Lumped Parameter Models for Numerical Simulation of the Dynamic Response of Hoisting Appliances Giovanni Incerti, Luigi Solazzi, Candida Petrogalli Abstract—This paper describes three lumped parameters models for the study of the dynamic behavior of a boom crane. The models here proposed allows to evaluate the fluctuations of the load arising from the rope and structure elasticity and from the type of the motion command imposed by the winch. A calculation software was developed in order to determine the actual acceleration of the lifted mass and the dynamic overload during the lifting phase. Some application examples are presented, with the aim of showing the correlation between the magnitude of the stress and the type of the employed motion command. Keywords—Crane, dynamic model, overloading condition, vibration. I. I NTRODUCTION A S is known, the application of a load to a hoisting device generates vibrations due to the rope and structure elasticity [1], [2], [3], [4], [5]. This aspect is of a general nature and is independent from the type of structure and from the mode of application of the load; the dynamic effect, instead, is strongly influenced by these factors. For hoisting devices the phenomenon is particularly important as it generates dynamic actions whose wrong assessment, forgetfulness or omission could compromise the structure both as regards the maximum stress, the instability, the fatigue and the overall balance of the structure itself. Large literature on the subject has been prepared by many research groups [6], [7], [8], [9] as the problem, although overlooked at the design stage in the past, now plays a progressively more important role. In this paper, we deepens the study through the use of computational models with lumped parameters, that allow the designer to simulate the dynamic effects in function of the parameters of the hoisting system (mass, stiffness, natural frequencies, damping, etc.) and in functions of the motion law imposed by the winch to the load. These phenomena may be applied to other type of hosting machine like elevating work platform and it is independent of the material used to made the hoisting machine [10], [11]. The following paragraphs describe the mathematical models (with one or two degrees of freedom) and the resolution methods (analytical and numerical) of the motion equations generated by these models. Some practical examples of application of these models are finally shown, using as a reference a particular type of crane, which, depending on the position of the load and the lifting height, a) b) c) M m s k s c α R s x l x M m r k r c α R 0 = s x l x M m r k s k r c s c α R s x l x presents different dynamic behaviors as regards the stiffness of the structure and regards the stiffness of the rope. II. DYNAMIC MODELS To analyze the dynamics of a crane during the hoisting phase the designer can use one of the three models shown in Fig. 1. The choice of model depends on the stiffness of the components; in fact, if the stiffness of the ropes k r is much higher than the stiffness of the structure k s , the one degree of freedom (1 DOF) model in Fig. 1 (a) can be used; instead if the stiffness of the structure is large compared to the stiffness of the ropes, it is convenient to use the scheme in Fig. 1 (b), which considers the structure rigidly connected to the ground and the load elastically suspended. Finally, if both stiffnesses have the same order of magnitude, it is necessary to use the two degrees of freedom model (2 DOF) shown in Fig. 1 (c), where both the load and the structure are elastically suspended. In the following subsections these mathematical models are analyzed in detail, with particular reference to the deduction of the motion equations and to the solution techniques. A complete list of symbols used in Fig. 1 is shown in Table I. A. One DOF model with rigid rope and elastic structure For this type of model (Fig. 1 (a)) we use as free coordinate the displacement x s of the structure; since the rotation α of the drum is known, the load displacement x l is given by: x l = x s + Rα (1) Fig. 1. Lumped parameter models of the crane G. Incerti, L. Solazzi and C. Petrogalli are with the Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy (e-mail: candida.petrogalli@unibs.it). World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering Vol:9, No:11, 2015 1900 International Scholarly and Scientific Research & Innovation 9(11) 2015 ISNI:0000000091950263 Open Science Index, Mechanical and Mechatronics Engineering Vol:9, No:11, 2015 publications.waset.org/10002646/pdf