Simulation analysis of the signicance and interaction of inuencing factors on mixing uniformity of double drum recycling mixing plant

: The mixing uniformity of the double drum recycling mixing plant has an important 11 effect on the quality of recycled asphalt mixture. The mixing uniformity of the double drum 12 recycling mixing plant not only depends on the axial installation angle of the blade, the radial 13 installation angle of the blade, the phase angle of the stirring arm, the inclination angle of the drum, 14 and the rotation speed of the drum, but also on the interaction between these factors. In order to 15 further clarify the relationship between the mixing uniformity and the above factors, the 16 significance and interaction of influencing factors of mixing uniformity were studied based on 17 EDEM and response surface methodology (RSM). The result shows that the factors affecting the 18 mixing uniformity of the aggregates are significantly different when the aggregate size is different. 19 Therefore, when studying the mixing uniformity of a mixing plant, it is not comprehensive to 20 conduct research on a certain factor in a single-sided manner. Instead, the main factors and the 21 interaction between the factors should be considered comprehensively.


25
The mixing uniformity of double drum recycling mixing plant largely determines the quality of the recycled asphalt 26 mixture, and its structural parameters and working parameters have an important influence on the mixing uniformity 27 of the asphalt mixture.Therefore, many scholars have conducted a lot of research. Ma et al [1] analyzed the 28 influence of the single factor of structure parameter and working parameter on the uniformity of mixing. Liu et al 29 [2] analyzed the stress of the recycled asphalt mixture in the double-drum recycling mixing plant, and qualitatively 30 analyzed the accumulation of the mixture on the mixing blades, and determined the installation range of the blade 31 inclination. Zhao et al [3] optimized the structure of the drying drum of the asphalt mixing equipment, and analyzed 32 the parameter matching of the asphalt mixing machine blades based on the discrete element method (EDEM).  In the actual mixing process, the mixing uniformity of the mixing drum is affected by the interaction of its 73 structural parameters and working parameters.

74
For this reason, this paper establishes a simulation model based on the discrete element method (DEM) that meets 75 the actual working conditions. Based on the analysis of the influence of each single factor on the uniformity of 9 aggregate mixing, a mathematical model between the discrete coefficient of aggregate and each factor is established 77 by using the response surface methodology (RSM), and the significant relationship between each factor and its 78 interaction on the uniformity of aggregate were analyzed. Furthermore, the influences of the rotating speed of the 79 drum, the inclination angle of the drum, the axial installation angle of the blade, the radial installation angle of the 80 blade, the phase angle of the mixing arm and other factors on the mixing uniformity are studied, which provides a 81 reference for further understanding of the mixing mechanism and reveals the movement law of particles on the 82 mixing blade.

104
When blade radial angle   0  and axial angle is  ,The force analysis of the mixing unit on the blade is shown 105 in Fig.2(a). When    , and blade radial angle is  , the force analysis of the mixing unit on the blade is shown in 106 Fig.2(b). Where F is the force on the asphalt mixture, f is friction between blade and aggregate, 1 F is axial force, it 107 mainly causes the axial movement of the mixture. 2 F is tangential force, it mainly causes the circumferential movement 108 of the mixture. 3 F is radial force, it mainly causes radial movement of the mixture. 4 F is tangential force, it mainly 109 causes circumferential motion of the mixture. As shown in Fig.3, in order to realize the axial movement of the 110 mixture, it will meet the requirements: 0 . Where  is friction coefficient. For the same reason, 9 the condition for the mixture to achieve radial movement shall be:

117
Material pile formed on the face of blade during mixing as shown in Fig.3, where AB and BC are the side edges of 118 the pile, the mixture moves along the side edges.  is the axial installation angle of the blade,  is the angle of the 119 drum; W is the width of the blade;b is blade height; and  is the angle between the side edges of the pile and the 120 horizontal plane, that is, the mixture accumulation angle.

126
The mixing speed coefficient is used to describe the axial and circumferential movement of the mixture, as shown in (1 (1) 131 In order to maximize the axial and circumferential velocity of the mixture, if

137
The rotation speed of the inner cylinder is controlled within a certain range, and the mixture will fall from the blade 138 when it reaches a certain height.The force analysis of the mixing unit on the blade is shown in Fig.4. If the mixture 139 is in the self falling state, the sliding force of material unit should overcome the centrifugal force and friction force.

