Optimization Design and Test Analysis of Rice Electric Binder Knotter Based on ADAMS

Abstract

The knotter, as a core module for the knotting function of a rice electric binder, has structural parameters and spatial configurations that significantly impact the efficiency and quality of rice collection, making the in-depth analysis and optimization of these parameters, and their spatial relationships, crucial for enhancing the operational quality of the rice electric binder. At present, rice binders still face the issues of a low bundling efficiency and quality, which affect the progress of rice harvesting during the harvest season. Through theoretical analysis and calculation, this study determined the main parameters affecting the knotter’s knotting process and their value ranges. Based on the ADAMS software, a simulation model of the knotter operation was constructed. Using the Box–Behnken design (BBD) method and response surface analysis of variance, a regression prediction model for knotter operation evaluation indicators was established, and the multi-objective optimization of the knotter’s operation quality was performed. The prediction results showed that, under the optimal structural parameter combination of a 30.23° angle between the knotting pincer and rope guard axes, a −3.75 mm rope clamping board position, and a 40.75° inclination angle of the knotting pincer convex platform, the knotter’s knotting quality reached the best state, with an average knot end protrusion of 9.10 mm and a maximum tension of 134.25 N on the knotting rope. The field tests results showed an average knot end protrusion of 9.60 mm and a maximum tension of 127.87 N on the knotting rope, with average relative errors of 5.82% and 4.72% compared to the theoretical values, respectively. After optimizing the knotter, the average knot end protrusion increased by 14.48% and the maximum tension of the knot rope was reduced by 11.27%. Meanwhile, the knotter achieved an average bundling rate as high as 99.3%. The bundling success rate also increased by 2.7%. These results fully verify the reliability and accuracy of the regression model, and demonstrate the reasonableness of the knotter structural parameter optimization design, providing a theoretical basis and reference for improving the operational quality of the rice electric binder.

1. Introduction

The knotter is a key module of the bundling operation in a rice electric binder, mainly forming knots by executing precise looping actions to tie the harvested rice stalks into bundles, thereby reducing the intensity of physical labor and saving on labor costs, thus increasing the benefits of rice cultivation. The knotting quality of the knotter is closely affected by factors such as the motion and geometric parameters of the structure, and the interaction forces between the knotting rope, knotting pincer, rope guard, and other structures [1]. If the knotter’s structural design or position layout is improper, it will directly lead to knotting failure or reduced knot quality, thus affecting the operational effect of the rice binder. Therefore, the in-depth exploration of the spatial positions of the various internal structures of the knotter and their impact on knotting performance is of crucial significance for improving the bundling quality of the rice binder.

The knotter is mainly classified into C-type and D-type knotters. At present, many scholars at home and abroad have conducted extensive and in-depth research on D-type knotters, covering multiple dimensions such as knotting simulation [2], timing analysis [3,4], component optimization design [5,6,7], load analysis [8], reliability design [9,10], new design exploration [11,12,13], and spatial structural parameter optimization [14,15,16,17], with the research focusing on the latter two dimensions. For example, Li H et al. [11] designed a φ-type knotter and conducted knotting rate experiments, demonstrating the good performance of the designed φ-type knotter. A new rope knotting method was proposed by Ma, S. et al. [12], who applied the TRIZ theory to analyze and design a new type of knotter. The tests showed that the knotter had a good durability and far exceeded the corresponding standards. Zhang, J. et al. [13] integrated the advantages of two devices to design a new type of buckle knotter. A test bench was fabricated and knotter tests were carried out. The results showed that the knotting performance met the design requirements. This provides a reference for the further optimization of the structure. Zhang A et al. [14] used spatial analytical methods to thoroughly analyze the spatial and motion relationships between the rope clamping plate and knotting pincer, and experimentally verified the accuracy of the parameter matching. Yin J et al. [15] constructed a kinematic model of the rope clamping–looping–clamping actions, systematically analyzed the timing and position relationships in the knotting process, and explored the key factors affecting the knotting quality. Li H et al. [16] established a parameterized model based on the working principle of the D-type knotter and experimentally verified the effectiveness of the model. Zhang A et al. [17] further investigated the influence of the structural parameters of the unknotting operation on rope unknotting and verified the accuracy of the relevant theoretical model.

In summary, the research on the D-type knotter has been quite comprehensive, but there is a scarcity of studies on the C-type knotter. Mecortale Company was among the pioneers in the design and research of knotters, and their knotting system, specifically the C-type knotter, has been widely adopted in the market [18]. Yang S [19] conducted research on the C-type knotter, but only made improvements and virtual model designs for some of the vulnerable components. An in-depth study of the C-type knotter’s structure was not conducted. Although there have been numerous studies on the optimization of the structural parameters for D-type knotters, the research on the structural parameters of C-type knotters remains scarce. Despite the similarity in the main components between these two types of knotters, there are significant differences in their structures. The spatial relationships between the various components of the C-type knotter, as well as their cooperative actions during the knotting process and the matching relationships of the main structural parameters, are still not well understood. The impact of these factors on rice harvesting is also unknown. This has prompted the present study to focus on the structural optimization of the C-type knotter.

This paper first introduces the structure and knotting principle of the C-type knotter; then, a synergistic action model of the main components of the knotter is established using numerical and analytical methods. Based on this model, the main structural factors affecting the knotting process are identified. Additionally, a dynamic model of the knotter is created using ADAMS 2020 software, and simulation experiments are conducted. Orthogonal tests are utilized to obtain the optimal structural parameter combination for the C-type knotter. Finally, field tests are carried out to verify the reliability of this parameter combination. The study reveals how the shape and size of the knotting principle and the spatial relationships between components synergistically affect the knotting process. Through the optimization of the structural parameters of the C-type knotter, this study aims to significantly improve the knotting rate, thereby enhancing the bundling efficiency and quality of the rice electric binder. Additionally, the findings provide a reference for subsequent related designs.

2. Materials and Methods

2.1. C-Type Knotter

The C-type knotter [20,21] has a larger knotting pincer compared to other types, but its overall size is smaller and it is easy to operate. The knot it forms is a slipknot, which can release automatically, with less tension on the knotting rope and a relatively low bundle density, making it suitable for environments where the strength of the knot is not highly demanding. However, its knot strength is relatively low, and it may not meet the needs for fast and continuous knotting in high-output environments. The D-type knotter [22] forms a fixed knot, with less tension on the binding rope and a lower bundle density, making it particularly suitable for applications that endure heavy loads or high tension. However, its complex structure makes manufacturing difficult, leading to higher costs, and its operation and maintenance are more complex. The double knotter [23] can form two knots in one knotting action, significantly improving the stability and strength of the knot. This technology is suitable for situations where safety requirements are extremely high, offering a double guarantee. But its knotting speed is slower, and it has higher costs and maintenance requirements, making it less suitable for situations that require fast knotting and agricultural production. In hilly and mountainous areas, the main requirements for a knotter are high adaptability, low cost, easy maintenance, and relatively modest performance demands. The C-type knotter, with its compact overall structure, lower cost, simple design, and capability to meet bundling needs, is therefore more suitable for use in such regions. The core modules of the bundling operation in the rice electric binder in this study include the transmission operation, C-type knotter, rope-feeding operation, and straw-collecting operation, as shown in Figure 1a. The C-type knotter is a core component of the bundling operation, integrating elements such as the knotting pincer, rope guard, frame, driving gear disk, and rice collection platform. When the knotter starts working, rice stalks are continuously conveyed to the straw-collecting space of the bundling operation, and the pressure on the bundle release rod (i.e., the clutch control element) gradually increases. When the pressure value reaches the preset threshold of the system, the clutch control rod rotates around its axis to the predetermined angle, and the rope-feeding needle carrying the knotting rope starts a rotational motion, tightly wrapping around the stalk group to form a stable bundle. It then completes the knotting action through the knotting pincer. After the rope guard rotates one revolution, the knotting rope is cut off by the cutting knife, completing the bundling operation, as shown in Figure 1b.

