The cylindrical shape of the ore bin is selected as the research object, and the size is (100{text{mm}} times 50{text{mm}}). When the excitation displacement (*H*) is 0.05 m, 0.10 m and 0.15 m respectively, the change of force and acceleration during the movement of the ore pan is shown in Fig. 3, and the regular change between the resistance coefficient (*VS*_{D}) of the ore bin and the Reynolds number(*Re*) is shown in Fig. 4.

When the acceleration is 0, only the relationship between the drag coefficient and the force can be considered. Figure 3 shows the changes in force and acceleration under different excitation displacements with *Re*= 15,000. It can be seen in Figure 4 that when the acceleration is 0, the greater the excitation displacement, the smaller the corresponding force value. Figure 4 is the change-of-law diagram of the ore bin resistance coefficient and Reynolds number. It can be seen from the figure that when the excitation displacement is constant, the resistance coefficient decreases with increasing Reynolds number. This is because when the Reynolds number is small, the ore bin has a strong viscous effect, and a larger force is required to maintain motion, so the resistance coefficient is large at this time. As the Reynolds number increases, the effect of viscosity on the ore bin weakens, so the coefficient of resistance decreases. As the excitation displacement changes, increasing the excitation displacement will reduce the overall drag coefficient of the ore bin. This is because when the excitation displacement increases, the excitation speed does not change, the excitation frequency becomes smaller, the effect of the inertial force is weakened, the overall force of the system is reduced, and the resistance coefficient shows a downward trend. In this experimental study, when the Reynolds number is very large (up to 60,000), the resistance coefficient will remain stable and will not change with increasing Reynolds number. When the excitation displacements are 0.05 m, 0.10 m and 0.15 m respectively, the drag coefficients are stable around 0.41, 0.50 and 0.60 with increasing number of Reynolds.

### The law of variation of the drag coefficient under different aspect ratios

The other five ore bins were selected as research objects, and their sizes were (150{text{mm}} times 50{text{mm}}),(150{text{mm}} times 100{text{mm}}),(200{text{mm}} times 50{text{mm}}),(200{text{mm}} times 100{text{mm}}),(200{text{mm}} times 150{text{mm}})the corresponding length-diameter ratios (*D*/*L*) were 0.33, 0.66, 0.25, 0.5 and 0.75. The regular changes between the ore bin resistance coefficient and the Reynolds number under the same excitation displacement with different length-diameter ratios are shown in Fig. 5.

It can be seen in Fig. 5a–c that changing the size of the ore bin will not change the original law of variation of the drag coefficient, i.e. the drag coefficient decreases gradually with increasing Reynolds number and stabilizes within a certain range, reducing the excitation displacement will increase the resistance coefficient of the ore bin. Under the same excitation displacement, the smaller the length-diameter ratio, the greater the resistance coefficient. Indeed, it can be seen in Figure 6 that the smaller the length-diameter ratio, the greater the force generated by the system and the greater the corresponding coefficient of resistance. Similarly, when the Reynolds number increases to a certain extent, the coefficient of resistance decreases to a stable value. The stable value under different length-diameter ratios is shown in Table 1.

### The law of variation of the drag coefficient in different external forms

Cylindrical (200 × 150 mm) and rectangular (200 × 200 × 150 mm) ore silos were selected as research objects, with the same characteristic length and different external shapes, and the length-diameter ratio is 0, 75. When the excitation displacement is 0.05 m, 0.10 m and 0.15 m respectively, the smooth changes between the ore bin resistance coefficient and the Reynolds number are shown in Fig. 7.

As can be seen from Fig. 7, when the characteristic length of the ore bin is the same and the external shape is different, its original law does not change. It does not matter whether the shape is rectangular or cylindrical, the coefficient of resistance decreases with increasing Reynolds number and eventually stabilizes around a certain range. It can be seen in Fig. 8 that when the characteristic length of the ore bin is the same, the corresponding force value in the condition of 0 m/s^{2} does not change much, but the force area of different forms of ore bin is different. The rectangular shape is slightly larger than the cylindrical shape, so the resistance coefficient of the cylindrical shape is higher than that of the rectangular shape. In real working conditions, the influence of the ore bin on the longitudinal vibrations and the transverse towing of the mining pipe must be considered simultaneously. For the longitudinal vibration, the large coefficient of resistance can generate large resistance to movement, consume the longitudinal excitation force, and reduce the vibration amplitude. In the process of transverse towing, the shape of the side of the ore bin is streamlined, which can reduce the force of the mining pipe during towing and shorten the distance of the transverse deflection. Therefore, the cylindrical shape is selected as the outer shape of the ore silo.

### The law of variation of the drag coefficient under different additional weights

Cylindrical (200 × 150 mm) and rectangular (200 × 200 × 150 mm) ore silos were selected as research objects, with the same characteristic length and different external shapes, and the length-diameter ratio is 0, 75. When the ore pan was attached to objects of different weights (as shown in Fig. 9), the regular changes between the ore pan’s coefficient of resistance and the Reynolds number are shown in Figs. 10 and 11.

As can be seen in Figure 9, weight blocks are attached to the side of the simulated ore silo, each weight block weighs 1 kg, and 2, 3, 4 weight blocks are successively added. The law of variation of the coefficient of resistance under different additional weights has been studied. It can be seen in Figs. 10 and 11 that it does not matter whether the ore tank is cylindrical or rectangular, the increase in the additional weight does not modify the law of variation of the coefficient of resistance. At the initial stage of the Reynolds number, the added weight has a great influence on the drag coefficient, and increasing the added weight will increase the drag coefficient. However, at high Reynolds number, the drag coefficient will become stable and its value will not change with increasing added weight. Tables 2, 3, 4 show the stable values of the high Reynolds number resistance coefficient under different excitation displacements, indicating that as long as the external shape of the ore bin is determined, the resistance coefficient will not change so significant at high Reynolds number, while the stable value of the cylindrical resistance coefficient is large at high Reynolds number under the same excitation displacements. In the field production of the mining system, the ore bin is a transfer station for the collection and transmission of resources from the seabed, and the additional weight is constantly changing. Research on the relation between the additional weight and the coefficient of resistance has an important orientation role in real working conditions.

In summary, based on the assumptions and theories of Sect. 2, the test device built for testing the longitudinal resistance coefficient can better measure the law of variation of the resistance coefficient under different aspect ratios, shapes and additional weights, which verifies the rationality of the hypothesis and the theoretical application, but the next step is to find the law of modification of the inertia force coefficient, in order to obtain better results.