Optimization of Molding Process Parameters of Caragana korshinskii Kom. Based on Box-Behnken Design

Abstract

In this study, using the Box-Behnken design (BBD) experimental method, a plunger-type three-roller pelletizer was employed to explore the optimal pelletizing parameters for biomass fuel pellets with Caragana korshinskii Kom. strip as the raw material. The moisture content of the raw material, the length-to-diameter ratio of the forming die, and the rotational speed of the ring mold were identified as the experimental factors. The relaxation density of the biomass fuel (BMF) pellets and the productivity of the pelletizer were set as the experimental indicators. The study aimed to uncover the influence patterns of these factors on the pelletizing outcomes and establish regression equations between various factors and indicators. The results revealed that when Caragana korshinskii Kom. strip was used as the raw material in this pelletizer, the optimal pelletizing parameters were as follows: a moisture content of 15.5%, a forming die length-to-diameter ratio of 5.3, and a ring mold rotational speed of 30 rpm. Under these conditions, the relaxation density, mechanical durability, and productivity reached 1.139 g/cm³, 96.21%, and 6.278 t/h, respectively. The energy consumption per ton of pellets did not exceed 41.3 kWh. The significance of this study is its potential to expand the utilization range of Caragana korshinskii Kom., reduce environmental pollution at the same time, and make a certain contribution to carbon peak and carbon neutrality.

1. Introduction

Biomass energy is the third largest energy source on the planet after coal and oil [1]. It constitutes approximately 14% of global energy consumption [2]. Utilizing this renewable and environmentally friendly resource can significantly reduce net carbon emissions. To some extent, biomass offers an excellent alternative to fossil energy [3]. The world is abundant with forests and agricultural resources that can be used to produce biomass fuels [4]. However, the low relaxation density of biomass limits its direct application, as using this raw material can pose challenges in storage, transportation, and utilization [5,6]. Various densification methods have been applied to overcome these shortcomings and increase the relaxation density of biomass fuels [7]. In recent years, an increasing amount of crop residues such as straw, rice husks, and wheat straw, as well as forestry residues like wood chips, sawdust, bamboo scraps, fruit peels, and nut shells, have been used to produce biomass solid fuels, providing an effective pathway for the large-scale application of biomass energy [8,9,10,11,12,13]. Although various feedstocks have been reported as being used for pellet production, those studies concentrated solely on the incorporation of binders and the combustion characteristics of the pellets, neglecting to mention the pelleting process itself [14].

Caragana korshinskii Kom. is a shrub of the genus Caragana in the legume family. It is a kind of tree widely distributed in the arid and desert areas of northwest China, and it plays an important role in wind prevention, sand fixation, and soil and water conservation [15,16,17]. In recent years, with the increase in research on renewable energy and biomass energy, Caragana korshinskii Kom., whose calorific value can reach 18,770–19,270 kJ/kg, has received more and more attention as a potential biomass fuel source [18]. The surface of the branches of Caragana korshinskii Kom. has a waxy layer, which makes it easy to ignite with vigorous flames and a high combustion value.

Due to its remarkable drought resistance, cold tolerance, and salt-alkali tolerance, Caragana korshinskii Kom. plays a crucial role in sand-fixing and windbreak. It is an indispensable forestry resource in northwest China. However, perennial Caragana korshinskii kom. loses its nutritional value after lignification and is no longer suitable for forage use. To promote its growth and rejuvenation, annual pruning generates a large amount of branch waste. This waste, characterized by its hard wood and high fiber strength, is particularly suitable for processing into solid molded fuel [19]. Realizing the energetic utilization of this waste not only contributes to environmental protection, but also promotes effective recycling of resources, holding profound significance.