2.2. Factors Influencing Knotter Operation Performance

2.2.1. Knotting Operation Process

At the beginning of the knotting operation, the knotting rope comes into contact with the lower jaw of the knotter pincer. Under the combined effect of its own tension and the rotation of the knotter, it slides slowly along the surface of the lower jaw. The frictional force hinders the sliding and the normal positive pressure gradually increases. As the knotter rotates, the position of the knotting rope changes, and its sliding speed and direction vary with the dynamic balance among the pulling force F, the frictional force f, and the normal positive pressure FN. The direction of f is along the tangent direction of the contact point between the convex platform surface and the knotting rope, which is oppo-site to the relative motion trend, and it changes with the change in the posture of the knot-ting rope. The change in the pulling force component affects the sliding state of the knot-ting rope. When the knotting is completed, the frictional force and the normal positive pressure between the knotting rope and the knotter reach a new balance, stabilizing the knot. The knotting process is also influenced by many other factors. For example, in a hu-mid or dusty environment, the friction coefficient μ between the knotting rope and the knotter may change. The magnitude of the frictional force affects the stability of the knot. If it is too small, the knot is likely to come loose under the action of external forces or vibrations. If it is too large, it may cause the excessive wear of the knotting rope and affect the quality. At the same time, the interaction between the two affects the knotting efficiency. Unsmooth movement will reduce the efficiency. By optimizing the design of the knotter, such as adjusting the shape and size of the convex template and improving the trajectory of the knotting rope, the energy loss of the relative motion between the rope and the mechanism can be reduced, thus increasing the efficiency.

Therefore, this article focuses on the influence of the structural parameters of the knotter on the knotting effect. The timing relationship between the rope pressing, looping, and clamping actions of the knotting rope has a significant impact on the knot quality of the knotter [24]. To accurately analyze this relationship, set the arc angle occupied by the incomplete bevel gear on the driving gear disk as ψ, and the angle between the axes of the knotting pincer and rope guard as δ. When the driving gear disk rotates in the predetermined direction (as shown in Figure 2), the phase difference ε between the actions of the knotting pincer and rope guard is as follows:

$$\epsilon =\delta$$

(1)

When the gear disk rotates one revolution, the incomplete bevel gear located on it will also drive the knotting pincer and rope guard to rotate one revolution. If the incomplete bevel gear of the gear disk is initially engaged with the knotter bevel gear when the gear disk rotates by an angle β, the rotation angle α₂ of the knotter at this time is as follows:

$${{\displaystyle \alpha }}_2={\displaystyle \frac{2\pi \beta }{\psi }}$$

(2)

where ψ is the arc angle occupied by the incomplete bevel gear, measured to be 60°.

The knotting rope is a flexible object, and during the looping and knotting process, the position of the rope placing point m on the knotting pincer changes dynamically. If the position of point m at any instant is approximated by circular arcs of different sizes and directions, the continuous connection of these circular arcs constitutes the geometric shape of the knot loop. To obtain the dynamic position of the rope placing point m, the following two spatial coordinate systems are established on the C-type knotter: a static coordinate system O-XYZ and a dynamic coordinate system O₁-X₁Y₁Z₁, as shown in Figure 3. In the static coordinate system, the axis lines of the driving gear disk, knotting pincer, and rope guard all intersect at point O, which is defined as the origin of the coordinate system O-XYZ, with the X-axis being the axis line of the driving gear disk, and the Z-axis located in the plane formed by the axis lines of the knotting pincer and rope guard. For the dynamic coordinate system O₁-X₁Y₁Z₁, its origin O₁ is set at the contact point between the knotting pincer axis line and the frame, with the X₁-axis located in the symmetry plane of the knotting pincer and the Z₁-axis being the axis line of the knotting pincer. The directions of the Y- and Y₁-axes are determined according to the right-hand rule. In terms of the spatial position, the angle between the Z₁- and Z-axes is α₁, and the angle between the Y₁- and Y-axes is α₂. The coordinates of O₁ relative to O are (b₁, 0, b₂), and point O₂ is the intersection of the rotation center axis of the upper and lower jaws of the knotting pincer with the plane X₁O₁Z₁, while point J is the center point of the cylindrical tail of the upper jaw of the knotting pincer.

In the dynamic coordinate system O₁-X₁Y₁Z₁, the contact points of any segment of the knot loop with the surface of the lower jaw of the knotting pincer are m₀ and m₁, respectively, with the coordinates of m0 being (a₁, 0, c₁), where a₁ is the perpendicular distance from point m₀ to the plane X₁O₁Z₁, and c₁ is the perpendicular distance from point m₀ to the plane X₁Y₁Z₁. During the process of forming a loop with the binding rope, at any given moment, the rope will wrap around the upper and lower jaws of the knotting nozzle as it rotates, making contact at points m₀ and m₁. These two contact points are located at the ends of the diameter of the rope loop formed, and the spatial distance between them can be considered as the diameter of the rope loop created by the knotting process.

During the knotter operation process, the coordinates of the rope placing points m₀ and m₁ on the knotting pincer in O-XYZ are as follows [15]:

$$\left[\begin{array}{c}{{\displaystyle x}}_{m0}\\ {{\displaystyle y}}_{m0}\\ {{\displaystyle z}}_{m0}\\ 1\end{array}\right]=\left[\begin{array}{c}{{\displaystyle a}}_1\cos {{\displaystyle \alpha }}_1\cos {{\displaystyle \alpha }}_2+{{\displaystyle c}}_1\sin {{\displaystyle \alpha }}_1+{{\displaystyle b}}_1\\ {{\displaystyle a}}_1\sin {{\displaystyle \alpha }}_2\\ {{\displaystyle -a}}_1\sin {{\displaystyle \alpha }}_1\cos {{\displaystyle \alpha }}_2+{{\displaystyle c}}_1\cos {{\displaystyle \alpha }}_1+{{\displaystyle b}}_2\\ 1\end{array}\right]$$

(3)

$$\left[\begin{array}{c}{{\displaystyle x}}_{m1}\\ {{\displaystyle y}}_{m1}\\ {{\displaystyle z}}_{m1}\\ 1\end{array}\right]=\left[\begin{array}{c}{{\displaystyle k}}_1\cos {{\displaystyle \alpha }}_1\cos {{\displaystyle \alpha }}_2+{{\displaystyle k}}_2\sin {{\displaystyle \alpha }}_1+{{\displaystyle b}}_1\\ {{\displaystyle k}}_1\sin {{\displaystyle \alpha }}_2\\ {{\displaystyle -k}}_1\sin {{\displaystyle \alpha }}_1\cos {{\displaystyle \alpha }}_2+{{\displaystyle k}}_2\cos {{\displaystyle \alpha }}_1+{{\displaystyle b}}_2\\ 1\end{array}\right]$$

(4)

$$\left\{\begin{array}{l}{{\displaystyle k}}_1=(5\cos {{\displaystyle \alpha }}_2+12)\sin ({{\displaystyle \tau }}_0+\tau )-{{\displaystyle a}}_2\\ {{\displaystyle k}}_2=(5\cos {{\displaystyle \alpha }}_2+12)\cos ({{\displaystyle \tau }}_0+\tau )-{{\displaystyle c}}_2\end{array}\right.$$

(5)

where α₁ is the angle between the Z₁- and Z-axes, taking the value of δ/2; τ₁ is the initial angle between O₂E and the Z₁ coordinate axis, measured to be 75°; τ is the swing angle of the cylindrical tail of the upper jaw of the knotting pincer; a₂ and c₂ are the distances from O₂ to the planes Y₁O₁Z₁ and X₁O₁Y₁, respectively, measured to be 11 mm and 27 mm.

