Contact Forces in a Screw Feeding Process

.e contact force between particles is analysed in this paper. Firstly, theoretical analysis is carried out based on theHertz–Mindlin (no slip) model. Secondly, the normal force and tangential force are, respectively, simulated in single/double-flight screw feeders with the discharging device at three rotating speeds (60 rpm, 90 rpm, and 120 rpm) using different diameter particles (3mm, 5mm, and 7mm) by the extended distinct element method (EDEM) software. Finally, the simulation results show that the particle diameter has the biggest impact on average contact force in the feeding process. .is research provides theoretical basis for the study of the rule of bulk material movement in the screw feeder and the development of the high-precision feeding machine.


Introduction
e screw feeder is widely used in the short distance transportation of bulk material in agricultural and biological engineering [1][2][3][4][5][6].It is mainly composed of trough, bin, and screw shaft.It has the advantages of simple structure, airtight conveying, and controllable feeding quantity.However, the instability and the periodic fluctuation of the feeding quantity limit its industrial application.Nowadays, the contact force of granular matter inside the feeder in the feeding process has raised global scholars' interests.For example, Zheng et al. [7][8][9] studied the contact force between viscoelastic ellipsoidal particles based on the contact mechanics and finite element method.Fernandez et al. [10] considered the material forms of motion from the hopper to trough and simulated the variable pitch and variable diameter screw conveyor using the discrete element method (DEM).Yang and Cheng [11] investigated the contact force and coordination number distributions for granular materials under breakage during one-dimensional compression using the DEM.However, there are few reports on the contact force between particles in feeding process.
e motion of bulk material in trough is a discrete nonclassical medium movement.It is important to study the contact force between particles and its changes [12].e changes of normal force between particles reflect the friction resistance changes, and the changes of tangential force between particles reflect the sliding ability changes, which can all indirectly reflect characteristics of the particle motion in the screw feeder.Meanwhile, the DEM has been widely used in the industrial engineering [13][14][15].DEM has been successfully applied in simulating and predicting the process of conveying granular solids.Although the linear springdashpot-slider system is the most common contact force model, more detailed contact force models have been applied, which is based on the classical Hertz's theory for the normal direction and on simplifications of the model developed by Mindlin and Deresiewicz for the tangential direction [16][17][18][19].
erefore, this paper studies the contact force between particles in the screw feeding system with the discharging device.
e simulations are, respectively, carried out in single-flight and double-flight screw feeders at three rotating speeds (60 rpm, 90 rpm, and 120 rpm) when feeding different diameter particles (3 mm, 5 mm, and 7 mm).

Theoretical Analysis for Contact Force
roughout this paper, the Hertz-Mindlin (no slip) model is considered.As shown in Figure 1, the particle 1 contacts the particle 2 at the point C and relatively moves.e dashed line indicates the initial position, while the solid line indicates the final position.e coupler is utilized to simulate the relationship of paired particles.If the tangential force F t exceeds the yield value, the two particles will slide under the normal force F n and the frictional resistance, which is simulated by the slider damper [20].
e normal and tangential decomposition of the motion of particle contact process is carried out.We decompose the vibrating motion of particle contact process in the normal and tangential directions.e normal equation of motion of the particle is given as follows [21]: e tangential vibrational motion of the particle contact process is characterized by tangential sliding and particle rolling.e tangential equation of motion of the particle and the rolling are given by where m 1,2 is the equivalent mass; I 1,2 is the equivalent moment of inertia; s is the turning radius; u n and u t are the normal and tangential relative displacements, respectively; θ is the angle of rotation; F n and F t are the normal and tangential components, respectively; M is the external torque of particles; K n and K t are the normal and tangential coe cients of elasticity, respectively; c n and c t are the normal and tangential damped coe cients.e friction between the particles a ects the tangential sliding of the particles and the rolling of the particles.e sliding model has the limit condition of the tangential sliding and rolling of the particles: where μ is the particle friction coe cient and sgn[] is the symbolic function is

The Screw Feeding Discrete Element Model
In order to improve the stability of discharging quantity, the screw feeder is installed the "discharging device" at the outlet.e "discharging device" is xed to the trough and does not rotate with the screw shaft.It contains six thin ba es, which uniformly distributes on the sleeve.As shown in Figure 2, the diameter of the screw and the screw shaft are 65 millimeter and 20 millimeter, respectively.ickness of the ight is 3.5 millimeter.e inner diameter of the trough is 67 millimeter, and the single-ight screw pitch is 70 millimeter.e doubleight screw pitch is 35 millimeter.e feeding process of the single-ight and double-ight screws is simulated at three rotating speeds (60 rpm, 90 rpm, and 120 rpm) with 3-, 5-, and 7-millimeter diameter particles.It is important to note that the feeding method in this paper is turning the screw shaft 60 °and then stopping for 0.5 s, and it is repeated.
e coe cient of restitution, Poisson's ratio, and other parameters are shown in Tables 1 and 2 [22].In order to control the running time, xed time step is set as 20% of the Rayleigh time step and the grid length is twice of the radius of the particle.As shown in Figure 3, the simulation data of contact force are collected when the choke section (black box area) lling rate is full.

e Contact Force between Particles at Di erent Speeds.
Figure 4 shows the average of the contact force distribution between particles at three di erent speeds in the single-ight screw feeding using 5-millimeter diameter particles.Figure 4 shows that the average normal forces are stronger than the average tangential forces in the same moment.Meanwhile, there is an average contact force obviously stronger than others at the speed of 60 rpm.e reason is that the average overlap between particles is biggest at the speed of 60 rpm. 2 Advances in Materials Science and Engineering

e Contact Force between Particles in Single/Double-Flight Screw
Feeders. e average of the contact force distribution between particles in single/double-flight screw feeders using 5-millimeter diameter particles is as shown in Figure 5. e average contact forces in the single-flight screw feeding at the speed of 120 rpm are stronger than those in the double-flight screw feeding, causing the particles to be tumble more easily in the single-flight screw feeding.e reason is that the discharging device has larger space hindrance function in the single-flight screw feeding.

3.3.
e Contact Force between Particles with Different Diameters.Figure 6 shows the average of the contact force distribution between particles with three different diameters at the speed of 60 rpm in the single-flight screw feeding.As the diameter is increased, the strongest average contact force increased so that the smaller particles easily maintain motion morphology.

Conclusions
In conclusion, the average contact force is investigated using both theoretical analysis and simulations.Among the three factors in this paper, the biggest impact on average contact force is the particle diameter, which leads the biggest impact on motion morphology in the progress of the screw feeding.In industrial production, in order to get accurate feeding quantity, the screw feeder which has faster rotating speed,     Advances in Materials Science and Engineering

Figure 2 :
Figure 2: e geometry model of the screw feeder.

Figure 6 :
Figure 6: e contact force between particles with three di erent diameters in the single-ight screw feeder.

Table 1 :
Material parameters used in the simulation.

Table 2 :
Contact parameters used in the simulation.