•A stretching hub-beam model for the 1st deployment of IKAROS solar sail is proposed.•A structure-preserving method is used to study the dynamic behaviors of the model.•Coupling dynamic behaviors of ...the flexible stretching hub-beam system are reproduced.
In the 1st stage deployment of the IKAROS solar sail, the flexible beam with comparable mass relative to the mass of the rotor is stretching actively in the axial direction, which brings new challenge in the dynamic analysis for the 1st stage deployment of the IKAROS solar sail. Considering the active axial stretching of the flexible beam, a simplified coupling dynamic model for the 1st stage deployment of the IKAROS solar sail is proposed based on the non-holonomic Hamilton least-action principle firstly. And then, a structure-preserving approach combining the generalized multi-symplectic method and the symplectic Runge-Kutta method is constructed to simulate the evolution of the transverse vibration of the beam as well as the evolution of the rotation of the hub. Finally, the associated numerical results in three stages are reported. From the numerical results, it can be found that the coupling effects between the deformation of the beam, the active stretching of the beam and the rotation of the hub are reflected in the stretching stage. In this stage, the transverse vibration of the beam is enhanced by the stretching effect of the beam, and the increase of the energy of the beam in this stage is derived from the decrease of the rotational energy of the hub. In addition, the structure-preserving properties and the validity of the numerical results are verified by the tiny relative energy dissipation of the flexible stretching hub-beam system in the stretching stage.
•The least-action principle is a better way to define contact resistance.•Conventional formula may result in negative thermal contact resistance.•New method is suitable for calculating the melting ...area in railguns.
This paper considers the resistance to the heat flow between two thick solids with a high contact ratio in a vacuum. Based on the least-action principle, we derive closed-form mathematical expressions for the temperature distribution and non-dimensional thermal contact resistance, both expressed as functions of the radii ratio. Furthermore, the thermal contact resistance is investigated as a function of contact pressure and microhardness. A comparison of the conventional and proposed methods reveals that the proposed method is more accurate for calculating the thermal contact resistance with a high contact ratio. In equipment with high contact pressure, such as electromagnetic launch, we compare armature melting models using different calculation methods for contact resistance. Small and all contact models were established based on the traditional and proposed methods, respectively. The melting morphology of the armature obtained from the all contact model is highly consistent with the experimental results. During the experiment, in areas where the armature did not melt, the small contact model incorrectly calculated the melting of the armature. The all contact model can describe the strong cooling effect of the rail on the armature, preventing the armature from melting. The all contact model obtained higher heat sources, contact thermal conductivity, and contact pressure in the melting region. Under the combined effect of the three factors, a deeper and more concentrated melting morphology was obtained. This morphology is more consistent with the experimental results.
•General nonlinear calibration framework of robot based on POE formula.•Geometric error model of over-constrained robot considering internal deformation.•Explicit interaction between internal ...deformation and geometric errors.•Pose errors decrease by about 95% after calibration in a 5-DOF hybrid robot.
In the over-constrained robot with geometric errors, internal forces would occur and lead to deformation due to redundant constraints and common constraints. In current kinematic calibration approaches, since the deformation, geometric errors and pose errors cannot be described in a unified framework, the error propagation fails to be solved intuitively and generically. In this article, a general calibration framework of over-constrained robots is proposed to unify geometric errors and internal deformation through the least action principle. In the framework, considering the interaction between errors and deformation, the difference map between geometric errors and pose errors is explicitly and analytically revealed. The mapping matrix can degenerate to be consistent with the previous research under non-over-constrained robots. In addition, the error forward propagation method and the error identification algorithm are proposed to solve the error nonlinear propagation and the ill-posed identification equations, respectively. Finally, the calibration simulation and experiment results of a 5-DOF over-constrained hybrid robot show that the proposed method can accurately predict the pose of the end-effector under geometric errors robustly and effectively.
Rotating, sliding or both? Ye, Xin; Lou, Bendong
Applied mathematics letters,
August 2023, 2023-08-00, Volume:
142
Journal Article
Peer reviewed
We consider a bar standing on a frictionless inclined plane, and study the next motion of the bar after being released from some initial states. We show that the bar will slide downward without ...rotating if and only if the bar is perpendicular in the beginning to the inclined plane; otherwise it will slide and rotate at the same time.
This study presents an equivalent test method of long/short pulse width impact based on energy accumulation during the elastoplastic response of the stepped beam. Through finite difference ...calculation, the stepped beam simplified from the sensitive unite of accelerometer used in this work is in the elastic response phase under the uniformly distributed impact load. Comparing the peak energy and the energy cumulative index based on the work of external force, it was found that the peak energy was not sensitive to the impact peak, while the energy cumulative index was affected by both the impact peak and the pulse width. Combined with Least Action Principle, the relationship between the impact peak and the pulse width was fitted to T = C · P 2 , and then the equivalent model of long/short pulse width impact was verified by Hopkinson Bar and live firing tests with the error less than 10%. The selection of overload parameters in the dynamic impact test can get timely guidance, and the engineering process of the simulation equivalent test of extreme overload environment can be further promoted under the equivalent model.
We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. ...These theories have in common that, in addition to the tetrad or metric, they employ a flat connection as additional field variable, but dthey iffer by the presence of absence of torsion and nonmetricity for this independent connection. Besides the different underlying geometric formulation using a tetrad or metric as fundamental field variable, one has different choices to introduce the conditions of vanishing curvature, torsion, and nonmetricity, either by imposing them a priori and correspondingly restricting the variation of the action when the field equations are derived, or by using Lagrange multipliers. Special care must be taken, since these conditions form non-holonomic constraints. Here, we explicitly show that all of the aforementioned approaches are equivalent, and that the same set of field equations is obtained, independently of the choice of the geometric formulation and variation procedure. We further discuss the consequences arising from the diffeomorphism invariance of the gravitational action, and show how they establish relations between the gravitational field equations.
•Propose the concept of irreversibility indicator for transport processes.•Entropy generation cannot measure irreversibility of standalone transport processes.•Entropy generation-based optimization ...may deteriorate process performance instead.•Irreversibility of a transport process should be measured by its energy dissipation.
The entropy generation has been widely used for evaluating irreversibility of transport processes and optimize their performance. However, there still exist challenges against this methodology. This work revisits the irreversibility evaluation in typical transport processes. The irreversibility indicator of transport processes is proposed combining aspects of physical essence and practical application. It is expected to be able to recover the constitutive relation, characterize the evolution direction of process, and optimize standalone transport processes. The entropy generation rate is examined against these conditions, and results show that it fails to meet them. These failures challenge the legitimacy of entropy generation rate in characterizing transport processes’ irreversibility. In contrast, the irreversibility of heat, mass, and momentum diffusion processes can be measured by the entransy dissipation, mass entransy dissipation, and momentum entransy dissipation, respectively. A one-dimensional “volume-to-point” heat conduction and a mass diffusion optimization problem are numerically studied, respectively. Results show that the entransy dissipation-based optimization reduces the average temperature by 3–5 K, giving a better performance than entropy generation optimization, which increases the average temperature up to 17.55 K. In the mass diffusion problem, the mass entransy dissipation-based optimization reduces the average concentration by 3.67%, showing a much better performance than the entropy generation optimization, which yields a 26% increase. Finally, these irreversibility indicators are found to be equivalent to their corresponding energy dissipations.
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