When the knotting rope loops and knots, the fitting radius of any segment of the knot loop is as follows:

$${{\displaystyle r}}_t={\displaystyle \frac{1}{2}}\sqrt{{{\displaystyle \left({{\displaystyle x}}_{m0}-{{\displaystyle x}}_{m1}\right)}}^2+{{\displaystyle \left({{\displaystyle y}}_{m0}-{{\displaystyle y}}_{m1}\right)}}^2+{{\displaystyle \left({{\displaystyle z}}_{m0}-{{\displaystyle z}}_{m1}\right)}}^2}$$

(6)

It can be known from Equation (6) that, when the rotation angle β of the gear disk is at 1° intervals, the knot formation as the knot loop loops and knots with the knotting pincer is closely related to the following factors: the angle (δ) between the axes of the knotting pincer and rope guard, the position of the rope placing point m0 (a₁, c₁), and the swing angle τ of the cylindrical tail of the upper jaw of the knotting pincer. In addition, the literature [25] shows that the inclination angle (θ) of the convex platform of the knotting pincer also affects the looping and knotting quality. Since the swing angle τ of the cylindrical tail of the upper jaw of the knotting pincer is a fixed value each time the rotation angle β of the gear disk rotates by 1°, and the position of the rope placing point m0 is influenced by the position (d) of the rope clamping board, this paper only analyzes the influence of the angle (δ) between the axes of the knotting pincer and rope guard, the position (d) of the rope clamping board, and the inclination angle (θ) of the convex platform of the knotting pincer on the cutting and bundling operation quality when analyzing the binder’s cutting and bundling operation quality.

2.2.2. Working Parameter

• Angle between the axes of the knotting pincer and rope guard (δ)

To ensure that the knotting pincer can smoothly complete the looping and knotting action, the following condition must be met: when the upper jaw of the knotting pincer rotates to intersect with the plane where the knotting rope is located, the rope-guiding ring of the rope guard must have rotated above that plane to ensure that the rope-guiding ring can effectively guide the rope index into the angle of the knotting pincer. At this point, the tip of the upper jaw of the knotting pincer is just in contact with the knotting rope, as shown in Figure 4a. The schematic diagram of the motion angle at the knotting pincer is shown in Figure 4b, and the phase angle satisfies the following relationship:

$$\left\{\begin{array}{l}{{\displaystyle \phi }}_1=\arcsin {\displaystyle \frac{{{\displaystyle L}}_1}{{{\displaystyle L}}_2\sin \delta }}\\ {{\displaystyle \phi }}_3=i\delta +{{\displaystyle \phi }}_2\\ {{\displaystyle \phi }}_3\le 320-{{\displaystyle \phi }}_1\\ {{\displaystyle \delta }}_{\min }\le \delta \le \psi -{\displaystyle \frac{{{\displaystyle \phi }}_2}{i}}\end{array}\right.$$

(7)

where, i is the gear ratio of the incomplete bevel gear on the driving gear disk to the small bevel gear; δ_min is the minimum angle between the knotting pincer and rope guard.

For the C-type knotter of the self-propelled rice electric binder (GFK-50), the number of teeth of the incomplete bevel gear on the driving gear disk is 8, occupying an arc angle of ψ = 60°. The cone angle of the small bevel gear is 75°, the number of teeth is 8, and the transmission ratio I = 6. When δ changes, the spatial position changes in the rope placing point and rope pressing point are extremely small. For the convenience of the subsequent research, it is assumed that the positions of these two points remain unchanged. The vertical distance from the rope placing point to the rope pressing point is L₁ = 15 mm, the distance from the driving gear disk center to the rope placing point is L₂ = 100 mm, and the maximum opening angle of the knotting pincer is 20°. When the rope-guiding ring of the rope guard just rotates to the position where it pushes the knotting rope into the angle of the knotting pincer, the rotation angle of the rope guard is φ₂ = 100°. When the generatrices of the small bevel gears of the knotting pincer and rope guard are parallel, the angle between the axes of the knotting pincer and rope guard is the smallest, at δ_min = 30°. At this time, when the knotting pincer rotates 190°, the rope guard starts to rotate, and its rope-guiding ring can smoothly push the knotting rope into the angle. Before the cutting blade of the rope guard touches the knotting rope, the knotting shaft has stopped rotating, and the knot can be normally released. Substituting the measured parameters into the formula, the value range of the angle between the axes of the knotting pincer and rope guard is obtained as 30° ≤ δ ≤ 34°

2.

Position of the rope clamping board (d)

During the process when the installation position of the rope clamping board moves from point o to point d₁, the knotting pincer rotates, and the rope pushing point gradually moves towards the tip of the knotting pincer. When the rope clamping board is fixed at position d₁, the knotting rope cannot be smoothly lifted by the knotting pincer, resulting in the rope falling off and knotting failure. During the process when the installation position of the rope clamping board moves from point o to point d₂, although the knotting rope can be smoothly lifted by the knotting pincer and participate in the knotting process, when the rope clamping board is at point d₂, after the knotting pincer completes the clamping action, the knotting rope at the end of the knot-tightening rope cannot smoothly pass through the narrow gap between the rope clamping board and the rice collection platform, leading to unknotting failure. The rope clamping point positions in both situations are shown in Figure 5:

To study the effective range of the rope clamping board position, a spatial rectangular coordinate system was constructed at point O on the axis line of the knotting pincer axis. In this coordinate system, the XOZ plane is parallel to the rope clamping board surface, the negative direction of the X-axis points to the rope guard, the positive direction of the Y-axis is set as the direction along the axis line pointing to the rice collection platform and perpendicular to the rope clamping board, and the negative direction of the Z-axis points to the ground. Point C is on the XOZ plane, as shown in Figure 6. Set the rope placing point on the knotting pincer as A, the rope clamping point on the rope clamping board as B, and the tip point of the knotting pincer as C, with their coordinates being A(x₁, y₁, z₁), B(x₂, y₂, z₂), and C(x₃, 0, z₃), respectively.

During the knotter operation process, the operating trajectory of the tip point C of the knotting pincer in space is a circular path, and the trajectory equation of point C is

$$\left\{\begin{array}{l}{{\displaystyle (x-{{\displaystyle x}}_3)}}^2+{{\displaystyle (z-{{\displaystyle z}}_3)}}^2={{\displaystyle R}}^2\\ R=\sqrt{{{\displaystyle {{\displaystyle x}}_3}}^2+{{\displaystyle {{\displaystyle z}}_3}}^2}\end{array}\right.$$

(8)

The parametric equation of the spatial line AB is

$$\left\{\begin{array}{l}x={{\displaystyle x}}_1+\lambda ({{\displaystyle x}}_2-{{\displaystyle x}}_1)\\ y={{\displaystyle y}}_1+\lambda ({{\displaystyle y}}_2-{{\displaystyle y}}_1)\\ z={{\displaystyle z}}_1+\lambda ({{\displaystyle z}}_2-{{\displaystyle z}}_1)\end{array}\right.,(\lambda \in R)$$

(9)

