Optimum analysis of inclined angle of mixing blades in planetary mixer based on discrete element method

Abstract

Based on production practice, it is known that the mixing scraper is an important mechanical part that the planetary mixer directly contacts with the concrete. Its structural shape will directly affect the mixing effect of the mixer, and the inclination angle of the mixing scraper is one of the most important factors affecting the mixing efficiency of the mixer. In this paper, based on the discrete element numerical analysis method, a three-dimensional simulation model of the vertical axis planetary concrete mixer is established, and the concrete mixing process is simulated, and the inclination angle of the mixing scraper is optimized based on the simulation results. An automatic precast concrete mixing experiment platform was built, and the simulation results were verified experimentally. The research results show that the experimental data and the simulation results are very consistent, which verifies the accuracy of the discrete element dynamics simulation model. It can be seen from the simulation and experimental results that the mixing efficiency of the mixer is the highest when the inclination angle of the mixing blade is 45°, and the number of collisions between different types of material particles in the mixing tank is the highest.

Keywords

Planetary mixer structure optimization mixing efficiency mixing blade inclined angle

Introduction

The forced mixers for mixing dry hard concrete in the market can be roughly divided into two types: horizontal shaft type and vertical shaft type. Compared with the earlier ribbon and paddle horizontal shaft mixers, the vertical shaft planetary mixer can significantly improve the mixing efficiency and uniformity of concrete materials.^1–4 Generally, the vertical shaft planetary mixer is composed of a low-speed revolving sun wheel mixing part and a high-speed self-rotating planetary wheel mixing part, whose trajectory of the scraper is more complex and changeable, and can realize multiple mixing modes such as shearing, tumbling, and diffusion of materials, and can mix higher-quality concrete.^5–7 Therefore, planetary mixers have been widely used in dry hard concrete brick production lines with high quality requirements.

However, even though with the relatively high mixing efficiency of the vertical shaft planetary mixer, it still significantly lags behind the production efficiency of the brick machine in the supporting automatic brick production line, which makes the production capacity of the entire production line unable to be fully released. Therefore, it’s needed to optimize the structure of the vertical shaft planetary mixer to improve its mixing efficiency. However, due to the complexity of the structure of the planetary mixer itself (compared to horizontal shaft mixer and rotating disk mixer) and the particularity of the concrete material itself, it is difficult to directly sample and measure concrete during mixing. Therefore, it is difficult to analyze it experimentally. At present, there are only a few articles on the mixing efficiency and structural optimization of vertical shaft planetary concrete mixers. For example, Valigi and Gasperini⁸ established a dynamic simulation environment for planetary concrete mixers to predict the behavior and service life of concrete mixers through geometric and physical parameters. Cazacliu⁹ explored the relationship between the mixing state of concrete materials in a planetary mixer and the mixing power. André et al.¹⁰ discussed the criteria for judging the degree of homogenization of powder mixed by planetary mixers, and proposed dimensional analysis with mixing time and power consumption as the target variables. Valigi et al.^11,12 analyzed the wear resistance of the mixing blades in the vertical shaft planetary mixer, and proposed a structural improvement plan for the blades to improve their wear resistance. Liang et al.¹³ analyzed factors such as blade clearance, helix angle, and rotation mode of a double-blade planetary mixer, and obtained their influence on mixing power consumption. Zhang et al.¹⁴ designed a new dry particle planetary mixer based on ADAMS optimization of conventional mixer blade parameters, whose mixing blade can change the angle of attack at any time during the rotation process to achieve multi-degree of freedom movement of the blade. He and Wang¹⁵ proposed a side scraper shape optimization scheme for a planetary mixer based on the analysis of the movement trajectory and mixing uniformity of the mixing material. In the early stage of the research, Zheng et al.,¹⁶ members of the research group, analyzed from the perspective of kinematics and proposed an optimization scheme for the planetary arm of the planetary mixer. Ulteriorly, this paper will carry out the structural optimization of the mixing blade of planetary mixer from the perspective of dynamics. The concrete planetary mixer is very popular among civil engineering field because of its complex transmission system to realize the full coverage of the mixing track in the mixing tank, but this also leads to the complexity of its internal mechanical structure, the difficulty of optimization and the high manufacturing cost. According to production practice, the inclined angle of the mixing blade is one of the most important factors affecting the mixing efficiency of the mixer. Compared with improving other internal mechanical structures of the mixer, adjusting the inclined angle of the mixing blade is not only low in manufacturing cost and easy to implement, but also significantly improves the mixing efficiency. Therefore, this paper will focus on the influence of the inclined angle of the mixing blade on the mixing efficiency.

