THREE-DIMENSIONAL COUPLED DYNAMIC ANALYSIS OF DEEP OCEAN MINING SYSTEM

Original scientific paper A new three-dimensional coupled dynamic model of the deep ocean mining system is developed. The seafloor tracked miner is built as a 3D single-body vehicle model with mesh element track-terrain interaction mechanics model, which not only can realize the fast dynamic simulation in contrast to traditional 3D multi-body model, but also can allow the loading of the seafloor sediment special terramechanics model. The mining pipeline is built as a 3D multi-body discrete element model that is divided into rigid elements linked by flexible connectors, also can realize the fast dynamic simulation for such long pipeline. New integrated mining operation modes for the total system are proposed and simulated, which show that during the whole operation processes, the synchronized stable motion of the total system can be kept well. The dynamic simulation analysis in the paper can provide important theoretical basis and technical reference for structure design, performance evaluation and operation control of the practical deep ocean mining system.


Introduction
With gradual exhaustion of land-based mineral resources, the deep seafloor extremely rich mineral resources have aroused great interest of global mining industry.So far, it is generally regarded and recommended that the system configuration with a seafloor tracked miner, flexible hoses, a buffer, rigid pipes, submerged pumps and a mining ship is the most promising continuous mining system [1].Fig. 1 illustrates a 1000 m deep ocean mining system configuration.
For the seafloor miner researches, Hong et al. developed a simplified transient 3D dynamic model of tracked vehicle crawling on seafloor soil and investigated its straight-line and steering motion performances through real-time simulations [2].Kim et al. developed a novel method using Euler parameters for dynamic analysis of the tracked vehicle on seafloor [3].Li et al. built a multibody virtual prototype model of a pilot miner, performed dynamic simulation analysis to evaluate its trafficability and maneuverability on the seafloor [4].Schulte et al. evaluated the trafficability of a seafloor tracked miner, calculated its static sinkage and dynamic sinkage [5].Kim et al. proposed and used the subsystem synthesis method to dynamic analysis of a complex multi-body tracked miner on the seafloor [6].Besides, dynamic modeling methods for the tracked vehicles on the land surface soft soils can be referenced.Solis et al. developed a trackterrain interaction model for transient dynamic analysis of the tracked vehicle [7].Liu et al. presented a systematic method to establish the kinematics model for a tracked mobile manipulator on grounds with consideration of the dynamic interactive motions between tracks and terrain [8].
For the pipeline, Cheng et al. used an improved discrete element method for a frequency analysis of a 1905m vertical deep ocean pipe [9].Rustad et al. used finite element method to build a mathematical model of an ocean pipeline system consisting of a tension leg platform, a pair of risers, environmental forces and hydrodynamic interaction [10].Hong et al. developed a novel method for analysis of 3D nonlinear dynamic of marine riser and pipes [11].dynamic positioning control of a large ocean mining shippipe system [12], and further proposed the research subject on how to perform the motion and positioning control of the total deep ocean system [13].Hong et al. performed analysis on the coupled dynamics of the tracked vehicle and flexible riser [14].However, it still remains a crucial problem to be further resolved, that is how to obtain and investigate the complex dynamic characteristics of the integrated operation processes of the total deep ocean mining system, so as to evaluate its design scheme, continuous operation performance and propose optimal mining operation modes, since it is very difficult to perform insitu tests and impossible to establish a similar laboratory experimental system.The dynamic simulation is undoubtedly an effective way.Reliable and efficient dynamic models for subsystems and then coupled for the total system will be developed in the paper.