Let the coordinates of the intersection point H of AB on the XOZ plane be (x₄, 0, z₄). Substituting point H into the above equation, we obtain

$$\left\{\begin{array}{l}{{\displaystyle x}}_4={{\displaystyle x}}_1+{\displaystyle \frac{{{\displaystyle ({{\displaystyle x}}_2-{{\displaystyle x}}_1)y}}_1}{({{\displaystyle y}}_2-{{\displaystyle y}}_1)}}\\ {{\displaystyle z}}_4={{\displaystyle z}}_1+{\displaystyle \frac{{{\displaystyle y}}_1({{\displaystyle z}}_2-{{\displaystyle z}}_1)}{({{\displaystyle y}}_2-{{\displaystyle y}}_1)}}\end{array}\right.$$

(10)

When the knotter rotates to contact the knotting rope, if point H is located inside of the trajectory circle of point C, the looping action can proceed smoothly. Substituting the coordinate values of point H into the equation, we obtain

$${{\displaystyle ({{\displaystyle x}}_4-{{\displaystyle x}}_3)}}^2+{{\displaystyle ({{\displaystyle z}}_4-{{\displaystyle z}}_3)}}^2\le {{\displaystyle {{\displaystyle x}}_3}}^2+{{\displaystyle {{\displaystyle z}}_3}}^2$$

(11)

To obtain the coordinate values of points A, B, and C, a measurement test was conducted on the C-type knotter. The measurement method is as follows. Firstly, the contact point between the bundle rope and the lower jaw of the knotter is defined as point A. Since the x₁ value of point A is difficult to measure directly, we use the projection of point A on the XOZ plane, denoted as A’. The distance of OA’ along the X-axis is the x₁ value, and the coordinate values y₁ and z₁ can be directly measured from the scale. Secondly, the coordinate value y₂ and the fixed distance d₁ at point B can be directly measured. Finally, the coordinate value of point C is directly measured. Each coordinate point was measured three times, and the average value was taken as its coordinate. The measurement results are shown in

Table 1. Measured values of the spatial coordinates.

Test No.	A	B	C	d1
1	(11, −8, −10)	(x2, 3, −11)	(11, −8, −10)	10
2	(10, −7, −11)	(x2, 4, −11)	(10, −7, −11)	11
3	(10, −6, −10)	(x2, 3, −13)	(10, −6, −10)	11
Average of Experiments	(10, −7, −10)	(x2, 3, −12)	(10, −7, −10)	11

below.

From Table 1, it can be seen that the coordinates of points A, B, and C are as follows: A(10, −7, −10); B(x₂, 3, −12); C(18, 0, −23), unit: mm. Substituting the coordinate values of A, B, and C into Equation (11), the coordinates of point H are solved as (3 + 0.7x₂, 0, −11.4)mm.

According to the previous calculation, the limit position d₁ of the rope clamping board on the rice collection platform is 17 mm. At the same time, through the precise measurement of the knotter, the limit distance d₂ is determined to be 11 mm. Therefore, the position d of the rope clamping board relative to the distance from the knotter axis line is −11 mm ≤ d ≤ 17 mm.

3.

Inclination angle of the knotting pincer convex platform (θ)

At any instant during the looping and knotting operation executed by the knotting pincer, the relative motion between it and the contact point with the knotting rope can be regarded as an object sliding along an inclined surface, as shown in Figure 7.

When the knotting pincer rotates 90°, the knotting rope is subjected to the pulling force F, the normal positive pressure F_N along the contact point on the curved surface of the lower jaw of the knotting pincer, and the friction force f of the curved surface of the convex platform of the lower jaw of the knotting pincer on the knotting rope, as shown in Figure 8. Among them, the magnitudes of the pulling force F of the knotting rope along the X-axis, Y-axis, and Z-axis directions are

$$\left\{\begin{array}{l}{{\displaystyle F}}_X=F\cos {\lambda }_1\\ {{\displaystyle F}}_Z=F\cos {\lambda }_2\end{array}\right.$$

(12)

where λ₁ and λ₂ are the angles between F and Fx, and Fz, respectively.

The magnitude of the normal positive pressure F_N along the contact point on the curved surface of the lower jaw of the knotting pincer is

$${{\displaystyle F}}_N={{\displaystyle F}}_{X2}+{{\displaystyle F}}_{Z2}$$

(13)

Substituting Equation (13) into (12), we can obtain

$${{\displaystyle F}}_N=F\cos \alpha \sin {\lambda }_1+F\cos {\lambda }_2\cos \theta$$

(14)

When the knotting rope does not slide upward along the curved surface of the lower jaw of the knotting pincer, the critical condition that needs to be satisfied is

$$\left\{\begin{array}{l}{{\displaystyle F}}_{Z1}<{{\displaystyle F}}_{X1}+f\\ f=\mu {{\displaystyle F}}_N\end{array}\right.$$

(15)

where μ is the friction coefficient between the knotting pincer and the knotting rope, which is taken as 0.18 in this paper [25].

Substituting Equations (12) and (14) into (25), we can obtain

$$F\cos {\lambda }_2\sin \theta -F\cos {\lambda }_1\cos \theta <\mu (F\cos {\lambda }_1\sin \theta +F\cos {\lambda }_2\cos \theta )$$

(16)

Further simplifying, the following formula can be obtained:

$$\theta <\arctan {\displaystyle \frac{\mu \cos {\lambda }_2+\cos {\lambda }_2}{\cos {\lambda }_2-\mu \cos {\lambda }_2}}$$

(17)

From Equations (16) and (17), it can be seen that, to ensure that the position of the knotting rope on the surface of the lower jaw of the knotting pincer remains unchanged, the knotting rope must maintain force balance in the direction of the friction force. That is, the inclination angle of the knotter convex platform is related to the posture angle of the knotting rope and the friction force generated between them.

Through measurement (Figure 9), it can be known that the posture angle of the knotting rope is λ₁ = 80° and λ₂ = 78°. Substituting them into the equation, it can be calculated that θ < 60.34°.

Considering that, when the knotting pincer rotates to the position intersecting with the knotting rope, the knotting rope needs to be smoothly accommodated by the gap formed by the lower jaw and convex platform of the knotting pincer, as shown in Figure 10, the measured minimum inclination angle θ_min of the knotting pincer convex platform at this time is 26°. Therefore, the rounded and adjusted range of the knotter convex platform inclination angle is determined to be 26° ≤ θ ≤ 60°.

2.3. Simulation Model

In the ADAMS 2020 simulation environment, the force model of the binder knotting rope is established by using the discrete rigid body connection method. The method is as follows: a cylinder model of the first segment of the rope is constructed in the three-dimensional design software SolidWorks; in the ADAMS software, macro-commands are used to automatically process the first segment cylinder and create a knotting rope model with no direct connection between segments. To simulate the flexibility characteristics of the knotting rope, bushing forces are applied between the small cylinders, whose magnitudes are dynamically adjusted according to the inherent properties of the material (such as the modulus of elasticity and the shear modulus of elasticity), the relative displacement, the angle change, the velocity, and the angular velocity. In this research, the knotting rope adopted by the knotting operation is a polypropylene rope with a diameter D = 2 mm, a modulus of elasticity E = 1.32 × 10³ MPa, a shear modulus of elasticity G = 0.49 × 10³ MPa, and Poisson’s ratio u = 0.35, while the torsional damping coefficient (C₄, C₅, and C₆) is taken as 0.1 N·m·s/rad [26]. The tensile damping coefficient (C₁, C₂, and C₃) has a limited impact on the dynamic performance of the knotting rope and is set to 2% of the corresponding stiffness coefficient value; the torsional damping coefficient has a non-negligible influence on the motion performance of the knotting rope. The smaller its value, the stronger the rope’s resistance to bending [27]. Through calculation by Equation (18), this paper determines the Bushing force settings of the knotting rope, as shown in

Table 2. Bushing force parameters.

