Design and Experimental Evaluation of a Pulsating Rubbing-Based Banana Fiber Extractor

Abstract

Banana fiber, as a naturally biodegradable material, exhibits excellent mechanical properties and considerable application potential. However, conventional rotary blade scraping extractors often cause significant fiber damage during extraction, thereby reducing fiber quality. To enhance fiber integrity and extraction efficiency, this study developed a pulsating rubbing-based banana fiber extractor. The device comprises a rubbing device with two grass-textured belts and a pulsating pressing device driven by a cam mechanism. Through the synergistic action of periodic pressing and rubbing, flexible fracture of banana stems and efficient fiber separation are achieved. The fiber extraction process was simulated using the RecurDyn rigid–flexible coupling analysis method to verify the dynamic behavior of stem slices during rubbing. Structural parameters were optimized based on the Box–Behnken experimental design, with 17 groups of tests conducted, each repeated three times and averaged. The results indicated that, when the spring outer diameter was 30 mm, the feeding interval of stem slices was 4 s, and the clamping angle between the stem slices and the rubbing belts was 90°, the fiber extraction rate reached 61.35%, the impurity rate was 9.01%, and the integrity rate was 96.22%. These findings verify the feasibility of the equipment structure and process parameters, achieve a favorable balance between extraction efficiency and fiber quality, and provide a novel technical pathway and equipment support for the high-value utilization of banana stem resources.

1. Introduction

The banana, a plant of the Musa genus in the Musaceae family, is cultivated in over 130 countries worldwide. The unique geographical and climatic conditions of Hainan Province are particularly favorable for producing high-quality bananas [1]. By the end of 2023, the banana planting area in Hainan Province reached approximately 35,000 hectares, with an annual output of about 1.18 million tons, accounting for 28.6% of the province’s total fruit production [2]. After bananas are harvested, a large amount of banana plant stems is discarded or burned as waste, which not only leads to resource waste but causes severe environmental pollution [3]. In recent years, the comprehensive utilization of banana stems has gained increasing attention. Among various approaches, extracting fibers from banana stems is regarded as a key method of resource utilization [4,5]. By extracting fibers from banana stems, agricultural waste can be effectively reduced, while providing a new type of natural fiber material for industries such as papermaking and textiles [6,7,8], offering both economic and environmental benefits.

The process of banana fiber extraction mainly involves the degumming and separation of banana fibers. Existing degumming techniques for plant fibers typically rely on chemical agents—such as inorganic acids, alkalis, and oxidants—or on microorganisms and the enzymes they secrete, to remove pectin, lignin, and other non-cellulose components from banana stems [9]. Reference [10] treated banana fibers with sodium hydroxide and used response surface methodology and analysis of variance to investigate the effects of temperature, concentration, and treatment time. Their results showed that the alkaline treatment significantly enhanced the adhesion between banana fibers and the polylactic acid matrix, thereby improving the overall performance of the composite material. Reference [11] extracted eco-friendly thyme fibers via a chemical soaking method and employed chemical analysis and X-ray Diffraction (XRD) to explore their feasibility as bio-composite materials. They found that fibers extracted after 90 h of soaking exhibited the highest activation energy and thermal stability. Reference [12] pretreated banana fibers through warm-water retting and studied optimal conditions for the process. By analyzing the physical properties of different parts of the banana stem and fibers during retting, the influence of bacteria and enzymes in various stages was investigated. The results indicated that, after 11 days of retting, the tensile strength of the banana fiber peaked, and after 21–25 days of soaking, the fiber met processing requirements, while the tensile separation stress of the stem was minimal—indicating the ideal endpoint for retting. Reference [13] treated banana fibers using xylanase–pectinase enzymes. They observed that, when the enzyme doses produced by the bacterial isolates were 15 IU for xylanase and 4.8 IU for pectinase, the fibers demonstrated significantly improved water absorption capacity and optimal optical properties. Reference [14] developed a process for the supply and processing of wet-stored fiber plants, offering an alternative to traditional field retting and reducing the process risks associated with unfavorable weather. While chemical degumming is often associated with high energy consumption and pollution—as well as reduced mechanical performance of the extracted fibers—biological retting methods, though environmentally friendly, suffer from significantly lower degumming efficiency.

