Design and Testing of Segmented Spiral Total Mix Ration Mixer

Abstract

To address the challenges of non-uniform mixing in total mixed diet forage and the high power consumption of the required device, we developed a segmented spiral total mixed diet device. This development involved theoretical analysis to determine the structural parameters of the main body of the segmented spiral blades, the churn, and the creation of a test bed for the segmented spiral total mixed diet device. Taking mixing speed, mixing time, filling coefficient, and segmented spiral blade spacing as test factors and mixing uniformity and energy consumption per unit mass as test indexes, the optimal combination of operating parameters of the device was determined by using a four-factor, three-level orthogonal test method. The results of the validation test showed that the mixing uniformity of the device under these conditions was 93.41%, the energy consumption per unit mass was 4723.69 J, and the errors between the mixing test values of the device and the optimized values of the model were all less than 5%. This study can provide a reference for improving the working quality of the segmented spiral TMR mixer.

1. Introduction

Xinjiang serves as a pivotal hub for the production of animal products in China. The region boasts some of the nation’s highest cattle and sheep inventories. Various methods are employed for sheep farming, primarily direct feeding, prolonged grass short feeding, coarse and fine feeding, and total mixed ration (TMR) feeding [1]. Direct feeding, prolonged grass short feeding, and coarse and fine feeding are considered traditional approaches among these techniques. Throughout the production process, issues such as dyspepsia, selective eating, and metabolic diseases are frequently encountered [2], in addition to low forage utilization and elevated breeding costs. In light of these drawbacks associated with traditional feeding practices, TMR feeding has progressively emerged as the predominant method, particularly given the increasing scale and intensity of farming operations [3,4,5]. TMR mixers, machines designed to chop, knead, and blend straw with a concentrate to create TMR feed, play a central role in TMR feeding [6,7]. A blended feed can enhance the nutritional value of cattle and sheep feed, reduce the overall cost of stable feeding, and enhance the feed conversion rate. A TMR mixer’s mixing performance directly links to the quality and productivity of the TMR feed [8,9]. Consequently, enhancing mixing uniformity and reducing the power consumption of TMR mixers are of utmost importance [10].

Prior research on TMR mixers has predominantly centered on investigating the impact of structural design, spindle speed, processing duration, and other variables on the uniformity of forage mixing [11,12,13,14,15,16,17]. Building upon this foundation, domestic and international scholars have explored strategies to enhance the uniformity of TMR mixers. Hyunwoong [18] utilized the standard deviation and coefficient of variation methods to assess mixing uniformity, focusing on crude protein concentration. They evaluated the mixing performance of a 2.5 m³ flat-bottomed vertical TMR mixer and determined optimal and minimal mixing times through the curve slope method. Xia [19] employed CFD software for a three-dimensional (3D) flow field simulation inside a horizontal ribbon mixer. By adopting the CFD approach [20]. This analysis revealed the presence of turbulence at the intersection of inner and outer ribbons, promoting convective mixing. Yang [21] examined the physical dimensions and contact parameters between corn straw skin, pith, leaves, corn flour, salt, and rice straw. It was accomplished by creating a discrete element model using EDEM software to simulate the mixing process in a rotary TMR mixer, thereby identifying the primary factors influencing mixing uniformity and tracer selection criteria. Nevertheless, the factors influencing the mixing uniformity of segmented spiral TMR mixers remain unexplored.

This study aims to enhance the mixing uniformity and reduce the operational energy consumption of the segmented spiral TMR mixer. In this research, we conducted TMR feed mixing experiments using an existing segmented spiral TMR mixer. The second chapter of the paper deduces the key factors affecting uniformity and losses through theoretical analysis. The mixer parameters were optimized in the third chapter using the response surface analysis method. Subsequently, an evaluation of the optimal mixer parameters was performed, providing valuable insights for improving the mixing uniformity of the mixer.

2. Materials and Methods

2.1. Structure of the Machine

2.1.1. Entire Structure

The segmented spiral TMR mixer device used in this study primarily consists of segmented spiral agitators (agitator shaft tube, segmented spiral blades, and plum blades), fixed knives, a case, a frame, a motor, and other components, as shown in Figure 1. Its external dimensions are 2100 mm × 650 mm × 950 mm, with the agitator’s outer diameter measuring 380 mm. The device holds a sufficient volume of 0.26 m³, and

Table 1. Parameters of sectional spiral TMR mixer.

Item	Parameter
Appearance size/mm × mm × mm	2100 × 650 × 950
Tank volume/m3	0.26
Churn length/mm	1000
Outer diameter of the churn/mm	380
Inner diameter of the churn/mm	114
Number of segmented spiral blades/one	10
Number of plum blades/one	30

outlines the specific parameters of the device. By controlling the device parameters and collecting experimental data, adjustments can be made by changing the bottom casing with varying radii to control the clearance between the casing and blades. Additionally, the motor speed of the agitator can be controlled by adjusting the frequency using a variable frequency drive, thus enabling control of the agitator’s churn speed, as seen in Figure 2.

2.1.2. Working Principle

The primary working purpose of the segmented spiral TMR mixing device is to knead and mix the materials put into the feed box to make TMR feed for sheep. When working, the motor provides the power, the churn makes a clockwise circular motion, the bolt fixes the bottom shell, puts the material into the upper part of the box, and the material is subjected to the centrifugal force of the segmented spiral blades to carry out the circumferential movement. At the same time, arrange the segmented spiral blades in a centrosymmetric manner within the churn, displace the material on the axis to the central part of the box, and part of the material is dislocated in the gap of the segmented spiral blades and piled up in the central part of the box to form an accumulation to reach a certain angle. When the pile in the middle reaches a certain angle, the material slides down along the pile angle, and so on, repeatedly to realize the mixing of materials.