In recent years, the use of discrete element simulation to analyze the mixing efficiency of mixers has been verified to be very efficient and reliable by many researchers. When using the discrete element method to analyze the problem of particle motion, the derivation of complex constitutive equations can be avoided, and the state of motion at each moment inside the particle can be observed, thereby providing an accurate basis for structure optimization. Hassanpour et al.¹⁷ applied the discrete element method to analyze the mixing mode of material particles in a twin-shaft mixer, and verified the effectiveness of the simulation method through particle tracking experiments. Alian et al.¹⁸ studied the influence of factors such as the material filling rate of the oblique cone mixer, the speed of the agitator, and the tank on the mixing efficiency. Ebrahimi et al.¹⁹ conducted a discrete element analysis on the influence of the blade installation angle of the single horizontal shaft mixer on the mixing efficiency. Tsugeno et al.²⁰ used the discrete element method to analyze the influence factors such as ribbon width, blade speed, lateral angle, and pitch angle of a horizontal-axis ribbon mixer and a ribbon-blade hybrid mixer. Long et al.²¹ characterized the mixing performance and power consumption of a non-viscous particle double-blade planetary mixer by discrete element method. Jadidi et al.²² used the discrete element method to investigate the effects of blade angle, width, and clearance on the mixing performance of a twin-shaft mixer. Garneoui et al.²³ used discrete element simulation to quantitatively analyze the influence of material filling type and number of paddles on the different mixing rates of a single-shaft paddle mixer along the mixing cycle. Bao et al.²⁴ used the discrete element method to analyze the influencing factors of the soil mixer’s flying knife speed, spindle speed, number of blades, and flying knife diameter, and proposed a structural optimization scheme for the mixer. In summary, the discrete element simulation method has been applied reliably in the field of concrete mixing. Therefore, it should be very suitable and effective to apply it to the structural analysis and optimization of the vertical axis planetary mixer whose mixing process is very difficult to be observed, but at present there is almost no such research.

Therefore, in this study, the discrete element simulation method will be used to analyze the mixing process of a vertical shaft planetary concrete mixer with a mixing volume of 1000 L. Firstly, the three-dimensional model of the mixer and the particle model of the concrete material particles are established, and then the contact model between the material particles is selected, and the contact coefficient in the model is determined through the mutual verification of simulation and experiment. Then, through the simulation analysis and experimental test of the working efficiency of the mixer equipped with mixing blades with different inclined angles, the optimal value of the mixer blade inclined angle is determined.

Simulation model

Planetary mixer model

The mixer involved in this research is a 1000 symmetrical planetary mixer produced by a company. The effective mixing volume of this type can reach 1000 L, and the structure size and rotation of the two planetary frames are the same, but opposite to the direction of the outer box of the gearbox. As shown in Figure 1(a) and (b), it is the basic composition system and simplified three-dimensional model of the mixer. Figure 1(c) shows the top view of the main mixing structure, and Table 1 shows the names and parameters of the corresponding structures.

Figure 1.

EDEM 3D model of symmetric planetary mixer: (a) planetary mixer, (b) 3D simulation mode and (c) schematic diagram of planetary mixer.

Table 1.

Key mixing structure parameters of planetary mixer.

Parameter symbol	Parameter name
a	Planetary arm length
b	Bottom blade arm length
c	Side blade arm length
d	Distance from input shaft to output shaft
l ₁	Mixing blade width
$ω_{0}$	Input shaft angular velocity
$ω_{1}$	Angular velocity of output shaft 1
$ω_{2}$	Angular velocity of output shaft 2
B ₁	Mixing blade on planetary arm 2
B ₂	Mixing blade on planetary arm 2
B ₃	Mixing blade on planetary arm 1
B ₄	Mixing blade on planetary arm 1
B ₅	Bottom blade

It should be noted that EDEM software was used in the study to conduct simulation analysis on the vertical shaft planetary mixer. This is a mature commercial discrete element simulation software, which is widely used in engineering fields such as civil engineering, pharmaceuticals, and chemical engineering. Its simulation process is shown in Figure 2.

Figure 2.

