decomposition, which can be implicitly used to update the model. We empirically validate our approach using real data from a 2-degrees-of-freedom flexible manipulator, demonstrating consistent improvements in feedforward controller performance.

This paper proposes a method for cable failure detection in cable-driven parallel robots (CDPRs) with arbitrary architecture, which is based on the estimates of the motor load torques, together with machine learning algorithms. By just exploiting the dynamic model of each actuator in the conditions of no load, an open-loop load torque observer is designed for each motor to estimate the presence of a load coupled through a cable. Since such a load instantaneously goes to zero for the motor with a broken cable, a simple but effective and robust signature of failure can be inferred to provide reliable detection even in the case of various model mismatches. Additionally, the load torque observer is not computationally demanding since just motor measurements are required, thus avoiding any direct measurement (and a dynamic model as well) on the end-effector. The detection of a failure is made through supervised classification algorithms based on artificial intelligence. The training of the machine learning algorithm is based on a “hybrid” approach: the dataset includes several failure cases, which are numerically generated through a system digital twin developed through the multibody system theory, together with measurements of the real system in nonfailing conditions. Different classification algorithms are considered, together with different sets of input variables to be fed to the classifier. Four numerical examples are proposed by showing the method capability in handling both fully actuated and redundantly actuated CDPRs under cable failure, both rigid and flexible cables, and also evaluating the response in the presence of cable slackness.

A digital twin should be and remain an accurate model representation of a physical system throughout its operational life. To this end, we aim to update (physically interpretable) parameters of such a model in an online fashion. Hereto, we employ the inverse mapping parameter updating (IMPU) method that uses an artificial neural network (ANN) to map features, extracted from measurement data, to parameter estimates. This is achieved by training the ANN offline on simulated data, i.e., pairs of known parameter value sets and sets of features extracted from corresponding simulations. Since a plethora of features (and feature types) can be extracted from simulated time domain data, feature selection (FS) strategies are investigated. These strategies employ the mutual information between features and parameters to select an informative subset of features. Hereby, accuracy of the parameters estimated by the ANN is increased and, at the same time, ANN training and inference computation times are decreased. Additionally, Bayesian search-based hyperparameter tuning is employed to enhance performance of the ANNs and to optimize the ANN structure for various FS strategies. Finally, the IMPU method is applied to a high-tech industrial use case of a semi-conductor machine, for which measurements are performed in closed-loop on the controlled physical system. This system is modeled as a nonlinear multibody model in the Simscape multibody environment. It is shown that the model updated using the IMPU method simulates the measured system more accurately than a reference model of which the parameter values have been determined manually.

The intricate dynamic characteristics of a flexible multibody system (FMBS) have a profound influence on the dynamic behavior of the system. In this paper, a topology optimization approach is proposed to confront the challenge of manipulating the eigenfrequencies of an FMBS. Firstly, an accurate dynamic model of an FMBS is established through the perspective of the absolute nodal coordinate formulation (ANCF). Within the mathematical framework, the eigenvalue problem is appropriately extracted, thereby the frequencies and the corresponding mode shapes of an FMBS can be obtained. To firmly verify the dynamic model and the modal solution, an in-depth validation is carried out by comparing the modal analysis of a four-bar mechanism with the results in ABAQUS. Secondly, the modal solution method and the density-based topology optimization method are combined to formulate a generalized topology optimization problem for the eigenfrequencies of an FMBS. The sensitivities for a single eigenfrequency and multiple repeated eigenfrequencies of an FMBS are derived for efficient optimization computation. Finally, the dynamic characteristic topology optimization of a rigid–flexible inflatable structure is conducted to strongly demonstrate the effectiveness and efficiency of the proposed topology optimization approach, which maximizes the first eigenfrequency and the gap between two consecutive eigenfrequencies of the inflatable structure.