2.2. Segmented Spiral Agitator

The segmented spiral agitator constitutes the primary working component of the segmented spiral TMR mixing device, comprising essential parts such as the agitator shaft tube, segmented spiral blades, plum blades, bolts, and other components, as illustrated in Figure 3. The segmented spiral blades are securely affixed to the agitator shaft tube through welding, while the plum blades are fastened with bolts and mounted on the segmented spiral blades. Each segmented spiral blade is equipped with three plum blades. In this study, we adopted a central symmetrical arrangement along the spiral line to place the segmented spiral blades [22,23], totaling ten sets. The two adjacent sets of segmented spiral blades have an equal axial spacing, as shown in Figure 4. The agitator should be horizontally mounted within the device’s material box during operation.

The segmented spiral TMR mixing device primarily relies on segmented spiral churn to convey materials during operation. Subsequently, it leverages its central symmetrical structure to transport the materials to the central region, creating a three-dimensional circulation of materials and facilitating their mixing. The material conveying capacity of the segmented spiral churn impacts mixing efficiency significantly. The material conveying capacity of full-face spiral blades is related to parameters such as the churn speed, the filling coefficient, and the pitch, as expressed in Equation (1) [22,23].

$$Q=\frac{\pi D^2}{4}6047\phi \cdot s\cdot n\cdot {\gamma }_r\cdot C=D^2\cdot \phi \cdot s\cdot n\cdot {\gamma }_r\cdot C$$

(1)

where: Q represents the conveying capacity in t/h; D stands for the diameter of segmented spiral blades in meters, with a value of 0.38 m in this study; φ denotes the material volume filling coefficient; s represents the spacing between segmented spiral blades in meters, with a value of 0.3 m in this study; n signifies the churn speed, rpm; γ_r signifies the material bulk density in t/m³. C represents the inclined conveyor trimming coefficient, which is taken as 0.62 based on the table in this paper.

Given the gaps between the segmented spiral blades and the blades, a portion of the material is expected to slide into these gaps, thereby enhancing the device’s diffusion mixing capability. Consequently, the actual material conveying capacity of the segmented spiral churn should account for the amount of material that slips into these gaps. Therefore, the material conveying capacity of the segmented spiral churn is calculated as follows [23]:

$$Q=47D^2\cdot \phi \cdot s\cdot n\cdot \gamma \cdot C-Q_{\mathrm{s}}=0.45\cdot \phi \cdot n-Q_{\mathrm{s}}$$

(2)

where: Q_s represents the amount of material slipped in the gap between the segmented spiral blades, t/h.

The energy consumption required during the operation of the segmented spiral TMR mixing device is determined by the device’s power and processing time. The power required during the operation of the segmented spiral churn is as follows [23]:

$$P=\frac{Qg(W_{0}L+H)\eta \times {10}^{-3}}{t}=\frac{(\phi \cdot n-Q_{\mathrm{s}})(W_{0}L+H)\eta }{227}$$

(3)

where: P represents the power required for the segmented spiral TMR mixing device in kilowatts, η denotes the overall efficiency of the drive and transfer system with a value of 1.13 for a 30-degree inclination, Q stands for the conveying capacity in tons per hour, W₀ represents the coefficient of material’s gravitational resistance typically taken as 1.2, L represents the horizontal conveying distance of the material in meters with a value of 1 m in this study, H denotes the lifting height of the material with 0 m in this study, and t represents the duration of operation in hours.

By analyzing Equations (1)–(3), it is evident that the conveying capacity and required power of the segmented spiral churn are closely related to parameters such as the diameter of the spiral blades, the churn speed, the filling coefficient of the material box, the gap size between the segmented spiral blades, and the processing time. The spacing of these blades on the agitator shaft tube determines the gap between the segmented spiral blades. Therefore, adjusting the segmented spiral churn’s conveying capacity and energy consumption is possible by regulating parameters such as the segmented spiral blade arrangement distance, the churn speed, the filling coefficient, mixing time, and more. In turn, it allows for control over the mixing performance of the device.

2.3. Theoretical Analysis of the Mixing Process

2.3.1. Material Circumferential Force Analysis

To gain a deeper understanding of the circumferential motion of materials within the material box, the working area of the device around the circumference is divided into four regions labeled I, II, III, and IV, as shown in Figure 5. Choose a specific material for force analysis at any position within these four regions. From region I, the material enters and initially experiences the force of its weight, represented by G, causing it to descend. The segmented spiral churn provides the material with a supporting force, F_N1. Transfer the energy from the rotating churn to the material. The material experiences friction force f₁ between the spiral blades and static friction force f₂ between adjacent materials to the left. The friction force f₁ between the material and the segmented spiral blades overcomes the static friction force f₂ between materials as the churn moves from region I to region II. As the material moves to region II, it experiences the centrifugal force, f_l, generated by the segmented spiral blades, leading to a certain degree of scattering and promoting diffusion mixing. At the same time, the material encounters the shearing force, f_h, from the segmented spiral blades, with an angle α formed between the direction of shearing force and the direction of gravity. This shearing action causes shear mixing between material layers. At this point, the material continues to descend to region III, aided by the force of gravity G. In region III, the bottom casing’s supporting force, F_N2 supports the material, preventing further descent. It also experiences the pressure force, F_p, from the segmented spiral blades and plum blades. At this stage, significant forces act upon the material, capable of breaking up clumps or entangled materials. Additionally, the material exhibits an upward movement tendency due to the centrifugal force, f_l, exerted by the segmented spiral blades. Driven by the segmented spiral blades, it moves towards region IV. As the material reaches region IV, it encounters frictional forces from the housing, f_m, and centrifugal force, f_l, from the segmented spiral blades, directed towards region I. Furthermore, the gap between the segmented spiral blades and the casing widens in the central part of region IV, which serves as a transitional area between the bottom casing and the material box. The kinetic energy accumulated in the lower portion of the material is released, leading to a macroscopic scattering phenomenon directed upward. It promotes diffusion mixing among the materials. At this point, the material is propelled from region IV to region I, thus achieving the repetitive circumferential mixing of materials.

