Dynamic Traction of Deep-Sea Polymetallic Nodule Collector

Abstract

The ocean is extremely rich in mineral resources. To cope with the shortage of land mineral resources, countries are focusing on the development of deep-sea mineral mining technology. Owing to its superior traction performance, the deep-sea polymetallic nodule collector (DPNC) has become the preferred solution for ocean mining. This paper proposes a dynamic traction calculation model to address the shortcomings in the classical static traction calculation model with consideration of the dynamic variation rule of grouser–soil interaction in the DPNC process. Lab tests were conducted to formulate materials similar to deep-sea soil, and the corresponding shear stress–displacement models were established using the discrete element method (DEM) and Magic Formula to describe the “shear stress–displacement” relationship more accurately. Considering Kunlong 500, which is a Chinese DPNC, as an example, the periodicity and dynamics of the dynamic traction force were analyzed and compared with the numerical simulation results. The dynamic traction force was smaller than the static traction force and fluctuated significantly when considering the dynamic grousers–soil interaction. The magnitude and fluctuation of the dynamic traction force were influenced by the ratio of the grouser height to the spacing. In the DPNC design, the ratio of the grouser height to the spacing should be optimized according to the properties of the deep-sea subsoil to improve the traction performance and stability of the DPNC.

1. Introduction

Since the beginning of the last century, countries around the world have been discovering a wide variety of solid mineral resources with rich reserves buried in the deep seabed, mainly including polymetallic nodules, cobalt-rich crusts, and polymetallic sulfides. The Pacific Ocean alone contains more than 16 billion tons of polymetallic nodules, and deep-sea solid mineral resources have enormous commercial potential [1]. Polymetallic nodules are commonly found in deep-sea plains or basins with relatively flat terrain at 4000–6000 m underwater [2], but the low level of mineral resource enrichment on the seabed, coupled with the existence of extremely high seawater pressure, makes mining extremely difficult. The polymetallic nodule collector is the primary segment in the deep-sea polymetallic nodule mining system. Currently, the DPNC is the most promising deep-sea mining equipment because it has the characteristics of large grounding area, easy access to a large traction force, and obvious superiority in seabed operations.

The traction force of the DPNC is provided by the grousers shearing the soil. Therefore, an accurate shear stress–displacement model of the soil is key for evaluating the traction performance of the DPNC. Bekker [3], Wong [4], and other scholars have proposed several classical shear stress–displacement models based on wet, soft land soil. These models are widely used and involve different ground conditions such as loose sand, saturated clay, and disturbed soil. However, unlike land soil, the occurrence of polymetallic nodules is mainly in under-consolidated soft sediment, which has the characteristics of significant looseness, high water content, high sensitivity, and easy liquefaction [5]. Because of the different physical and mechanical properties of deep-sea sediments, the existing land soil shear model is not suitable for deep-sea sediments. For deep-sea sediments, Wang [6] verified the applicability of the existing shear stress–displacement model based on the track shear test, analyzed the main external forces on the DPNC, and proposed a saturated soft-plastic soil model. Based on the soil–track interaction system, Baek [7] investigated the soil thrust mechanism of cohesive soil and proposed a prediction model of deep-sea soil thrust. Ma [8] investigated the traction performance of grousers shearing the soil under different grouser spacing, grouser height, and grounding pressure using a traction characteristic tester and predicted the “shear stress–displacement” curve by combining the traction model parameters. Enno [9] mixed bentonite with water at a certain ratio to prepare simulated sediments. The “shear stress–shear displacement” relationship was measured experimentally. Subsequently, the traction of the seabed sediments that can be supplied to the track was calculated, and the static and dynamic subsidence of the track was analyzed in detail.