In addition, the lignification degree of Caragana korshinskii Kom. is high and its fiber content is rich, which provides a good raw material basis for the forming of biomass. Caragana korshinskii Kom. has a high calorific value and a low ash content, which makes it an excellent biomass fuel. Studies show that 1.63 kg dried Caragana korshinskii Kom. has a calorific value equivalent to 1 kg standard coal, which further proves its potential as a biomass fuel. Some research affirms that Caragana korshinskii Kom. can be used as a raw material in producing biomass molding fuel. Zhang [20] analyzed the effects of the force applied, particle size, temperature, and moisture content on the briquette density of Caragana korshinskii Kom. using Statistical Analysis System (SAS 9.4) software and Duncan multiple range tests, and obtained the primary and secondary relations of various factors. Xu [21] utilized Caragana korshinskii Kom. powder as the primary ingredient and wheat bran as the binder, employing the following optimal molding process parameters: a wheat bran content of 9%, a moisture content of 20%, and a molding temperature of 140 °C. Under these conditions, the resulting MBF pellets exhibited a relaxation density of 1.209 g/cm³ and a mechanical durability of 97.2%. Wu [22] conducted an analysis to determine the optimal conditions for particle size, moisture, temperature, and pressure to maximize the pressure density effect when preparing solid briquettes from Caragana korshinskii Kom. By applying the Taguchi method, the best combination of parameters was found to be a particle size of less than 0.63 mm, a moisture content of 8% (wet basis), a temperature of 130 °C, and a pressure of 120 MPa. Under these conditions, the relaxation density reached its maximum value of 1.152 g/cm³.

Biomass molding fuel made from Caragana korshinskii Kom. can be used as a clean and renewable energy source to replace traditional fossil fuels such as coal and oil. This helps reduce carbon emissions and mitigate global climate change. The development and application of biomass molding fuel made from Caragana korshinskii Kom. can promote the economic development of rural areas and increase the income level of farmers. At the same time, it can also provide a stable energy supply for rural areas and improve the rural energy structure. The industrialization of biomass molding fuel can promote the rapid development of the biomass energy industry and provide strong support for the optimization and upgrading of energy structures. However, at present, the processing and production costs of Caragana korshinskii Kom. biomass molding are relatively high, and there are still some technical bottlenecks in the process of Caragana korshinskii Kom. biomass molding, such as the wear of molding equipment, high energy consumption, and low relaxation density [23]. This limits its large-scale application. In order to reduce costs and improve the relaxation density of BMF, it is necessary to further optimize the production process and equipment and improve the molding efficiency and product quality.

There are various types of machines that are currently used for biomass densification and briquetting, primarily including screw extrusion, piston pressing, and die-roller pelletizing machines. Among them, die-roller pelletizing machines boast the highest production capacity, reaching up to 1500 kg/h. However, roller-ring die pelletizing machines encounter several issues during the molding process, such as uneven material distribution, easy upward displacement of raw materials, uneven pressure distribution, and frequent blockage of molding die holes. These issues greatly limit the promotion and application of biomass molding technology. This study focuses on the three-press roller pelletizer, using Caragana korshinskii Kom. strips as the raw material. Based on the Design-Expert BBD (Box-Behnken Design) experimental design method, the moisture content of Caragana korshinskii Kom. strips, the length-to-diameter ratio of the forming die, and the rotational speed of the ring mold are taken as the experimental factors. The relaxation density of the BMF pellets and the productivity of the pelletizer are selected as the experimental indicators. The influence of these factors on the indicators is explored, providing a theoretical basis and reference for the optimal design of forming process parameters for the three-roller pelletizer and accelerating the large-scale industrialization of Caragana korshinskii Kom.

2. Materials and Methods

2.1. Experimental Materials

In this study, Caragana korshinskii Kom. aged five years and older was harvested in the autumn of 2023 from Ulanqabu City (Lat. 42.53° N, Long. 112.36° E, and Alt. 1612 m), Inner Mongolia Autonomous Region, China. After being harvested, Caragana korshinskii Kom. branch and twig samples were cut into strips of 5–10 mm in length, which were then dried at ambient temperature. The naturally air-dried Caragana korshinskii Kom. strips are illustrated in Figure 1. The chemical composition analysis of Caragana korshinskii Kom. is shown in

Table 1. The chemical composition analysis of Caragana korshinskii Kom.