Simulation process of EDEM software.

Small-sized structures such as small-sized chamfers, bolts, screws, and countersinks in the mixer components have very limited influence on the mixing effect, but they will cause a significant increase in the number of meshes in the simulation model, resulting in a significant increase in solution time. This is very bad for simulation. Therefore, before importing the 3D model of the mixer into the discrete element simulation software, it is necessary to simplify the structure of the mixer model, delete the small structures that are not related to the mixing effect, and then fill in the missing parts and integrate them into the large-scale structure.

Particle model

The process of concrete mixing mainly involves the movement of four types of particles, sand, gravel, cement, and water molecules, and the agitation of the mixing blades of the mixer. The basic material properties of the four particles and the mixer structure need to be set in the pre-processor of the EDEM software. As shown in Table 2, the densities, Poisson’s ratios, and shear moduli of the five materials are given.

Table 2.

Material properties.

Material	Density (kg/m³)	Shear modulus (109 Pa)	Poisson’s ratio
Stone	2650	5	0.215
Sand	2500	0.63	0.25
Cement	3000	0.1	0.25
Water	1000	0.1	0.01
Steel	7850	79	0.3

After comprehensively considering the effectiveness and efficiency of simulation calculation, the size and shape of various particles in the simulation are appropriately simplified to simplify the calculation and speed up the solution process. Among them, the stones are set as non-uniformly distributed particles with a maximum radius of 15 mm, and are randomly generated according to the particle size ratio range of 1–0.3. Sand and cement particles are uniform non-spherical particles, wherein the radius of sand particles is set to 6 mm, the radius of concrete particles is set to 4 mm, and the radius of water particles is set to 4 mm. Figure 3(a) to (d) respectively show the three-dimensional models of four kinds of particles established in EDEM.

Figure 3.

EDEM 3D model of stone (a), sand (b), cement (c), and water particles (d).

Particle contact model of different materials

The contact model is mainly used to describe the contact form between particles and calculate the size of the contact force. For different working conditions, there are different contact forms between particles, and the selected contact models are also different. The correct selection of the contact model of particle elements is the key factor to obtain a good simulation structure. In the discrete element simulation software, the built-in contact models mainly include the following types, and the respective application occasions are shown in Table 3.

Table 3.

Applicable occasions of common contact models.

Common contact models	Applications
Herz-Mindlin (no slip)	The most basic contact model, suitable for regular particle contact
Herz-Mindlin with bonding	Suitable for simulation analysis of crushing and fracture problems
Herz-Mindlin with JKR cohesion	Suitable for occasions where bonding and agglomeration occur due to moisture content
Linear spring	Suitable for rapid calculation and qualitative analysis of conventional particles
Hysteretic spring	Suitable for occasions where particles undergo plastic deformation due to compression
Herz-Mindlin with heat conduction	Suitable for occasions where temperature is analyzed

The contact model is mainly used to describe the contact form between particles and calculate the magnitude of the contact force. The correct selection of the contact model of the particle unit is the key factor to obtain a good simulation structure.

The Herz-Mindlin (no slip) model is the default model used in the EDEM system and is accurate and efficient in force calculations. The model mainly calculates the normal force component, tangential force component, tangential friction force, and rolling friction force when the particles are in contact. This model is suitable for the calculation of contact force of most dry particles, so the contact form of particles in the process of concrete dry mixing can be described by this model. Among them, the calculation expression of F_n (the normal force) when the particles are in contact is²⁵:

F_{n} = \frac{4}{3} E^{*} \sqrt{R^{*}} δ_{n}^{\frac{3}{2}}

(1)

Where, $δ_{n}$ is the normal overlap, the equivalent Young’s modulus E*, and the equivalent radius R* are defined as:

\frac{1}{E^{*}} = \frac{(1 - v_{i}^{2})}{E_{i}} + \frac{(1 - v_{j}^{2})}{E_{j}}

(2)

\frac{1}{R^{*}} = \frac{1}{R_{i}} + \frac{1}{R_{j}}

(3)

Where, $E_{i}$ and $E_{j}$ are Young’s moduli, $v_{i}$ and $v_{j}$ are Poisson’s ratios, $R_{i}$ and $R_{j}$ are the radii of the contact spheres.