However, the traction force of the DPNC is not only related to the mechanical properties of the soil, but the grousers–soil interaction also directly affects the traction performance. The design parameters of the DPNC, such as the grouser height [10], grouser spacing [11], inclination angle, and grouser shape [5], are different. The strength and deformation characteristics of the soil are also different. Additionally, unlike conventional tires, the traction force of the DPNC is dynamic and periodic during operation. At a certain time, the shear of each grouser acting on the soil is not synchronized, the action time is different, and the corresponding shear displacement and traction force provided are also different. To describe the real-time traction performance of the DPNC with satisfactory accuracy, it is necessary to establish a dynamic traction model.

Based on the above analysis, this study addresses the problem of driving traction and describes the mechanical performance of deep-sea soil under different grouser parameters using a mathematical model based on classical theory and the DEM. A dynamic traction calculation model is proposed to provide a theoretical reference for DPNC design.

2. Classical Static Calculation Model of DPNC

During the subsea operation of the DPNC, under the action of the track [12], the soil undergoes shear deformation (j) and generates shear stress (τ) to form the soil thrust (F_s), and shear between the soil is generated along the grounding area (Figure 1). At grouser 1, the track is only in contact with the soil when the shear deformation of the soil behind the grouser is zero. The subsequent grousers have sheared soil relative to the ground for a certain time; the shear displacement increases cumulatively along the track length and reaches a maximum value (j_max) at the last part of the grounding area (grouser N). To quantitatively investigate the generation of shear displacement under the track, the slip rate (i) of the track is first defined as follows:

$$i=1-\frac{v}{r\omega }=\frac{v_j}{v_T}$$

(1)

where v_T is the theoretical speed determined by the angular velocity of the sprocket (ω) and the radius (r) of the track pitch circle; v_j is the slip speed of the track relative to the ground.

The classical traction force calculation model is based on the inextensibility of the track during the straight-line, steady-state operation of the DPNC and considers the slip rate at each point of the track to be essentially the same. The shear displacement at each point of the grounding area during the operation is expressed as follows:

$${j=v}_j\cdot \frac{x}{v_T}=\mathit{ix}$$

(2)

where i is the slip rate of the DPNC; x is the distance from each point of the grounding area to the track front (see Figure 1).

Assuming that the track contact area is always in full contact with the ground, the integral of the shear stress on the entire grounding area can obtain the traction force provided by the deep-seabed soil to the miner as follows:

$$F_{\mathrm{s}}=B{\int }_0^L\tau \mathrm{d}x$$

(3)

where B is the track width; L is the track grounding length; τ is the shear stress.

As shown in Figure 1, the classical traction calculation model (Equation (3)) calculates the static traction at a certain moment during the movement of the DPNC and ignores the cyclic periodicity of the shear soil of the grousers. Considering the above-mentioned problems, this study attempts to establish a dynamic traction model.

3. Dynamic Traction Force of DPNC

3.1. Construction of Dynamic Traction Model

The typical case of DPNC operation as a tracked vehicle works like this. When the segment meshes with the terminal rollers (front and rear) or meshing gears in the landing gear system, the drive torque from the motor is delivered via the drive sprocket to the track, which results in a pulling force being developed at the tracks’ segments. The ‘transmitting power’ process commences only after the motion has started, and the motion of the track can be called rolling. This generates traction and forward movements. In this process, the track rotation is dynamic and periodic (Figure 2). The periodic description of the track rotation is as follows: the time when a certain grouser (Figure 2a, grouser 1) completely sinks in the soil is considered as the initial time t₀. After time T, the subsequent track grouser 1′ reaches the same state, and T is a time cycle. The shear distance of the DPNC in a single time cycle is s′, and the sliding displacement is s. Because the traction force is generated by the shear stress of the grouser acting on the soil in the time period (t₀, t₀ + T), the shear displacement of the grouser to the soil changes dynamically with time, and the shear stress also changes dynamically. Therefore, the traction force also changes dynamically with time, exhibiting dynamics and periodicity. This study constructed a dynamic traction calculation model based on the following assumptions:

(1)

The track plate is an inextensible rigid plate which is in horizontal contact with the soil;

(2)

The track grounding pressure is a uniform load;

(3)

The influence of the head and tail end of the track grousers on the traction force is ignored;

(4)

The top portion of the track in contact with the soil is completely free of soil carryover.