Moisture Content	Crude Protein	Crude Fat	Crude Fiber	Nitrogen-Free Extract	Ash	Phosphorus	Potassium
6.51%	15.13%	2.43%	39.67%	37.18%	5.39%	4.32%	2.31%

[24].

2.2. Experimental Equipment and Instruments

The plunger-type three-roller pelletizer developed in the laboratory is shown in Figure 2. In addition, a SIEMENS MICROMASTER 440 inverter (Siemens AG, Munich, Germany), SC69-02 moisture rapid tester (Shanghai Green Instrument Co., Ltd., Shanghai, China), vernier caliper (Chengdu Lianggong Measuring Tools Co., Ltd., Chengdu, China), DT300A electronic balance (Changzhou Henglong Instrument Co., Ltd., Changzhou, China), and TCS-100 stainless steel folding industrial electronic platform scale (Yongkang Qianju Industry and Trade Co., Ltd., Jinhua, China) were needed during the experiment.

As shown in Figure 3, the overall structural diagram of the pelletizer clearly illustrates its working principle. The core components of this pelletizer include three rolls, plungers, a ring mold, and forming dies, which work together to complete the compression and molding process of biomass materials. The three rolls are equipped with uniformly distributed plungers, and the ring mold is processed with molding holes evenly distributed according to a specific gear ratio. To ensure that the biomass raw materials can be smoothly filled into the ring holes without affecting the plunger bodies’ work on the pressure rolls, the engagement between the ring mold and the three rolls is installed at a certain angle, with the angle between the line connecting the two axial centers and the vertical direction being 45°. The three rolls and the ring mold rotate in the same direction, driven by idler gears. To ensure that the plungers on the rolls and the molding holes on the ring mold can engage accurately at a certain speed ratio, the relative position and angle between them need to be precisely adjusted to guarantee smooth cooperation during operation, thereby achieving effective compression and molding of biomass materials. During co-rotation, the plungers and straight molding holes engage slowly, with the plungers reaching the maximum engagement depth during rotation. The relationship between the speed ratio and diameter ensures that the rolls and ring mold have the same tangential linear velocity at the engagement point, achieving a gear-like transmission effect and thus avoiding motion interference. To ensure that the plungers and ring mold holes can smoothly engage one by one and safely separate during rotation while avoiding any form of interfering contact, chamfers are applied to the tops of the plungers and the entrances of the ring die holes, and the taper angle of the molding hole openings is set to 30°. Inside the ring mold holes, the materials are filled under the combined influence of gravity and the centrifugal force generated by the rotation of the ring mold. Subsequently, through the continuous and precise engagement movement between the ring mold and roller plungers, these materials are extruded into regular pellets.

The main design parameters of the pelletizer are shown in

Table 2. The main design parameters of the pelletizer.

Design Parameters	Value of Calculation
Theoretical efficiency	$\ge$1500 kg/h
Diameter of pellets	20 mm
Relaxation density	$\ge$1.15 g/cm3
Mechanical durability	$\ge$96.3%
Motor power	132 kW
Number of ring mold rows	6
Number of rollers	3
Ring mold hole distribution	60/row
Diameter of plungers	20 mm
Engagement circle’s diameter of ring mold	1100 mm
Engagement circle’s diameter of rollers	440 mm
Maximum revolution speed of ring mold	60 rpm
Percentage of forming	$\ge$90%
Energy consumption per ton	$\le$50 kWh

.

2.3. Experimental Methods

2.3.1. Control of the Length-to-Diameter Ratio of the Forming Mold

In this study the pelletizer adopts a sleeve-type combined ring mold structure. The double-layer forming mold is embedded into the base, and the upper and lower closure plates are fixed with bolts to form a single-layer raceway ring mold. This design enhances durability, stability, and efficiency. Based on the experimental design, three specifications of forming dies were processed, with length-to-diameter ratios of 5, 5.25, and 5.5, respectively.

