Abstract
The present paper addresses the derivation of a 3 DOF mathematical model of a spherical pendulum attached to a crane boom tip for uniform slewing motion of the crane. The governing nonlinear DAE-based system for crane boom uniform slewing has been proposed, numerically solved, and experimentally verified. The proposed nonlinear and linearized models have been derived with an introduction of Cartesian coordinates. The linearized model with small angle assumption has an analytical solution. The relative and absolute payload trajectories have been derived. The amplitudes of load oscillations, which depend on computed initial conditions, have been estimated. The dependence of natural frequencies on the transport inertia forces and gravity forces has been computed. The conservative system, which contains first time derivatives of coordinates without oscillation damping, has been derived. The dynamic analogy between crane boom-driven payload swaying motion and Foucault’s pendulum motion has been grounded and outlined. For a small swaying angle, good agreement between theoretical and averaged experimental results was obtained.
Highlights
Payload swaying dynamics during crane boom slewing is within the objectives and scope of many academic and industrial research programs in the fields of mechanical, electrical, and control engineering, and theoretical mechanics
Mathematical descriptions of relative and absolute payload swaying motion during crane boom rotation require the introduction of design models for a spherical pendulum with a suspension point following a horizontal circular trajectory
The motion of Foucault’s pendulum is shown in Figure 7, where x2y2z2 is the heliocentric inertial reference frame, x1y1z1 is the geocentric noninertial reference frame, and xyz is a noninertial reference frame, located at the geographic latitude y1z; Astz is a local vertical; BD is the radius of the circle of the pinning point; BM is the cable length; and ωe is the angular velocity of the Earth diurnal rotation
Summary
Payload swaying dynamics during crane boom slewing is within the objectives and scope of many academic and industrial research programs in the fields of mechanical, electrical, and control engineering, and theoretical mechanics. Today payload swaying problems attract the great attention of such applied mathematicians and mechanical engineers as Abdel-Rahman et al [1,2,3], Adamiec-Wojcik et al [4], Al-mousa et al [5], Allan and Townsend [6], Aston [7], Betsch et al [8], Blackburn et al [9, 10], Blajer et al [11,12,13,14,15,16,17], Cha et al [18], Chin et al [19], Ellermann et al [20], Erneux and Kalmar-Nagy [21, 22], Ghigliazza and Holmes [23], Glossiotis and Antoniadis [24], Grigorov and Mitrev [25], Gusev and Vinogradov [26], Hong and Ngo [27], Hoon et al [28], Ibrahim [29], Jerman et al [30,31,32,33], Ju et al [34], Kłosinski [35], Krukowski et al [36, 37], Lenci et al [38], Leung and Kuang [39], Loveykin et al [40], Maleki et al [41], Maczynski et al [42,43,44], Marinovicet al. Palis [58], Perig et al [59], Posiadała et al [60], Ren et al [61], Safarzadeh et al [62], Sakawa et al [63], Sawodny et al [64], Spathopoulos et al [65], Schaub [66], Solarz and Tora [67], Uchiyama et al [68], Urbas [69], and others
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