Type	Value (Unit)
Tension Rigidity Coefficient K11	2073.45 (N/mm)
Torsional Rigidity Coefficient K22, K33	769.69 (N/mm)
Shear Rigidity Coefficient K44	6.72 (N∙mm/deg)
Bending Rigidity Coefficient K55, K66	9.05(N∙mm/deg)
Tension Amping Coefficient C11	41.47 (N∙s/mm)
Torsional Amping Coefficient C22, C33	15.39 (N∙s/mm)
Shear Amping Coefficient C44	0.1 (N∙s/rad)
Bending Amping Coefficient C55, C66	0.1 (N∙s/rad)

. At the same time, the force model of the real knotting rope is batch-created using macro-commands.

$$\left\{\begin{array}{l}{{\displaystyle K}}_{11}={\displaystyle \frac{EA}{L}}\\ {{\displaystyle K}}_{22}={{\displaystyle K}}_{33}={\displaystyle \frac{GA}{L}}\\ {{\displaystyle K}}_{44}={\displaystyle \frac{G\pi {{\displaystyle D}}^4}{32L}}\\ {{\displaystyle K}}_{55}={{\displaystyle K}}_{66}={\displaystyle \frac{E\pi {{\displaystyle D}}^4}{64L}}\\ G={\displaystyle \frac{E}{2(1+U)}}\end{array}\right.$$

(18)

In the formula, E represents the knotting rope of the binding rope, G is the knotting rope of the binding rope, A is the cross-sectional area of the knotting rope, D is the diameter of the knotting rope, L is the length of each micro-segment of the knotting rope, and U is Poisson’s ratio of the knotting rope.

The three-dimensional model of the knotter was constructed in the Solidworks2021 software. Since the rice collection platform of the knotter interferes with the observation of the knotting rope posture, when constructing the simulation model, the rope clamping board region is retained, while other non-critical regions are reduced to optimize the simulation calculation efficiency of ADAMS. To simulate the actual working state of the knotting rope, a knotting rope model is designed, consisting of 100 small cylinders with a diameter and length of 2 mm, connected by Bushing forces. According to the knotting rope shape after the rope-feeding needle completes the rope feeding, one end of the knotting rope is attached to the rope pressing region of the rope guard, and the other end is kept in contact with the rope clamping board, as shown in Figure 11. At the same time, gravity effects and Boolean operations are applied to the model, and corresponding material properties are set for each component (the material parameters for steel can be obtained from the ADAMS simulation, the density of polypropylene is 0.895 to 0.912 g/cm³ [28], and, for this study, 0.90 g/cm³ is taken), as shown in

Table 3. Material parameters added to the ADAMS parts.

Material Specification	Added Part	Value
		Density	Young’s Modulus	Poisson’s Ratio
Steel	2, 3, 4, 5, 6, 7, 8, 9	7.8 × 10−6 kg/mm3	2.07 × 105 Mpa	0.29
Polypropylene	1, 10, 11	9.0 × 10−7 kg/mm3	1.32 × 103 Mpa	0.35

.

Based on the dynamic interaction relationship between the components of the knotter during the actual knotting operation process, kinematic pairs and drives were added to the ADAMS simulation model to accurately simulate the physical behavior in the knotter operation. The parameter settings are shown in

Table 4. Constraints and drives applied between each pair of components.

Apply Between Components A and B		Constraint (Drive) Type
Part A Number	Part B Number
1	2, 5, 6, 7, 8, 9	Contact force
2	4, 5, 9	Revolute joint
3	5, 9	Gear pair
4	2, 6	Contact force
5	6	Contact pair and revolute joint
2, 7, 8	ground	Fixed joint
10	ground	Translational joint and drive
11	ground	Translational joint

.

During the simulation process, to eliminate the non-physical penetration phenomenon between two interacting components, it is necessary to clearly define the contact relationship between the relevant motion components. ADAMS provides three methods for calculating contact forces, namely, the impact function method (Impact), the restitution coefficient method (Restitution), and the user-defined method, to meet the requirements of the contact force calculation in different scenarios. In this research, the knotting rope needs to maintain continuous and close contact with the knotter. Under the condition of continuous contact, the impact function method (Impact) can most effectively simulate this dynamic interaction process. Therefore, the impact function method was selected to calculate the contact force between the knotting rope and the knotter and its components. The specific expression of the impact function is shown in the following equation:

$${{\displaystyle F}}_{\mathrm{j}}=\left\{\begin{array}{cc}0& x>{{\displaystyle x}}_0\\ k{{\displaystyle ({{\displaystyle x}}_0-x)}}^e-{{\displaystyle c}}_{\max }{\displaystyle \frac{dx}{dt}}step(x,{{\displaystyle x}}_0-{{\displaystyle d}}_{\max },1,{{\displaystyle x}}_0,0)& {{\displaystyle x\le x}}_0\end{array}\right.$$

(19)

where x₀ is the initial distance between two colliding objects, unit: mm; x is the actual distance between the two objects during the collision process, unit: mm; d_x/d_t is the relative velocity between the two objects, unit: mm/s; k is the contact stiffness coefficient, unit: N·mm^−3/2; e is the collision index; c_max is the damping coefficient, unit: N·s·mm⁻¹; d_max is the penetration depth, unit: mm.

Here, step(x, x₀ − d_max, 1, x₀, 0) is a function adopted to ensure the continuity of the damping force during the collision process, and its calculation formula is

$$\left\{\begin{array}{l}\begin{array}{cc}\begin{array}{c}{{\displaystyle h}}_0\\ {{\displaystyle h}}_0+{{\displaystyle ({{\displaystyle h}}_1-{{\displaystyle h}}_0)\Delta }}^2(3-2\Delta )\\ {{\displaystyle h}}_1\end{array}& \begin{array}{c}{{\displaystyle t\le t}}_0\\ {{\displaystyle {{\displaystyle t}}_0<t<t}}_1\\ {{\displaystyle t\ge t}}_0\end{array}\end{array}\\ \Delta ={\displaystyle \frac{(t-{{\displaystyle t}}_0)}{({{\displaystyle t}}_1-{{\displaystyle t}}_0)}}\end{array}\right.$$

(20)

where h₀ is the initial value of the function; h₁ is the final value of the function; t is the time variable of the function; t₀ is the initial value of the time variable; t₁ is the final value of the time variable.

The specific value of the contact stiffness coefficient k is generally calculated using the theoretical formula of the Hertz elastic impact model [29], as follows:

$$\left\{\begin{array}{l}{\displaystyle \frac{1}{R}}={\displaystyle \frac{1}{{{\displaystyle R}}_1}}+{\displaystyle \frac{1}{{{\displaystyle R}}_2}}\\ {\displaystyle \frac{1}{E}}={\displaystyle \frac{1-U_1^2}{{{\displaystyle E}}_1}}+{\displaystyle \frac{1-U_2^2}{{{\displaystyle E}}_2}}\\ {{\displaystyle k}}^2={\displaystyle \frac{16R{{\displaystyle E}}^2}{9}}\end{array}\right.$$

(21)

In the above equation, R₁ and R₂ are the radii of the curvature of the knotting pincer and knotting rope, taken as 10 mm and 1 mm, respectively; E₁ and E₂ are the moduli of elasticity of the knotting pincer and knotting rope; u₁ and u₂ are the Poisson ratios of the knotting pincer and knotting rope.

Calculated by Equation (21), the final parameter settings of the contact force parameters in ADAMS are shown in

Table 5. Contact force parameters.

