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Advanced Materials Research ISSN: 1662-8985, Vols. 1006-1007, pp 308-312 doi:10.4028/www.scientific.net/AMR.1006-1007.308 © 2014 Trans Tech Publications, Switzerland Submitted: 2014-06-12 Accepted: 2014-06-15 Online: 2014-08-13 Analysis of the blade structure on the influence of the particle movement Lei Huang1,2,a, Jingfa Lei1,b, Hui Li1,c, Congsheng Chen1,d and Xuehui Chen 1,e 1 Anhui Jianzhu University mechanical and electrical engineering college, Hefei, Anhui, 230601, China 2 Hefei University of technology Hefei, Anhui, 230009, China a [email protected], [email protected], [email protected], d [email protected],[email protected], Keywords: Cone mixer, Particles, mix, Discrete element method. Abstract. This article studied the blade structure on the influence of particle movement, as well as the force between blade and particles. Cone mixer is one of the commonly used equipment for powder mixed, usually, its blade’s movement driven by motor to stir particles, the structure of the blade to powder mixture has important effect, thus it’s important significance to explore the structure of the blade. The result based on the discrete element method to calculate the particle motion and stress with different blade structure, provides important help and reference for the design of the mixer blade. Introduction Cone mixer is one of the commonly used equipment for powder mixed, usually, its blade’s movement driven by motor to stir particles. There are different forms of blade structure, such as turbine, pusher, anchor, screw conveyor, screw and so on. Cone mixer used spiral blade structure commonly. Under the effect of blade agitation, the particle can be thought of as in three kinds of mechanism of mixing (i.e., mixed convection, diffusion, mix and shearing). The three mechanism of particle movement is closely connected with the blade structure, so the different blade structure parameters for particles mixture have practical significance. Three equation of elastic contact model Cundall and Strack put forward the discrete element method (DEM) for the first time in 1979, and DEM is used to solve the movement of particles in soil, but then this technology was applied widely in other areas, a lot of scientific researchers put forward numerous improved DEM model, but in these models, the most of them are still very incomplete. Discrete element method model has a lot of birth defects, so its hindered the development of the method, and the defects in the existing model also reduced the accuracy of the method in different degrees, such as in most of the models, the influence of the rolling friction is not taken into account. Only recently rolling friction was introduced to the discrete element model, its importance is also fully confirmed and in the new model, the interparticle forces are fully considered, including the normal contact force, tangential contact force and moment, can be called three equation model. So far, three equation model is a relatively perfect model. According to the elastic damping properties of a soft ball model can be generally divided into two kinds, namely linear model and nonlinear model, the linear model is the simplest and the most widely used model. This paper adopts the model of particles in mixer to make a numerical simulation. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 130.203.136.75, Pennsylvania State University, University Park, USA-17/05/16,14:48:31) Advanced Materials Research Vols. 1006-1007 309 1.1 Force Analysis on particles In simple particle system, the particle in the process of movement mainly affect by two kinds of force, namely, its own gravity and collision contact force between particles. Collision contact force is divided into normal contact force Fn,ij and tangential contact force F nt ,ij , the equations of each particle transport as follows: n dv = g + ∑ (F m m dt i i i i n ,ij j =1 + F t ,ij ) (1-1) In addition, the particles are affected by two kinds of torque, the tangential force torque T t,ij and rolling friction torque T r ,ij , and the rotary motion equations of each particle is: n dw I i m dt = m g + ∑ (T i i i i j =1 t ,ij + T r ,ij ) (1-2) Under the action of the force and moment, the speed of the particles, rotation speed and position can be represented by the following formula: dw ∆t dt dw v =v + ∆t dt xyz = xyz + v ∆t w i ,t i ,t = wit1 + (1-3) i ,t i ,t it 1 i ,t it 1 i (1-4) (1-5) The model adopts the three equations of linear elastic damping model, considering the normal contact force and tangential contact force (including the sliding friction) and rolling friction torque, each force and moment can be simplified to a spring, a damping and a slider. The numerical test conditions There a lot of structure for Cone mixer blade, here only study single screw blade mixer. On the upper plane, the diameter of 0.2m, the bottom diameter of 0.1m, height of 0.45m, selected two kinds of particles diameter were 0.009 m (small particles) and 0.012 m (large particles), the volume ratio of 1:1, the filling rate of about 35%, blade