Owing to the different shear displacement j relative to the soil at each time (Figure 2b), according to the shear–deformation relationship of the soil, it can be seen that the shear stress generated by the soil sheared by the grousers is different. In the cycle shown in Figure 2a, the shear displacement generated by grouser 1 of the miner at t₀ + t is j(t), and the instantaneous traction F_d(t) can be obtained by integrating the shear stress as follows:

$$F_{\mathrm{d}}\left(t\right)=B{\int }_{j\left(t\right)}^{j\left(t\right)+L}\tau \mathrm{d}x$$

(4)

where B is the total width of the track; τ is the stress–displacement relationship (as discussed in Section 3.2.2).

3.2. Direct Shear Test and DEM of Soil

3.2.1. Direct Shear Test and DEM Parameter Calibration

This study used the DEM to analyze the mechanism of the grousers–soil interaction. The main principle of the particle flow method is derived from molecular dynamics theory, which is a type of particle DEM. The mechanical characteristics of the materials are simulated by the interaction between the movement of the spherical (3D) or disc (2D) particle units and the contact between the units [13]. Therefore, regardless of its shape, as long as the object can be considered a particle, for macroscopic continuous or discontinuous problems, the microscopic characteristics of the physical motion and the mechanical mechanism of the particle medium level can be solved by DEM modeling.

First, it is necessary to obtain the physical and mechanical properties of the soil. Owing to the difficulty of in situ soil sampling, the physical properties of deep-sea sediment are typically assessed by testing similar materials. Bentonite with silty clay properties was used to simulate the soil samples in the laboratory, and the shear strength of the simulated soil samples was tested by direct shear testing. Thus, it was found that the similar soil samples with 120% water content, cohesion c = 4.32 kPa, and internal friction angle φ = 3.76° conformed to the physical and mechanical properties of deep-sea sediment.

The DEM direct shear model was used to simulate the laboratory direct shear test. The direct shear test model (Figure 3) had a size of 1:1 relative to the laboratory test and generated eight rigid wall boundaries through the “wall create” command to form a 61.8 × 20 mm shear specimen boundary. Two walls were set between the upper and lower shear, staggered to prevent particle overflow during the shear process. Then, overlapping particles with specified porosity and particle size were generated using the “ball distribute” command. After the particles were generated, radius repulsion was carried out to make the overlapping particles diffuse and fill the model boundary. The advantage of this method is that it can generate particles quickly and efficiently. Additionally, because the number of particles in the DEM directly affects the calculation speed of the numerical simulation, it is necessary to enlarge the particle radius at a certain proportion during the simulation. Many studies [14,15,16] have shown that, if the actual soil particle radius is used, hundreds of thousands or even millions of particles are generated, resulting in a significant decrease in the calculation rate. When the ratio of the minimum particle size to the boundary size of the sample is less than 0.03, the results of the numerical test have good stability, and the size effect of the model can be ignored.

According to the strength characteristics of the investigated deep-sea soil, the linear contact bond model was selected because it reflects the actual macroscopic mechanical properties of cohesive materials more accurately. The selection of microscopic parameters in the contact model directly affects the validity of the simulation. However, owing to the complexity of particle interaction, microscopic parameters cannot be obtained by theory or experiment. To ensure that the particle characteristics in the DEM model satisfy the deep-sea soil conditions, it is necessary to calibrate the parameters of the particle contact model. The effects of the contact modulus (emod), friction coefficient (fric), stiffness ratio (kratio), and bond strength (shear/normal strength) on the shear stress were analyzed under different values (Figure 4). As can be seen, in the process of direct shear testing using the DEM, the mesoscopic parameters that greatly influence the stress–displacement curve are the contact modulus, friction coefficient, and bond strength, and the mesoscopic parameter that has the smallest influence is the contact modulus. The influence of the stiffness ratio on the stress curve is negligible.