2.3.2. Material Axial Force Analysis

During the operation of the segmented spiral TMR mixing device, materials are subjected to the thrust force, F_T, exerted by the segmented spiral churn. This thrust force induces axial movement in the materials. In axial movement, their inherent properties and the forces acting on them influence the materials. Figure 6 illustrates the axial force experienced by the materials under the influence of the segmented spiral churn. The materials experience thrust force, F_T, from the segmented spiral blades directed toward the spiral rotation. Simultaneously, they encounter resistance force, Fr, from other materials that have already been pushed ahead of them, as well as friction forces, f₂, between materials, friction forces, f₁′, between materials and the device, friction forces, f₂, between materials, and pressure force, F_p, from the device, as well as support force, F₁′, from the materials below the material in question. Additionally, they receive support force, F_N1, from the segmented spiral churn. The thrust force, F_T, is resolved into circumferential force, F_y, and axial force, F_z. The materials are subjected to the axial force, F_z [24,25], resulting in displacement along the axial direction. This displacement continues until the materials accumulate at the center due to the segmented spiral churn’s central symmetric design. When the materials reach a certain angle of accumulation, they start sliding downward. Upon reaching the ends of the churn, they are once again influenced by F_z and transported back to the center, thus achieving repeated convective mixing along the axial direction. It is important to note that in the axial direction, there are gaps between the segmented spiral blades, and in these gaps, the pressure, F_p, from the segmented spiral blades on the materials vanishes. At this point, the direction of material movement is no longer in the direction of F_T, and some materials may move within the gaps between the segmented spiral blades, sliding directly into the previous spiral range. This phenomenon leads to the diffusion mixing of materials.

2.3.3. Motion Analysis

Materials subjected to the action of the segmented spiral churn experience motion, and the efficiency of the device’s mixing process is directly related to the magnitude of material movement speed. Consider any specific material point, denoted as “O”, located at any position along the segmented spiral churn. The motion of this material point under the influence of the segmented spiral blades primarily involves movement along the axial direction of the churn and the generation of circumferential motion within the blades, as illustrated in Figure 7. As shown in Figure 7, the distance from material point O to the axis of the segmented spiral churn is denoted as “r_z”. Under the effect of the segmented spiral churn, the material points experience a tangential velocity, V₀, which represents the linear velocity of the material at point O. The formula for calculating V₀ is as shown in Equation (4). The overall motion speed of the material is denoted as V_l, with its calculation formula given in Equation (4). Given the numerous contacts between materials in actual working conditions, friction forces need to be considered. At this point, the actual material motion direction deviates by an angle, γ, from V_l. Consequently, the actual material velocity is represented as V_s, with its calculation formula provided. To further break down the velocity into two directions—axial and tangential—the axial motion speed is denoted as V_z, and the tangential motion speed is represented as V_y. Their respective calculation formulas are given in Equation (4) [26].

$$\left\{\begin{array}{l}{V}_0=\frac{2\pi r_{\mathrm{z}}n}{60}\\ V_l=V_0\sin \beta \\ V_{\mathrm{s}}=\frac{V_l}{\cos \gamma }\\ V_y=V_s\cdot \sin (\beta +\gamma )\\ V_z=V_s\cdot \cos (\beta +\gamma )\end{array}\right.$$

(4)

where: V₀ denotes the material’s implicating speed, m/s; r_z denotes the distance between the material and the axis of segmented spiral churn, mm; n denotes the segmented spiral churn speed, rpm; V_l denotes the speed of the material without considering material friction, m/s; β denotes the angle between V_l and V_z, (°); V_s denotes the speed of the material when considering material friction, m/s; γ denotes the angle between V_l and V_s, (°); V_y denotes the material tangential movement speed, m/s; V_z denotes the material axial movement speed, m/s.

Therefore, it can be concluded that

$$\left\{\begin{array}{l}{V}_y=\frac{2\mathit{\pi }{r}_{z}n}{60}\cdot \frac{\sin \beta \sin (\beta +\gamma )}{\cos \gamma }\\ V_z=\frac{2\mathit{\pi }{r}_{z}n}{60}\cdot \frac{\sin \beta \cos (\beta +\gamma )}{\cos \gamma }\end{array}\right.$$

(5)

From Equation (5), it becomes evident that the motion of materials inside the device, both in the circumferential and axial directions, is influenced by factors such as the churn speed, pitch, the position of the material, and the friction between materials. By controlling these parameters, it is possible to regulate the speed at which materials are conveyed during device operation, thereby allowing for adjustments in the mixing efficiency.

