Nonlinear Dynamic Analysis Of Horizontal Vibrating Centrifuge

Collisionvibration between components of engineering machinery is a common phenomenon.This phenomenon can be beneficial sometimes,but it can also be harmful.How to draw on advantages and avoid disadvantages is a heated research subject in mechanical engineeringat present.In recent years,many domestic and overseas experts and scholars have made a relatively deeper research on collision vibrationphenomenon in low degree-of-freedom system and the research of bifurcation chaos in low degree-of-freedom system has made great achievement.However,the research on working machinery mechanism.in high degree-of-freedom system is relatively less.Non-linear dynamics study of horizontal vibrating centrifuge which is a kind of frequently-used centrifugal dewatering equipment in industry was presented in this paper.The main work of this paper was in the following:The history and working mechanismof centrifuge was simply described in this paper.Following that is thedomestic and overseasresearch progress and the main problems of collisionvibration system.The theoryof non-linear dynamics and its main research method including the judgment data of fixed point and stability,bifurcation phenomenon,Poincarémapping and chaos phenomenon were presented in this paper,which lays the foundation for the non-linear dynamics study.The working process of horizontal vibrating centrifuge was simplified into left-right2-DOF,left-right 3-DOF and up-down 2-DOFcollision vibration systemdynamical model and its differential equationswere achieved by applying the math,physics and mechanics knowledge.Solutions of the differential equationswere achieved according to the boundary conditions in the working process,thus the Poincaré mapping and Jacobimatrix were deduced.The simulation was conducted by using MATLAB based on the process principle of solving the system equation.The motion of the physical model was studied through numerical theory.According to 2D(3D)bifurcation diagrams and Poincare mappingcross section diagramsin the process of collision vibration,complex dynamics features of system motion statetransferring to chaos were theoreticallydiscussed combined withthe number and positions ofcharacteristic value of the Jacobi matrix surpassing the unit circle.Through comparison and analysis,it is found that there are various kind of bifurcations in the process of system transferring from periodic motion to chaos,among which the most common types are Hopfbifurcation,period doubling and torusdoublingbifurcation.There is also codimension-two bifurcation,including Hopf-Hopfbifurcation,Hopf-Flip bifurcation,etc.For horizontal vibrating centrifuge,according to the result of computer numerical simulation,parameters such as driving frequency w,collision clearance b,mass ratio ?m,stiffness ratio ?k,and recovery coefficient R have a huge impact on system dynamic behavior.For centrifuge,working under chaotic state is more appropriate and choosing the right parameters can reduce the energy consumption of the machine and raise the efficiency.The exact value of parameters on bifurcationstate and chaosstate were given in this paper,which can provide certain reference basis for the design,optimization and manufacturing of the centrifuge.