140
As shown in Fig. 4 Before the inner cylinder speed reaches the critical speed, the conditions for the mixture to meet the self falling are 144 as follows:

147
Where  is Material glide angle， R is blade end rotation radius， g is gravitational acceleration． 26

151
Substituting the above parameters into (4), the critical speed of the drum is 13.4 r/min. According to the speed 152 requirements, the primary drum speed is 6-10 r/min.  Under the action of gravity, the particles of the mixture do parabolic motion at a certain initial speed. The initial velocity 0 V is composed of the relative velocity r V and the implicated velocity ω V , that is 0rω  162 Established the coordinate system as shown in Figure 5. The X axis is parallel to the ground, and the Z axis coincides 163 with the mixing axis.The particle is thrown out at the initial speed from point 0 P (  (1 / 2) sin sin cos( ) The falling point of particles is the intersection of the curve described in (4) and the inner wall of the outer cylinder, 172 corresponding to the coordinate system shown in Figure 7, the cylinder equation is 2 2 2 x y R .Thus, the time p t 173 is particle movement from 0 P to 1 P is obtained.
The projection of the trajectory of the mixture on the XOY plane is shown in Fig The simulation model is established based on DEM, the contact relationship of DEM generally includes particle to 189 particle and particle to geometry, as shown in Figure 7.  I is the equivalent moment of inertia; r is the revolving 207 radius;unis the relative displacement normally, and us is the tangential one;  denotes rotational angle for itself, n F is 208 the normal components of particles acted on by outside force, s F is the tangential one; M is the external moment of 209 particles, n K is the normal elastic coefficient in contact model, s K is the tangential one; n c is the normal damping 210 coefficient; s c is the tangential one. 211 The friction force between contacting particles has an effect on the tangential sliding and rolling of particles.

212
Through the sliding model, the limiting conditions of tangential sliding and rolling can be obtained as shown in 213 equation (6):

217
Simulation model of double drum regeneration mixing equipment is established by EDEM software, as shown in 218 Fig.10.In order to improve the simulation speed, the aggregate in the mixture is simplified as a single spherical particle 219 model. Three kinds of aggregate with different particle size range are used to simulate the mixture. The particle size 220 range is 2.36-4.75 mm, 4.75-9.5 mm ,and 9.5-19 mm, respectively. Named aggregate 1, aggregate 2, and aggregate 3.

221
According to the production efficiency and gradation, the production rate of each particle factory is

249
In the mixture distribution diagram shown in Figure 11, the right side is the feed port and the left side is the 250 discharge port. Due to the setting of the particle factory, small particles (green and pink particles in the figure) are 9 distributed in the bottom layer, that is, the mixture enters the mixing chamber in the state of segregation. It can be seen 252 from Figure 11 that the segregation of the mixture is gradually improved along the axial direction of the mixing 253 chamber, that is, the extension of the mixing time is conducive to the improvement of the mixture uniformity. As 254 shown in Fig.11 (a) and (b), the aggregate segregation is serious and almost runs through the whole mixing chamber.

255
With the increase of rotation speed, the mixture uniformity is improved to some extent as shown in Fig.11 (c) . When n 256 is 9r/ min and 10r / min, as shown in Fig.11(d) and (e), there is almost no obvious segregation in the middle of the 257 mixing chamber and after.

258
The average velocity of the particles in the mixing chamber at different speeds is shown in Fig.13.It can be seen from

272
As shown in Figure 13, the drum speed has a great influence on the mixing uniformity of the mixture.When the 273 rotating speed of drum increases from 6r/min to 9r/min, the dispersion coefficients of three kinds of aggregate decrease, 274 and the dispersion coefficients of aggregate 1 and aggregate 3 decrease obviously.Because aggregate 1 and aggregate 3 275 are relatively fine and coarse particles, and the number of particles is relatively small, it is easy to produce 276 segregation.When the rotating speed of the drum is low, the distribution of particles is less disturbed. With the increase 277 of the rotating speed of the drum, the aggregate throwing increases correspondingly, the large-scale cross movement 278 among particles becomes more intense, and the renewal frequency of particle position increases.Because the number of 279 particles in aggregate 2 is relatively large and the particle size is moderate, its particle distribution has strong anti-280 interference ability and small fluctuation range of dispersion coefficient.When the drum speed changes from 9r/min to 281 10r/min, the decrease range of the dispersion coefficient of aggregate 1 and aggregate 3 becomes smaller, and the 282 dispersion coefficient of aggregate 2 increases slightly, that is to say, the influence of drum speed on the uniformity of 283 aggregate is nonlinear. When the rotating speed of the drum reaches a certain value, the mixture distribution tends to be 284 stable, and further increasing the rotating speed will not have a great positive effect on the improvement of mixing 285 uniformity.

300
As shown in Figure 15, the greater the inclination of the drum, the more particles of the mixture retained in the 301 drum.Due to the constant feed rate of the feed port, the increase of the number of particles in the mixing drum indicates 302 that the axial movement speed is weakened and the retention time of the mixture is prolonged.

303
The feed rate of particle factory is reduced by 30%, and other parameters remain unchanged. The uniformity of 304 mixture is analyzed when the inclination of roller is 6 °.

305
The dispersion coefficients of aggregate 1, 2 and 3 are 0.427, 0.184 and 0.683 respectively, which are lower than 306 before the feed rate is reduced.It shows that the filling ratio of the mixing chamber is high when the inclination angle 307 of the drum is 6 ° without the decrease of the feeding rate. It can be concluded that increasing the inclination of the 308 drum can prolong the mixing time of the mixture. However, the retained mixture is easy to cause a large filling ratio in 309 the mixing drum, which is not conducive to mixing.