2.3.4. Kinetic Analysis

The mixing process mainly relies on the segmented spiral churn to produce a conveying and centrifugal effect on the material so that the kinetic energy of the segmented spiral churn is transferred to the material, and its kinetic energy is greater than the energy required to overcome the friction between the materials, the material produces motion. According to the law of conservation of momentum and the kinetic energy theorem [27,28], there are

$$\left\{\begin{array}{l}V=\frac{2\pi rn}{60}\\ E=\frac{1}{2}M{V}^2\\ M_1{V}_1+m_w{v}_q=M_1{V}_2+m_1{v}_h\\ \Delta E=E_1-E_2-E_3\\ \Delta E=\frac{1}{2}{\left(\frac{2\pi r}{60}\right)}^2\left[M_1{n}_1{}^2-M_1{n}_2{}^2-\frac{M_1{}^2}{m_w}{\left(n_1-n_2\right)}^2\right]\end{array}\right.$$

(6)

where: V is the material speed, m/s; n is the churn speed of the segmented screw churn, rpm; E is the kinetic energy of the material, J; M is the mass of the material, kg; M₁ is the mass of the segmented screw blades, kg; V₁ is the speed of the material before the action of segmented spiral churn, m/s; m_w is the mass of the material subject to the action of segmented spiral blades, kg; V_q is the speed of the material subject to the action of segmented spiral churn, m/s, and the material is subject to the action of the bottom shell support force after entering the tank, which is regarded as 0; V₂ is the speed of the material after the action of segmented spiral churn, m/s; V_h is the speed of the material after being subjected to the action of segmented spiral churn, rpm; ΔE is the kinetic energy consumed by the mixture, J; E₁ is the kinetic energy before the action of the segmented screw blade on the material, J; E₂ is the kinetic energy after the action of the segmented screw blade on the material, J; E₃ is the kinetic energy after the action of the segmented screw churn received by the material, J; n₁ is the churn speed o before it acts on the material, rpm; n₂ is the churn speed after acting on the material, rpm.

By the impulse theorem, the combined force on the material is:

$$F_1=N\frac{2M_1\pi r\left(n_1-n_2\right)}{60t_h}$$

(7)

where: F₁ is the kneading force on licorice stalks, N; N is the number of segmented helical leaves; t_h is the processing time, s; r is the radius of the segmented screw churn, mm.

The material is subjected to a friction force of:

$$F_f={\mu }_z\frac{M_1{}^2{\pi }^2{r}^2{\left(n_1-n_2\right)}^2}{900m_w\left(r+h\right)}$$

(8)

where: F_f is the friction force on the material, N; μ_z is the friction coefficient between the material and the device; h is the gap between the segmented spiral blade and the bottom shell, mm, which in this paper is 15 mm.

Analyzing the Equations (6)–(8), it can be seen that the kinetic energy consumed by the material mixing, the combined force, and the friction force are related to the radius of the segmented spiral agitator, the mass, the churn speed, the quality of the material, the mixing time and other parameters, and the quality of the material is closely related to the filling factor of the material tank in the actual operation.

In summary and, combined with the actual conditions, we outlined how to control the churn speed, mixing time, filling coefficient, segmented spiral blade arrangement distance to adjust the mixing performance of the device to improve the quality of material mixing.

3. Results

3.1. Test Materials and Equipment

To improve the mixing degree of the mixer, in conjunction with the relevant literature [15,27] and the current situation of sheep farm research, this experiment used a total mixed diet composed of three materials: crushed licorice stem, silage, and corn flour. Therein, licorice stem and silage constituted 25% and 45% of the roughage, respectively, and corn flour constituted 30% of the concentrate. The churn speed was adjusted during the test using a Zhengtai NVF2G inverter. The churn torque was measured and gathered using the NJTY3 agricultural machinery general dynamic telemetry system. Figure 8 shows the test bench for the segmented spiral TMR mixer used in the test.

3.2. Pilot Program

Mixing uniformity is an essential technical parameter for measuring the mixing performance of the TMR mixer, and its superiority is an advantage of TMR feeding. Further, power consumption reflects the efficiency of the mixing process of the mixer; therefore, in this test, mix uniformity and energy consumption per unit mass were selected as the evaluation indices for mixing performance.

Following the ‘JB/T 11438-2013 TMR mixer’ standard [29], rice was used as a tracer and the rice and the material were placed in the feed box during the test, adding 3% of the total material. After the test, ten samples weighing 1000 g each were evenly extracted from multiple locations in the feed box as test samples for determining material mixing uniformity. Four materials in each sample were screened and weighed using a vibrating screen. Multiple samples appeared to have a similar overall percentage of each of the three materials with rice. Therefore, by calculating the percentage of rice mass in each sample to the total sample mass, the mixing uniformity of the remaining three materials was expressed by calculating the rice mixing uniformity using Equations (9) and (10). The greater the mixing uniformity, the more uniformly the materials are mixed and the better the mixing performance of the equipment.

$$S_h=\sqrt{\frac{{\displaystyle \sum _{i=1}^{ni}{(X_i-\overline{X})}^2}}{ni-1}}$$

(9)

where: S_h represents the standard deviation of the sample; n_i represents the number of samples; X_i represents the percentage of tracer mass and sample mass in the sample, %; and $\overline{X}$ denotes the average of the percentages of tracer mass and sample mass in the sample, %.

$$M_h=\left(1-\frac{S_h}{\overline{X}}\right)\times 100\%$$

(10)

where: M_h represents mixing uniformity, %.

Energy consumption per unit mass refers to the energy required for mixing unit mass materials, which can yield the energy consumed by the device during operation [27,28] and thus reflect the device’s efficiency in terms of the task of mixing. The calculation Equations for the same is

$$W=\frac{T{\omega }_{j}t}{m_l}=2\pi n{t}_h\frac{{\displaystyle \sum _{i=1}^u{T}_i}}{60u{m}_l}$$

(11)

where: W denotes the energy consumption per unit mass, J/kg; T denotes torque, N m; ω_j denotes the angular velocity of the segmented spiral churn, rad/s; t_h denotes mixing time, min; m_l denotes the material quality, kg; n denotes the churn speed, rpm; $u$ denotes the number of torque data collected in a single test; and T_i denotes the instantaneous torque collected at the i-th time, N m.

