Dynamic Modeling And Analyses Of An Axially Moving And Spinning Beam Based On The Variable-length Elements

Axially moving and spinning(AMS)beam,which means a beam that is axially moving and spinning simultaneously,is widely used in certain fields of engineering,such as automatic drilling sampling mechanism in the Lunar soil sampling mission,and drilling system in the petroleum industry.Generally,the force status of an AMS beam is quite complex,and the beam would produce deformations of tension and compression,bending and torsion.Dynamic problem of an AMS beam can be abstracted as the dynamic problem of a variable mass and circular cross-section(CCS)beam which is axially moving and spinning simultaneously.At present,dynamic research of an AMS beam mainly concern structural dynamics and focus on the vibtation behavior and stability of the beam.Mechanical products should have the functions of implementting specific motion and transmitting the load at the same time in general case,and the flexible multibody dynamic model of the products should be established in the design phase.Structural dynamic model of an AMS beam in the literature has a certain limitation on satisfing the requirement of building the flexible multibody dynamic model of mechanical products.In this dissertation,two variable-length beam elements incorporating the spinning effect based on the absolute nodal coordinate formulation(ANCF),Euler-Bernoulli and Rayleigh beam threoies and arbitrary Lagrangian–Eulerian(ALE)description are established to build the dynamic model of an AMS beam,the two elements are variable-length Euler beam-shaft element and variable-length Rayleigh beam-shaft element,respectively.All of the existing ANCF-based variable-length tether/beam elements neglect beam spinning effect,which means the rotation of the cross section around the central axis of the beam,therefore,they cannot be applied to the dynamical modeling the simulation of an AMS beam.In this dissertation,rotation angle of the cross section around the element axis is introduced into the paremetres to describe the motion of an element compared to the variable-length beam element of Hong Difeng,and the rotation angles of the two nodes are also introduced into the nodal coordinates of this element.The rotation angle of arbitrary cross section in the element can be interpolated using a linear polynomial by the rotation angles of the two nodes.This new element is referred to as a variable-length Euler beam-shaft element(VLEBSE)to reflect the introduction of both bending and spinning effects.This element is verified by three series of typical dynamical problems concerning free falling analysis of a flexible pendulum with a contracting boundary,free torsional vibration analysis of a cylindrical shaft and dynamic response of a spinning shaft subjected to an axially moving and rotating load.Because the rotational angle of the cross section of the VLEBSE is interpolated using linear polynomials only,the change rate of the rotational angle inside the element remains invariant with positon,and the continuity of the change rate of the rotational angle and corresponding torque on the common node between two elements cannot be guaranteed,the ability of the element to describing the torsion effect is relatively weak.In order to break through such limitation,derivatives of the rotational angle with respect to the material coordinate(change rate of the rotational angle)of two nodes are also introduced into the nodal coordinates of the element,and the rotational angle of the cross section of the element is interpolated using the same three order polynomials as the position vector,which would improve the VLEBSE.The free torsional vibration analysis results of a cylindrical shaft demonstrate that the ability of the improved VLEBSE to describe the torsion effect of a CCS beam is significantly superior to that of the original element.The dynamic analysis results of an AMS cantilever Euler beam by using the the improved VLEBSE are almost the same as the results by using the Hamilton principle and the Galerkin method given in the literature,which further verifies the element.The cross-section of a VLEBSE is simplified into a concentrated mass on the central axis of the element and a rotatory inertia around the axis,and neglect the rotatory inertia around the neutral axis.When the VLEBSE be used in the the dynamic analysis of an AMS beam with large rotatory inertia around the neutral axis,obvious errors may occur in the results.To solve this problem,above simplification can be abandoned and the Rayleigh beam threoy can be introduced in the element,which means that the virtual work of the inertia force of the element can be obtained by integrating that of every material point,in this way,the novel variable-length Rayleigh beam-shaft element(VLRBSE)can be established.The dynamic analysis results of an AMS cantilever Rayleigh beam by using the VLRBSE are almost the same as the results by using the Hamilton principle and the Galerkin method given in the literature,which confirms the correctness of the VLRBSE.Rayleigh theory is more general than the Euler-Bernoulli theory on the dynamics of a beam,therefore,the VLRBSE is more accurate and reliable than the VLEBSE when be used in a beam with small slenderness ratio,which can be proved by comparison of the dynamic analysis results of the same AMS cantilever Rayleigh beam by using the two elments.However,the VLRBSE would consume more computer resources than the VLEBSE and its computational efficiency is relatively low.Both of the two variable-length beam elements incorporating the spinning effect proposed in this dissertation,could correctly describe the dynamic behavior of variable mass and CCS beam which is axially moving and spinning simultaneously in certain conditions,and provide convenient and effective numerical modeling method for an AMS beam based on the flexible multibody dynamics.Compared to the solving method aimed at an AMS cantilever beam based on the structural dynamics by using the Hamilton principle and the Galerkin method given in the literature,when the loading condition and constraint condition are altered,the dynamic equations and the constraint equations need only be adjusted correspondingly and can be solved directly,therefore,the solving process of the method in this dissertation is more programmed.In the solution of the practical engineering problems,the elements should be selected and used according to the concrete conditions to achieve balance between the solving accuracy and computational efficiency.The two elements enrich the element library of ANCF and allows this modeling method to be used in more types of dynamic applications in the field of flexible multibody systems.In the end of this dissertation,theoretical analysis using both the VLEBSE and the VLRBSE is carried out aiming at the dynamic problems of the drill stem related to the amplitude limiting mechanism in the lunar soil drilling sampler which is used to obtain the soil on lunar surface,and the influence rule of the amplitude limiting mechanism to the dynamic behavior of the drill stem is obtained.It is demonstated that the influence rule of the actual product is consistent with the result of the theoretical analysis by the drill stem dynamic response experiment carried on the ground experimental prototype,which also prove the correctness of the theoretical analysis.