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2024 | OriginalPaper | Chapter

The Influence of the Load Modelling Methods on Dynamics of a Mobile Crane

Authors : Andrzej Urbaś, Krzysztof Augustynek, Vasyl Martsenyuk

Published in: Perspectives in Dynamical Systems I — Applications

Publisher: Springer International Publishing

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Abstract

A mathematical model for the dynamics analysis of a mobile crane is presented in the paper. The proposed model of a mobile crane is in the form of a tree structure of a kinematic chain with closed-loop subchains. The carried load is treated in the two cases, as a lumped mass and a rigid body. The formulated model takes also into account the flexibility of wheels, outriggers, drives and rope(s). Dry friction in joints is also considered. The formalism of joint coordinates and homogeneous transformation matrices are used to describe the kinematics of the crane. The equations of motion are derived using the Lagrange equations of the second kind. These equations are supplemented by the Lagrange multipliers and constraint equations formulated for each cut-joint.

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previous chapter Nonlinear Dynamic Vibration Absorber Applied in a High-Speed Elevator System
next chapter A Nonlinear Analysis of an Aeroelastic Three Degrees of Freedom Model
Literature
1.
Urbaś, A., Augustynek, K.: Modelling of the dynamics of grab cranes with a complex kinematic structure, taking into account the links’ flexibility and advanced friction models. Proceedings of the 13th World Congress on Computational Mechanics (WCCM XIII) and 2nd Pan American Congress on Computational Mechanics (PANACM II), New York, USA (2018).
2.
Urbaś, A., Augustynek, K.: Mathematical model of a crane with taking into account friction phenomena in actuators. Multibody Dynamics 2019: Proceedings of the 9th Eccomas Thematic Conference on Multibody Dynamics. Springer International Publishing, 299–306 (2020).
3.
Kacalak, W., Budniak, Z., Majewski, M: Stability assessment as a criterion of stabilization of the movement trajectory of mobile crane working elements. International Journal of Applied Mechanics and Engineering 23(1), 65–77 (2018).CrossRef
4.
Cekus, D., Kwiatoń, P.: Effect of the rope system deformation on the working cycle of the mobile crane during interaction of wind pressure. Mechanism and Machine 153:104011 (2020).CrossRef
5.
Åström, K.J., Canudas-de-Witt, C.: Revisiting the LuGre model. IEEE Control Systems Magazine, Institute of Electrical and Electronics Magazine, 28(6), 101–114 (2008)CrossRef
6.
Wittbrodt, E., Szczotka, M., Maczyński, A., Wojciech, S.: Rigid Finite Element Method in Analysis of Dynamics of Offshore Structures. Ocean Engineering & Oceanography, Springer, Berlin-Heidelberg (2013)
Metadata
Title
The Influence of the Load Modelling Methods on Dynamics of a Mobile Crane
Authors
Andrzej Urbaś
Krzysztof Augustynek
Vasyl Martsenyuk
Copyright Year
2024
Book
Perspectives in Dynamical Systems I — Applications

Print ISBN: 978-3-031-56491-8

Electronic ISBN: 978-3-031-56492-5

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-56492-5_41

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