In addition, the mechanical extraction of banana fibers avoids the use of chemical reagents and offers higher production efficiency [15]. Reference [16] designed an early-stage banana fiber extractor composed of components such as a frame, pedal, sprocket, flywheel, and blade drum, which enabled the mechanical extraction of banana fibers. Reference [17] developed a transverse-feeding ramie fiber extractor and optimized its technical parameters through multi-objective tests based on the Box–Behnken design. Reference [18] developed a rice straw fiber extraction machine and used EDEM software to conduct discrete element simulations of the extraction process. Reference [19] developed a banana fiber extraction device based on a combined beating and pressing mechanism. By optimizing the drum rotation speed and the number of beating blades, the device achieved a fiber extraction rate of 88% and a yield of 8.6 kg/h under conditions of 750 rpm and 10 blades, with good fiber straightness and integrity. Reference [20] designed an electric-powered banana fiber extractor driven by a 2-horsepower motor, in which fiber was extracted by drum-based striking of the banana stem slices. Testing showed that the machine could extract banana fibers with thicknesses ranging from 4.0 mm to 10 mm within 27 to 42 s. Reference [21] designed a rotary blade scraping-type banana fiber extraction machine and used a wet-laid nonwoven web device to prepare the extracted banana fibers into homogeneous reinforced materials for evaluating their mechanical properties. Reference [22] designed a mobile, full-feed banana stem fiber extractor, consisting mainly of a stem conveying device, feeding mechanism, rolling and pressing unit, fiber scraping system, and discharge mechanism. It was capable of processing longer stem slices through feeding, dewatering, and mechanical beating/scraping. Reference [23], inspired by the physiological structure of praying mantis forelimbs, applied bionic design principles to develop a similarly shaped toothed blade. With the improved blade, the fiber preparation rate of the machine increased from 13% to 15%, and the impurity content decreased from 14% to about 11%, while maintaining more stable efficiency when processing multiple fiber slices simultaneously. Currently, most mechanical methods for banana fiber extraction rely on beating and scraping, which often lead to issues such as fiber entanglement and clogging. Moreover, the scraping process tends to damage the fibers, compromising their mechanical properties and thus limiting the broader application of banana fibers.

At present, the processes and equipment for extracting fibers from banana stems remain underdeveloped, with issues such as low extraction efficiency and unstable fiber quality still persisting. Although previous studies have continuously explored structural designs and extraction methods, research on low-damage extraction mechanisms that ensure fiber integrity remains limited, particularly concerning flexible extraction approaches for banana stem fibers and their effective implementation. To improve extraction efficiency and quality, and to achieve stable acquisition of high-integrity, high-purity fibers, there is an urgent need to develop efficient and low-damage fiber extraction technologies and equipment for promoting the high-value utilization of banana stem resources. Therefore, this study designed a pulsating rubbing-based banana fiber extractor that uses PVC grass-textured belts to perform periodic compression and rubbing on retted banana stem slices, achieving thorough fiber separation while reducing mechanical damage, thereby providing reliable equipment support for such applications.

2. Materials and Methods

2.1. Structure and Working Principle

2.1.1. Overall Machine Structure

The schematic diagram of the pulsating rubbing-based banana fiber extractor is shown in Figure 1. The machine mainly consists of a rubbing device, a pulsating pressing device, a transmission system, a motor, and a frame. The rubbing device comprises two rubbing belts arranged vertically, each driven by rollers. The pulsating pressing device includes a camshaft, springs, and a set of pressing rollers, installed at the rear of the frame and aligned with the center of the upper rubbing belt. The main technical parameters of the machine are listed in

Table 1. Main technical parameters of the pulsating rubbing-based banana fiber extractor.

Technical Parameter	Design Value
Overall dimensions/mm	2160 × 913 × 773.6
Motor power/kW	0.75
Maximum output speed/rpm	120–150
Machine weight/kg	850
Extraction rate/%	≥65
Impurity rate/%	≤25
Integrity rate/%	≥85

.

2.1.2. Working Principle

In this study, the designed fiber extractor operates as follows: Banana stems are first sliced into thin slices. After powering on, the motor runs unloaded until stable operation is achieved. The stem slices are then placed on the protruding upper surface of the lower rubbing belt. Driven by the lower belt’s conveying action, the slices are fed into the gap between the upper and lower rubbing belts. Due to the speed difference between the two belts and the friction provided by their rough, grass-textured surfaces, the slices undergo rubbing and abrasion, causing surface fibers to separate from impurities. Meanwhile, the spring-pressed squeezing roller assembly applies downward pressure. Under the camshaft’s drive, the squeezing rollers move up and down reciprocally, causing the gap between the two rubbing belts to periodically change. This creates a pulsating squeezing effect on the stem slices, promoting the breakdown of impurities within the slices. Finally, the processed fibers and impurities exit from the rear of the rubbing belts and fall into the collection device.