Based on the laboratory shear test, numerical simulations under the vertical stress σ = 25 kPa, 50 kPa, 75 kPa, and 100 kPa were carried out using the DEM. The numerical simulation results were compared with the laboratory test results, as shown in Figure 5. As can be seen, the two results are essentially consistent. The numerical test results are in good agreement with the laboratory results with regard to mechanical performance. The overall error is within a reasonable range, which validates the established numerical model and method. The parameters adopted in the numerical test are listed in

Table 1. Mesoscopic parameter values of DEM under different vertical stress.

Particle Parameter		Mesoscopic Parameter	Vertical Stress (kPa)
			25	50	75	100
Particle modulus (MPa)	1	Contact bond modulus (MPa)	4	2	1	1
Particle stiffness ratio	1	Contact bond ratio	1	1	1	1
Minimum radius (mm)	0.1	Contact bond normal strength (kPa)	0.8	1	1	1
Maximum radius (mm)	0.4	Contact bond shear strength (kPa)	0.8	1	1	1
Density (kg/m3)	2650	Friction coefficient	0.04	0.03	0.03	0.03

.

3.2.2. “Shear Stress–Displacement” Relationship

When the torque is applied to the track sprocket, track–ground shear occurs. To predict the traction, the relationship between the shear stress and the shear displacement can be determined by a shear test. The accuracy of the quantitative expression between the shear stress and the shear displacement directly affects the traction calculation. Based on a considerable number of land soil test data, three types of “shear stress–shear displacement” relationships are typically observed:

1. For loose sand, saturated clay, and most disturbed soils, the characteristics of the “shear stress–displacement” relationship are as follows: The shear stress initially increases sharply with the shear displacement and then approaches a constant value as the shear displacement increases. For this type of ground, the exponential function proposed by Janosi and Hanamoto [17] can be used to describe the corresponding “shear stress–displacement” relationship as follows:

$$\tau =\left(c+\sigma \tan \phi \right)\cdot \left(1-e^{-j/K}\right)$$

(5)

where c is the bond strength of soil; φ is the internal friction angle of soil; σ is the vertical stress; K is the shear displacement coefficient;

2. For organic ground with biological vegetation on the surface and a saturated peat layer beneath it, the shear stress initially increases rapidly with the increase in shear displacement and reaches peak shear stress. At this time, the ground surface starts being cut off, and the shear stress continuously decreases as the shear displacement increases further. This type of shear behavior can be expressed as follows [4]:

$$\tau ={\tau }_{\max }\left(j/K_{\mathsf{\omega }}\right)\exp \left(1-j/K_{\mathsf{\omega }}\right)$$

(6)

where K_ω is the shear displacement corresponding to the maximum shear stress;

3. For dense sand, silt, and frozen snow, the shear stress may initially increase rapidly and reach the maximum shear stress at a specific shear displacement. However, as the shear displacement increases further, the shear stress decreases and gradually approaches a constant residual value. This type of shearing behavior is described by the following function table proposed by Wong [12]:

$$\tau =\left(c+\sigma \tan \phi \right)\cdot K_{\mathrm{r}}\cdot \left\{1+\left[\frac{1}{K_{\mathrm{r}}\left(1-e^{-1}\right)}-1\right]e^{\left(1-j/K_{\mathsf{\omega }}\right)}\right\}\cdot \left(1-e^{-j/K_{\mathsf{\omega }}}\right)$$

(7)

where K_r is ratio of peak shear stress to residual shear stress.

The traditional shear model discussed above is widely used to describe the shear characteristics of land soils, but the applicability of the shear model to deep-sea seabed soils in complex environments requires further investigation. Based on the DEM direct shear test model and verified particle contact parameters, this study constructed a track shear model and investigated the relationship between the soil strength and the shear displacement under different grouser height/spacing ratios (λ = h/b) by changing the relationship between the grouser height h and spacing b (Figure 6). The design of an excessively large λ makes the grouser arrangement overly dense, and the design of an excessively small λ leads to a small number of track grousers, which is not in line with the actual engineering requirements. Therefore, λ was set to 0.4–1.4 in the DEM models.