In addition, the expression of $F_{n}^{d}$ (the damping force component of the normal force) is:

F_{n}^{d} = - 2 \sqrt{\frac{5}{6}} β \sqrt{S_{n} m^{*}} v_{n}^{rel}

(4)

m^{*} = {(\frac{1}{m_{i}} + \frac{1}{m_{j}})}^{- 1}

(5)

Where, $m^{*}$ is the equivalent mass, $v_{n}^{rel}$ is the normal component of the relative velocity, and the expressions of β and S_n (normal stiffness) are as follows:

β = \frac{\ln e}{\sqrt{\ln^{2} e + π^{2}}}

(6)

S_{n} = 2 E^{*} \sqrt{R^{*} δ_{n}}

(7)

Where, e is the restitution coefficient. The $F_{τ}$ (tangential force) depends on $δ_{τ}$ (the tangential overlap) and $S_{τ}$ (the tangential stiffness).

F_{τ} = - S_{τ} δ_{τ}

(8)

S_{τ} = 8 G^{*} \sqrt{R^{*} δ_{n}}

(9)

Where, $G^{*}$ is the equivalent shear modulus. Furthermore, the tangential damping force is expressed as:

F_{τ}^{d} = - 2 \sqrt{\frac{5}{6}} β \sqrt{S_{τ} m^{*}} v_{τ}^{vel}

(10)

Where, $v_{τ}^{vel}$ is the tangential velocity of the relative velocity. The tangential force is limited by $μ_{s} F_{n}$ (Coulomb friction), and μ_s is the coefficient of static friction. For the simulation, rolling friction is also an important parameter, which is considered by applying a moment on the contact surface.

τ_{i} = - μ_{r} F_{n} R_{i} ω_{i}

(11)

Where, μ_r is the coefficient of rolling friction, R_i is the distance from the contact point to the center of mass, and ω_i is the unit angular velocity vector of the object at the contact point.

During the wet mixing process of concrete, the cohesion between particles increases due to the addition of water. At this time, the Herz-Mindlin (no slip) model will not be applicable. The Herz-Mindlin with JKR cohesion model takes into account the cohesion between moisture-containing particles, and can better simulate the strong viscous state of water-containing concrete. Therefore, the model will be used during this churning phase.

First of all, what needs to be known is that the JKR model uses the same method as the Herz-Mindlin model to calculate the tangential elastic force, normal dissipative force, and tangential dissipative force generated when particles contact. The calculation of the normal force of the JKR model is based on the overlap δ and the interaction parameters α and surface energy γ.

F_{JKR} = - 4 \sqrt{π γ E^{*}} α^{\frac{3}{2}} + \frac{4 E^{*}}{3 R^{*}} α^{3}

(12)

δ = \frac{α^{2}}{R^{*}} - \sqrt{\frac{4 π γ α}{E^{*}}}

(13)

When the surface energy γ (in equation (12)) is zero, the same calculation result as the Herz-Mindlin model can be obtained:

F_{JKR} = F_{Herz} = \frac{4}{3} E^{*} \sqrt{R^{*}} δ^{\frac{3}{2}}

(14)

The model provides attractive cohesion even when the particles are not in direct contact. The maximum gap between particles with non-zero cohesion is calculated by the following formula:

δ_{c} = \frac{α_{c}^{2}}{R^{*}} - \sqrt{\frac{4 π γ α_{c}}{E^{*}}}

(15)

α_{c} = {[\frac{9 π γ R^{* 2}}{2 E^{*}} (\frac{3}{4} - \frac{1}{\sqrt{2}})]}^{\frac{1}{3}}

(16)

When the JKR model is used to simulate wet particles, the force required to separate two wet particles depends on the liquid surface tension γ_s and the wetting angle θ.

F_{pullout} = - 2 γ_{s} \cos θ \sqrt{R_{i} R_{j}}

(17)

This force can be equated with the maximum cohesive force of the JKR model, so in the EDEM software, we need to set the surface energy value γ required in the model settings. Therefore, it is necessary to calibrate the value (γ) through experiments in order to improve the accuracy of the simulation model.

Determination of particle surface contact parameters

As mentioned in the previous section, when we use EDEM software to simulate wet particles such as concrete, the Herz-Mindlin with JKR cohesion model will be used to simulate the mutual contact force between particles. For this model, the only parameter that needs to be set in the software is the particle’s surface energy value γ .The size of this value is related to many factors such as the change of water content on the particle surface, particle shape, and contact state, and it is difficult to directly deduce it theoretically.