2.2. Key Component Design

2.2.1. Design of the Rubbing Device

The structural schematic of the rubbing device is shown in Figure 2. The function of the rubbing device is to move the banana stem slices placed on the lower rubbing belt backward and feed them beneath the upper rubbing belt. Then, the speed difference between the upper and lower rubbing belts causes a rubbing action on the banana stem slices, which facilitates fiber separation within the slices under frictional force. To increase the friction coefficient between the rubbing belts and the stem slices, two grass-textured conveyor belts are used as the rubbing belts for the rubbing device [24]. To ensure consistent deflection of the rubbing belt, an adjustable height support plate was installed. This allows the support position to be adjusted according to the operating conditions, maintaining the uniformity of the belt surface tension.

The rubbing device utilizes the difference in linear velocities between the upper and lower rubbing belts to exert periodic shear and frictional forces on the banana stem slices clamped between them. Under sufficient contact pressure, energy is transferred to preliminarily separate the fibers (Figure 3).

The linear velocities of the upper and lower belts are $v_1$ (upper) and $v_2$ (lower), respectively. When $v_1\ne v_2$, the stem slices undergo tensile deformation, forming a velocity shear layer, whose shear rate is defined as follows:

$$\dot{\gamma }={\displaystyle \frac{v_1-v_2}{h}}$$

(1)

where $h$ denotes the clamping thickness between the two rubbing belts. According to the theory of viscoelasticity, the shear stress $\tau$ experienced by a unit volume of stem slice is related to the shear rate $\dot{\gamma }$ as follows:

$$\tau =\eta \dot{\gamma }$$

(2)

where $\eta$ represents the effective viscosity coefficient of the stem tissue. When this shear stress acts within the tissue and $\tau \ge {\tau }_c$ (the bonding strength between fiber and pith), delamination occurs in the tissue, and the fiber is pulled out.

To realize the above process, design manuals were consulted and the relevant studies and literature were referenced. Based on this, the technical parameters of the rubbing device were determined, as shown in

Table 2. Technical parameters of the rubbing device.

Technical Parameter	Design Value
Stroke of lower rubbing belt/mm	1800
Stroke of upper rubbing belt/mm	1000
Roller diameter/mm	60
Speed of lower rubbing belt	200–250 mm/s
Speed ratio of upper to lower belt	2

.

2.2.2. Design of the Pulsating Pressing Device

The pulsating pressing device is responsible for periodically pressing down the lower surface of the upper rubbing belt at a certain frequency [25], forcing changes in the gap between the two rubbing belts. This creates a pulsating pressing effect on the stem slices, promoting the breakdown of the impurity components within. Two spring pressure plates are fixed on the frame, and the springs provide a downward force to ensure tight contact between the follower bearing and the cam. Four guide rails are vertically fixed to the frame, and the sliders are connected to the roller bracket to ensure that the rollers always move in the vertical direction (Figure 4).

During operation, the two sprockets rotate synchronously to ensure that the two camshafts operate at the same frequency and in the same phase. Driven by the cam mechanism, the pressing drums mounted on the roller support periodically press downward. The downward stroke of the upper rubbing belt is $s=10 \mathrm{m}\mathrm{m}$, which can be approximately described as simple harmonic motion, and is calculated as follows:

$$y\left(t\right)=A\mathit{sin}\left(2\pi ft\right)$$

(3)

The corresponding acceleration is calculated as follows:

$$a\left(t\right)=-A{\left(2\pi f\right)}^2\mathit{sin}\left(2\pi ft\right)$$

(4)

The equivalent normal pressure is calculated as follows:

$$N\left(t\right)=N_0+ma\left(t\right)$$

(5)

Let the unit contact area be $A_c$, then the cyclic pressure applied to the stem slice is calculated as follows:

$$p\left(t\right)={\displaystyle \frac{N\left(t\right)}{A_c}}={\displaystyle \frac{N_0+ma\left(t\right)}{A_c}}$$

(6)

This cyclic pressure exerts a fatigue damage effect. Even if the average pressure is not high, the non-fibrous tissue structures will gradually weaken due to fatigue failure. According to the material fatigue theory, under the action of the cyclic stress $p\left(t\right)$, the damage degree $D$ accumulates as follows:

$$D=\sum _{i=1}^n{\displaystyle \frac{1}{N_i}}$$

(7)

where $N_i$ is the allowable fatigue life under stress ${\sigma }_i$. When $D\ge 1$, structural failure occurs in the tissue.