The stress–displacement curve obtained by the numerical simulation of the shear model is shown in Figure 7. With the increase in shear displacement, the shear stress can be divided into the stages of growth, decrease, and stability. With the decrease in λ, the shear area of the soil between the grousers increases, the shearing action against the track becomes more obvious, and τ_max, τ_res, and K_ω exhibit an increasing trend. Additionally, owing to the large pores in the sample, the particles are staggered and rearranged under the influence of shear, and the shear displacement required for the stress in the decreasing stage also increases as λ decreases.

By using the classical “shear stress–displacement” relationship (Equations (5)–(7)) to fit the numerical simulation data (Figure 8), it can be seen that the three “shear stress–displacement” relationships, which generally characterize land soils, cannot accurately describe the shear stress behavior of deep-sea soil. The “shear stress–displacement” relationship (Equation (7)) exhibits a trend of stress growth and attenuation to stability after reaching the peak, which approximately reflects the “shear stress–displacement” relationship of deep-sea soil. However, the response of the double exponential mathematical model to the growing and decreasing stages of the actual stress performance is relatively slow; therefore, the expression of the “shear stress–displacement” relationship of marine soil must be described more accurately.

To describe the variation characteristics of the shear strength of deep-sea soil with λ and j, we noted that the Magic Formula used by Pacejka [18] to fit the moment model has similar curve characteristics, and the feature parameters used in the Magic Formula can control the curve more flexibly; so, we chose Magic Formula to fit the stress–displacement curve based on the simulation data. The Magic Formula is a semi-empirical formula that expresses the test curve by modifying the sine wave as follows:

$$\tau ={\tau }_{\max }\sin \left\{C\arctan \left[Dj-E\left(Dj-\arctan \left(Dj\right)\right)\right]\right\}$$

(8)

where τ_max is the maximum shear stress; j is the shear displacement; C is the shape coefficient; D is the peak coefficient; E is the curvature coefficient.

Based on the numerical simulation curve, the particle swarm optimization (PSO) algorithm model was used to fit parameters C, D, and E in the Magic Formula. The essence of the parameter fitting problem is function optimization. Traditional algorithms are not ideal for solving such complex functions with high latitude and multiple local extreme values. For most nonlinear functions, the PSO algorithm has good performance in terms of accuracy and optimization speed [19]. In this study, MATLAB was used for fitting, and the fitting curve is shown in Figure 9.

By comparing the fitting degree of the Magic Formula and traditional equation to the simulation results, we show that the Magic Formula can express the “shear stress–displacement” relationship more accurately. As shown in Figure 9, for the “shear stress–displacement” relationship under the conditions λ = 1.2 and λ = 0.4, Equation (7) is poorly fitted, and the dispersion R = 0.52 and 0.27, respectively. The Magic Formula (Equation (8)) fits the simulation data well, and the dispersion R reaches 0.92 and 0.90. The shape coefficient C in the Magic Formula controls the amplitude of the curve change and affects the residual value of the “shear stress–displacement” curve in the stable stage. When C is 1.8–2.0, the curve exhibits an obvious trend of decaying to a stable value after the peak. The curvature coefficient E affects the curvature of the descending section of the curve. With a smaller E, the curve decrease becomes slower. As the peak coefficient D increases, the K_ω corresponding to the peak value of the curve becomes smaller. Considering the excellent performance of the Magic Formula for fitting the simulation data, we used the Magic Formula to calculate the dynamic traction force (Equation (4)).

4. Case Analysis and Discussion

4.1. Case Analysis

Based on the Kunlong 500 DPNC model (Figure 10), this study selected the self-propelled DPNC as the research object. The Kunlong 500 polymetallic nodule collection system is a hydraulic collection device developed by the Changsha Institute of Mining and Metallurgy, and it is suitable for a sea depth of 6000 m; its parameters are listed in

Table 2. Parameters of Kunlong 500 [20].

