Study On Longitudinal Vibration And Vibration Reduction Of Lifting Pipe In Deep-sea Mining

As an important part of connecting the middle-module and mining vessel,lifting pipe bears huge environmental load.The top of the lifting pipe is connected with the mining vessel,and it heaves with the mining vessel.Because it is affected by the load of ocean current and wave,it vibrates in the longitudinal direction.Longitudinal vibration of lifting pipe has an important impact on the safety and reliability of deep-sea mining system.Therefore,it is necessary to determine the longitudinal vibration of the lifting pipe,study a simple and easy-to-achieve vibration reduction scheme.Firstly,Stokes wave is selected to describe the wave,Morrison formula is determined to calculate the wave load,the expression of ocean current and the calculation formula of the load on the lifting pipe are determined,the formulas of gravity and buoyancy of the pipeline are deduced,and the materials and parameters of each part of the deep-sea mining system are determined.The static and dynamic analysis of the lifting pipe is carried out by using the finite element method.According to the stress condition of the lifting pipe,the finite element model of the lifting pipe is set up as a beam model,and the overall stiffness matrix is established.The axial and radial equivalent loads of the lifting pipe are deduced by using the principle of virtual work.The overall load matrix of the lifting pipe is established.And The boundary conditions are determined.The static analysis of the lifting pipe are carried out.The variation of the axial force,displacement,stress,bending moment and bending stress with the position of the lifting pipe with equal diameter and stepped shape are obtained.The results show that the distribution of the axial displacement of the hoist pipe with equal diameter increases gradually from top to bottom,the distribution of the axial force is maximum at the top,minimum at the bottom and equal at the middle.The distribution law of the axial stress of the hoist pipe with equal diameter is the same as that of the axial force.The distribution of the transverse displacement increases gradually from the top to the bottom.The distributions of bending moment are as follows:the maximum bending moment is at the top,and the bending moment at other locations is much smaller than that at the top.The distribution of the axial displacement of the stepped lifting pipe is gradually increasing from top to bottom.The distribution of axial force is that the maximum axial force is at the top and the minimum is at the bottom.The axial force changes with the position in a step-like manner.The distribution rule the axial stress is that the maximum stress is at the top,the minimum stress is at the lowest,the change of the axial stress with the position is stepped.The distribution of lateral migration increases gradually from the top to the bottom.and the overall distribution trend of bending moment of stepped lifting pipe is similar to that of equal diameter lifting pipe.The results show that the maximum axial stress and bending normal stress of the stepped lifting pipe are less than those of the same diameter lifting pipe,and the stress of the stepped lifting pipe is better than that of the same diameter lifting pipe.The integral damping matrix and integral mass matrix are established,and the modal analysis of the lifting pipe is carried out by using subspace iteration method,and the natural frequencies and natural formations of the lifting pipe are obtained.The dynamic equation of the lifting pipe is established,and the variation trend of the longitudinal vibration of the lifting pipe with time is studied by using Newmark method and ABAQUS software simulation.The results show that the vibration of the lifting pipe can be seen as a simple harmonic motion.Longitudinal vibration of lifting pipe is not synchronized,and the time to reach the vibration amplitude from the top to the bottom of the lifting pipe is gradually delayed,and the vibration amplitude is reached at the bottom at the latest.The vibration amplitude of the lifting pipe decreases gradually from top to bottom.The maximum amplitude appears at the top of the lifting pipe and the minimum amplitude appears at the bottom of the lifting pipe.Aiming at the problem of longitudinal vibration reduction of lifting pipe,the dynamic vibration absorber is used to reduce the longitudinal vibration of lifting pipe.The mechanical model of the dynamic vibration absorber is established.The dynamic vibration absorber is set on the pump of lifting pipe and simulated by software.The vibration curve of the lifting pipe with additional dynamic vibration absorber is obtained.The results show that the longitudinal vibration of the lifting pipe with additional dynamic vibration absorber has the following characteristics:the vibration curve of the lifting pipe with additional dynamic vibration absorber shows a simple harmonic curve with time.The vibration of the lifting pipe with DVA decreases gradually from top to bottom,the maximum vibration position appears at the top,and the minimum vibration position appears at the bottom of the lifting pipe.The vibration of each position of the lifting pipe with DVA is not synchronous.From the top to the bottom,the response time of the lifting pipe begins to delay,and the lowest end starts to vibrate at the latest compared with other locations.The longitudinal vibration of the lifting pipe is compared with that without additional dynamic vibration absorber.The results show that the dynamic vibration absorber can effectively reduce the longitudinal vibration of the lifting pipe.