If the equivalent stress amplitude is denoted as ${\sigma }_a$, according to the Basquin equation:

$$\begin{array}{c}{\sigma }_a={\displaystyle \frac{{\sigma }_{max}-{\sigma }_{min}}{2}}\\ N_f={\left({\displaystyle \frac{{\sigma }^{\prime }}{{\sigma }_a}}\right)}^{{\displaystyle \frac{1}{b}}}\end{array}$$

(8)

where ${\sigma }_a$ and $b$ are material fitting constants. This indicates that even if $p\left(t\right)$ is insufficient to crush the tissue immediately, repeated cycles can still accumulate damage and eventually lead to tissue failure, thereby promoting fiber separation.

Based on the above principles, and with reference to design manuals and relevant studies, the technical parameters of the pulsating pressing device were determined, as shown in

Table 3. Technical parameters of the pulsating pressing device.

Technical Parameter	Design Value
Cam spacing/mm	430
Slider stroke/mm	10
Pressing drum diameter/mm	60
Pulsating pressing frequency/Hz	4–6

.

2.2.3. Transmission System Design

The transmission system of the pulsating rubbing-based banana fiber extractor is required to fulfill the functional principles outlined above. It must feature a compact structure, low power consumption, and reasonable power distribution, such that both the rubbing device and the pulsating compression device can operate at appropriate speeds under the drive of a single motor. The configuration schematic of the transmission system for the designed fiber extractor is shown in Figure 5 [26].

The power is output from the motor and transmitted to the drive drum of the lower rubbing belt through a belt transmission mechanism, driving the operation of the lower rubbing belt. The drive drum then transfers the power to the gear half-shaft via gears, while also reversing the direction of rotation. The gear half-shaft transmits the power to the drive drum of the upper rubbing belt through a belt transmission mechanism (serving as a speed increaser), thereby driving the upper rubbing belt and ensuring differential motion between the two belts. Meanwhile, the motor output shaft also transmits power to the front camshaft via a belt transmission mechanism. The front camshaft then transfers power to the rear camshaft through a chain transmission mechanism to ensure synchronized phase operation of the two camshafts.

2.3. Simulation Analysis of the Pulsating Rubbing Process

To verify that the designed pulsating rubbing-based fiber extractor can effectively break down banana stem slices for fiber extraction, the fiber extraction process involving the rubbing device and the pulsating compression device was simulated using the RecurDyn 2023 software with a rigid–flexible coupling approach.

2.3.1. Simulation Model Establishment

The Belt component in the Toolkit module of RecurDyn 2023 provides a convenient method to quickly create a rigid–flexible coupling simulation model of the belt system [27]. This component was used to rapidly build a model that includes the belts, drive drums, idler drums, and pressing drums. The belt was created using the Shell type, which is essentially a finite element flexible body (F-Flex), while all drums were set as rigid bodies [28].

The 3D model of the support plate was drawn using Creo 10.0 and then imported into RecurDyn. It was kept as a rigid body to prevent downward deformation of the lower rubbing belt under pressure during operation, which could otherwise reduce the available friction force. The banana stem slice model was imported in the same way, set as an F-Flex body, and meshed. The assembled simulation model is shown in Figure 6.

The material properties of the rubbing belts were defined based on the characteristics of soft PVC, while the pressing drums and support plate were assigned the properties of steel [29]. According to the relevant literature [30], the material properties of banana stems were determined, as shown in

Table 4. Material properties of banana stems.

Density/(kg/m3)	Poisson’s Ratio	Elastic Modulus/Pa
137	0.41	1.35 × 109

, which were used to set the properties of the banana stem slices and to establish contact relationships.

According to the motor speed and the transmission system, the rotational speed of the lower rubbing belt driving drum is 74 rpm, and that of the upper rubbing belt driving drum is 148 rpm. Driving equations are established respectively to control the revolute joints of the drums to rotate around their axes, thus completing the construction of the simulation model.