Parameter Name	Value
	Rope and Other Rigid Components	Interacting Rope-Tying Section
Contact stiffness coefficient	3607.3	377.1
Exponent	2	2
Damping coefficient	1.52	1.52
Penetration depth	0.3	0.3
Coefficient of static friction	0.37	0.37
Coefficient of kinetic friction	0.18	0.18

.

After completing all of the parameter settings and configurations, the force simulation model of the knotter was constructed in the ADAMS software environment. In the simulation model, the dynamic evolution process of the knotting rope under the synergistic action of the various components of the knotter can be intuitively observed and analyzed, that is, the gradual transition from the initial slack state to the final stable knotting state, as shown in Figure 12.

2.4. Optimising Test Methods

2.4.1. Experimental Arrangement

Based on the theoretical analysis in Section 2.2, taking the angle δ (X₁) between the axes of the knotting pincer and rope guard, the position d (X₂) of the rope clamping board, and the inclination angle θ (X₃) of the knotting pincer convex platform as test factors, and the maximum tension force on the binding rope (F_max) and the knot end protrusion length (L_S) as evaluation indicators, a three-factor three-level quadratic orthogonal test was conducted using the Design-Expert 13.0 software. The number of test groups was 17, and the factor level coding table is shown in

Table 6. Experimental factors and codes.

Factor Level	Angle Between the Axes of the Knotting Pincer and Rope Guard (X1)/(°)	Position of the Rope Clamping Board (X2)/(mm)	Inclination Angle of the Knotting Pincer Convex Platform (X3)/(°)
−1	30	−11	26
0	32	3	43
1	34	17	60

.

2.4.2. Experimental Indices

• The maximum tensile force on the binding rope (F_max)

The smaller maximum tension on the knotting rope during the knotting process (the maximum tensile force on the binding rope for the knotter before the improvement was measured to be about 145 N), the higher the density of the final bundle, the more stable the knot, and the higher the knotting efficiency.

2.

The knot end protrusion length (L_S)

The maximum distance from the knot point to the end of the knot after knotting (the knot end protrusion length for the knotter before improvement was measured to be about 8.5 mm) was used to measure the quality of the knotting and the utilization rate of the binding rope so to ensure that, after the actual bundling, the binding rope could overcome the outward tension of the bundle during tying. The greater the extension, the more stable the knot [30].

2.5. Field Verification Test Method

To verify the accuracy of the identified optimal structural parameters, a knotter was prototyped based on the best combination of parameters. In order to enhance the working stability of the knotter, the manufacturing and processing accuracy of the components were ensured to strictly meet the design requirements during the prototyping process, thus reducing assembly errors. Subsequently, both the improved and previous versions of the C-type knotter were installed on the rice electric binder, ensuring that all parts were properly aligned and secured, with bolts, nuts, and other fasteners selected appropriately and tightened correctly. In addition, the structure at the connection between the knotter’s transmission box and the bottom of the cutting platform was reinforced, and vibration dampers were added to reduce the vibration and improve the knotting quality. In September 2024, a field harvesting and bundling test was conducted at the rice field test base of the Wanxin Family Farm in Pucheng County, Fujian Province, as shown in Figure 13. The test object of this test was rice at the mature stage, with the variety being Shan You 6, and the average plant height was 0.88 m. Before the test, the layout position of the knotting rope and the tightness of the pressing plate were adjusted, and a polypropylene rope with a diameter of 2 mm was adopted as the test knotting rope. During the test process, the forward speed of the binder was set to 0.5 m per second. The test conditions and methods were implemented in accordance with the requirements of the Chinese national standard “JB/T9702-2010 Knotters of Rectangular Balers” [31] and the agricultural machinery promotion appraisal outline “DG/T 179-2023 Binder” [32]. During the test, a rope ring was used to connect the knotting rope to the sensor shackle (Figure 14a). The maximum tension on the knotting rope was obtained by measuring the force on the sensor, and a ruler was used to directly measure the length of the knot end after the knotting was completed (Figure 14b). Each test was conducted for 10 s, and the average values of the maximum tension on the knotting rope and the knot end protrusion length measured during the test process were used as single test data. The experiment was divided into the following two groups: one before optimization and one after optimization, with each group repeated five times, recording the data each time.

After the operation of the rice binder was completed, 100 rice bundles were continuously collected as a sampling unit, and this was repeated 3 times. The number of successful bundles in each of the 3 tests was recorded. The method of judging the knot was as follows: apply 400–500 N of tension at both ends of the knot. If the knot is not pulled apart, it is judged to be a successful knot; otherwise, the knot fails, as shown in Figure 15. The bundling rate was calculated according to the following formula:

$${{\displaystyle \eta }}_d={\displaystyle \frac{{{\displaystyle n}}_1}{{{\displaystyle n}}_0}}\times 100\%$$

(22)

where η_d is the bundling rate, unit: %; n₀ is the total number of test bundles, unit: bundles; n₁ is the number of bundled bundles, unit: bundles.

3. Test Results and Analysis

3.1. Regression Prediction Model of Bundling Quality

A total of 17 sets of simulation tests were conducted in the ADAMS software, with each set repeated three times, to obtain the maximum tension (F_max) on the knotting rope and the knot end protrusion length (L_s) during the knotting process of the knotter. The results are shown in

Table 7. Test protocols and results.

Test No.	Factor Level			Ls (mm)	Fmax (N)
	X1	X2	X3
1	30	−11	43	8.9	138
2	34	−11	43	6.7	148
3	30	17	43	8.1	145
4	34	17	43	7.5	153
5	30	3	26	8.8	135
6	34	3	26	6.9	146
7	30	3	60	9.0	154
8	34	3	60	7.8	162
9	32	−11	26	7.7	142
10	32	17	26	7.0	152
11	32	−11	60	7.9	168
12	32	17	60	7.8	169
13	32	3	43	8.4	140
14	32	3	43	8.4	142
15	32	3	43	8.3	141
16	32	3	43	8.3	142
17	32	3	43	8.5	141

. Based on the analysis of variance (ANOVA), all of the experimental data were statistically analyzed with the Design-Expert 13.0 software, and the results of the regression models, the significance, and the fitting of the maximum tension (F_max) on the knotting rope and the knot end protrusion length (L_s) were obtained. The analysis of variance (ANOVA) results are shown in

Table 8. The ANOVA results for the experimental indices.

Source of Variance	LS			Fmax
	Mean Square Error	F-Value	p-Value	Mean Square Error	F-Value	p-Value
Model	0.8244	47.89	<0.0001 **	183.86	116.47	<0.0001 **
X1	4.35	252.77	<0.0001 **	171.13	108.40	<0.0001 **
X2	0.08	4.65	0.0680	66.13	41.89	0.0003 **
X3	0.5512	32.02	0.0008 **	760.50	481.76	<0.0001 **
X1 X2	0.64	37.18	0.0005 **	1.00	0.6335	0.4522
X1X3	0.1225	7.12	0.0321 *	2.25	1.43	0.2714
X2 X3	0.09	5.23	0.0561	20.25	12.83	0.0090 *
X12	0.0032	0.1850	0.6801	14.41	9.13	0.0193 *
X22	1.29	74.66	<0.0001 **	186.20	117.95	<0.0001 **
X32	0.2179	12.66	0.0092 **	412.67	261.42	<0.0001 **
Lack of fit	0.0308	4.40	0.0930	2.75	3.93	0.1097

Note: ** indicates extremely significant (p < 0.01); * indicates significant (0.01 ≤ p < 0.05).

.