2.3.2. Control of Moisture Content

The control of the moisture content of Caragana korshinskii Kom. is a critical step in the biomass forming process, as it directly affects the flowability, the formability of the raw material, and the quality of the final product. According to the experimental protocol, the cut and naturally air-dried Caragana korshinskii Kom. is adjusted by adding water in a certain proportion to control the moisture content at 10%, 15%, and 20%. After adjustment, the strip is sealed and allowed to stand for a week. Using a DT300A electronic balance, the mass of the tray provided by the SC69-02 rapid moisture tester is measured as m₁. A certain amount of material is loaded onto the tray, and the combined mass is measured as m₂. The tray is then placed into the SC69-02 rapid moisture tester for drying. The tray is removed every 15 min to measure its weight, and when the weight remains unchanged for three consecutive measurements, this weight is recorded as m₃. Therefore, the moisture content of the material is calculated as follows:

$$Y={\displaystyle \frac{m_2-m_3}{m_2-m_1}}\times 100\mathrm{\%}$$

(1)

The average moisture content values measured for the three materials with different moisture contents were 9.89%, 15.28%, and 20.94%, respectively. The maximum difference from the adjusted moisture content did not exceed 0.94%, meeting the requirements of the experiment.

2.3.3. Control of Rotation Speed

In this experiment, to facilitate the control of motor speed, a SIEMENS MICROMASTER 440 frequency converter was used to alter the motor’s frequency, with three settings of 10 Hz, 20 Hz, and 30 Hz, corresponding to motor speeds of 30 rpm, 45 rpm, and 60 rpm, respectively.

2.4. Experimental Index

Based on the experimental items and methods described in the literature [25,26,27], the process parameters of the pelletizer and the formed pellets were tested.

2.4.1. Relaxation Density of Pellets

Randomly select 5 pellets from the sample, measure the mass of each pellet using an electronic balance, and measure the length of each pellet using a vernier caliper. Calculate the relaxation density of each pellet using Equation (2) and take the average value.

$$\rho ={\displaystyle \frac{4000m}{\pi d^{2}l}}$$

(2)

where:

• ρ—relaxation density of the formed pellets, in g/cm³;
• m—average mass of the formed pellets, in g;
• d—average diameter of the formed pellets, in mm;
• L—average length of the formed pellets, in mm.

2.4.2. Productivity

During the production process, collect and weigh the pellets from the discharge outlet every 5 min, and calculate the productivity of the pelletizer using Equation (3).

$$\mathrm{Q}=3600{\displaystyle \frac{\mathrm{m}(1-\mathrm{H})}{\mathrm{t}(1-0.2)}}$$

(3)

where:

• Q—productivity, in kg/h;
• M—mass of the collected sample, in kg;
• H—moisture content of the formed pellets, in %;
• T—time taken to collect the sample, in seconds.

2.4.3. Energy Consumption

To calculate the energy consumption per ton of the pelletizer, use Equation (4):

$$W=1000{\displaystyle \frac{P}{Q}}$$

(4)

where:

• W—energy consumption per ton of the pelletizer, in kW·h/t;
• P—average power consumption during the operation of the pelletizer, in kW;
• Q—productivity, in kg/h.

2.4.4. Mechanical Durability

The mechanical durability of the pellets was determined using Equation (5). According to the ISO 17831-1 [28] standard, attrition tests involve placing a 0.5 kg test sample in a cylindrical box that is 500 mm in length and has a diameter of 500 mm. The box rotates at 50 revolutions per minute (rpm) for 10 min, during which time the BMF particles collide with each other and the internal surface of the box. After the test, the sample is sieved, and the oversize fraction, which is 3.5 mm or larger, is weighed.

$$D={\displaystyle \frac{m^{″}}{m^{’}}}\times 100\%$$

(5)

where:

• D—mechanical durability, in %;
• m″—mass of the pellet lumps whose sizes are not less than 3.5 mm after the test, in kg;
• m′—total mass of the formed pellets before the test, in kg.

