Nonlinear Similarity Design Of Slender Telescopic Booms

With the increasing carrying capacity of the telescopic cranes in recent years and the rising of the hoisting height,their booms have increasingly large slenderness ratios.This structural form makes the approximate displacement analysis method commonly used in practical engineering produce larger errors and is no longer applicable.In addition,under the actual working conditions of the telescopic boom,the lateral force and the axial force received by the arm end are staggered and affect each other.Therefore,the large-displacement and large-deformation theory is needed to analyze the telescopic boom.At present,the cycle of domestic companies digesting foreign advanced technologies has a long period of time,and the input of human and material resources is large and inefficient.So this paper applies the similar theory to the design process of crane telescopic boom.Aiming at the problem that the classical similarity theory has theoretical imperfections in the non-linear field and leads to limited applications,the design knowledge of existing telescopic boom products can be used to rapidly design new high-end technologies and enhance the benchmarking products after optimization.The inheritance of the benchmark products after optimization should be strengthened to achieve the goal of rapid product design and serialization.The main research content is as follows:(1)This article starts from the overall structure of the research object and explains the structure,working principle and bearing force characteristics of the telescopic boom.According to the characteristics of the load under the operating conditions of the jib,the form of the action and the degree of influence on the telescopic arm,the force model of the telescopic arm is established.The typical nonlinear characteristics of the telescopic boom are discussed.Based on the theory of large displacement,the description is given and the transformation method of global coordinates and local coordinates is introduced.The basic equations of large displacement theory are deduced.(2)Based on the theory of large displacement and the assumption of small deformation,the general expression of the equation of motion of the unit is deduced.Using the principle of virtual work,the equations of motion of the unit have been rewritten in the following coordinate system.The Euler Bernoulli beam theory was used to establish the beam element.The first-order stiffness matrix was deduced according to the general deflection law.The interpolation function was used to obtain the shape function of the displacement field,and then the pure displacement theory was used to rewrite the axial displacement relationship to derive the axial displacement under large displacement conditions.The additional stiffness resulting from the displacement gives the corrected stiffness matrix and the balance equation is derived on the basis of this.The Simulink simulation model was compiled,and the calculation results of the nonlinear method and the classical method were compared through the example calculation of the typical boom and working conditions.(3)The article describes the initial single-valued conditions,substituting the balance differential equations of the telescoping boom into the equation analysis method,deriving the corresponding similarity constraint equations,and defining the invariant properties of the similarity criteria obtained by the partial dimensional analysis method to supplement the part similar relations.Then the similarity test program is compiled and the similarity criterion is used to test and summarize the local similarity relationship.The nonlinear displacement similarity ratio formula is constructed as the calculation basis of similar design of the telescopic boom.(4)Four sets of box arm models were designed and manufactured.Several experiments were performed with different elevation angles and different loads.The actual elevation angles were recorded under the working conditions of the booms.The displacements of the characteristic points were measured by distance sensors mounted on specific positions on the boom.The displacement similarity ratio prediction was carried out based on the similar relationship derived from the research and the experimental model size data.The calculated results were compared with the experimental measurement results,and the theoretical errors that may exist in the similar design methods were analyzed.This paper combines non-linear problems with similarity theory and derives nonlinear similarity relationships to guide the rapid and serialized design of telescopic arms.It has high theoretical significance and application value.