From the analysis in Table 8, it can be seen that the p-values of the models for the knot end protrusion length (L_s) and the maximum tension (F_max) on the knotting rope are both less than 0.0001, indicating that the models reach an extremely significant level, the constructed regression models are significant, and the fitting degree is good. The p-values of the lack-of-fit terms for both models are > 0.05, indicating that the errors generated during the experimental process are within an acceptable low-level range, further verifying the effectiveness and reliability of the regression analysis. The significant factors affecting the knot end protrusion length (L_s) are X₁, X₃, X₁X₂, X₁X₃, X₂², and X₃²; the significant factors affecting the maximum tension (F_max) on the knotting rope are X₁, X₂, X₃, X₂X₃, X₁², X₂², and X₃². Excluding the factors that have no significant influence on the response variables, the regression prediction models for the knot end protrusion length Ls and the maximum tension Fmax on the knotting rope are obtained as follows:

$$\left\{\begin{array}{l}{{\displaystyle L}}_{\mathrm{s}}=8.38-{{\displaystyle 0.1\mathrm{X}}}_2+0.26{{\displaystyle \mathrm{X}}}_3+0.4{{\displaystyle \mathrm{X}}}_1{{\displaystyle \mathrm{X}}}_2+0.18{{\displaystyle \mathrm{X}}}_1{{\displaystyle \mathrm{X}}}_3-0.55{{\displaystyle \mathrm{X}}}_2^2-0.23{{\displaystyle \mathrm{X}}}_3^2\\ {{\displaystyle F}}_{\max }=141.2+4.63{{\displaystyle \mathrm{X}}}_1+2.88{{\displaystyle \mathrm{X}}}_2+9.75{{\displaystyle \mathrm{X}}}_3-2.25{{\displaystyle \mathrm{X}}}_2{{\displaystyle \mathrm{X}}}_3-1.85{{\displaystyle \mathrm{X}}}_1^2\\ \begin{array}{cc} & +6.65{{\displaystyle \mathrm{X}}}_2^2+9.9{{\displaystyle \mathrm{X}}}_3^2\end{array}\end{array}\right.$$

(23)

According to the results of the analysis of variance, the mean square error (MSE) is a key metric in the analysis of variance (ANOVA), and a factor with a larger mean square typically has a significant impact on the experimental outcomes. The order of influence of individual factors on the knot end protrusion length is as follows: the angle between the axes of the knotting pincer and rope guard > the inclination angle of the knotting pincer convex platform > the position of the rope clamping board, while the order of influence on the maximum tension on the knotting rope is as follows: the inclination angle of the knotting pincer convex platform > the angle between the axes of the knotting pincer and rope guard > the position of the rope clamping board.

3.2. Analysis of the Influence of Factor Interactions on Evaluation Indicators

To further analyze the influence of two-factor interactions on the evaluation indicators, the remaining factor was set to the level-zero value, and only significant factors were considered. The interactions of significant influencing factors on the knot end protrusion length and the maximum tension on the knotting rope were obtained, as shown in Figure 16.

As shown in Figure 16a, when the position of the rope clamping board remains unchanged, as the angle between the axes of the knotting pincer and rope guard gradually increases, the protrusion length of the knot end shows a gradually decreasing trend. When the angle between the axes of the knotting pincer and rope guard is within the range of 30–31°, the protrusion length of the knot end is the largest. If the angle between the axes of the knotting pincer and rope guard is kept constant, as the position of the rope clamping board gradually increases, the protrusion length of the knot end first increases and then decreases. In particular, when the position of the rope clamping board falls within the range from −4 mm to −11 mm, the protrusion length of the knot end reaches its minimum value. The main reason may be that, as the angle between the axes of the knotting pincer and rope guard increases, the timing of the knotting pincer clamping the knotting rope is correspondingly delayed, resulting in a decrease in the protrusion length of the knot. The change in the position of the rope clamping board affects the looping position, causing it to tend towards the tip of the lower jaw. Whether this position moves closer or further away, it will have an adverse impact on the smoothness of the knot formation process, thereby reducing the protrusion length of the knot.

From Figure 16b, it can be seen that, when the angle between the axes of the knotting pincer and rope guard remains unchanged, as the inclination angle of the knotting pincer convex platform increases, the protrusion length of the knot end first increases and then decreases; when the inclination angle of the knotting pincer convex platform remains unchanged, as the angle between the axes of the knotting pincer and rope guard increases, the protrusion length of the knot end gradually decreases. The main reason may be that, when the inclination angle of the knotting pincer convex platform increases, the friction force experienced by the knotting rope during the loop formation process decreases, leading to a delay in the time node when it is clamped, thereby reducing the protrusion length of the knot; when the inclination angle of the knotting pincer convex platform decreases, the knotting rope cannot smoothly enter the predetermined accommodating gap, causing the loop formation completion point to shift towards the lower jaw tip, reducing the release radius and thus reducing the protrusion length of the knot.

From Figure 16c, it can be seen that, when the position of the rope clamping board remains unchanged, as the inclination angle of the knotting pincer convex platform increases, the maximum tension on the knotting rope shows a trend of first decreasing and then increasing. When the inclination angle of the knotting pincer convex platform is within the range of 34.5–43°, the maximum tension on the knotting rope has a minimum value; when the inclination angle of the knotting pincer convex platform remains unchanged, the maximum tension on the knotting rope also increases with the increase in the position of the rope clamping board, showing a trend of first decreasing and then increasing. When the position of the rope clamping board is within the range from −4 mm to −11 mm, the maximum tension on the knotting rope has a minimum value. The main reason for this phenomenon may be that the increase or decrease in the inclination angle of the knotting pincer convex platform causes the knotting rope to easily fall off or fail to smoothly enter the predetermined accommodating gap, leading to the entanglement of the knotting rope and increasing the maximum tension on the knotting rope. Secondly, the adjustment of the position of the rope clamping board directly affects the radius of the loop. When the position increases, the increase in the radius of the loop leads to an increase in the maximum tension on the knotting rope. When the position decreases, the tension end of the rope may have difficulty smoothly passing through the rope-pulling space of the rice collection platform, which also increases the maximum tension.

3.3. Optimal Parameter Combination and Verification

To determine the best structural parameter combination for the knotter, taking the maximum tension on the knotting rope and the knot end protrusion length as optimization objectives, and limiting the level range of significant influencing factors, a mathematical optimization model for the operation quality of the electric rice binder was established, as shown below:

$$\left\{\begin{array}{c}{{\displaystyle L}}_{\mathrm{s}}=\max f({{\displaystyle \mathrm{X}}}_1,{{\displaystyle \mathrm{X}}}_2,{{\displaystyle \mathrm{X}}}_3)\\ \begin{array}{l}{{\displaystyle F}}_{\max }=\min f({{\displaystyle \mathrm{X}}}_1,{{\displaystyle \mathrm{X}}}_2,{{\displaystyle \mathrm{X}}}_3)\\ s.t.\left\{\begin{array}{l}{{\displaystyle 30\le \mathrm{X}}}_1\le 34\\ {{\displaystyle -11\le \mathrm{X}}}_2\le 17\\ {{\displaystyle 26\le \mathrm{X}}}_3\le 60\end{array}\right.\end{array}\end{array}\right.$$

(24)

Using the Design-Expert 13.0 software to solve and analyze the optimization model, the relatively optimal knotter structural parameter combination was obtained as follows: the angle between the axes of the knotting pincer and rope guard is 30.23°, the position of the rope clamping board is −3.75 mm, and the inclination angle of the knotting pincer convex platform is 40.75°. At this time, the knot end protrusion length obtained from the prediction model is 9.10 mm and the maximum tension on the knotting rope is 134.25 N.