2.5. Experimental Design

The experimental design employed a Box-Behnken design (BBD) method with three factors at three levels. Based on the relevant literature and previous experimental results [21,29,30,31,32], this study selected the moisture content of the raw material, the length-to-diameter ratio of the forming mold, and the rotational speed of the ring mold as the experimental factors. The experimental indices were set as the density of the formed particles and the productivity of the pelletizer. The factor levels are represented by 1, 0, and −1, respectively, leading to the coded table shown in

Table 3. The level coding table of the experimental factors.

Coding Level	Factors
	Moisture Content (%)	Length-to-Diameter Ratio of Forming Die	Rotational Speed of Ring Mold (rpm)
−1	10	5	30
0	15	5.25	45
1	20	5.5	60

.

3. Results

3.1. Experimental Results

The produced BMF pellets made from Caragana korshinskii Kom. using the three-roller pelletizer are shown in Figure 4.

This experiment utilized the Design-Expert 8.05b data analysis software to process and analyze the experimental results. The experimental arrangements and outcomes are presented in

Table 4. The experimental arrangement and results.

Sequence Number	X1 (%)	X2	X3 (rpm)	Y1 (g/cm3)	Y2 (t/h)
1	15	5.5	60	0.934	4.78
2	10	5.25	60	0.921	4.36
3	15	5	30	1.127	6.35
4	10	5.25	30	0.918	4.33
5	15	5.25	45	1.078	5.94
6	20	5.25	60	0.736	3.93
7	15	5.25	45	1.145	6.58
8	20	5.5	45	0.807	3.64
9	20	5	45	0.979	5.61
10	10	5.5	45	0.896	5.36
11	15	5	60	0.726	3.72
12	20	5.25	30	0.909	4.47
13	10	5	45	1.033	5.23
14	15	5.25	45	1.158	5.58
15	15	5.25	45	1.003	5.71
16	15	5.25	45	1.118	6.28
17	15	5.5	30	0.963	5.33

Note: X₁, X₂, and X₃ represent the moisture content, the length-to-diameter ratio of the forming mold, and the rotational speed of the ring mold, respectively. Y₁ and Y₂ represent the relaxation density of the BMF pellets and the productivity of the pelletizer, respectively.

.

3.2. Regression Equation for the Relaxation Density of Formed Particles

The regression equation for the relaxation density of the BMF pellets is shown in Equation (6), and the results of the analysis of variance (ANOVA) are presented in

Table 5. A variance analysis table of the relaxation density of the forming grain.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Modal	0.2458	9	0.0273	4.78	0.0255	Significant
X1	0.0142	1	0.0142	2.49	0.1588
X2	0.0088	1	0.0088	1.54	0.2549
X3	0.045	1	0.045	7.88	0.0262
AB	0.0003	1	0.0003	0.0537	0.8235
AC	0.0077	1	0.0077	1.36	0.2823
BC	0.0346	1	0.0346	6.06	0.0433
A2	0.0597	1	0.0597	10.46	0.0144
B2	0.0116	1	0.0116	2.04	0.1964
C2	0.0512	1	0.0512	8.98	0.02
Residual	0.04	7	0.0057
Lack of fit	0.0244	3	0.0081	2.08	0.2455	Not significant
Pure error	0.0156	4	0.0039
Cor total	0.2857	16

. As can be seen from Table 5, the model’s p-value is less than 0.005, indicating that the model’s regression equation is significant. The lack-of-fit p-value is 0.2455 (greater than 0.05), which is not significant [33]. Furthermore, the R² value of the model is 0.88602 (greater than 0.8), indicating that the equation fits the experimental data well and there is a significant correlation between the experimental factors and the response variable [34,35]. The excellent degree of fit suggests that this model is suitable for predicting the relaxation density of the BMF pellets.

$$Y_1=1.01-0.0421x_1-0.0331x_2-0.0750x_3-0.0088x_1{x}_2-0.0440x_1{x}_3+0.0930x_2{x}_3-0.1191x_1^2-0.0526x_2^2-0.1103x_3^2$$

(6)

3.3. Regression Equation for the Productivity of the Pelletizer

The regression equation for the productivity of the pelletizer is shown in Equation (7), and the results of the analysis of variance (ANOVA) are presented in