Therefore, we decided to simplify the solution process of this value by combining experiments and simulations. As shown in Figures 4 and 5, we established a funnel model in EDEM and manufactured an experimental prototype with the same dimensions. In order to obtain a more accurate particle surface energy, different values of γ (in equation (12)) in the JKR model are taken at equal intervals during the simulation. The value range is 0–5 J, and the value interval is 1 J. Fill the funnel with irregularly shaped sand particles with a particle size of 2 mm and gravel particles with a maximum particle size of 20 mm. When the simulation starts, the material in the hopper gradually falls and accumulates in a cone on the platform below. The angle between the generatrix of the cone and the bottom plate is the material accumulation angle, and the larger the angle, the greater the surface energy between the material particles.

Figure 4.

Comparison between experiment and simulation of accumulation angle of wet sand.

Figure 5.

Comparison between experiment and simulation of accumulation angle of wet stones.

The steps of the experiment are similar to the simulation process. First, fill the funnel with sand or gravel materials, and then release the mouth of the funnel to let the materials fall freely. As shown in Figure 4, comparing the experimental and simulation results, it can be seen that the surface energy of wet sand is approximately 0.43 J. Similarly, it can be obtained from Figure 5 that the surface energy of wet stones is about 2 J.

The hydration reaction of cement particles after absorbing water causes significant changes in their chemical properties and shape. Therefore, the interaction force between particles cannot be described by a unified contact model. However, considering that the distribution of cement particles in the mixing tank is basically uniform after the mixing enters the wet mixing stage, the size of its surface energy has little effect on the final mixing uniformity. Therefore, its surface energy value can be set based on the surface energy value of wet sand.

Simulation results and analysis

Mixing uniformity evaluation standard

Mixing uniformity, also known as mixing quality, is an important indicator for evaluating the performance of mixers, and the level of mixing uniformity also directly reflects the quality of concrete. After the concrete material is stirred by the mixer for a period of time, the aggregate mortar is mixed and bonded. It is difficult to judge whether the mixing uniformity is good or bad by naked eyes. Therefore, in order to avoid subjective judgment errors, it is necessary to introduce statistical analysis methods to scientifically analyze the mixing uniformity.

As shown in Figure 6, in the post-processing stage of the simulation, the accumulation area of the material at the bottom of the mixing tank is meshed. The cube grid is a single-layer 10 × 10 distribution form. In the post-processing program, statistical analysis can be performed on the number, quality, and velocity of particles in the grid. The mixing uniformity of concrete materials can be judged according to the mass ratio of each material in each grid. The reason why it is not directly judged according to the quality is that the material quality in each unit grid is constantly changing due to the mixing effect during the mixing process. However, when the material is fully stirred evenly, the mass proportion of each material in a certain space volume is constant, so it is more appropriate to use the mass fraction of each component to analyze the degree of mixing uniformity.

Figure 6.

Mesh division of the material area.

Assuming that the mass of a certain material particle in the grid unit n (n = 1, 2, 3 …) is $m_{i}$ , and the total weight of the grid particle is $M_{i}$ , then the mass fraction of the material particle in the sample n is $ϕ_{n}$ for:

ϕ_{n} = \frac{m_{i}}{M_{i}}

(18)

The average value of its mass fraction in all grids is $μ$ , then $σ$ (the standard deviation of the mass fraction of the material particles in the grid) can be obtained as:

σ = \sqrt{\frac{1}{N} \sum_{n = 1}^{N} {(ϕ_{n} - μ)}^{2}}

(19)

Where, N is the total number of divided grids, and its value is 100 in the simulation case. In the post-processing program, the particle information in each grid unit is exported as a data table and calculated according to demand.

Structure optimization scheme

As shown in Figure 7, the angle values of the bevel angles of the mixing blades of the asymmetrical vertical shaft planetary mixer were set, taking four angles of 30°, 45°, 60°, and 75° respectively. It is a relatively common usage in the same type of mixer. As shown in Figure 8, they are the three-dimensional model of the mixing blade after the modification of the mixing blade structure of the prototype machine. Except for the different inclined angle of the mixing blade, the other structures of the mixer model are the same, and the initial positions of the two planetary frames are perpendicular to each other. The value of inclined angle is determined by the angle between the bottom surface of the mixing scraper and the front surface. As shown in Figure 8, $β_{1}$ equals 30°, and $β_{2}$ equals 45°, and $β_{3}$ equals 60°, and $β_{4}$ equals 75°.