To verify the reliability of the parameter optimization results, in the constructed simulation model, the angle between the axes of the knotting pincer and rope guard was adjusted to 30.23°, the position of the rope clamping board was set to −3.75 mm, and the inclination angle of the knotting pincer convex platform was set to 40.75°. A knotting operation simulation performance test was conducted. At this time, the test results showed that the knot end protrusion length was 9.18 mm and the maximum tension on the knotting rope was 134.32 N, which were consistent with the values of the prediction model, verifying the reliability of the parameter optimization results.

3.4. Field Verification Test Results and Analysis

After the measurement was completed, a comparative analysis with the simulation optimization results was conducted, as shown in

Table 9. Comparison of optimization results and test values.

Test Index	Test Number	Theoretical Value	Test Results	Relative Error/%
The end protrusion of the knot (LS/mm)	1	9.10	9.60	5.49
	2	9.10	9.36	2.86
	3	9.10	9.71	6.70
	4	9.10	9.82	7.91
	5	9.10	9.66	6.15
	Average value	9.10	9.63	5.82
The maximum tension on the knotting rope (Fmax/N)	1	134.25	130.65	2.68
	2	134.25	125.43	6.57
	3	134.25	127.39	5.11
	4	134.25	129.91	3.23
	5	134.25	126.18	6.01
	Average value	134.25	127.91	4.72

.

Analyzing Table 9, it was found that the experimental value of the knot end protrusion length in the field test was higher than the simulated value, and the experimental value of the maximum tension on the knotting rope was lower than the simulated value. The average relative errors compared to the experimental values were 5.82% and 4.72%, respectively, indicating that the established regression prediction model for the bundling performance can effectively predict the actual values of the knot end protrusion length and the maximum tension on the knotting rope with a good accuracy and reliability. The main reasons for the errors may be the influence of external factors, such as the flatness of the soil in the rice field, the growth condition of the crops, the proficiency of the operator, and the ambient temperature and humidity during the experiment. These factors may all affect the knotting state of the knotter, thereby reducing the bundling effect.

The comparison and analysis of the experimental results before and after optimization are shown in

Table 10. Comparison and analysis of the experimental results before and after optimization.

Test Index	Test Number	Results Before Optimization	Result After Optimization	Improvement Rate/%
The end protrusion of the knot (LS/mm)	1	8.46	9.60	13.48
	2	8.22	9.36	13.87
	3	8.53	9.71	13.83
	4	8.38	9.82	17.18
	5	8.47	9.66	14.05
	Average value	8.41	9.63	14.48
The maximum tension on the knotting rope (Fmax/N)	1	144.32	130.65	9.47
	2	146.44	125.43	14.35
	3	142.39	127.39	10.53
	4	141.86	129.91	8.42
	5	145.75	126.18	13.43
	Average value	144.15	127.91	11.27

.

According to Table 10, the end protrusion of the knot of the knotter increased from 8.41 mm to 9.63 mm, and the average maximum tensile force on the knotting rope decreased from 144.15 N to 127.91 N, indicating a significant improvement in the performance of the knotter after optimization, with increases and decreases of 14.48% and 11.27%, respectively. Firstly, this indicates that the optimized knotter is capable of forming more secure knots, which will lead to a higher success rate in bundling during the rice harvesting process. After the bundles are tied and air-dried, they are less likely to come apart during subsequent collection and threshing operations, which is beneficial for improving the overall work efficiency. Secondly, the reduction in the average maximum tensile force suggests that the optimized knotter can maintain the integrity of the knot while applying less force to the binding twine. This not only enhances the overall performance of the knotter but also implies that the components of the knotter exert less pressure on the binding twine, potentially increasing the service life and durability of both the twine and the machine. Lastly, the significantly improved performance of the optimized knotter is better equipped to meet the challenges of its intended functions, reducing the likelihood of bundling failure and enhancing the overall quality of the final product, the rice combine harvester. This is of great significance for improving the efficiency and economic benefits of rice harvesting.

From

Table 11. Bundling test results.

Test Number	Before Optimization		After Optimization		Standard Requirements
	The Bundling Numbers (η1)	The Bundling Rates (ηd)	The Bundling Numbers (η1)	The Bundling Rates (ηd)	The Bundling Rates
1	97	97%	100	100%	>95%
2	96	96%	99	99%
3	97	97%	99	99%
Average of Experiments		96.6%		99.3%

, it can be seen that the average bundling success rate of the rice electric binder before optimization was 96.6%, and the bundling rate of the rice electric binder field test 1 was 100%, while the bundling rates of tests 2 and 3 were both 99%, with an average bundling rate of 99.3%. The bundling success rate of the rice electric binder increased by 2.7% after optimization. These data indicate that the rice electric binder demonstrated high bundling efficiency and stability during the field trials. It also provides strong evidence of the success of the optimization efforts, and offers a certain reference for the advancement of knot-tying technology and the development of related industries.

To further verify the performance reliability and stability of the machine after optimization, multiple field tests were conducted from September to October 2024 in the rice paddy planting bases of the Wanxin Family Farm and Fuling Longqing Agricultural Machinery Professional Cooperative in Pucheng County, Fujian Province. After each test, the experimental errors were analyzed and improvements were made to the machine, such as adjustments to the knotting rope path, the tightness of the binding rope, and the optimization of the rope feeding needle. The tests covered a variety of weather conditions and different field conditions, including the flatness of the fields, the degree of mud, the rice varieties, and the plant heights. Under these diverse conditions, the knotter, after adjustments and improvements, performed excellently, ensuring its reliability in a range of actual field situations.

4. Conclusions

This research aimed to improve the operational quality of the rice electric binder knotter. Through theoretical analysis, knotting process simulation, and field test methods, the structural parameters of the rice electric binder knotter were optimized and designed, and the best structural parameter combination was determined, significantly improving the operational quality of the rice electric binder, while also providing methods and a theoretical basis for similar knotting studies. The specific conclusions are as follows:

• Through a theoretical analysis of the influence of the spatial position relationship and structural characteristics among the components of the knotter on the knotting performance, the key factors affecting the knotting quality were clarified, and a simulation model capable of simulating the dynamic process of interaction between the knotter and knotting rope, and the formation of knots, was constructed.
• Using the quadratic orthogonal test design method, regression prediction models based on the two key evaluation indicators of the knot end protrusion length and maximum tension on the knotting rope were constructed, realizing the quantitative analysis of the relationship between the knotter structural parameters and evaluation indicators. The research results showed that the first-order term of the rope clamping board position, the second-order term of the angle between the axes of the knotting pincer and rope guard, and the interaction term between the rope clamping board position and the inclination angle of the knotting pincer convex platform had significant effects on the knot end protrusion length. The interactions of the angle between the axes of the knotting pincer and rope guard with the other two factors also had significant effects on the maximum tension on the knotting rope.
• The optimal structural parameter combination for the rice electric binder was determined as follows: the angle between the axes of the knotting pincer and rope guard was set to 30.23°, the position of the rope clamping board was adjusted to −3.75 mm, and the inclination angle of the knotting pincer convex platform was set to 40.75°. Under this parameter combination condition, the knot end protrusion length reached 9.10 mm and the maximum tension on the knotting rope was 134.25 N. Then results from the field experiments indicate that the relative errors between the experimental values and theoretical values for the two evaluation indicators are 5.82% and 4.72%, respectively. Additionally, the improvement rates of the two evaluation indicators before and after optimization are 14.48% and 11.27%, respectively. Simultaneously, the bundling success rate of the rice electric binder increased by 2.7% after optimization, indicating that the constructed knotter simulation model had a high accuracy and reliability.