3D dynamic model of seafloor tracked miner 2.1 Single-body vehicle model with mesh element trackterrain interaction mechanics model
In contrast to traditional 3D multi-body dynamic model of tracked vehicle, a 3D single-body dynamic model is developed for the following considerations.Firstly, all commercial codes for multi-body dynamic simulation of tracked vehicle only provide one type of soft soil mechanics model to represent land surface soft soil types, but it is definitely unsuitable for exhibiting the special mechanics of the seafloor extremely cohesive soft soil.Secondly, the multi-body dynamic model has a large number of DOFs and needs extremely long time for numerical simulation computation.Finally, it is reasonable to regard the miner as a single-body model of the total system's multi-body model, and most attention for the miner in the total system is given to its overall dynamic behavior rather than its internal detailed dynamic interaction characteristics.The detailed track-terrain interaction dynamic model is shown in Fig. 3. OXY is the ground horizontal coordinates, O is the vehicle's turning center, G and C are the vehicle's gravity center and geometric center.o 1 x 1 y 1 and o 2 x 2 y 2 are coordinate systems fixed to and moving with vehicle located at the longitudinal centerlines of the inner and outer tracks and at a distance S o from the gravity center of the vehicle.The offset distance S 0 will be determined from the dynamic equilibrium of the vehicle in the lateral direction during the turning.O i and O o are instantaneous turning centers of the inner and outer tracks, which respectively deviate certain lateral distances in opposite directions from geometric centers O 1 and O 2 of inner and outer tracks due to slip.Based on above detailed model analysis, a method is considered and adopted to dynamic modeling the trackterrain interaction as shown in Fig. 4. The track-terrain interface is partitioned into a certain number of mesh elements, which is determined by the number of road wheels.The o t -x t y t z t is the track-fixed coordinate system located at the rear of the track contact patch.A mesh point x i is assigned to the center of each mesh element, and the value of x i represents its fixed distance relative to the origin o t of the coordinate system o t -x t y t z t .Three mutually perpendicular forces F ni , F longi and F lati represent the normal force, longitudinal and lateral shear forces respectively.
The normal force F ni is computed by multiplying the normal pressure p xi acting on the point x i by the area of each mesh element: To compute the shear forces F longi and F lati , the shear displacements developed along the track-terrain interface should be determined firstly.For the mesh element model, the longitudinal shear displacement j xi needs to be computed at each mesh point x i as follow and applied to the whole surface of the mesh element: where v jxi is the longitudinal slip velocity of mesh point x i , v xi is the actual velocity of the point, r s and ω s are the radius and angular velocity of the sprocket.
The longitudinal shear force F longi acting on each mesh point x i is computed by multiplying the shear stress by the area of each mesh element: where 'sgn' is the signum function, τ xi is the longitudinal shear stress acting on the mesh point x i .
The lateral shear displacement at each mesh point x i can be computed as: where v jyi is the lateral slip velocity of the mesh point x i , v yi is the lateral velocity, v jyi and v yi are the same for lateral motion.
The lateral shear force F lati acting on each mesh point x i is computed as follow and in the opposite direction to the lateral shear displacement: where τ yi is the lateral shear stress acting on the mesh point x i .

Laboratory experimental validations
A small-scale tracked vehicle was manufactured and used for trafficability and mobility studies on soft terrain as shown in Fig. 5.
The vehicle utilizes two 1,2 kW permanent magnet synchronous servo motors (PMSM) by which the left and right tracks can be rotated independently.The servo motors are equipped with absolute optical encoders.Each motor speed is controlled by a servo driver, which transmits velocity and torque information to the lower computer, a Siemens S7-1200 PLC module.The PLC module communicates with the host computer through wireless Ethernet.A Honeywell 3-axis digital compass HMR3000 is installed on the vehicle chassis to measure the heading, pitch and roll angles of the vehicle, and transfers data to the PCL module through the serial port RS232.A single axis gyroscope is installed on the vehicle to measure its turning angular velocity, and a single axis acceleration sensor is used to measure its acceleration and can be integrated to get its actual velocity.The corresponding 3D dynamic model of the vehicle can be established by the above proposed modeling method.Laboratory soft terrain is dry sand, whose mechanics properties can be expressed by the Bekker's pressure-sinkage relationship [15] and Janosi's shear stress-shear displacement relationship [16].
For the motion experiment, the theoretical input velocities for inner and outer tracks are respectively set to 0,05 m/s and 0,16 m/s.Fig. 6 shows the vehicle motion trajectories, turning angular velocities and headings.
It is measured in situ in the experiment that the vehicle's turning radius is about 0,63 m, which is about 0,61 m in simulation.Also, the simulation results of the vehicle's turning angular velocity and heading agree with the experiments.

Application to dynamic modeling seafloor tracked miner
According to the design parameters of the tracked miner, its single-body model structure and mesh element track-terrain interaction force model is established as shown in Fig.The dynamic equations of the miner can be written as: where M is miner mass, I z is inertia moment about z axis, subscript 1 and 2 respectively denote the inner and outer tracks, N is the partitioned mesh element number, F longi , F lati and F ni are the longitudinal shear force, lateral shear force and normal force, ΔF longi is the longitudinal additional shear force, F R1 and F R2 are longitudinal motion resistances on inner and outer tracks, F bi is lateral bulldozing resistance, F h is hydrodynamic force, R in is internal motion resistance.
Through laboratory stimulant experiments, the pressure-sinkage relationship and shear stress-shear displacement of the seafloor sediment have been obtained.
For each mesh element, F ni is computed as: where b is the smaller dimension of the contact area, k c is the soil cohesion deformation modulus, k φ is the soil friction deformation modulus, Δz i is the sinkage, n is the soil deformation exponent, ΔA i is the area of each mesh element.
F longi is computed by multiplying shear stress by area of each mesh element: 1) where K r is the ratio of residual shear stress τ res to the maximum shear stress τ max , K ω is the shear displacement where the maximum shear stress τ max occurs.Similarly, F lati is computed as: The additional shear force acting on each mesh element can be computed as: The compaction force can be computed as [17]: where M is total weight of miner, n w is the number of the supporting wheels per each track, p is the track pitch, d is the diameter of the supporting wheel.
The bulldozing resistance is computed using earth pressure theory [18]: where γ is soil density, K c and K γ are coefficients of passive earth pressure.Through ocean in-situ surveys and laboratory stimulant experiments, detailed mechanics parameters of sediment are obtained and used in the simulation [19,20].
The hydrodynamic force acting on miner is composed of drag and inertial forces linearly added: where ρ w is seawater density, C d and C m are drag coefficient and added mass coefficient, v c and c v  are current velocity and acceleration, v m and m v  are miner velocity and acceleration, A m and V m are miner projection area and volume.