	Object		Value
Kunlong 500	Overall quality	M	9.50 t
	Drainage volume	Mw	8.00 t
	Underwater quality	W = M − Mw	1.50 t
	Track grounding length	L	2.75 m
	Track gauge	2b0	2.00 m
	Single track width	B	0.75 m
	Grouser height	h	0.13 m
	Grouser spacing	b	0.21 m
	Total area of track grounding	A = 2LB	4.13 m2

.

The static traction F_s (Equation (3)) and dynamic traction F_d (Equation (4)) were calculated, respectively, and the traction was compared and analyzed using the Kunlong 500 model (Figure 11). As can be seen, F_d is dynamic with time, and the absolute error between F_d and F_s is 5.25% at most and 0.11 % at least. The reason for the error is that the stress value of the soil behind the grousers does not have a fixed interval during the movement of the DPNC but, instead, changes with the shear time of the grousers and fluctuates significantly in the rotation period T of the track.

4.2. Periodic and Fluctuant of Traction Force

The periodicity and fluctuation of dynamic traction are affected by the track parameters as follows: the larger the λ, the stronger the fluctuation of dynamic traction and the more obvious the periodicity, and the average traction increases first and then decreases with the increase in λ. To investigate the track parameters under the optimal traction performance of DPNC based on the parameters of Kunlong 500, the influence of the track parameters on the traction performance was investigated using different λ values. In time cycle T, the cyclic periodic displacement increases as λ decreases, and the periodic (Figure 12) and fluctuant (Figure 13) of the dynamic traction force are different. Additionally, because the dynamic traction force calculation does not consider the process of unearthing the end track, there is a sudden increase between the cycles of the dynamic traction force curve. The track shear data under different working conditions in the DEM were compared with the calculation results obtained by Equation (4). The results reveal that the traction force in the numerical simulation exhibits periodicity and fluctuation similar to the theoretical calculation results, which validates the dynamic traction calculation.

From the ratio of the dynamic traction F_d to the static traction F_s (Figure 12), it is understood that there is an error between the traction calculated by the dynamic traction model and the classical traction model. The error increases with λ. When λ is 1.4–0.4, the absolute error between F_d and F_s is 0.7–5.6%. This also confirms that the classical traction model can only be used as a traction reference under certain conditions.

The box plot (Figure 13) intuitively shows the fluctuation range, skewness, and tail weight of the data. When λ is 0.9–1.4, the dynamic traction force has a small displacement distance in a single cycle, and the fluctuation of the dynamic traction force is not obvious. The absolute fluctuation value is 0.03–0.06, and the traction force exhibits an upward distribution. When λ is 0.4–0.8, the soil has more displacement space against the track shear, which indicates greater strength. Therefore, the dynamic traction distribution close to the upper quartile exhibits strong volatility, and the absolute value is in the range of 0.095–0.53.

4.3. Discussion on Shear Influence Range

The above-mentioned dynamic traction model comprehensively considers the dynamics and periodicity of the interaction between the grousers and the soil on the basis of classical theory but does not consider the influence of the shear influence range of the soil. Owing to the elastic–plastic properties and large pores of the soil, the shear displacement of the soil does not increase linearly along the longitudinal direction of the entire track. When the grouser spacing is large, particularly for the front end that has just entered the soil, the shearing of the soil occurs only within a certain range, while Equation (3) considers the entire track–soil contact surface to be sheared, which is unreasonable and leads to overestimation. The calculated result can be considered as the traction force under certain working conditions, but the actual working traction force is often different to the calculated value. Because it is difficult to obtain the shear influence range of soil by direct shear testing in the laboratory, the DEM can be used to determine the displacement field of the soil particles. From the DEM direct shear model detail map (Figure 14), it can be seen that, in the process of shearing the soil, the displacement of the particles in the middle of the soil sample after the shear is smaller than that after the plate, and the contact between the particles in the middle is closer. The contact bond between the particles behind the two side plates is broken, and an obvious fractured area appears (Figure 14d).

