Download Analysis of the blade structure on the influence of the particle

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.
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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
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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