Dynamic Analysis Of Rope-pulley System Of Hoisting Mechanism For Polar Crane

During construction and operation of a nuclear power plant(NPP),a polar crane is an important lifting device used inside a reactor.It serves to lift and handle objects through its hoisting mechanisms during installation and maintenance of mechanical equipments and fuel replacement in a reactor.Since its operation site and the objects to be lifted are special,a polar crane is required to have a very high positioning accuracy.Rope-pulley system is an important part of a hoisting mechanism.The layout of rope-pulley and the pattern of rope winding are critical factors affecting the positioning accuracy of a polar crane.There have been research achievements in positioning accuracy of general crane types.However,existing research has simplified rope-pulley systems excessively or only considered the kinematic perspective,and the existing solutions for rope-pulley systems are not stable and mature enough to ensure high positioning accuracy for polar cranes.Therefore,this paper looks at dynamic modeling and simulation of the rope-pulley systems in a polar crane’s hoisting mechanisms in a systematic manner,based on the characteristics of the systems.First,this paper analyzes the common problems in dynamics of rope-pulley systems.In conventional methods,a rope’s motion is usually described by material description,which assumes that nodes of rope elements are bound with the material points on the rope and describes the moving rope’s deformation and forces acting on it by tracking the motion of these material points.There are intractable difficulties in solving a rope-pulley system:how to enable rope elements to accurately describe rope’s deformation into a straight segment and deformation into a circular segment at the same time,and how to describe the dynamic contact between rope and pulley.To solve these,this paper presents a moving rope element whose nodes are not bound with material points on the rope,thus avoiding the assumption made in conventional methods and allowing the rope to be divided into elements based on the its spatial position.Each rope element can be given a relatively large length in order to reduce the degrees of freedom of the system.Adding several intermediate nodes to the middle of each element can improve accuracy.Compared to conventional rope elements,this rope element is not only able to deal with shape constraints and describe the motion of a rope-pulley system in more detail,but also greatly simplifies the analysis process for the hoisting mechanisms of a polar crane.In light of the structural characteristics of the components coupled with the rope in a polar crane’s hoisting mechanism and their relative positions,dynamic models are constructed for components such as pulley,winch,and block frame based on theories relevant to dynamics of multibody system.First,pulleys(fixed,movable,and guide pulleys)are modeled independently,which facilitates description of rope parameters with pulley parameters.The pulley elements constructed not only take into account the type and structural characteristics of pulleys,but also consider details such as changes at the entrance and exit points of rope on a pulley and the swing angle.For the circular rope segment in contact with a pulley,the concepts of material velocity and spatial velocity are employed to describe the constraints between them as follows:the material velocity of the circular rope segment equals the material velocity of corresponding points on the pulley.Then the dynamic equation for the circular rope segment can be created from pulley parameters.Later,the kinematic parameters of rope’s entrance point on winch are determined based on the role of winch in a hoisting mechanism,with the winch’s position relative to rope being considered.Given the characteristics of pulley block in a hoisting mechanism,block frame and different types of pulleys are modeled separately so that the dynamic model for block frame is not limited by the number of pulleys,making pulley block modeling simpler and more flexible.An urgent issue arises in dynamic modeling for the rope,pulley,and winch in a rope-pulley system:how to relate rope to pulley and winch,or essentially to solve the problem of boundary conditions for the dynamic contact between pulley and rope and between winch and rope.There is currently no referential results about how to address this issue.Therefore,based on the relationship between material velocity and spatial velocity,boundary conditions for the dynamic contact between pulley and rope and between winch and rope are proposed.The condition that there is no relative sliding between rope and pulley in the tangential direction can be described as follows:the components of the rope’s material velocity along the pulley surface at the entrance and exit points are equal to the tangential components of the pulley’s velocity at corresponding points on the pulley surface.For a smooth-faced winch,the condition that there is no relative sliding between rope and winch can be described as follows:the rope and the smooth-faced winch have equal material velocity at the contact points between them.For a helically grooved winch,the condition that there is no relative sliding between rope and helical groove can be described as follows:the rope and the helically grooved winch have equal material velocity at their contact points along the spiral helical groove.These boundary conditions connect different components of the rope-pulley system into an organic whole,which addresses the inefficiency of traditional contact force models.They not only provide a solid support for developing a stable,mature solution to dealing with rope-pulley systems,but also can extend the applications of rope-pulley systems.Furthermore,dynamics simulation software for the rope-pulley system in a polar crane’s hoisting mechanism was written based on the proposed approach.This simulation software was applied to dynamic analysis of two typical hoisting mechanisms in polar cranes.The numerical results were then compared with theoretical values and the results obtained with simulation software ADAMS.The comparison verifies the validity of the dynamic models constructed for moving rope,pulley,winch and block frame,as well as the boundary conditions for the ropepulley system proposed in this paper.The proposed methodology not only provides a dynamics approach for analyzing the trajectory of lifting point in a polar crane,but also offers certain reference value for the operation and control of the hoisting mechanisms.