一个展示直线振动筛筛板上单质点运动情况的仿真实验外文文献翻译

附录A virtual experiment showing single particle motion on a linearly vibrating screen-deckZHAO Lala , LIU Chusheng, YAN JunxiaSchool of Mechanical and Electrical Engineering, China University of Mining & Technology, Xuzhou 221008, China1 IntroductionVibration screening is a complicated process used in the mineral processing area that is affected by the vibration and other technical parameters of the screen and by the processed materials properties. The motion of the material on the screen deck has a direct relation to the quality of the screening process. Factors such as the penetration probability of the particles and the productivity of the apparatus are important. So investigating the theory of motion and the properties of the screened materials is of great significance for choosing reasonable kinematic parameters that ensure an effective screening process.The sieving experiment forms the foundation of screening theory. The traditional experimental methods have the disadvantages of being complex to operate, being easily influenced by outside conditions and being difficult to carry out accurately in small scale. Virtual experimental technology, on the other hand, has the advantages of low cost, of having no limits in the field related to the available time and number of tests and of affording the simulation of complex processes. Virtual techniques have been widely applied in studies within military, medical and industrial fields.We describe a virtual screening experimental system built upon physical simulation principles. The motion of a single particle on a linearly vibrating screen deck was studied. The influences of kinematic parameters on the state of motion were discussed. These results could provide a reference for the convenient study of vibrating screen theory and sieving practice.2 Theory of linear motion on a vibrating screenDifferent kinematic parameters, such as the vibration frequency, f, the amplitude, , the inclination angle of the screen plate, a0, or the direction angle of vibration, , may be changed to affect the motion of material on the screen deck. A motion that is static, positively sliding, negatively sliding or throwing can be obtained. The throwing motion provides good segregation performance, good screening and higher sieving efficiency and productivity. Hence, a throwing motion is adopted for most vibrating screens.Fig. 1 shows a kinematic model of a linear vibration screening process. The vibration motion is sinusoidal and linear. Its displacement is given by: (1)where is the amplitude of screen motion along the vibration direction, mm； the circular frequency of vibration, rad/s； t time, s； and the vibration phase angle, .Fig. 1 Kinematic model of a linear vibration screening processWe let the particle fall freely under the influence of gravity from its initial position until it hits the vibrating screen deck. The particle will then undergo a continuous throwing motion after elastic-plastic collisions with the vibration deck. Let the time of the ith collision between the particle and the screen be ti and ignore the time required for the collision process itself. Then, based on the law of conservation of energy, the particle velocity along the normal direction of the screen deck after the collision is given by: (2)where is the direction angle of vibration, ； the y-direction velocity of the particle before the ith collision, m/s； the screen deck velocity at the ith collision, m/s； and e the elastic coefficient of restitution of the colliding particle.Conservation of energy requires that the thrown height relative to the screen deck after the collision is: (3)where g is the gravitational acceleration constant, m/s2； and a0 the inclination angle of the screen deck, . The theoretical average thrown height of the particle is then: (4)where n is the number of collisions of the particle. Because there is no collision along the screen deck direction (the x-direction) for the particle, the theoretical average throwing height of the particle is determined by: (5)where iD is the throwing coefficient； and D the throwing index.3 Simulation and discussionThe situation for simulation of a single particle on a cylindrical-bar type linear vibrating screen deck is shown in Fig. 2a. A global coordinate system (unit: cm) was adopted and the center of the scene at ground level was set as the origin of the coordinate system. The initial position of the screen and of the particle is (0, 0, 15) and (-25, 0, 30), respectively. The screen deck area is 60 cm30 cm, the screen aperture size (a) is 2 cm, the particle diameter (d) is 4 cm and the elastic coefficient of restitution (e) is 0.5. Fig. 2b shows the trajectory of the particle through space during the screening process.Taking the trajectory in the z-direction