Table 6. A variance analysis table of the productivity of the pelletizer.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value	Source
Modal	11.73	9	1.3	4.25	0.0348	Significant
X1	0.3321	1	0.3321	1.08	0.3328
X2	0.405	1	0.405	1.32	0.2884
X3	1.7	1	1.7	5.55	0.0507
AB	1.1	1	1.1	3.59	0.0999
AC	0.0812	1	0.0812	0.2647	0.6228
BC	1.08	1	1.08	3.52	0.1026
A2	3.53	1	3.53	11.49	0.0116
B2	0.0858	1	0.0858	0.2796	0.6133
C2	2.9	1	2.9	9.46	0.0179
Residual	2.15	7	0.3069
Lack of fit	1.47	3	0.4902	2.9	0.1655	Not significant
Pure error	0.6773	4	0.1693
Cor total	13.88	16

. According to Table 6, the model’s p-value is 0.0348, indicating that the model’s regression equation is significant. The lack-of-fit p-value is 0.1655 (greater than 0.05), which is not significant. Additionally, the R² value of the model is 0.8453 (greater than 0.8), demonstrating that the model fits the data well with minimal experimental error. This indicates that the model is appropriate and can be used to predict the productivity of the pelletizer.

$$Y_2=6.02-0.2037x_1-0.2250x_2-0.4612x_3-0.5250x_1{x}_2-0.1425x_1{x}_3+0.5200x_2{x}_3-0.9153x_1^2-0.1428x_2^2-0.8302x_3^2$$

(7)

4. Discussion

4.1. The Primary and Secondary Effects of the Experimental Factors on the Experimental Response Variables

The contribution rates of each experimental factor to the experimental response variables are shown in

Table 7. The experimental factors’ rates of contribution to the experimental indexes.

Experimental Index	Value of Contribution Rate of Experimental Factors			Ranking of Contribution Rate
	X1	X2	X3
Y1	2.49	1.54	7.88	X2 > X3 > X1
Y2	1.08	1.32	5.55	X1 > X2 > X3

. The contribution rates of each experimental factor to the response variables can be determined based on the F-test values. For the relaxation density of the BMF pellets, the contribution rates of the experimental factors are as follows: ring mold rotational speed > moisture content > length-to-diameter ratio. For the productivity of the pelletizer, the contribution rates of the experimental factors are as follows: ring mold rotational speed > length-to-diameter ratio of forming die > moisture content.

For the relaxation density of the BMF pellets, the rotation speed of the ring mold contributes the most, as it directly affects the flow and molding speed of the material; the moisture content follows, as it serves as a binder during molding and has a significant impact on the interlocking and embedding of particles; the length–diameter ratio contributes relatively less, but still has a notable effect on relaxation density within a certain range [11,13,21,25,26,27]. As for the productivity of the pelletizer, the ring mold rotation speed, again, contributes the most, as it directly influences the material throughput speed and the pelletizer’s production capacity; the length–diameter ratio is second, due to its impact on the material compression ratio and friction resistance; moisture content contributes relatively less, but still has an influence on productivity within a certain range [29,34,35,36,37,38].

4.2. The Impact of Interactions Between Experimental Response Variables

Utilizing the Design-Expert data analysis software, we can delve into the intricate interactions among various experimental factors and their impacts on the test indicators, subsequently generating response surface plots and contour plots. These graphical representations offer a visual insight into how individual factors collectively influence the test indicators and the intricate interplay among them. By analyzing these response surface plots and contour plots, we can discern the patterns of how the interactions between different experimental factors affect the test indicators, thereby providing a theoretical foundation for optimizing the molding process parameters of the pelletizer.