2.3.2. Simulation Results and Analysis

Since the finite element flexible body cannot accurately reproduce the fiber distribution and complex layering within the banana stem slices [31], the working performance of the machine is mainly evaluated by analyzing the stress conditions of the stem slices.

As shown in Figure 7, from the feeding of the stem slice to its discharge, the entire process lasts about 3.44 s. During this period, the friction force acting on the stem slice is shown in Figure 7b.

It can be observed that the friction force acting on the stem slice generally exhibits a periodic variation. The friction force on the upper contact surface remains positive throughout the process, indicating that the faster upper rubbing belt continuously tends to drive the stem slice forward. The friction force on the lower contact surface is positive during the initial cycles but later becomes negative. This suggests that, in the early stage, when the stem slice moves at a low speed, the lower rubbing belt helps to push it forward. As the stem slice accelerates and its speed exceeds that of the lower rubbing belt, the lower belt starts to resist its motion. At this point, the stem slice is subjected to opposite friction forces on its upper and lower surfaces, creating a shearing effect that promotes the destruction of the layered structure of the stem slice. This result aligns well with the intended working principle.

By examining the stress distribution of the stem slice, it is found that, due to the squeezing and friction effects of the rubbing belts, the stress is mainly concentrated in the upper and lower layers of the stem slice, while the stress in the middle part is relatively low. According to the previous mechanical property tests of banana stem slices, the shear strength of banana stem slices after 35 days of retting is 0.52 MPa. Based on Figure 8, when the stem slice is compressed, most areas of its surface layer are subjected to stress exceeding 0.528 MPa. As the surface layer peels off, the newly exposed inner layer becomes the new outer layer, thereby gradually destroying the layered structure of the stem slice and achieving fiber extraction [32].

3. Results and Discussion

3.1. Prototype Manufacturing and Preparation of Banana Stem Material

As shown in Figure 9, a prototype of the pulsating rubbing-based banana fiber extractor was fabricated, and performance tests were carried out. Mature, disease-free Brazilian banana stems produced in Haikou, Hainan Province, were selected as raw materials. The leaf sheaths were separated layer by layer using knives, and water retting was performed indoors at the Engineering Training Center of Hainan University for a total of 83 days. To facilitate subsequent processing and analysis, the retted leaf sheaths were cut into stem slices with a length of 150 mm and a width of 50 mm using knives, which were used as test materials [12].

3.2. Evaluation Indicators

Referring to the Chinese national standard “Test Methods for Jute and Kenaf Fibres” (GB/T 12411-2006) [33], and considering the material characteristics of banana stem fibers, the evaluation indicators for the tests were determined as extraction rate, fiber impurity content, and integrity rate. The specific test methods are described in below.

3.2.1. Extraction Rate

The extraction rate indicates the proportion of fibers extracted by the designed prototype relative to the total fiber content in the stem slices. An electronic balance (Model: YHM-5003, manufacturer: Wuxi Ying Heng Electronics Co., Ltd., Wuxi, China) was used to measure the total mass $m_1$ of the retted banana stem slices before processing. After processing, the impurities attached to the extracted fibers were manually scraped off. The fibers were then dried using a drying oven (Model: LC-202/101, manufacturer: Shanghai Lichen Instrument Technology Co., Ltd., Shanghai, China), and the total mass $m_2$ of the dried fibers was measured. The extraction rate $R$ was calculated using the following formula:

$$R={\displaystyle \frac{m_2}{\mu m_1}}\times 100\%$$

(9)

where $R$ is the extraction rate; $m_1$ is the total mass of the banana stem slices before processing, g; $m_2$ is the total mass of the extracted dried fibers, g; and $\mu$ is the fiber content of the banana stems, which is 3.8% for the banana variety used in this experiment [18].

3.2.2. Impurity Rate

The fiber impurity rate represents the proportion of impurities contained in the extracted fibers by the designed prototype. After processing the stem slices with the prototype, the obtained fibers are divided into two groups of equal mass. One group is directly dried using a drying oven, and the total mass $m_3$ is measured using an electronic balance. The impurities attached to the fibers of the other group are manually removed, and the cleaned fibers are dried using the drying oven, with the total mass $m_4$ measured. The impurity rate $W$ can be calculated using the following formula:

$$W={\displaystyle \frac{m_3-m_4}{m_3}}\times 100\%$$

(10)

where $W$ is the impurity rate; $m_3$ is the mass of the fibers without removing impurities, g; and $m_4$ is the mass of the fibers after removing impurities, g.