angle of 0 degree. After the loading, the blade rotate around its axis. This article made numerical experiments with diameter of blade and pitch, each of these experiments made four groups tests. First study of the blade pitch, numerical experiment of blade structure such as table 1 310 Advanced Manufacturing and Industrial Engineering Table 1 Selection of blade parameter classification 1 2 3 4 Screw pitch D/m 0.065 0.075 0.085 0.095 Blade radius S/m 0.08 0.085 0.09 0.095 Figure 1 Particle movement under the action of a blade 2.1 The simulation results of different blade parameters Table 2 Experimental results of the first group The same pitch: X direction force of blade Y direction force of blade A particle velocity in the Z direction Blade diameter 0.08m, pitch 0.08m Blade diameter 0.085m, pitch 0.08m Blade diameter 0.09m, pitch 0.08m Blade diameter 0.095m, pitch 0.08m Above for the blade pitch is 0.08 m, the radius is changed, the author obtain blade force situation in x and y, and a particle movement speed in z axis .Through the second column in the table, when the radius of the blade in 0.08m, the force of blade in X, Y direction has maximum stress, the force drive the peer particles mixing in the XY plane. The speed of the particles in Z direction is affected by selecting the location of the particles, from the fourth column in the graph can be found in the rate of reaction in the Z direction, this can be explained convection exchange in particles at the role of blade. Advanced Materials Research Vols. 1006-1007 311 Table 3 Experimental results of the second group The same radius X direction force of blade Y direction force of blade A particle velocity in the Z direction Blade diameter 0.095m, pitch 0.065m Blade diameter 0.095m, pitch 0.075m Blade diameter 0.095m, pitch 0.085m Blade diameter 0.095m, pitch 0.095m Table 3 react mixing effect with different parameters of pitch, the influence of blade force and particle velocity at constant in the blade radius. Pitch can be seen obviously from the above that affect the particles movement, at the same time the blade stress also has the certain fluctuation. And the speed of the particles is most obviously with different pitch, and it with twice larger fluctuations can be seen from the fourth column. Analyzing the results of the experiment The first group, when the blade pitch is 0.08m, different radius of blade has different effects on the particle movement. Analyze from the stress of the blade and particle velocity, the best convective motion is the blade of radius of 0.09m. The second group with blade radius of 0.95m, show that the different pitch has different influence to particle movement, when the blade pitch in 0.085m made a good relatively effect to particle motion. Investigate its reason, radius of blade embodies the contact area with the particles, and affects the whereabouts of particles and blind angle of sport. When the blade has a large radius, particles and blade contact area is large, it can drive the more particles, but if the radius is too large will affect the settlement of particles, and it is advantageous to the mix of particles; But if the blade radius is too small, will make smaller contact area among particles and blade, and the blind angle is 312 Advanced Manufacturing and Industrial Engineering large too, and easy making the mixture of particles is not uniform. Screw pitch affect friction and contact area among the particles and blade, and thus affect the motion of particles. If blade pitch is too large, the contact area with the particles in the same space is small, big pitch can make particles rebound at the same time, and those situations can’t reach the ideal mixing effect. Summary Through the numerical simulation, the author found that pitch of the propeller and blade radius have a large effect on the particle motion, took the larger radius of blade, can promote the flow of particles, but will affect the settlement of small particles at the same time, and cause unevenly mixed; Pitch value is too small, particles are prone to sideslip, it is unfavorable to particle movement, so in the design of blade, engineers should choose reasonable blade radius and pitch according to the size of the mixer bulk, References [1]Cundall P.A.,Strack O.D. L.A discrete numerical model for granular assemblies [J].Grotechnique,1979. [2]Ting J.M.,Corkum B.T.Computational laboratory for discrete element geomechanics [J].Journal of Computing in Civil Engineering,1992,6:129·146. [3]Wightman C.Dry , Powder Mixing in a Cylindrical Vessel Undergoing Rotational and Rocking Motions.New Jersey:The State University of New Jersey.1997.1-50 [4]Lacey P.M.C.Developments in the theory of particle mixing [J].Journal of Applied Chemistry, 1954,4(5):257-268 . [5]Guoming Hu. Discrete element method analysis of particle systems,Wuhan university of science and technology press,2010.7 Advanced Manufacturing and Industrial Engineering 10.4028/www.scientific.net/AMR.1006-1007 Analysis of the Blade Structure on the Influence of the Particle Movement 10.4028/www.scientific.net/AMR.1006-1007.308