单轴振动筛运动模拟及筛面上单颗粒运动规律

建立直角坐标系，其坐标原点与筛机质心重合，y轴由筛机质心指向激振器旋转中心。通过对单轴振动筛受力分析和微分方程求解，得到筛机上任意点的位移解析表达式，发现筛机的质心处为圆运动，而y轴上点(0，－R′)的运动为直线往复运动，其幅值与质心运动圆半径相等。因此，筛机的运动可用曲柄-连杆-滑块机构中的连杆模拟；利用几何作图法，能够找出筛机上任意点曲柄转过任意角度时的位移，从而描绘出该点的运动轨迹；利用连杆的速度瞬心法，能够得到筛机上任意点任意时刻的运动速度；利用颗粒运动抛物线和时间步长减半法，可以得到颗粒及筛面的运动状态，进而找到颗粒落回筛面的接触点，得到颗粒被抛起后相对筛面的运行距离，将筛机及颗粒的复杂运动变得简单、直观。

Simulation of single-shaft vibrating screen and the movement law of a particle on the screen surface

Rectangular coordinate system was established，and its origin of coordinates was the centroid of the screen，y-axis points to the center of vibration exciter.Through the force analysis and solving differential equation of single-shaft vibrating screen，it could get the analytical expressions of the displacement of the screen at any point，it is found that motion of centroid of the screen is the circular and the motion of point(0，－R′) is straight reciprocating motion，the amplitude is equal to the radius of the circle，the motion of single-shaft vibrating screen could be simulated by the connecting rod of crank-connecting rod-slide block mechanism.Using the geometrical method，it could identify displacement of any point on the screen，thus it depicts the trajectory of the point.Using the method of instantaneous center of velocity of connecting rod，it could get the velocity of any point of the screen at any time.Using the particle motion parabola and method of time half step，it could find the instantaneous position of the particle and the screen surface at any time，the complex movement of the particle and the screen surface gets simple and intuitive.