4.2.1. The Influence of Experimental Factors on the Relaxation Density

Figure 5 presents a response surface plot illustrating the effects of two experimental factors on the relaxation density of the BMF pellets, with the third factor held at its central level. As evident from Figure 4, the surface slope is most pronounced when the ring die rotational speed varies, while changes in the moisture content of the Caragana korshinskii Kom. also lead to a noticeable slope. In contrast, alterations in the length-to-diameter ratio result in a relatively gentle slope. This indicates that the order of influence of the three experimental factors on the relaxation density of the BMF pellets is as follows: rotational speed of ring mold > moisture content of caragana > length-to-diameter ratio. When the length-to-diameter ratio remains relatively constant, reducing the rotational speed of the ring mold or increasing the moisture content of the Caragana korshinskii Kom. significantly enhances the relaxation density. Additionally, decreasing the ring die rotational speed can notably reduce energy consumption in actual production [26]. Figure 6 depicts the corresponding contour plots of the response surfaces, which reflect the significance of interactions between factors. Straighter contour lines suggest weaker interactions between parameters, whereas saddle-shaped or elliptical contour lines indicate stronger interactions [39]. It can be observed that the interactions among the three factors are all pronounced.

4.2.2. The Influence of Experimental Factors on Productivity

Figure 7 presents a response surface plot illustrating the influence of two experimental factors on the productivity of the pelletizer, with the third factor held at its central level. From the figure, it is evident that the surface slope is steepest when the ring mold speed varies, indicating a strong influence on productivity. The ring mold speed, the length–diameter ratio of the forming die, and the moisture content of the raw material have an impact on the productivity of the pelletizer [40]. Among them, ring mold speed has the greatest impact on the productivity of the pelletizer. During the biomass molding process, the design of the ring mold’s rotational speed needs to take into account various factors such as the particle molding rate, the type of material, and its stability. Excessively high rotational speed can reduce the molding rate, increase centrifugal force, affect the stability of the machine, and subsequently decrease the productivity of biomass densification molding. Conversely, excessively low rotational speed may increase the molding rate, but could lead to low production efficiency due to a reduced amount of material processed per unit of time [41]. Therefore, the rotational speed of the ring mold should be reasonably set according to the type, characteristics, and molding requirements of the material to achieve optimal molding effects and productivity.

When the length–diameter ratio changes, the surface undergoes a noticeable tilt, demonstrating its moderate influence. In contrast, alterations in moisture content result in a relatively gradual slope, signifying a lesser impact. Consequently, the order of influence of these three factors on the pelletizer’s productivity can be ranked as follows: ring mold speed > length–diameter ratio > moisture content. When the moisture content remains relatively stable, moderately reducing the length–diameter ratio or increasing the ring mold speed can significantly enhance productivity. However, to minimize energy consumption in practical production, appropriately decreasing the ring mold speed may be a viable option [42].

Figure 8, which corresponds to the response surface plot, presents a contour plot that reflects the significance of the interactions between factors. Straighter contour lines suggest weaker interactions between parameters, whereas saddle-shaped or elliptical contours indicate stronger interactions. It can be observed that the interaction between the length–diameter ratio and moisture content is not pronounced. In contrast, the interactions between the ring die speed and length–diameter ratio, as well as between the moisture content and ring die speed, have a notable impact on the forming pressure. In this scenario, appropriately decreasing both the ring die speed and the length–diameter ratio can lead to a noticeable reduction in the pelletizer’s productivity while also lowering energy consumption.

4.3. Optimization of the Pelletizing Process Parameters

Using Design-Expert 13 data analysis software, the forming parameters were optimized. After fitting the model and discussing the experimental results, considering both the relaxation density of the formed particles and the productivity of the pelletizer during the production process under the constraints of a moisture content range of 10% to 20%, a length–diameter ratio of the forming mold between 5 and 5.5, and a forming roller speed of 30 to 60 rpm, the optimization aimed to maximize both the relaxation density of the formed pellets and the productivity of the pelletizer. The optimized forming parameters were determined as follows: a moisture content of 15.58%, a length–diameter ratio of the forming mold of 5, and a forming mold speed of 34.70 rpm. Under these conditions, the density of the formed pellets reached 1.142 g/cm³, and the productivity of the pelletizer was 6.419 t/h.