Figure 7.

Schematic diagram of mixing blades with different inclined angles.

Figure 8.

EDEM simulation of mixing process with mixing blades of different inclined angles: (a) 30°, (b) 45°, (c) 60°, and (d) 75°.

Simulation results analysis

As shown in Figure 9, it is a graph showing the relationship between the mixing uniformity and the mixing time of different mixer models with different mixing blade angles of 30°, 45°, 60°, and 75°. By comparing and analyzing the trends of these curves, it can be found that the standard deviation of the mass fraction of the material particles under different mixing blade angles decreases with the increase of the mixing time after the material particles are put in, and the change of the mixing blade angle affects the change of the standard deviation of the mass fraction of the material particles.

Figure 9.

Variation of mixing uniformity under mixing blades of different inclined angles.

It can be seen from the figure that within the mixing time 0–5 s, the three materials finished feeding in order, and the standard deviation of the mass fraction of the material particles in the mixing barrel rose rapidly and reached the maximum at this time. In the mixing time 5–10 s, the materials in the mixing barrel start to mix with each other by the mixing device, and the standard deviation of the mass fraction drops rapidly, and the mixing effect is good. During the mixing time of 10–20 s, it can be seen that the standard deviation of mass fraction of 30° mixing blade is the largest among the four angles of mixing blades, and it continues until the end of simulation, which means that the mixing effect of 30° mixing blade is the worst. During this period, the standard deviation of the simulated mass fraction of 45°, 60°, and 75° mixing blades was basically the same and continued to decrease. When the mixing time exceeds 20 s, it can be seen that the overall standard deviation of mass fraction of 45° mixing blade is the smallest and the change is small, while the standard deviation of simulated mass fraction of 60° and 75° mixing blade has increased, which indicates that the mixing effect of 45° mixing blade is the most ideal among the four angles of mixing blades.

As shown in Figure 10, the frequency of stone-sand collisions under different angles of mixing blades is compared, from which it can be found that the effect of different angles of mixing blades on the trend of the frequency of collisions with mixing time is not the same. After the mixing time reaches 20 s, the frequency of stone-sand collisions under different angles of mixing blades appears to be different, and it can be found that the frequency of inter-particle collisions of 45° mixing blades will be higher than that of other angles of mixing blades. This indicates that the 45° mixing blade of the mixer, the most frequent contact between the particles, higher mixing, reducing the standard deviation of the material mass fraction, more conducive to the material particles to achieve uniform mixing.

Figure 10.

Frequency of stone-sand collisions under mixing blades of different inclined angles.

Experimental verification

Experimental equipment

As shown in Figure 11, a vertical axis planetary mixer dry hard concrete production and preparation experiment platform built by a company, its main components include: material storage warehouse, material transport conveyor belt, mixer workbench, vertical axis planetary mixer, water adding device, material recovery bins, and consoles.

Figure 11.

Concrete preparation production line: (a) storage, (b) feeding direction, (c) water adding device, (d) planetary mixer, (e) internal structure of planetary mixer and (f) mixing blade.

Figure 11(a) shows the material storage bin for fresh concrete preparation and production. The two hoppers above are used to store stone and sand materials respectively, and the bottom is a weighing table for accurate control of the quality of the materials put in. Figure 11(b) shows the material transportation conveyor, which is mainly used to transport the materials required for mixing from the bottom of the material storage bin to the inlet of the vertical shaft planetary mixer. Figure 11(c) shows the production table for fresh concrete preparation, which is used to place the vertical axis planetary mixer and the water filling device, and the remaining space at the bottom of the table is used to place the material recovery bin. Figure 11(d) shows the main machine of the vertical shaft planetary mixer, which is surrounded by the feeding port, observation port, and ventilation port, and the discharge port at the bottom of the mixing tank, and its technical parameters are shown in Table 4. Figure 11(e) shows the internal mechanical structure of the vertical shaft planetary mixer with 75° mixing blades. Figure 11(f) shows the physical diagram of the mixing blades with different inclined angles, the specific inclined angles are 30°, 45°, 60°, and 75°.

Table 4.

1000 type mixer technical parameters.

