Comparison of the Absolute Nodal Coordinate and Geometrically Exact Formulations for Beams

The modeling of flexibility in multibody systems has received increase scrutiny in recent years. The use of finite element techniques is becoming more prevalent, although the formulation of structural elements must be modified to accommodate the large displacements and rotations that characterize multibody systems. Two formulations have emerged that have the potential of handling all the complexities found in these systems: the absolute nodal coordinate formulation and the geometrically exact formulation. Both approaches have been used to formulate naturally curved and twisted beams, plate, and shells. After a brief review of the two formulations, this paper presents a detailed comparison between these two approaches; a simple planar beam problem is examined using both kinematic and static solution procedures. In the kinematic solution, the exact nodal displacements are prescribed and the predicted displacement and strain fields inside the element are compared for the two methods. The accuracies of the predicted strain fields are found to differ: The predictions of the geometrically exact formulation are more accurate than those of the absolute nodal coordinate formulation. For the static solution, the principle of virtual work is used to determine the solution of the problem. For the geometrically exact formulation, the predictions of the static solution are more accurate than those obtained from the kinematic solution; in contrast, the same order of accuracy is obtained for the two solution procedures when using the absolute nodal coordinate formulation. It appears that the kinematic description of structural problems offered by the absolute nodal coordinate formulation leads to inherently lower accuracy predictions than those provided by the geometrically exact formulation. These observations provide a rational for explaining why the absolute nodal coordinate formulation computationally intensive

State estimation in a hydraulically actuated log crane using Unscented Kalman Filter

Abstract Multibody system dynamics approaches together with state estimation methods can reduce the need for a large number of sensors, especially in the digital twin of working mobile machinery. To demonstrate this, a hydraulically actuated machine was modeled using the double-step semi-recursive multibody formulation and lumped fluid theory in terms of system independent states. Next, because of the high non-linearity of the modeled system and with respect to the reported performance degradation of the Extended Kalman Filters (EKF), which are mostly related to the linearization procedure of this filter, the Unscented Kalman Filter (UKF) was implemented to achieve high accuracy and performance. The methodology of the proposed approaches was applied to a mobile log crane model PATU 655. The implementation of the proposed estimation algorithms is demonstrated with three different multibody based simulation models: the synthetic real system producing the artificial measurements, the simulation model, and the estimation model. Encoders and pressure sensors, installed on the synthetic real system, provided synthetic sensor measurement data. To mimic real-world conditions, the estimation and simulation models used in the processing of the state estimation algorithm were assumed to have errors in the initial conditions and force model. The proposed UKF was applied to the estimation model with the synthetic sensor measurement data. The minimum percent normalized root mean square errors in the associated measured and unmeasured states of case example were 0.11% and 1.86%, respectively. The UKF using the multibody system dynamics formulations is able to estimate the case example states despite 15% and 60% errors in mass and inertial properties of bodies and Payload, respectively, confirming the accuracy and performance of the algorithm

Comparison of numerical and computational aspects between two constraint-based contact methods in the description of wheel/rail contacts

Abstract The numerical and computation aspects of the Knife-edge Equivalent Contact (KEC) constraint and lookup table (LUT) methods are compared in this paper. The LUT method implementation uses a penetration-based elastic contact model for the flange and a constraint-based formulation at the wheel tread. For the KEC method, where an infinitely narrow rail contacts an equivalent wheel, regularization of the tread-flange transition is adopted to simultaneously account for tread and flange contacts using constraints. A comparison between the two methods is carried out using well-known numerical integrators to show the applicability and limitations of both methods. Two fixed-step-size integrators, the explicit Runge–Kutta (RK4) and the predictor–corrector Adam–Bashforth–Moulton (ABM) methods, and two variable-step-size Matlab built-in function integrators, the explicit ode45 and implicit ode15s, were applied to get the numerical solutions to the dynamic problems and study the relative numerical performance of the two contact description methods. To complete the railway vehicle model, both contact methods were implemented for the multibody model of a benchmark railway vehicle (the Manchester wagon 1). Numerical results were obtained for different railway tracks with and without irregularities. Profiles of the S1002 wheel and LB-140-Area rail, which demonstrate the two-point contact phenomenon, were considered. Both methods were implemented in Matlab and validated against commercial simulation software. The kinematic results for both approaches show good agreement, but the KEC method was up to 20% more efficient than the LUT method regardless of integrator used

Experimental investigation into the state estimation of a forestry crane using the unscented Kalman filter and a multiphysics model

Abstract To increase productivity, reduce energy use, and minimize unplanned maintenance, manufacturers of heavy machinery must instrument their products. As explained in the literature, state and parameter estimators can successfully integrate machine sensor signals with simulation results from computational models. This leads to comparable or improved observations even when fewer sensors are being used. This study introduces a state observer based on the unscented Kalman filter for the coupled mechanical and hydraulic systems. The resulting reality-driven simulation procedure is applied to a hydraulically actuated forestry crane that has been instrumented to provide the necessary sensor information. This study analyzes the performance of state observer in four different scenarios and recommends an optimal sensor configuration for the application. Estimation accuracy of observer in the simulation of the mechanics and hydraulics components is evaluated using the percent normalized root mean square error (PN-RMSE) and 95% confidence interval

Physics-based digital twins merging with machines:cases of mobile log crane and rotating machine

Abstract Real-world products and physics-based simulations are becoming interconnected. In particular, real-time capable dynamic simulation has made it possible for simulation models to run in parallel and simultaneously with operating machinery. This capability combined with state observer techniques such as Kalman filtering have enabled the synchronization between simulation and the real world. State estimator techniques can be applied to estimate unmeasured quantities, also referred as virtual sensing, or to enhance the quality of measured signals. Although synchronized models could be used in a number of ways, value creation and business model development are currently defining the most practical and beneficial use cases from a business perspective. The research reported here reveals the communication and collaboration methods that lead to economically relevant technology solutions. Two case examples are given that demonstrate the proposed methodology. The work benefited from the broad perspective of researchers from different backgrounds and the joint effort to drive the technology development towards business relevant cases

Replaying evolutionary transitions from the dental fossil record

The evolutionary relationships of extinct species are ascertained primarily through the analysis of morphological characters. Character inter-dependencies can have a substantial effect on evolutionary interpretations, but the developmental underpinnings of character inter-dependence remain obscure because experiments frequently do not provide detailed resolution of morphological characters. Here we show experimentally and computationally how gradual modification of development differentially affects characters in the mouse dentition. We found that intermediate phenotypes could be produced by gradually adding ectodysplasin A (EDA) protein in culture to tooth explants carrying a null mutation in the tooth-patterning gene Eda. By identifying development-based character interdependencies, we show how to predict morphological patterns of teeth among mammalian species. Finally, in vivo inhibition of sonic hedgehog signalling in Eda null teeth enabled us to reproduce characters deep in the rodent ancestry. Taken together, evolutionarily informative transitions can be experimentally reproduced, thereby providing development-based expectations for character state transitions used in evolutionary studies