Research On Dynamics Modeling And Simulation Of Cable-pulley Multibody Systems

Cable-pulley mechanisms are widely used in many fields,such as construction machinery and aerospace industry.In order to meet the engineering needs,the research of dynamic modeling and simulation of the cable-pulley system has been gradually developed.However,there still remains some problems unsolved.The cable-pulley mechanism is a type of rigid-flexible multibody system.Dynamic modeling and simulation of this kind of system have some difficulties as follows:(1)The cable moves axially among several pulleys;(2)The bending modulus of the cable is very low so that transverse loads can only be sustained by increasing axial deformation or kinetic energy of the cable.(3)The contact zones between the cable and pulleys change frequently.The tranditional method models the whole cable as beam elements or a mass-spring system.Because no interpolation function can precisely describe an arc,the element number increases as much as possible to approach the arc in the tranditional method which results in the computation efficiency reduction.In this paper,dynamic modeling and simulation of the cable-pulley system are investigated deeply.In this paper,the cable of the cable-pulley system is divided into two types:the segment between two pulleys and the segment in contact with pulleys.For the cable segment between two pulleys,a cable element with time-varying length and moving boundary is proposed based on the space description.In terms of the virtual power principle and the relationship between space and material descriptions,the dynamic equation of the cable segment is established.For the contact segment of the cable,the contact constraint is transformed into a kind of shape constraint,based on the premise that there is no relative slip between the cable and pulleys and the cable segment is reshaped into an arc while in contact with pulleys.In this way,the motion of the contact segment of the cable can be described by the kinematics parameters of pulleys.In this paper,three common types of pulleys are considered and different kinematics parameters are selected to describe the spatial motion of each type of pulley.Then the dynamic equations of three types of pulleys are established by using the principle of virtual power.In addition,the solving method of common tangent between two spatial pulleys is presented to ensure the proper initial values of the cable-pulley system.As a rigid-flexible multibody system,the dynamic equations of the cable-pulley system are typical stiff ordinary differential equations(ODEs).The general numerical method for the stiff ODEs is to use the expression of position to describe the velocity and acceleration on the basis of the accurate physical model.Therefore,the numerical method for stiff ODEs can rapidly attenuate the high frequency responses.This paper presents a fast algorithm of filtering high frequency responses in the modeling phase of rigid-flexible multibody systems.The instantaneous stress that changes rapidly is replaced by the averaged stress during a short time.The numerical examples show that the proposed fast algorithm can improve computation efficiency and keep the system lower order modes.The order number of the system responses can be selected by adjusting the time size of the averaged stress.The fast algorithm is implemented in the dynamic modeling and numerical simulation of the cable-pulley system.Considering that the number of cable elements is enormous,the accelerations of the internal nodes of the cable are expressed by those of the boundary nodes.The final system equations only contain the degrees of freedom of the cable boundary nodes.At last,the overall dynamic equation of a whole cable-pulley system is assembled.Based on the dynamic modeling approach in this paper,a dynamics simulation softwarefor different types of cable-pulley systems is developed by using Matlab.Several examples are demonstrated and the numerical results are compared with ADAMS simulation and theoretical solutions.The comparison shows that the proposed method is feasible and has high computation efficiency and good numerical stability.It can provide theoretical basis and technical support for design,verification and assessment of cable-pulley mechanisms in engineering practice.