3.2.3. Integrity Rate

The integrity rate represents the proportion of unbroken fibers in the extracted fibers by the designed prototype. After processing the stem slices with the prototype, the obtained fibers are dried in a drying oven, and the total fiber mass $m_5$ is measured using an electronic balance. The length of each fiber is measured with a ruler, and fibers with a length less than 90% of the stem slice sample length are removed. The total mass of the remaining fibers $m_6$ is then measured again. The integrity rate $C$ can be calculated using the following formula:

$$C={\displaystyle \frac{m_6}{m_5}}\times 100\%$$

(11)

where $C$ is the integrity rate; $m_5$ is the total mass of the fibers, g; and $m_6$ is the total mass of the fibers after removing short fibers, g.

3.3. Selection of Experimental Factors

3.3.1. Spring Outer Diameter

The compression spring is an essential component of the pulsating pressing device. The spring stiffness directly affects the compressive force on the stem slice, thereby influencing the fiber extraction performance. For a cylindrical compression spring, its stiffness is calculated as follows:

$$P^{\prime }={\displaystyle \frac{G{d}^4}{8D^{3}n}}$$

(12)

where $P^{\prime }$ is the spring stiffness, N/mm; $G$ is the shear modulus of the material, Pa; $d$ is the spring wire diameter, mm; $D$ is the mean diameter of the spring, mm; and $n$ is the number of active coils in the spring.

When other conditions remain the same, as the spring’s outer diameter increases, the mean diameter of the spring also increases, leading to a decrease in the spring stiffness. Under the same compression length, the pressure provided by the spring decreases, which reduces the friction force between the rubbing belts and the stem slice, thus decreasing the extraction rate and integrity while increasing the impurity content, and vice versa.

The maximum allowable spring outer diameter for the device is 35 mm. If the spring size is too small, it may cause spring misalignment or even detachment. The experimental spring outer diameter range is set to 30–35 mm.

3.3.2. Feeding Interval of the Stem Slices

Reducing the feeding interval can improve the working efficiency but will increase the number of stem slices processed simultaneously in the device, reducing the pressure and friction force on each stem slice. This results in a lower extraction rate and integrity and a higher impurity content, and vice versa. Referring to the general process of banana fiber extraction [34], the experimental feeding interval is set to 4–6 s.

3.3.3. Clamping Angle Between the Stem Slices and the Rubbing Belts

The friction force provided by the rubbing belts is parallel to the conveying direction. The larger the clamping angle between the stem slices and the rubbing belts, the smaller the component of the friction force along the fiber direction, causing the impurities between the fibers to be mainly subjected to tensile forces. The smaller the clamping angle, the larger the friction force component along the fiber direction, causing the impurities to be mainly subjected to shear forces. When the fibers in the stem slice are parallel to the conveying direction, the angle is 0°; when the fibers are perpendicular to the conveying direction, the angle is 90°.

3.4. Box–Behnken Test

3.4.1. Test Design

Taking the extraction rate ($R$), the impurity rate ($W$), and the integrity rate ($C$) as the response indicators, and the spring outer diameter ($d$), the feeding interval of the stem slices ($t$), and the clamping angle between the stem slices and the rubbing belts ($\theta$) as the influencing factors, a Box–Behnken response surface test [35] was designed. The factor level table is shown in

Table 5. Factor level table.

№	$\mathbf{Spring} \mathbf{Outer} \mathbf{Diameter}$ X1/mm	$\mathbf{Feeding} \mathbf{Interval}$ X2/s	$\mathbf{Clamping} \mathbf{Angle}$ X3/°
−1	30	4	0
0	32.5	5	45
1	35	6	90

.

The experimental design was conducted using Design-Expert 13 software, with the influencing factors and response indicators set, and the number of center points per block set to 6. The experimental scheme is shown in

Table 6. Box–Behnken experimental scheme.