4.4. Experimental Verification

Taking into account the practicality of the experiment, the optimal forming parameters were adjusted to the following: a moisture content of 15.5%, a length–diameter ratio of the forming mold of 5, and a forming roller speed of 30 rpm. To verify the reliability of the optimized forming parameters, five sets of experiments were conducted using the adjusted parameters, and predictions were made using the regression equation. The experimental and predicted values are presented in

Table 8. Comparisons between the experimental values and the predicted values.

Relaxation Density Y1 (g/cm3)		Relative Error (%)	Productivity Y2 (t/h)		Relative Error (%)	Mechanical Durability (%)	Energy Consumption (kW·h/t)
Experimental Value	Predicted Value		Experimental Value	Predicted Value
1.146	1.142	0.349	6.342	6.419	1.214	97.03	40.9
1.141	1.142	0.088	6.505	6.419	1.322	96.88	40.1
1.139	1.142	0.263	6.278	6.419	2.250	96.21	41.3
1.143	1.142	0.0877	6.409	6.419	0.156	96.92	40.7
1.140	1.142	0.175	6.424	6.419	0.078	96.71	40.3

.

As can be seen from Table 8, the maximum relative error for the relaxation density of the formed pellets is 0.349%, and the maximum relative error for the productivity of the pelletizer is 2.250%. This indicates that the regression equations established in this experiment for the density of the formed pellets and the productivity of the pelletizer are reliable, and the experimental results can be effectively predicted through the regression equations.

When the moisture content of Caragana korshinskii Kom. is 15.5%, with a length–diameter ratio of 5 and a mold rotation speed of 30 rpm, the minimum relaxation density of the molded pellets is 1.139 g/cm³; the minimum productivity is 6.278 t/h; the lowest mechanical durability is 96.21%; and the highest energy consumption is 41.3 kW·h/t. In comparison to the experimental results (relaxation density: 1.15 g/cm³, mechanical durability: 96.28%, productivity: 75 kg/h, energy consumption: 56 kW·h/t) gained by Ning [24], the relaxation density and durability are only reduced by 0.96% and 0.072%, respectively, while the productivity is increased by 83.71 times and the energy consumption is reduced by 55.26%. ISO 17225-6 [43], specific to non-wood pellets, stipulates that the mechanical durability should be at least 97.5% for class A and 96.0% for class B. In accordance with ISO 17225-6, MBF pellets made from Caragana korshinskii Kom. powder are of high quality, fulfilling the necessary criteria for storage, utilization, and transportation. Research [44,45] has shown that to enhance the quality of formed pellets, additives are typically required during the molding process. However, this study demonstrates that satisfactory formed pellets can be obtained without binders, thereby simplifying the molding process and advancing the industrial application of Caragana korshinskii particles.

5. Conclusions

Based on the Box-Behnken design (BBD) experimental method, the influence of the forming process parameters on the forming effect of the piston ring die molding machine was discussed, the optimal configuration of the forming process parameters of the pelletizer was found, and the regression equation between the test factors and indexes was established. This research shows that when using Caragana korshinskii Kom. as the raw material and pressing BMF pellets using the pelletizer, the optimal molding process parameters are as follows: the moisture content of Caragana korshinskii Kom. is 15.5%, the length–diameter ratio of the forming die is 5.3, and the rotation speed of the ring mold is 30 r. The relaxation density, durability, and productivity of the molding particles can reach their ideal states of 1.139 g/cm³, 96.21%, and 6.278 t/h, respectively. Energy consumption per ton is not more than 41.3 kWh.

The test factors with the highest contribution rates to the relaxation density of the pellets, in descending order, are the ring mold speed, the moisture content, and the length-to-diameter ratio of the forming die. The test factors with the highest contribution rates to the productivity of the pelletizer, in descending order, are the ring mold speed, the length-to-diameter ratio of the forming die, and the moisture content. The maximum relative error between the experimental and predicted values for the relaxation density of the pellets is 0.349%, and the maximum relative error for the productivity of the pelletizer is 2.250%, indicating a high degree of agreement.