Mixer model	Feeding capacity (L)	Discharge capacity (L)	Mixing rated power (kW)	Hydraulic station power (kW)	Planetary/mixing blade
1000 type	1500	1000	37	3	2/4

Mixing process design

The actual production process of fresh concrete mainly has four stages, including: feeding, dry mixing, wet mixing, and discharging. The mixed material falls from the storage bin and is transported to the weighing platform. After weighing, it falls into the conveyor belt and passes through the conveyor belt. Transport it to the feed port of the vertical shaft planetary mixer on the mixing table. After a period of dry mixing in the mixer, the material reaches a preliminary uniformity. Then add water to the mixing tank for wet mixing until the final mixing is uniform. Finally, the freshly mixed concrete is discharged from the discharge port at the bottom of the mixer to the material recovery box. As shown in Table 5, the time schedule for a complete mixing process of the vertical shaft planetary mixer.

Table 5.

Field experiment mixing process arrangement.

Mixing process	Mixing time (s)	Remark
Feed stage	10–15	Complete the feeding work of all materials
Dry mixing stage	30	Timing after all the materials fall into the mixing tank; the signal acquisition equipment starts to work
Wet mixing stage	90	Calculate the wet mixing time from the time of adding water; the time of adding water is about 20 s
Discharge stage	30	Make sure that the material in the mixing tank is completely discharged

Through multiple on-site experiments on vertical shaft planetary mixers and signal acquisition, we have obtained multiple sets of experimental data on the current of the main engine of the mixer and the humidity of the materials in the mixing tank during the mixing process. After processing the experimental data by Origin (data processing software), the average value of the experimental data of the repeated group was taken for analysis, and the influence of different inclined angles of mixing blades on the actual mixing effect of the vertical shaft planetary mixer was compared.

Experimental results and analysis

As Figure 12(a) to (d) show the relationship between the humidity of the mixed material in the mixing tank and the mixing time during the mixing process of the vertical shaft planetary mixer when the mixing blade angle is 30°, 45°, 60°, and 75°, respectively. It can be seen from the figure that the humidity change trend of the mixing material in the mixing tank is similar during the actual mixing process of the mixer with different mixing blade angles. The humidity of the mixing material in the mixing tank reaches a preliminary stability after 30 s of dry mixing. About 10 s after the device started to add water, the humidity in the mixing tank began to rise rapidly. After a period of mixing, the humidity in the mixing tank finally stabilized, and the materials in the mixing tank reached a state of uniform mixing. However, the time for the humidity in the mixer with different angles of mixing blades to reach uniformity is different. From Figure 12, it can be seen that the time for the humidity of the mixing material in the mixer with 30° mixing blade to reach the final stability is about 110 s; the time for the humidity of the mixing material in the mixer with 45° mixing blade to reach the final stability is about 84 s; the time for the humidity of the mixing material in the mixer with 60° mixing blade to reach the final stability is about 92 s; the time for the humidity of the mixing material in the mixer with 75° mixing blade to reach the final stability is about 90 s. Through comparison, it can be easily seen that when the angle of the mixing blade is 45°, the mixing time required for the humidity of the mixing material to stabilize is the shortest, indicating that the mixing efficiency is the highest.

Figure 12.

Humidity change in field experiment of mixer with mixing blades of different inclined angles: (a) 75°, (b) 60°, (c) 45° and (d) 30°.

The mixing process of the vertical shaft planetary mixer needs to overcome the mixing resistance to do work. When the voltage is constant, the mixing process of the mixer can be reflected by the change rule of the mixing host current. During the mixing process, the resistance of the mixing blades is changing all the time. The fluctuation of the motor current reflects the fluctuation of the resistance of the mixing device. The greater the fluctuation, the stronger the mixing effect, and the magnitude of the motor current reflects the fluctuation of the mixing resistance. The larger the current value, the greater the mixing resistance.

