Research On The Stability And Geometric Nonlinearity Of The Crane Main And Jib Structure

In order to further increase the lifting height during crane operation,the truck crane is equipped with a fixed jib on the basis of the telescopic main boom.The introduction of the fixed jib effectively increases the lifting height of the truck crane,but also increases the slenderness ratio of the main jib structure composed of the telescopic main boom and the fixed jib.As a result,the ability to resist instability and deformation of the main and jib structure is weakened.At this stage,the research on the stability and geometric nonlinearity of the telescopic boom structure is relatively mature.However,there are few theoretical research results on the main jib structure composed of the telescopic main boom and the variable cross-section lattice fixed jib,and not directly guide engineering actual design.Therefore,this article takes the main jib structure composed of an n-section telescopic main boom and a lattice fixed jib with quadratic changes in the moment of inertia along the section as the research object,and conducts in-depth research on its stability and geometric nonlinearity.The main research contents and methods are as follows:(1)First,based on the vertical and horizontal bending theory,a differential equation for the deflection of the main jib structure with an n-section telescopic main boom and a fixed jib is established.The instability characteristic equation is derived from the boundary conditions,and the out-of-plane stability of the main jib structure composed of a telescopic main boom and a fixed jib is analyzed.Secondly,the MATLAB software is used to numerically solve the instability characteristic equation of the main and jib structure,and the finite element software ANSYS is used to analyze the eigenvalue buckling of the main and jib structure.Finally,the influence of the jib length and taper coefficient of the fixed jib on the structural stability of the main jib is discussed.The analysis result proves that the deduced instability characteristic equation is correct and can be applied to the stability analysis of main and auxiliary arm structures.(2)Based on the second-order theory,establish the mechanical model of the n-section telescopic main boom and the fixed jib under the action of axial force,lateral force and bending moment.The geometric nonlinearity of the main and jib structure is studied,and the deflection expression of the main and jib structure in the form of recursion is obtained.With the help of MATLAB software,the theoretically derived deflection expressions are solved,and two main and jib structure simulation analysis models are established with ANSYS.The theoretical formula solution and ANSYS simulation results are compared and analyzed.The deflection values of the main and jib structures of different jibs are analyzed by calculation examples,the influence of the web member parameters in the fixed jib on the accuracy of the non-linear deflection expression of the main jib structure is discussed,difference between the linear analysis method and the geometric nonlinear analysis method to calculate the deflection value of the main and jib structure is compared and analyzed.The analysis results show that the deflection expression of the main and jib structure taking into account the second-order effect of axial force in this paper is correct,that can be used for the deflection calculation of the main and jib structure of the actual structure,it also proved the necessity of calculating the non-linear deflection of the main and jib structure.Parameters such as the cross-sectional area of the web members and the arrangement angle of the web members have a certain effect on the non-linear deflection value of the main and jib structure,but the effect is small.(3)Provides a convenient and practical approximate formula for the stability and geometric linear analysis of the main and jib structure.Based on the energy method,derives the approximate formula for the stability of the main and jib structure.Based on the deflection amplification factor method,the nonlinear deflection approximate formula of the main and jib structure is derived.Through the analysis of calculation examples,the calculation results of the stability approximation formula and the geometric nonlinear approximation formula are compared with the simulation calculation results of ANSYS.The validity and practicability of the approximate formula are verified.(4)The analysis results of the structural stability and geometric nonlinear problems of the main jib consisting of a telescopic main boom and a variable cross-section lattice fixed jib show that,the instability characteristic equation and nonlinear deflection expression of the main and jib structure deduced in this paper have high accuracy.It can provide a theoretical basis for the revision of the crane design code GB/T3811-2008,and also provides necessary theoretical support for the design and calculation of the main and jib structure of the truck crane.