3.3. Determination of the Range of Test Factor Parameters

Many factors influence the mixing performance of the segmented spiral TMR mixer, including the churn speed, mixing time, material addition method, filling coefficient, the gap between the device and the bottom shell, segmented spiral blade arrangement distance and blade type. Despite the limitations of test conditions and test equipment, under the premise of preliminary theoretical analysis and pre-test, the mixing speed, mixing time, filling coefficient and segmented spiral blade arrangement distance were finally selected as the test factors of this study.

(1)

Churn speed

During operation, the churn speed directly impacts the material’s mixing quality. If the churn speed is high, the centrifugal force of the spiral blade is high, and the material is thrown to the outer side of the segmented spiral blade; if the axial conveying is fast, the material is quickly conveyed to the middle, reducing the shear mixing and diffusion mixing ability of the device. In contrast, the linear speed of the churn will increase, and the plum blade installed on the segmented spiral blade will produce more kinetic energy, increasing the acceptable powder rate after material processing and resulting in a TMR feed that is not conducive to animal rumination. Suppose the rotation speed of the churn is too slow. In that case, it heightens the extrusion effect between the materials, and the material agglomerates owing to the high-water content of the silage. At this point, the dispersion performance of the material will reduce along with the mixing performance of the device. Therefore, the churn speed parameter range should be thoroughly considered and reasonably chosen. Accordingly, in the present study, based on previous theoretical analysis and related research in conjunction with the pre-test results of the device, we set the speed range of the churn to 20–40 rpm.

(2)

Mixing time

The duration of the mixing time directly affects the moving distance of the material inside the device and, thus, the mixing quality. If the mixing time is longer, the material cannot be thoroughly mixed, convective mixing is not visible, and the material cannot fully move in the tank, resulting in low mixing uniformity and inability to meet TMR feeding requirements. If the mixing time is too long, it will cause excessive mixing of materials, generating the mixing phenomenon and increasing energy consumption. Based on the preceding considerations and the pre-testing results, we set the range for the mixing time level to 2–8 min.

(3)

Filling coefficient

The filling coefficient is the ratio of the amount of material added to the tank each time to its volume. When feed processing is performed in the device, if the filling coefficient is too small, the total amount of moving materials in space with the segmented spiral churn is too small; consequently, 3D circulation cannot be formed, or the 3D circulation effect is weak, and cannot fully utilize the segmented spiral churn for material mixing. It induces a low utilization rate of energy and low productivity. If the filling coefficient is too high, it will affect the flow speed of the 3D circulation of the material and increase the mixing time, both of which are detrimental to feed processing. The device, in contrast, uses a central symmetric design, with accumulation occurring in the middle during operation. If the filling coefficient is too large, accumulation will occur in the middle. When the accumulation forms, it is too large in the center, causing the material to overflow the material box. Based on the preceding considerations and the pre-testing results, the filling coefficient level range was set to 0.3–0.7.

(4)

Segmented spiral blade arrangement distance

The segmented spiral blade arrangement distance along the spiral line establishes the size of the segmented spiral blade spacing. During operation, the segmented spiral blades continuously transport the material to the center of the device for convective mixing. It moves in its gap for diffusion mixing. If the sectional spiral arrangement distance is too short, the gap is too small and not conducive to material diffusion in the gap. If the segmented spiral blades are arranged too far apart, the gap is too large, and the material conveying efficiency is low, reducing the working efficiency of the device. Based on the preceding considerations and the pre-testing results, the horizontal range of the segmented spiral blade arrangement distance was determined to be 140–160 mm.

3.4. Results and Analysis

In order to explore the optimal parameters of the device, the Box-Behnken experimental design method was used to carry out a four-factor, three-level quadratic orthogonal rotating center combination test using the churn speed, mixing time, filling coefficient, and segmented spiral blade arrangement distance as influencing factors, and the mixing uniformity and energy consumption per unit mass as the evaluating indexes, based on the experimental factor levels coded in

Table 2. Test factor level coding table.

Level	X1 Churn Speed /(rpm)	X2 Mixing Time /(min)	X3 Filling Coefficient	X4 Segmented Spiral Blade Arrangement Distance /(mm)
−1	20	2	0.3	140
0	30	5	0.5	150
1	40	8	0.7	160

. The experiment was designed with the experimental design software Design-Expert design four-factor three-level Box-Behnke test program; a total of 17 groups of tests were performed, including 12 groups of analytical factors, five groups of zero-point estimation error, and each group of tests was carried out three times with the average value presented as the final test results.

3.4.1. Mixing Uniformity

(1)

Result analysis of mixing uniformity

Using the Design-Expert software to analyze the mixing uniformity data presented in

Table 3. Test scheme and results.