№	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{Y}}_1$	${\mathit{Y}}_2$	${\mathit{Y}}_3$
1	−1	0	0	60.85	12.76	99.61
2	0	−1	−1	65.49	57.48	92.32
3	0	−1	0	79.17	57.21	93.24
4	−1	−1	0	96.47	50.87	91.41
5	0	1	1	64.08	60.22	65.58
6	1	1	0	47.36	64.86	89.62
7	0	0	0	77.40	18.60	59.64
8	0	1	0	50.62	66.79	97.22
9	0	0	−1	68.18	60.65	95.03
10	1	0	1	55.00	63.78	80.61
11	0	1	0	86.99	53.37	98.57
12	0	0	1	88.75	52.49	98.80
13	0	0	−1	63.99	63.72	99.49
14	0	0	0	72.23	58.63	74.66
15	0	1	−1	77.73	44.19	75.96
16	−1	0	0	52.47	59.63	81.25
17	0	−1	1	70.21	45.34	97.39

.

3.4.2. Analysis of Variance

The experimental results were fitted and analyzed. It was found that, for the extraction rate $Y_1$ and integrity rate $Y_3$, the cubic model exhibited confounding and was unusable, while the linear, 2FI, and quadratic models all had negative $R^2$ values, indicating very poor fit. Therefore, following the software’s recommendation, the mean model was selected, and the test results were averaged directly, yielding an extraction rate of 67.47% and an integrity rate of 90.84%.

For the fiber impurity content $Y_2$, the 2FI model was found to have the smallest sequential p-value of 0.0399 and the highest adjusted $R^2$ of 0.6009. Therefore, the 2FI model was selected as the basis and modified by removing non-significant terms while ensuring model hierarchy [36]. The corrected model is shown in

Table 7. Regression analysis of variance.

Source	Sum of Squares	Degrees of Freedom	Mean Square	F-Value	p-Value	Significance
Model	2790.68	5	558.14	6.58	0.0046	*
$X_1$	1039.82	1	1039.82	12.26	0.005	*
$X_2$	200.96	1	200.96	2.37	0.1519
$X_3$	424.32	1	424.32	5	0.0469	*
$X_1{X}_2$	651.58	1	651.58	7.68	0.0182	*
$X_1{X}_3$	474.01	1	474.01	5.59	0.0375	*
Residual	932.7	11	84.79
Lack of fit	614.28	7	87.75	1.1	0.4911
Pure error	318.42	4	79.61
Corrected total	3723.38	16

Note: * indicates statistically significant difference.

.

The p-value of the model is less than 0.05, indicating that the model is significant overall. The p-values for the spring outer diameter $X_1$, the clamping angle $X_3$, and the interaction terms $X_1{X}_2$ and $X_1{X}_3$ are all less than 0.05, showing that these terms have a significant effect on the model. The p-value for $X_2$ is greater than 0.05, indicating that the feeding interval has no significant effect, but it is retained in the model as a main effect of the significant interaction term, in order to ensure model hierarchy. The p-value of the lack-of-fit term is greater than 0.05, suggesting that the model has no obvious fitting defects and the fitting performance is good.

3.4.3. Response Surface Analysis

Based on the experimental data, a fitting equation was derived for the above-mentioned terms, as follows:

$$Y_2=-801.67932+25.73201X_1+170.93126X_2-3.30665X_3-5.10521X_1{X}_2+0.09676X_1{X}_3$$

(13)

The response surface of the interaction terms is shown in Figure 10, and all surfaces exhibit a saddle-shaped form. Regarding the interaction between the spring outer diameter $X_1$ and the feeding interval $X_2$, when $X_1$ is small, the impurity rate $Y_2$ increases with the increase of $X_2$; when $X_1$ is large, $Y_2$ decreases as $X_2$ increases. Likewise, when $X_2$ is small, $Y_2$ increases with increasing $X_1$; when $X_2$ is large, $Y_2$ decreases as $X_1$ increases. This phenomenon is caused by the following: when the spring outer diameter is small, the system’s pulsating extrusion force is weak. As the feeding interval of stem slices increases (i.e., fewer slices are processed at the same time), although the slices as a whole are subjected to relatively greater friction, the pressure is insufficient to press the slices tightly against the lower rubbing belt. This results in displacement of the stem slices, and the extrusion-friction force on each slice is limited, which fails to effectively break up the impurities, thus increasing the impurity rate. However, when the spring outer diameter is larger, the pulsating extrusion becomes stronger, and the displacement of stem slices is reduced. As the feeding interval increases, each slice receives more stable and sufficient extrusion force, promoting the removal of non-fibrous tissues and reducing the impurity rate.