As Figure 13 show the relationship between the motor current and the mixing time during the mixing process of the vertical shaft planetary mixer when the mixing blade angle is 30°, 45°, 60°, and 75°, respectively. It can be seen from the figure that the fluctuation of the motor current is small during the dry mixing stage, indicating that the material in the mixer is relatively stable at this stage. After the dry mixing is completed, the mixer starts to add water, and the water and cement form a hydration reaction in the mixing tank, the properties of the mixed materials change, and the viscous force between the mixed materials is greatly enhanced, resulting in increased resistance to the mixing device and motor current value rises rapidly. After a period of mixing, the motor current value tends to be stable but fluctuates greatly, indicating that the effect of the mixing device on the mixed materials is more obvious. Through the filter processing of the data processing software, the magnitude of the motor current value can be observed more intuitively. From Figure 13, it can be seen that the motor current reaches a stable average value of about 34 A during the mixing process of the mixer with 30° mixing blades; The motor current reaches a stable average value of about 35 A during the mixing process of the mixer with 45° mixing blades; the motor current reaches a stable average value of about 36.5 A during the mixing process of the mixer with 60° mixing blades; the motor current reaches a stable value of about 37 A during the mixing process of the mixer with 70° mixing blades. Comparing the results in the four pictures, it can be seen that the average value increases with the increase of the angle of the mixing blade when the current of the main engine is stable, indicating that the increase of the angle of the mixing blade will lead to the increase of the mixing resistance of the mixing device of the mixer, and the higher the power cost for completing the mixing.

Figure 13.

Working current of the mixer with mixing blades of different inclined angles.

In addition, the motor current value reflects the power efficiency of the mixer on the other hand. It can be seen from Figure 13 that the greater the inclination angle of the mixing blade, the greater the corresponding motor current value. This shows that when the mixing time is the same, the greater the inclination angle of the mixing blade, the greater the power consumption generated by the mixer. Taking into account the mixing time and the power consumption of the mixer, it can be seen that the mixing blades with different inclined angles have an impact on the power efficiency of the mixer. It can be seen from Figure 12 that the mixing time of the 45° mixing blade is shorter than that of the 60° and 75° mixing blades. However, according to Figure 13, it can be seen that the power consumption of the mixer with 45° mixing blades is less than that of 60° and 75° mixing blades. Therefore, the power efficiency of the mixer with 45° mixing blades is much higher than that of 60° and 75° mixing blades. Although the power consumption of the mixer with 45° mixing blades is slightly higher than that of 30° mixing blades, the mixing time is much lower than that of a 30° mixing blade. Therefore, the power efficiency of the mixer with 45° mixing blades is higher than that of 30° mixing blades.

Conclusions

In this study, the discrete element simulation analysis method was used to quantitatively analyze the mixing performance of the vertical shaft planetary concrete mixer, and the structural optimization design was carried out on the inclined angle of the mixing blade that affects the working efficiency of the mixer. In addition, an automatic concrete mixing platform for verifying the EDEM model was established, and the mixing uniformity of the concrete was detected by measuring the change of the concrete humidity value inside the mixer during the experiment. The research results showed that the experimental data and the simulation results were in good agreement, which verified the accuracy of the simulation model. The above simulation and experimental studies show that among the mixing blades with different inclined angles studied, the mixing efficiency of the mixer is the best when the inclined angle of the mixing blade is 45°.

The limitations of this study are mainly manifested in two aspects: first, in this paper, the water added in the production process with no fixed shape and size is equivalent to water particles, and some material property parameters and material contact coefficients of water particles are compared with sand particles. There is no rigorous theoretical derivation or experimental testing for the setting of stone, and the simulation model does not consider the hydration reaction of water and cement during the mixing process. Second, due to the limitation of experimental conditions, this paper only conducts experimental comparisons on some common mixing blade inclined angles. To obtain a more accurate relationship between mixing blade inclined angle and mixing efficiency, the scope of experiments needs to be further expanded.

Future work includes conducting more experiments to determine the value of water particle parameters, and the theoretical basis for water equivalent to water particles needs to be further improved. The improvement of these works will improve the accuracy of the particle model to better reflect the physical phenomena in the actual production process. In addition, the simulation model verified in this paper can also be used to study the relationship between the speed of the planetary mixer main engine and the mixing efficiency, and to explore how to sense the changes in the properties of the materials in the planetary mixer during the mixing process, and to continuously adjust the rotation speed of the main engine to make the mixing blade mix the material at the current best rate, and finally achieve the goal of improving the mixing efficiency and reducing the energy consumption of the mixing equipment.

Footnotes

Acknowledgements

We are grateful to the reviewers and editors for their valuable comments and suggestions.

Handling Editor: Aarthy Esakkiappan

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Quanzhou City Science and Technology Program of China (grant number: 2021C007R), and the Key Laboratory of Fluid Power and Intelligent Electro-Hydraulic Control, China (Fuzhou University).

ORCID iD

Wenmin Lu

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