Serial Number	X1 Churn Speed /(rpm)	X2 Mixing Time /(min)	X3 Filling Coefficient	X4 Segmented Spiral Blade Arrangement Distance /(mm)	Y1 Mixing Uniformity/(%)	Y2 Energy Consumption per Unit Mass/ (J/kg)
1	40	5	0.3	150	91.36	4852.69
2	30	5	0.7	140	83.54	3619.37
3	30	5	0.7	160	85.21	8454.32
4	30	5	0.5	150	90.79	4328.49
5	30	2	0.3	150	87.37	2829.9
6	40	5	0.5	140	91.59	5173.29
7	30	5	0.3	140	93.63	4263.76
8	30	5	0.3	160	86.27	6083.31
9	30	8	0.7	150	93.92	6336.69
10	20	5	0.7	150	83.9	4692.35
11	20	5	0.5	140	87.36	3596.57
12	30	8	0.3	150	92.16	4158.93
13	30	2	0.5	140	81.99	2119.35
14	30	5	0.5	150	89.9	4004.21
15	30	2	0.7	150	79.38	2968.9
16	20	5	0.5	160	85.38	7321.96
17	20	5	0.3	150	90.87	3144.94
18	20	2	0.5	150	80.1	1996.84
19	40	5	0.7	150	89.76	4833.31
20	30	5	0.5	150	90.35	4683.65
21	30	8	0.5	140	93.28	5407.63
22	20	8	0.5	150	91.02	5238.48
23	30	2	0.5	160	83.54	5963.17
24	30	5	0.5	150	90.52	4441.7
25	30	8	0.5	160	89.28	7959.58
26	40	8	0.5	150	94.71	6816.76
27	30	5	0.5	150	91.94	4157.55
28	40	2	0.5	150	88.29	3993.63
29	40	5	0.5	160	86.77	8427.37

and multiple regression fitting, we established regression equations of Y₁ to X₁, X₂, X₃, and X₄, and tested their significance.

Table 4. Regression equation analysis of mixing uniformity.

Source	Quadratic Sum	Degree of Freedom	Mean Square Deviation	F	Significance
Model	466.88	12	38.91	31.94	<0.0001
X1	47.40	1	47.40	3.92	<0.0001
X2	240.31	1	240.31	197.30	<0.0001
X3	56.12	1	56.12	46.07	<0.0001
X4	18.60	1	18.60	15.27	0.0013
X1X2	5.06	1	5.06	4.16	0.0584
X1X3	7.21	1	7.21	5.92	0.0271
X2X3	23.77	1	23.77	19.51	0.0004
X2X4	7.70	1	7.70	6.32	0.0230
X3X4	20.39	1	20.39	16.74	0.0009
X22	11.21	1	11.21	9.20	0.0079
X32	6.72	1	6.72	5.52	0.0320
X42	32.29	1	32.29	26.51	<0.0001
Residual	19.49	16	1.22
Lack of fit	17.15	12	1.43	2.44	0.2015
Pure error	2.34	4	0.5851
Correct total	486.37	28

presents the variance analysis results. p < 0.0001 for the Y₁ model under the Box–Behnken model shows that the regression model was highly significant.

The absolute R² coefficient is 0.96, indicating that the model can fit > 96% of the test results. The lack of fit p > 0.05 indicates a high quadratic regression fitting degree.

X₁, X₂, X₃, X₄, X₂X₃, X₃X₄, X₂² and X₄² had a highly significant impact on the mixing uniformity model, X₁X₃, X₂X₄, and X₃² had a significant impact on the mixing uniformity model, while X₁X₂ had an insignificant impact on mixing uniformity model. The order of the influence of each experimental factor on the mixing uniformity model in terms of the significance of the influence is mixing time, filling coefficient, churn speed, and segmented spiral blade arrangement distance. We eliminated the insignificant factors and analyzed them again, then obtained the quadratic regression coding equation for each variable concerning mixing uniformity, as shown in Equation (12).

$$\begin{array}{c}{Y}_1=90.27+1.99X_1+4.47X_2-2.16X_3-1.25X_4-1.12X_1{X}_2+1.34X_1{X}_3\\ +2.44X_2{X}_3-1.39X_2{X}_4+2.26X_3{X}_4-1.29X_2{}^2-0.10X_3{}^2-2.19X_4{}^2\end{array}$$

(12)

In the regression equation, the absolute value of the coefficient determines the factor’s influence on the qualified rate. Therefore, the order of the influence of each factor on the mixing degree is mixing time, filling coefficient, churn speed, and segmented spiral blade arrangement distance, which is consistent with the variance analysis results.

(2)

Surface analysis of mixing uniformity parameters

Figure 9a shows that the mixing uniformity reaches its maximum when the churn speed and mixing time are high. The main reason is that when the churn speed is high, the material transported by the axial churn to the middle increases, as does the centrifugal force and linear velocity generated by the circumferentially segmented spiral blade. Consequently, the material moves faster in the circumferential direction, strengthening shear mixing. This results in more intense material movement. The longer the mixing time, the longer the duration of the intensified material movement, and thus the more uniform the mixing.

As can be observed in Figure 9b, the maximum mixing uniformity is obtained when the churn speed is high and the filling coefficient is low. The main reason is that the material moves violently when the churn speed is high.

As shown in Figure 9c, when the filling coefficient is high and the filling coefficient and mixing time are both low, the mixing uniformity rapidly increases with increasing mixing time. When the filling coefficient is low and the mixing time is high, the mixing uniformity exhibits a slight downward trend. When the filling coefficient is high, the material moves quickly inside the device as the mixing time increases, and the interaction between the material and the material is also enhanced. The material has a high degree of diffusion and convection, and the material per unit time is more significant. Therefore, while it is easier to mix when the filling coefficient is low in the early stages of mixing, as time passes when the filling coefficient is high, the improvement rate of mixing uniformity is more significant than when the filling coefficient is low. When the filling coefficient is low and the mixing time is high, there are fewer materials inside the device currently, and the materials continue to exchange positions as time passes. However, because the uniform mixing of the materials occurs relatively quickly, the mixing uniformity grows slowly, and the mixing time process appears. Over-mixing causes re-stratification of the materials, as does decreased mixing uniformity.

