Theoretical Research On Motion Law Of A Particle Based On Motion Characteristics Of Screen

Cleaning and screening of particles is an important process in the agricultural production and the vibrating screen which is one of the main working parts in the cleaning system of combined harvester is the primary tool for cleaning and screening of particles that are different in size based on the moving screen.The vibrating screen contains two different types: plane vibrating screens and multi-degree-of-freedom vibrating screens.However,the plane reciprocating screen is still the main working part of the cleaning system in a combined harvester due to the complex structure of the multi-degree-of-freedom vibrating screen,its cost and imperfect relatively theoretical research.A motion mode of the plane reciprocating screen is a plane motion and the motion trajectory of the screen is the plane curve.The classical analysis of screen motion is based on the assumptions that the length of two hanger rods should be equal and the length of the hanger rods and the connecting rod is much larger than vibration amplitude of the screen,the trajectory of each point on the screen is same and is approximately on a straight line,and regards the screen motion as a simple harmonic motion.The motion status and behaviors of particles on the screen,screening quality and screen efficiency are directly affected by the motion characteristics of the screen when ignoring airflow and the intergranular friction.To study the effect of the screen motion on the force and motion status and behaviors of the particle on the screen,under the condition that some factors such as friction between motion pairs,the mass of the parts and air resistance were not taken into account and established a mathematical model to analyze the motion of the planar reciprocating screen.Moreover,a matrix method was employed to derive the motion equation of the planar reciprocating vibrating screen in this paper.The motion characteristics of the screen were obtained and verified based on the method of combining the numerical simulation by Matlab with high speed photography technology.The force of a particle on the screen was analyzed and when and where the motion status of a particlelike slipping forward,moving backward occurs were determined.Based on the nonlinear motion law of the particle,regions of different particle behaviors on the screen were obtained.The main research contest is as follows:(1)The mechanism of the plane reciprocating screen were simplified into a crank and rocker,the double rocker of the upper screen and the double rocker of the lower screen according to its structure.And the mathematical model was established to analyze the motion of the planar reciprocating screen.Moreover,a matrix method was employed to derive the motion equation of each point in the screen.The change laws of the tilted angle,velocity,acceleration,acceleration direction angle of screen were obtained by Matlab,which indicates the motion of the screen is a non-simple harmonic motion and the motion law of each point in the screen is different.(2)The tilted angle of screen is one of the important factors which effect the screening efficient.It was simulated numerically and we obtained that in the screening process,the tilted angle of screen is found to be between 3.5° and 6.5°,which is believed to be a result of superposition of multiple harmonic motions.And it also indicates that there are the translational motions in the X,Y directions,and an additionally rotational motion.This rotational motion causes the differences of velocity and acceleration between points in different locations of the screen.(3)The high speed camera was used to track the motion of three points in the longitudinal direction in the screen.And the velocity in X,Y direction obtained by the high speed camera is compared with that obtained by the numerical simulation based on Matlab.The result indicates that the velocities obtained from the numerical simulation are consistent with those of the test,which reveals that the motion screen is a non-simple harmonic motion.The feasibility and correctness of the matrix method for solving the motion profile of the vibrating screen are verified by experimental test.(4)The screening efficiency are directly affected by the motion status of particles on the screen.The forces on a single particle are analyzed in the different quadrants that the direction angle of acceleration based on the no-simple harmonic motion of the screen and simulated using Matlab.And Different status of particles motion like slipping forward,moving backward,and being thrown up on the different positions in the screen were analyzed(5)Based on the analyses with actual work conditions of the screen in the cleaning mechanism,a vibro-impact motion modelof a particle on the non-simple harmonic vibrating screen was established based on the nonlinear motion law of the particle.The stability of a particle bounding on the screen and the fixed point is equivalent.Based on the method of connecting the number with the shape,the existence of it was determined and the eigenvalues of Jacobin matrix of mapping equation was solved by Matlab numerically.Moreover,the stability of fixed points of a two-dimensional map was discussed.Regions of different particle behaviors on the screen such as the stable periodic motion,the period-doubling bifurcation motion,the Hopf bifurcation motion and the chaotic motion were obtained.In this paper,the motion law of the plane reciprocating screen and the status and behaviors of a particle on the screen are revealed,which provides the theoretical basis for the optimization design of the screen.