Based on the direct shear model, the relationship between the shear displacement j and the soil shear influence range l was investigated. The boundaries of the direct shear model were adjusted to 160 × 40 mm, respectively, and the interference of the long axis boundary was avoided by increasing the length of the model. The model was evenly divided into upper and lower shear boxes along the short axis, and the displacement of the particles with the same order of magnitude was measured to investigate the influence range of the shear particles in the shear process. As can be seen from the particle displacement (Figure 15), the shear influence range of the soil increased with the shear displacement. When the shear displacement increased to a certain extent, the shear influence range no longer changed significantly.

By observing the particle displacement field in the DEM, the shear displacement of the dynamic traction model can be modified (Figure 16). It is assumed that the shear displacement of the soil behind the grousers is linearly attenuated. Grouser 1 just begins to shear, and the range of influence l is small. The shear displacement difference between each grouser is s. As the displacement of the grouser increases, the influence range of the soil increases up to l_max. The shear influence range behind the subsequent grousers is considered to reach the maximum (if the grouser spacing b is less than l_max, then l_max = b). Notably, the soil stress obtained by the traditional calculation is the average stress. In fact, there is no obvious shear stress in every part of the soil. When a small shear displacement occurs in the soil; the soil is not all affected by shear, and it is difficult to provide soil thrust. Therefore, to determine the traction force more accurately, it is necessary to conduct a more in-depth study on the actual stress of the soil. With the change in the shear displacement relationship of the soil, the soil stress is different; therefore, the method of calculating the traction force using the continuous integral of soil stress is no longer applicable.

Based on the fluctuation and periodicity of the dynamic traction force under different λ in the above investigation, it can be seen that, as λ decreases, the fluctuation of the track traction force becomes more obvious. When λ is 0.4–0.6, the average traction force of the track is small and cannot provide an efficient and stable traction force for the DPNC. Therefore, the design λ of the track should be more than 0.6. However, research on the shear stress expression and shear influence range of the soil behind the grousers has shown that an excessive track height ratio not only reduces the soil stress, but also reduces the shear utilization efficiency of the soil. Therefore, when the design height-to-spacing ratio of the grouser is approximately 0.6–0.8, this not only ensures that the soil has a sufficient shear utilization range, but also provides better traction performance for the DPNC.

5. Conclusions

This study first investigated the dynamic mechanism between the grousers and the soil during the moving process of the DPNC. A dynamic traction model was proposed and reflects the internal mechanism of the traction force. Additionally, the proposed model can describe the traction performance more accurately, provides a theoretical reference for the design of the tractive mechanism, and can be useful in the field of deep-sea resource mining. The main conclusions drawn from this study are as follows:

(1) The “shear stress–displacement” relationship of the soil is very important for evaluating the traction performance of the DPNC. This study selected the classic “shear stress–displacement” empirical formula to verify the applicability of deep-sea soil. The results reveal that the existing shear model is not suitable for deep-sea soil. To solve this problem, the Magic Formula was used to describe the “shear stress–displacement” curve under different track designs. The results reveal that the Magic Formula can preferably describe the variation characteristics of the “shear stress–displacement” relationship of deep-sea soil;

(2) This study established a new dynamic traction calculation model. Based on the driving characteristics of DPNC, the model describes the traction from the time and displacement and gives the periodicity and dynamics of traction. Compared with the traditional traction model, the proposed model can be applied to the prediction of traction under different working conditions. The proposed model was validated by using the DEM to simulate the shearing of the track.

Based on the research status and the research content of this study, future studies can investigate the dynamic traction force during the operation process in relation to the following aspects: the actual stress distribution of the soil behind the grousers should be investigated in depth, and the influence of the failure mode of the soil on the traction force should be considered. Based on the particular mechanical properties of deep-sea sediments, the grounding pressure of the track is not linearly and evenly distributed, but the number and eccentricity of the supporting wheels should be considered. Subsequently, according to the grouser–soil dynamic indentation–shear relationship, the dynamic traction model can be further improved to investigate the improvement method of traction performance and the driving stability of the DPNC.