According to Figure 9d, when the mixing time is low, the mixing uniformity first increases and then decreases as the segmented spiral blade arrangement distance increases. When the mixing time is high, the mixing uniformity decreases directly to the arrangement distance of the segmented spiral blades. When the mixing time and the segmented spiral blade arrangement distance are low, the gap between the mixed segmented spiral blades is small, and the axial movement of the material is more intense, but the diffusion mixing ability is poor. As the distance between the blade gaps increases, more materials can move, and the diffusion mixing ability strengthens, improving mixing uniformity. However, as the arrangement distance increases, the distance in the middle of the segmented spiral blade shortens, reducing the accumulation ability of the material in the middle. Although the diffusion mixing ability improves, the convective mixing ability deteriorates, resulting in a downward trend in mixing uniformity. When the mixing time is high, the material can be fully convectively mixed under the action of a low-level arrangement distance, resulting in a downward trend in mixing uniformity.

As shown in Figure 9e, when the filling coefficient is low, the mixing uniformity decreases as the segmented spiral blade arrangement distance increases; when the filling coefficient is high, the mixing uniformity first increases and then decreases as the arrangement distance increases. When the filling factor is low, the device has fewer materials, and the mixing time is 0. If the materials are relatively sufficient, a conveyor with a shorter arrangement distance can transport them to the center for complete mixing via convection. Although the material diffusion capacity increases as the arrangement distance between the segmented spiral blades increases, the convective mixing capacity decreases, decreasing mixing uniformity.

3.4.2. Energy Consumption per Unit Mass

(1)

Result from the analysis of energy consumption per unit mass

Using Design-Expert software to analyze the mixing uniformity data in Table 3 and multiple regression fitting, the established regression equations of Y₂ to X₁, X₂, X₃ and X₄, and their significance were tested.

Table 5. Regression equation analysis of energy consumption per unit mass.

Source	Quadratic Sum	Degree of Freedom	Mean Square Deviation	F	Significance
Model	8.170 × 107	10	8.170 × 106	87.75	<0.0001
X1	5.475 × 106	1	5.475 × 106	58.81	<0.0001
X2	2.146 × 107	1	2.146 × 107	230.48	<0.0001
X3	2.587 × 106	1	2.587 × 106	27.78	<0.0001
X4	3.343 × 107	1	3.343 × 107	359.11	<0.0001
X1X3	6.137 × 105	1	6.137 × 105	6.59	0.01941
X2X3	1.039 × 106	1	1.039 × 106	11.16	0.0036
X2X4	4.172 × 105	1	4.172 × 105	4.48	0.0484
X3X4	2.273 × 106	1	2.273 × 106	24.42	0.0001
X12	1.067 × 106	1	1.067 × 106	11.46	0.0033
X42	1.413 × 107	1	1.413 × 107	151.77	<0.0001
Residual	1.676 × 106	18	93,098.62
Lack of fit	1.403 × 106	14	1.002 × 105	1.47	0.3839
Pure error	2.732 × 105	4	68,297.24
Correct total	8.337 × 107	28

displays the variance analysis results. The Box–Behnken model’s Y₂ model p < 0.0001 demonstrated that the regression model was highly significant.

The absolute coefficient R² is 0.98, indicating that the model can fit > 98% of the test results. Lack of fit p > 0.05 indicates a high quadratic regression fitting degree.

X₁, X₂, X₃, X₄, X₂X₃, X₃X₄, X₁² and X₄² had a significant impact, while X₁X₃ and X₂X₄ had an insignificant impact on the energy consumption per unit mass model. We eliminated the insignificant factors and analyzed them again. The quadratic regression coding equations for each variable concerning energy consumption per unit mass were obtained, as shown in Equation (13).

$$\begin{array}{c}{Y}_2=4137.30+675.49X_1+1337.19X_2+464.28X_3+1669.15X_4-391.70X_1{X}_3\\ +509.69X_2{X}_3-322.97X_2{X}_4+753.85X_3{X}_4+393.12X_1{}^2+1430.80X_4{}^2\end{array}$$

(13)

In the regression equation, the absolute value of the coefficient determines the factor’s influence on the qualified rate. Therefore, the arrangement distance of the segmented spiral blades, the mixing time, the churn speed, and the filling coefficient significantly influence the mixing degree. This is consistent with the variance analysis results.

(2)

Surface analysis of energy consumption per unit mass

As shown in Figure 10a, the energy consumption per unit mass first decreases and then increases as the churn speed increases. With an increasing filling coefficient, the energy consumption per unit mass increases. When the filling system is at total capacity, the amount of material in the device is large, and the churn speed is slow. The extrusion of the material is more intense than when the amount of material is less; hence, the downward trend of energy consumption is more significant. Increase the churn speed to 0. The increase in materials offsets the phenomenon of more significant extrusion pressure caused by the increase in churn speed, leading to an increase in energy consumption. Therefore, the energy consumption per unit mass increases, and the increased range is close. When the churn speed is low, the extrusion pressure of the device on the material increases as the number of materials increases. Therefore, when the churn speed is low, the upward trend in energy consumption per unit mass is more visible as the filling coefficient increases.

As shown in Figure 10b, the energy consumption per unit mass increases as the mixing time increases; an increasing trend is observed as the filling coefficient increases.

As shown in Figure 10c, the energy consumption per unit mass first decreases and then increases as the segmented spiral blade arrangement distance increases; when the mixing time is low, the energy consumption per unit mass is higher than when the mixing time is high, and the upward trend of the increase in the segmented spiral blade arrangement distance is more prominent. When the mixing time is short, the device subjects the material to a shorter period of churning force. When the filling coefficient is 0, as the segmented spiral blade arrangement distance increases, the spacing between the two segmented spiral blades in the middle decreases, increasing unit mass energy consumption. The rate of increase exceeds the increase in unit mass energy consumption caused by the increase in mixing time; hence, the energy consumption required when the segmented spiral blade arrangement distance is at a high level exceeds that at a low level. When a segmented spiral blade arrangement distance is low, the increase in unit mass energy consumption caused by an increase in mixing time is faster than when the arrangement distance is significant.

