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A quasi-static method to analyze equilibrium path and trajectory deflections for the load of polar crane in nuclear power plant is presented based on three-dimensional analyses. The governing equations of equilibrium path and the compatibility conditions of the rope-pulley system are provided in the method; properties and formulations of the variables involved in these equations are studied in detail. A method to describe general rope-pulley system is given, and a numerical method is derived to solve the common tangent between spatial pulleys, which was conforming to the rope reeving. Moreover, the rope lengths wound by the drum and left in the system are computed, and the transitive relation for rope velocities between two sides of the pulley is derived. Two numerical examples prove that the proposed method is reasonable and valid, and to a large extent, the method is universal and can be applied to general rope-pulley systems.

A systematic method for analyzing the dynamic of the rope-sheave system of polar crane for nuclear power plant is proposed taking physical structure of the system into account based on the virtual power principle in this paper. The dynamical equations of the spatial ropes are established by spline interpolation based on the spatial description parameters, which could be applied to the rope with variable length. For sheaves of different types, the corresponding essential parameters and the virtual power equations are given. Properties and formulations of the variables involved in these equations are studied in detail. In order to improve the solving efficiency, the high-frequency items are filtered out by replacing the instant strain by time- average strain in integral and the degree of freedoms (DOFs) of the spatial ropes are condensed to the boundary nodes of the ropes. Hence, the total virtual power equation in terms of the sheaves’ parameters is obtained. Two numerical examples, including lowering the load and hoisting the load for different types of rope-sheave systems, are given to verify the rationality and feasibility of the method.

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A systematic method to analyze the trajectory of hook block for polar crane in nuclear power plant (NPP) is proposed, in which dynamic equations of the system and the compatibility conditions for drum parameters are presented. Properties and formulations of the variables involved in these equations are studied in detail. A method to describe the rope-pulley system is given and a numerical method is derived to solve the positions and velocities of the common tangents that consistent with the reeving ropes between spatial pulleys. Based on these displacements and velocities, the angular speeds of pulleys are given to solve the difficulty to confirm the rotating directions of pulleys in some rope-pulley systems. A numerical example contrasting the dynamic model with corresponding static model is demonstrated to validate the systematic method. The proposed method is largely universal and can be a reference for designing and analyzing of polar cranes in NPP.