310
The dispersion coefficient of the three aggregates at the drum inclination angle is 4°and the rotation speed is 9r/min 311 is smaller than that of the three aggregates at the drum inclination angle is 2°and the rotation speed is 8r/min. Therefore, 312 in order to solve the problem of the increase of the filling ratio of the mixing drum caused by the increase of the 313 inclination angle of the drum, the speed of the drum can be properly increased without reducing the productivity.

362
As shown in Fig.19, the phase angle of the mixing arm increases, and the feeding cycle of the mixing equipment also 363 increases. The increase of picking period will increase the rolling stroke of mixture, and the segregation of large 364 particle will be intensified. Therefore, the phase angle of the mixing arm has a great influence on the uniformity of 365 large particles. As shown in Fig. 19 (a), the phase angle of the mixing arm is too small, and the distance between 366 adjacent blades is small. The mixing process is similar to the spiral conveying process, and the spraying of the mixture 367 is low, which is not conducive to the mixing of the mixture.

372
As shown in Fig.20, the larger the phase angle between the mixing arms is, the more the particles in the mixing drum 373 are. It shows that with the increase of the phase angle, the velocity of the mixture slows down gradually. The increase 374 of phase angle is easy to delay the mixing of the mixture, and increase the filling ratio of the mixing chamber.

375
The feed rate of particle plant is reduced by 30%, and other parameters are unchanged. The uniformity of mixture is 376 analyzed when the phase angle of the mixing arm is 60°. The dispersion coefficients of aggregate 1, 2 and 3 are 0.451, 377 0.316 and 1.038, respectively, which are lower than before the feed rate is reduced. It shows that when the feed rate is 378 constant and the phase angle of the mixing arm is 60 °, the filling ratio of the mixing drum is on the high side. As 379 shown in Fig.18 and Fig.20, when the phase angle of the mixing arm is 60 °, the high filling ratio of the mixing drum is 380 also the reason for the poor mixing uniformity of the mixture.

387
As shown in Figure 21, the dispersion coefficient of aggregate 1 and aggregate 2 has little change. The dispersion 388 coefficient of aggregate 3 is relatively large influenced by the radial installation angle of blade, but its fluctuation range 389 is also less than 0.11. It shows that the radial installation angle of blade has little influence on the uniformity of mixture.

390
The radial installation angle of the blade can make the mixture separate from the inner wall of the outer cylinder, 391 shorten the rolling distance and reduce the segregation of the coarse particles in the rolling process. Therefore, as 9 shown in Figure

429
According to the range of influence factors in Table 3,the simulation scheme and results obtained by Box Behnken 430 design test method as shown in Table 4:  The simulation results are analyzed by response surface method, the mathematical model between the discrete 433 coefficient and each factor of aggregate 1 is shown in eq.(7). The mathematical model between the discrete 434 coefficient and each factor of aggregate 2 is shown in eq.(8). The mathematical model between the discrete 435 coefficient and each factor of aggregate 3 is shown in eq. (9). Table 5, table 6 and table 7

462
In order to test the rationality of the fitting model, the randomness and normality of the residual are analyzed. The 463 relationship between residual and predicted value of aggregate fitting model is shown in Fig.24. The student residual is 464 randomly distributed on both sides of the predicted value, it shows that there is no correlation between residual and 465 predicted value, that is, residual is caused by random error. The residual normal probability distribution of aggregate 466 fitting model is shown in Fig.25

542
As shown in Fig.26 (a), Fig.27 (c), and Fig.28 (b), the interaction between the angle of drum and the phase angle of 543 mixing arm has a significant effect on the dispersion coefficient of the three kinds of aggregate. In order to improve the 544 mixing uniformity, the phase angle when the inclination of the drum is large should be smaller than that when the 545 inclination of the drum is small. When the inclination of the drum is constant, the phase angle corresponding to the low 546 point of the response surface of the discrete coefficient of aggregate decreases in turn, that is, a smaller phase angle 547 should be arranged for the mixing of large particles.

549
Taking the minimum value of discrete coefficient as the optimization objective, the values of each parameter are 550 obtained as follows:

551
The blade axial installation angle is 34.896°, the blade radial installation angle is 38.389°, the phase angle of the mixing 552 arm is 31.676°, the drum inclination angle is 5.999°, and the drum rotational speed is 9.997r/min. After rounding, the 553 blade axial installation angle is 35°, the blade radial installation angle is 38°, the phase angle of the mixing arm is 32°, 554 the drum inclination angle is 6°, and the drum rotational speed is 10r/min.

556
(1) Increasing the rotation speed and reducing the axial installation angle of the blade can reduce the dispersion 557 coefficient of the aggregate. When the feed rate is unchanged, only increasing the phase angle will cause the filling rate 558 of the stirring chamber to increase and the stirring uniformity to decrease. Therefore, in order to obtain better stirring 559 uniformity, the phase angle when the drum inclination angle is larger should be smaller than the phase angle when the 560 drum inclination angle is small, and it is not appropriate to use a larger phase angle for the stirring of large-size 561 particles.

562
(2) Through the response surface method, the significant relationship between the influence of each single factor and its 563 interaction on the discrete coefficients of the three aggregates is obtained. All data, models, and code generated or used during the study appear in the submitted article.