As shown in Figure 10d, when the segmented spiral blade arrangement distance is small, the energy consumption per unit mass slowly increases with increasing filling coefficient. The increase in energy consumption per unit mass with increasing arrangement distance is proportional to the increase in the filling coefficient. At 0, the segmented spiral blade arrangement distance has a more significant influence on the energy consumption per unit mass than the filling coefficient. The main reason for this is that as the segmented spiral blade and filling coefficient rise, it is affected by the increase in material. In contrast, it is influenced by the expansion of the blade spacing between and the clamping effect of the middle two spiral blades on the material, which causes the required energy consumption to increase faster.

3.5. Parameter Optimization

The analysis of the influence of the above parameter indexes on mixing performance reveals that the influence of different factors on mixing uniformity and energy consumption per unit mass has distinct characteristics. The test parameters must be optimized to improve the mixing performance of the segmented spiral TMR mixer.

Because mixing uniformity refers to the uniformity of the material after mixing, the higher the mixing uniformity, the stronger the mixing ability of the transposition to the material. Thus, achieving the maximum value of the mixing uniformity is essential; energy consumption per unit mass describes the amount of energy consumed during the operation that can reflect the device’s efficiency. Lower energy consumption per unit mass reduces the energy required for mixing. Therefore, the minimum energy consumption per unit mass is required. Further, to enhance productivity, the full coefficient range is set to 0.5–0.7, the churn speed is 20–40 rpm, the mixing time is 2–8 min, and the segmented spiral arrangement distance is 140–160 mm. Equation (14) establishes the constraint equation. The constraint equation is solved using the numerical function of Design-Expert software.

$$\left\{\begin{array}{l}20\le X_1\le 40\\ 2\le X_2\le 8\\ 0.5\le X_3\le 0.7\\ 140\le X_4\le 160\\ \max Y_1\left(X_1,X_2,X_3,X_4\right)\\ \min Y_2\left(X_1,X_2,X_3,X_4\right)\end{array}\right.$$

(14)

When the churn speed is 27.52 rpm, the mixing time is 7.42 min, the filling coefficient is 0.50, the segmented spiral blade arrangement distance is 144.89 mm, and the mixing uniformity is 93.41%. The energy consumption per unit mass is 4723.69 J/kg, according to the results. Currently, the mixing performance of the device is optimal. To validate the model’s reliability, based on the actual test conditions, the above parameters were rounded to the churn speed of 28 rpm, the mixing time of 7.5 min, the filling coefficient of 0.5, and the segmented spiral arrangement distance of 140 mm. Three verification tests were performed, with the results shown in

Table 6. Comparison of model optimized values with validation test values.

Item	Evaluating Indicator
	Mixing Uniformity (%)	Energy Consumption per Unit Mass (J/kg)
Model optimization value	93.41	4723.69
Verify test values	90.64	4497.26
Relative error (%)	2.97	4.79

.

The verification test results show that the error between the device mixing test value and the model optimization value is < 5%, indicating that the model optimization is feasible and fulfills the operational requirements of relevant standards [30,31], which can be used to guide the design and research on related devices.

4. Conclusions

(1)

We analyzed the circumferential force and axial force of the material during the working process of the segmented spiral TMR mixer, and analyzed the kinematics and dynamics of the device working process simultaneously. The results show that it is possible to control the quality of the material mixing by adjusting the parameters of churn rotation speed, mixing time, filling coefficient, and the distance of the segmented spiral blades to improve the mixing performance of the device, and to set up a test bed for the segmented spiral TMR mixing device to provide a device basis for the subsequent material mixing test.

(2)

To address the problem of low mixing uniformity and high-power consumption per unit mass of the segmented spiral TMR mixer, the quadratic multinomial influence model test method with four factors and three levels was used to design the test, and the Design-Expert software was used for data processing. Using variance analysis, we established and analyzed the regression mathematical model for mixing uniformity and energy consumption per unit mass. The primary and secondary factors influencing the mixing uniformity were the mixing time, filling coefficient, churn speed, and segmented spiral arrangement distance. The primary and secondary factors influencing the energy consumption per unit mass were the segmented spiral arrangement distance, mixing time, churn speed, and filling coefficient. The effect of mixing uniformity on the energy consumption per unit mass was investigated using a single-factor experiment.

(3)

The Box–Behnken combination test method was used to optimize the regression model based on the importance of the optimization target. The churn speed was 28 rpm, the mixing time was 7.5 min, the filling coefficient was 0.5, and the segmented spiral blade arrangement distance was 140 mm. Under these conditions, the mixing uniformity was 93.41%, and the energy consumption per unit mass was 4723.69 J/kg. According to the verification test results, the error between the device mixing test value and the model optimization value did not exceed 5%, indicating that the model optimization is feasible and fulfills operational requirements.

(4)

The mixer was designed with a single-shaft structure, and during operation, it experiences torque in the direction of shaft rotation. However, when there is an excess of feed or when the speed is too high, it can affect the balance of the device. In the future, a double-shaft design with a segmented spiral structure may be considered to enhance the overall stability of the device.

(5)

This paper is only for Xinjiang’s commonly used materials, licorice stalks, silage, and cornmeal; we used three materials to carry out the relevant research. In the later stage, it would be worth exploring the use of different areas and different materials in the study of mixing effects.