as our research object, the influence of vibration frequency and amplitude, inclination angle of the screen deck and vibration direction angle on the average particle velocity and average throwing height will be discussed.Fig. 2 Virtual experiment of a single particle sieving process3.1 Effect of vibration frequency, fThe influence of frequency on the particle trajectory is shown in Fig. 3 for constant amplitude, inclination angle and vibration direction. The average velocity and throwing height are listed in Table 1 as a function of frequency.Table 1 Influence of frequency on particle kinematicsf (Hz)12131415v (m/s)0.29780.54580.21400.2056Vd (m/s)0.28490.30870.33240.3562hz (cm)26.446825.196126.411922.6399Fig. 3 Influence of frequency on throwing trajectoryNote that the particle velocity initially increases as f decreases but then decreases for the final frequency increment. This is because increasing frequency of vibration causes the number of collisions between the particle and the screen deck to increase. The opportunity for random collisions then also increases and a back-throwing phenomenon after collision even appears. This causes an increase in the number of particle bounces and in the time spent to complete the screening process. When f is 13 Hz, the number of particle bounces is 6, the time spent to complete screening is the minimum value of 1.15 s and the particle average velocity is the maximum value of 0.5458 m/s. But when f is 15 Hz the particle bounces 16 times and the time spent to complete screening is the maximum value of 2.267 s. At this frequency both the average velocity and the average throwing height are at their minimum values.An analysis of the results in Table 1 shows that the correlation coefficient for the vibration frequency versus the average velocity is 0.494 and that the coefficient is 0.725 for frequency versus the average throwing height. This indicates that frequency has a greater influence on the average throwing height and has no significant influence on the particles average velocity. The highest average velocity and average throwing height is obtained when f is 13 Hz.3.2 Effect of amplitude, The influence of amplitude on the trajectory of a particle is shown in Fig. 4. The average velocity and average throwing height are listed in Table 2.Fig. 4 Influence of amplitude on throwing trajectoryFig. 4 and Table 2 show that an increase in X, which causes the relative velocity between the particle and the vibrating screen deck to increase, results in a gradual increase in the particle average velocity and height. The number of bounces decreases at the same time. These predictions are in reasonable agreement with related theories. When is 3.5 mm there are twenty bounces and the particle has low average velocity and height. The time needed to complete screening is the longest under this condition (2.417 s). As increases the incremental change in sieve time decreases as the time tends to about 1.6 s. And the particle average velocity and height increase rapidly when is 6.5 mm.An analysis of the results in Table 2 gives a correlation coefficient between amplitude and average velocity of 0.793 and between amplitude and height of 0.924. This indicates that the amplitude has some influence on particle average velocity and a significant influence on the average thrown height. Hence, amplitude should be selected according to the properties of the screened material. For materials difficult to screen relatively larger amplitude should be used to simultaneously obtain higher average velocities and throwing heights.Table 2 Influence of amplitude on particle kinematicsX (mm)3.54.55.56.5v (m/s)0.21070.20880.21400.2977vd (m/s)0.21160.24170.33240.3929hZ (cm)19.469421.548426.411940.9729h (cm)19.728519.835721.900124.20233.3 Effect of screen-deck inclination angle, a0The influence of deck inclination angle on the particle trajectory is shown in Fig. 5. The average velocity and height are listed in Table 3.Fig. 5 Influence of screen-deck inclination angle on throwing trajectoryFig. 5 and Table 3 show that as a0 increases the average velocity also increases and the number of collisions the particle undergoes decreases. The average height tends to decrease. When a0 is 0 the particle has twenty collisions with the screen and the average velocity is the minimum. The time needed to complete screening is then the longest (3 s). When a0 is 6 the average height of the particle is at its maximum value. For a0 equal to 9 the initial distance from the particle to the screen deck decreases and the relative velocity of the particle and screen deck is at a minimum, which causes a decrease in the thrown height.Table 3 Influence of screen-deck inclination angle on particle kinematics00 ()0369v (m/s)0.24770.291670.25090.3169Vd (m/s)0.29540.31390.33240.3512hz (cm)21.508222.697826.411915.1523h (cm)18.4471316.727921.900115.3953Correlation coefficients from data in Table 3 relating screening deck inclination angle to average velocity or to average height are 0.644 and 0.697, respectively. Hence, the screen-deck inclination angle influences both particle average velocity and throwing height. When the screening deck inclination angle is 36 high average velocity and high throw height can be obtained simultaneously.3.4 Effect of vibration direction angle, The effect of the angle of vibration the particle trajectory was also studied. Fig. 6 shows the trajectories. The average velocity and average height are listed in Table 4.Fig. 6 Influence of vibration angle on throwing trajectoryTable 4 Influence of vibrating-direction angle on particle kinematicsS ()30405060v (m/s)0.36720.52930.25090.1903vd (m/s)0.42220.38310.33240.2716hz (cm)19.828622.542526.411948.2712Fig. 6 and Table 4 show that the average height increases as increases but there is a decrease in the average velocity. When is 40, the average particle suffers six collisions and the average velocity is the maximum. In this situation the time spent for complete screening is the shortest (1.067 s). When is 60 the particle has minimum average velocity and suffers eleven collisions. The time spent for completion of screening is at the maximum (2.15 s). The increase in the normal component of the screen deck velocity causes the relative velocity of the particle after collision to increase. Thus, the average height increases in amplitude and reaches a maximum.From the data in Table 4 correlation coefficients for vibration direction angle versus average velocity and average throw-height may be found. They are 0.70 and 0.889 respectively. This indicates that direction angle, , influences particle average velocity and height. So, higher average velocity and throwing height may be simultaneously obtained by using a vibration angle of about 40.4 Conclusions1) A single particle on the vibrating screen deck has a complicated motion. The particle motion during the sieving process can be described well using elastic-plastic collision theory.2) The amplitude and the vibration direction angle have a great effect on the particle average velocity and the average throw height considered over the normal range of linear screen parameters. The vibration frequency and the inclination angle of the screen plate have a small influence. To obtain the ideal sieving effect for materials that are difficult to sieve the frequency and amplitude of vibration, the inclination angle of the screen plate and the vibration direction angle should be chosen as 13 Hz, 6.6 mm, 6 and 40, respectively.3) A virtual screening experiment based on physical simulation principles reflects the objective laws of the sieving process and can provide a simple and reliable means to study screening theory.一个展示直线振动筛筛板上单质点运动情况的仿真实验ZHAO Lala，LIU Chusheng，YAN Junxia机电工程学院，中国矿业大学，徐州 221008，中国1 简介振动筛分是矿物加工领域的一个复杂过程，它受振动情况、筛机的技术参数和物料的性质影响。筛分过程的效率直接影响物料在筛板上的运动状态。物料穿透概率和筛机的效率是很重要的影响因素。因此，研究运动理论和物料的性质具有重要意义，是选择合理的运动学参数，确保有效筛分的重要过程。筛分实验是筛分理论的基础。传统的实验方法有难以比较结果、容易被外界因素影响和难以取得精确数值的缺点，而仿真实验技术则有实验费用低、没有场地、时间以及实验次数限制，能够对复杂过程进行仿真等优点。仿真技术现在被广泛用于军事、医药和工业领域的研究。我们基于物理仿真理论建立了一个仿真筛分实验系统，用于研究直线振动筛筛板上单质点的运动状态， 质点运动的动力学参数的影响同样被考虑了。本研究的结果可以为振动筛理论和筛分实践的研究提供方便。2 振动筛上物料的直线运动理论不同的运动学参数，例如振动频率，f，振幅，筛面倾角，a0，振动方向角，的改变可能影响筛面上物料的运动状态。我们改变参数就能够得到完全静止、绝对滑行和绝对抛掷三种物料运动状态。抛掷运动状态能够使物料有效地分离，为振动筛提供更高的筛分效率和生产率，所以大部分振动筛都采用了抛掷的方式。图1显示了一个直线振动筛分过程的运动学模型，可以看出振动运动的轨迹是线性和正弦曲线的。其位移由下式给出： (1)式中振动方向的振幅，mm；振动的角频率，rad/s；t 时间，s；振动相位角，。图1 直线振动筛分过程的运动学模型我们让质点在重力的作用下做自由落体运动直到再次撞击到筛面为止，在质点与筛面碰撞后将做连续的抛掷运动。我们设质点连续两次碰撞之间的时间为ti同时忽略碰撞的时间。这样，根据能量守恒定律，质点在筛面正向的正常速度为： (2)式中 为振动的方向角，；y方向的撞击速度， m/s； 筛板在撞击时的速度， m/s； e质点撞击的回弹系数。能量守恒定律指出质点的抛射高度与质点与筛面的撞击有关： (3)式中g 重力加速度，m/s2；a0筛板的倾角， 。 则平均抛射高度为： (4)式中 n 质点的撞击次数。因为质点沿x方向没有撞击，从理论上定义平均抛射高度为： (5)式中 iD 抛掷系数；D为抛掷指数。3 仿真与讨论单质点在圆形棒条筛网的直线振动筛上的仿真条件见图2a。我们采用将一个三维坐标（单位：cm）的原点定在原坐标系的水平轴上。筛板和质点的初始位置分别为(0， 0， 15) 、 (-25， 0， 30)。筛面尺寸为60 cm30 cm，筛孔尺寸为 (a) 2 cm，质点的尺寸为(d) 4 cm回弹系数(e) 为0.5。图2b显示了质点在筛分过程中的运动轨迹。我们以z轴方向的轨迹为研究对象，我们将讨论在不同振动频率、振幅、筛面倾角、振动方向角下质点的平均速度、平均抛射高度。图2 单质点的筛分实验31 振动频率的影响， f恒定振幅、倾角、振动方向角条件下下振动频率对质点运动轨迹的影响见图3。平均速度和平均抛射高度作为振动频率的函数在表1中列出。表1 振动频率对质点的影响f (Hz)12131415v (m/s)0.29780.54580.21400.2056Vd (m/s)0.28490.30870.33240.3562hz (cm)26.446825.196126.411922.6399图3 振动频率对抛射轨迹的影响记录显示初始阶段质点速度随着频率的增大而增大，但之后随着频率的增大而减小。这是因为频率的提升引起质点与筛面的撞击次数增加，同时随机抛射现象增多，后抛现象出现。这导致了质点回弹现象的增多，增加了筛分过程的时间。 当 f 为13 Hz时，质点的回弹为6，完成筛分过程的时间为1.15s，质点的平均速度最大值为0.5458m/s。但是当 f 为15 Hz时回弹次数为16，完成筛分过程的最长时间为2.267 s。在这个频率下，质点的平均速度和平均抛射高度均为最小值。对表1的分析结果显示振动频率对平均速度的相关系数为0.494，对平均抛射高度的相关系数为0.725。这样的结果指出振动频率对抛射高度的影响较大，对质点的速度影响较小。最大平均速度和最大抛射高度是在振动频率为13Hz时获得的。3.2 振幅的影响，振幅对质点运动轨迹的影响见图4。平均速度和平均抛射高度在表2中列出。图4 振幅对质点运动轨迹的影响图4和表2显示振幅的提高导致质点和筛面之间的相对速度提高，从而提高了质点的速度和抛射高度，同时回弹现象减少。这个结果符合理论上的预判。 当 为3.5 mm