Regarding the interaction between the spring outer diameter $X_1$ and the clamping angle $X_3$, when $X_1$ is small, the impurity rate $Y_2$ decreases with the increase of $X_3$; when $X_1$ is large, $Y_2$ increases as $X_3$ increases. Likewise, when $X_3$ is small, $Y_2$ decreases with increasing $X_1$; when $X_3$ is large, $Y_2$ increases with increasing $X_1$. The reason for this phenomenon is as follows: when the spring outer diameter is small, the pulsating extrusion force is limited. If the clamping angle is small, the direction of friction is mostly aligned with the fiber direction, making it difficult for the impurities to separate, leading to a higher impurity rate. However, as the clamping angle increases, the frictional component perpendicular to the fiber direction becomes stronger, and the shear effect of the rubbing belt on the surface of the stem slice becomes more evident. Although the spring’s pressing ability is insufficient, the increase in friction caused by the clamping angle compensates for it, promoting the removal of non-fibrous tissues and thus decreasing the impurity rate. However, when the spring outer diameter is large, the system provides a stronger pulsating extrusion force. If the angle is too large, the internal layered structure of the stem slice may be damaged, resulting in a noticeable reduction in its hardness. Under the action of friction, the softened stem slice may be twisted and entangled, causing the impurities and fibers to bind closely together, thereby increasing the impurity content.

3.4.4. Parameter Optimization and Experimental Verification

Based on the fitting equation of Equation (13), the Optimization module of Design-Expert software was used to optimize the prototype parameters and to minimize the fiber impurity content, which is calculated as follows:

$$\begin{array}{c}\min g\left(X_1,X_2,X_3\right)=Y_2\\ \mathrm{s}.\mathrm{t}.\left\{\begin{array}{c}3\le X_1\le 3.5\\ 4\le X_2\le 6\\ 0\le X_3\le 90\end{array}\right.\end{array}$$

(14)

The program automatically generated 100 sets of solutions. The set with the lowest predicted value of $Y_2$ was selected, and the rounded values were taken as the final optimized parameters: $X_1=30 \mathrm{mm}$, $X_2=4 \mathrm{s}$, and $X_3=90°$, with a predicted $Y_2$ value of 5.04%. To verify the optimization result, a validation test was conducted using the same parameters and experimental methods as Group 1 in Table 6, since the optimized parameter combination was identical to that of this group. The results are shown in

Table 8. Validation test results.

Response Indicator	Test Result	Predicted Value	Error
Extraction rate	61.35%	69.24%	7.89%
Impurity rate	9.01%	5.04%	3.97%
Integrity rate	96.22%	87.67%	8.55%

.

Among them, the integrity rate exhibited the largest relative error between the experimental and predicted values, reaching 8.55%, while the impurity rate showed the smallest relative error of 3.97%, which is within the acceptable range. Therefore, the obtained optimized parameters are considered to be relatively reliable.

4. Conclusions

To address the demand for the high-value utilization of banana stem resources, this study designed a pulsating rubbing-based banana fiber extractor. Based on simulation analysis and performance testing, the following conclusions were drawn:

(1)

The structural scheme of the device was established, featuring key components, including a dual-belt differential-speed rubbing device and a cam-based pulsating pressing device, enabling periodic rubbing and pressing of the banana stem slices. A simulation analysis verified the mechanical feasibility of the extraction process, showing that the surface stress on the stem slices exceeded the shear strength, enabling effective fiber detachment.

(2)

Structural parameters were optimized using Box–Behnken experimental design. The results indicated that, when the spring outer diameter was 30 mm, the feeding interval was 4 s, and the clamping angle was 90°, the extraction rate reached 60.85%, the impurity rate was 12.76%, and the integrity rate reached as high as 99.61%. This demonstrated a good balance between extraction efficiency and fiber quality.

(3)

This study demonstrated the feasibility of flexible, low-damage fiber extraction. The proposed structural scheme and parameter optimization path provide a reference for processing similar crop stalks.

The limitations of this study include uncontrollable changes in stem slice posture during actual operation and the need for further verification of adaptability to different banana stem varieties. Future research could incorporate image recognition and other methods to optimize the feeding control strategy, further improving the equipment’s versatility and stability.

In conclusion, this study proposed a novel and effective low-damage banana fiber extraction technology and successfully designed and built a pulsating rubbing-based banana fiber extractor. It demonstrates both theoretical and practical innovation and offers reliable technical support for the resource utilization of banana stem materials.