Influence of structural parameters on pitching stability of a vertical shiplift

Abstract

To analyze the pitching stability of the fully balanced hoist vertical shiplift, this paper develops a fluid velocity potential and dynamical model of the vertical shiplift based on an improved energetic exponent method, to study the influence of the primary structural parameters on the pitching stability of an actual shiplift installed in GuoPitan shiplift (GuiZhou province, China). With the linearized potential theory and the undetermined coefficient method, the numerical analytical expression of the velocity potential is obtained by discussing the pitching motion of ship chamber. Applying the Lagrange equation of the second kind to establish a dynamical model of the shiplift having multiple degrees of freedom, the energetic calculated model for ship chamber in respect to the pitching motion is proposed. To accurately analyze the variation of the pitching stability, this paper develops the slope of energetic varied curve, based on the orthogonal polynomial approximation and the subsection averaging method. Also, the influence of the parameters is studied, including the distance of lifting point, the synchronous synchronous shaft stiffness, and the hoist radius, with the optimized design of these three structural parameters: a = 40.0 m, C = 2.0 × 109 N/m, and R = 1.8 m. The changing range of the absolute value of energetic exponent for the distance of lifting points is the largest of the three structural parameters (5.00–12.80), indicating that the distance of lifting points has the most remarkable influence on the pitching stability. Moreover, by the Runge–Kutta algorithm, the response of the angle displacement is analyzed before and after optimization, and then the reliability of results is demonstrated. The four angle displacements at the peak values close to 300 s decrease by 11.11%, 13.33%, 15.91%, and 10.86% respectively after optimization. It reveals that the pitching stability of shiplift is enhanced evidently after optimization.