This work presents a precise analytical solution of the Reynolds equation governing the lubrication of journal bearings, this solution is valid for either an infinitely long or an infinitely short bearing, based on the side leakage condition applied. The pressure distribution solution is analytically integrated to obtain the forces generated by the lubricant in supporting external dynamic loads in imperfect journal bearings joints. The analytical solution for both the pressure distribution and the forces generated by the lubricant has been corroborated through numerical validation. This solution was implemented on two distinct multibody mechanical systems: one comprising two bodies interconnected via a lubricated imperfect journal bearing, and the other being the conventional crank-slider mechanism with a lubricated imperfect joint. The outcomes are demonstrated for both long and short journal bearings. The results indicate that an increase in side leakage diminishes the pressure at the ends of the joints and amplifies the axial pressure gradient, which, in turn, elevates the eccentricity required to generate sufficient hydrodynamic forces from the lubricant to support the external load. When exposed to identical external dynamic loading, the central axis of a short journal bearing delineates a trajectory that manifests a pronounced lubricant force overshoot. This phenomenon arises from the diminished viscous damping in short journal bearings, attributable to increased side leakage, in contrast to their long journal bearing counterparts.

This paper presents a comparison among different flexibility models of elastic elements to be implemented in multibody simulations of compliant mechanisms. In addition to finite-element analysis and a pseudo-rigid body model, a novel matrix-based approach, called the Displaced Compliance Matrix Method, is proposed as a further flexibility model to take into account geometric nonlinearities. According to the proposed formulation, the representation of the elastic elements is obtained by resorting to the ellipse of elasticity theory, which guarantees the definition of the compliance matrices in diagonal form. The ellipse of elasticity is also implemented to predict the linear response of the compliant mechanism. Multibody simulations are performed on compliant systems with open-loop and closed-loop kinematic chains, subject to different load conditions. Beams with uniform cross-section and initially curved axis are considered as flexible elements. For each flexibility model, accuracies of displacements and rotations, and computational time, are evaluated and compared. The numerical results have been also compared to the data obtained through a set of experimental tests.

The nonlinear dynamics of electric scooters are investigated using a spatial mechanical model. The equations of motion are derived with the help of Kane’s method. Two control algorithms are designed in order to balance the e-scooter in a vertical position at zero forward speed. Hierarchical, linear state feedback controllers with feedback delay are considered. In the case of a delay-free controller, the linear stability properties are analyzed analytically, with the help of the Routh–Hurwitz criteria. The linear stability charts of the delayed controllers are constructed with the help of the D-subdivision method and semi-discretization. The control gains of the controllers are optimized with respect to the robustness against perturbations. The effects of the feedback delay of the controllers, the rake angle, the trail, and the center of gravity of the handlebar on the linear stability are shown. The performance of the control algorithms is verified by means of numerical simulations.

Force estimation in multibody dynamics relies heavily on knowing the system model with a high level of accuracy. However, in complex mechatronic systems, such as robots or mobile machinery, the values of model parameters may be only roughly estimated based on design information, such as CAD data. The errors in model parameters consequently have a direct effect on force estimation accuracy because the estimator compensates the erroneous inertia, friction, and applied forces by changing the value of estimated external force. The objective of this study is to present the workflow of system identification and state/force estimation of an open-loop multibody structure. The system identification utilizes a linear regression identification method used in robotics adapted to the multibody framework. The semirecursive multibody formulation, in particular, is studied as a formulation for both system identification and force estimation. The multibody state/force estimator is constructed using extended Kalman filter. The specific aim of this paper is to demonstrate the utilization of these per se known modeling, identification, and estimation tools to address their current lack of integration as a complete toolchain in virtual sensing of multibody systems. The methodology of the study is tested with both artificial and experimental data of Stäubli TX40 robotic manipulator. In the experimental analysis, an openly available benchmark data set was used. Artificial data were created by running an inverse dynamics analysis with inertia and friction parameters taken from literature. The results show that the multibody inertia and friction parameters can be accurately identified and the identified model can be used to produce decent estimates of external forces. The proposed multibody system identification method itself opens new opportunities in tuning the multibody models used in product development. Moreover, effective use of system identification together with state estimation helps to build more accurate estimators. When the system model is accurately identified, the capability of state estimator to observe unknown inputs, such as external forces, is significantly enhanced.