The dynamic analysis of load motion during the interaction of wind pressure
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MODELLING AND ANALYSIS OF MECHANICAL SYSTEMS DYNAMICS
The dynamic analysis of load motion during the interaction of wind pressure Dawid Cekus
. Paweł Kwiaton´
. Tomasz Geisler
Received: 20 February 2020 / Accepted: 20 August 2020 The Author(s) 2020
Abstract This work presents the analysis of the load motion during the interaction of wind pressure. The load was treated as a rigid body, and the rope system model as a non-deformed. The influence of effective area of wind pressure on load motion was considered. The theoretical model of load motion was presented, which may be an universal approach for transporting machines equipped with a rope-lifting system. To define the orientation of the movable Cartesian coordinate system related to the load, Bryant angles were used. An algorithm and computational program were developed to allow for analysis of dynamic phenomena. The initial problem was solved with the use of the ode45 calculation procedure in the Matlab software on the basis of the Runge–Kutta 4th Order Method. The obtained results were verified with the experimental ones achieved in the wind tunnel and Tracker program. Numerical calculations using commercial software SolidWorks were also presented. In the experiment, the spatial motion of the load was analysed. Experimental tests were carried out for gust
D. Cekus P. Kwiaton´ (&) T. Geisler Department of Mechanics and Machine Design Fundamentals, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa, Poland e-mail: [email protected] D. Cekus e-mail: [email protected] T. Geisler e-mail: [email protected]
of wind and constant temperature and humidity. In addition, the paper presents the application of the proposed method for a load carried by a rotary crane. After taking into account the control functions resulting from the nature of the work of any machine, the formulated model can be a full description of the carried load motion taking into account external forces. Keywords Wind pressure Load Experimental analysis Dynamics List of symbols m Mass of load (kg) q Density (kg/m3 ) W Bryant angle (X axis) # Bryant angle (Y axis) U Bryant angle (Z axis) a Length of the load (m) b Width of the load (m) c Height of the load (m) g Gravitational acceleration (m/s2 ) S Effective area of wind pressure (m2 ) C Load suspension point (rotary crane) G Gravity force (N) H Rotational momentum vector of the load (N m) r, v Rope length (m) V w Wind speed (m/s) C D Coefficient of aerodynamic resistance ac Total translational acceleration vector (m/s2 )
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Meccanica
Fn Mc Fr Fw xc c Jc
Resultant vector of all acting forces (N) Momentum vector of all acting forces (N m) Total vector of the tension in the rope (N) Wind force vector (N) Angular velocity vector (rad/s) Angular acceleration vector (rad/s2 ) Matrix of inertia momentum (kg m2 )
1 Introduction The impact of external forces, for example, the wind pressure, is essential during the process of load transfer and positioning. Dyn
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