3D dynamic model of pipeline
Discrete element method is adopted for development of the fast dynamic simulation model of the mining pipeline.Based on the multi-body dynamics and structural dynamics, the pipe is divided into numbers of rigid elements linked by flexible connectors.The number of the divided rigid elements is determined by the practical number of the segments of the pipeline.The flexible connector can be described by six spring elements [21].The external loads are applied to mass centers of corresponding rigid elements as shown in Fig. 8.

Figure 8 3D discrete element model of pipe
The equivalent stiffness coefficients shown in Fig. 8 are the axial spring stiffness k x , lateral spring stiffness k y and k z , torsional spring stiffness k rx , and rotational spring stiffness k ry and k rz , which can be expressed as: where E and G are Young modulus and shear modulus, A and L are cross-section area and length; I y and I z are second moments of area, I p is polar moment of inertia.The hydrodynamic force is calculated using Morison equation: where d is pipe outer diameter, v p and p v  are pipe velocity and acceleration.
According to design scheme of pipeline subsystem, to keep its optimal spatial shape so as to ensure its transmission efficiency and safety, two buoyancy modules are installed on the flexible hose to make its spatial shape like a saddle as shown in Fig. 9.One buoyancy module is located at a distance of 134 m to the buffer providing the buoyancy force of about 4,2×10 4 N, the other is located at a distance of 267 m to the buffer providing the buoyancy force of about 8,4×10 4 N. Considering the mass of the mining ship and the wave force acting on the ship are all much larger than the mass of the pipeline and the wave force acting on the pipeline respectively, it can be assumed that the motion of the mining ship is not influenced by the motion of the pipeline.Regarding the ship as a rigid body, its motions can be expressed as 6 DOFs as shown in Fig. 10.
However, it is generally regarded that the yaw motion has little influence on the ship and can be neglected, the roll and pitch motions can be compensated, the sway and surge motions can be conquered by dynamic positioning system, only the heave motion of the ship has the most influence on the pipeline.
The heave motion of the ship can be described as a harmonic motion equation with the same period as the ocean wave period.(16) where z h is the heave displacement of the ship, z ha is the heave amplitude of the ship which is determined by the ship structure, ship dimension, wave height etc., T is the wave period.According to design parameters of the mining ship, and assuming that the ocean state is the 4 level (the surface wave height is 2,5 m, the wave period is 8 s), the ship speed is about 1kn, then the heave motion of the ship can be determined, which also can be changed and determined accordingly with different ocean surface state.

Coupled dynamic analysis of total system
Integrating the above established dynamic models of subsystems in MSC.ADAMS, the 3D coupled dynamic simulation model of total system can be formed as shown in Fig. 11.In the practical deep ocean mining operation, the integrated motion mode of the total system is designed so that the seafloor miner moves along the predetermined mining paths, while the ship tows the pipeline subsystem to follow the miner, which is referenced for the designs and dynamic simulation analysis of the mining operation modes of the total system in the paper.
Two new mining operation modes for the total system are proposed as shown in Fig. 12.For the operation mode I, it is designed that the miner firstly moves along longitudinal straight line, then turns 90° and moves along the lateral straight line, while the ship tows the pipeline to follow the miner.For the operation mode II, the miner also firstly moves along longitudinal straight line, then turns about 180° and still moves along the longitudinal straight line, and so again.Fig. 13 shows the simulation motion trajectories of subsystems.It can be seen that during the whole operation processes, the motion states of all the subsystems are stable and within permissible areas, the synchronized stable motion of the total system can be kept well, so both of the two operation modes can be implemented well.
Fig. 14 shows the forces acting on the miner by the flexible hose.It can be seen for both of the two modes, the longitudinal forces acting on the miner all fluctuate in the range of about −5 kN ÷ 10 kN, the vertical forces all fluctuate around 17,5 kN all the time, and the maximum lateral forces are about 5 kN.15 shows the deflection angles of the rigid lifting pipeline relative to its initial vertical states, which is an important index for evaluating the transmission safety and performance of the pipeline.It can be seen that the change trends of the deflections angles for both of the two modes are similar.During the longitudinal straight-line motions, the deflection angles increase and reach about 2,7° in maximum, while during and after the turnings, the deflection angles are about 1,3° in maximum and keep it stable.According to the system design criteria and operation requirement, the deflection angle of the rigid lifting pipeline should not exceed 8° during the whole operation process.So, it is further proved that the newly proposed mining operation modes are feasible and efficient, and the pipeline can keep its spatial shape and transmit well during the whole operation processes.

Conclusions
The following conclusions can be drawn from the works: (1) The fast dynamic simulation of the seafloor tracked miner can be achieved by the newly established 3D single-body vehicle model with mesh element trackterrain interaction mechanics model in contrast to the traditional 3D multi-body model, also this new dynamic model can realize the loading of the seafloor sediment special terramechanics model that cannot be applied in all commercial codes.The new 3D multi-body discrete element dynamic model of the pipeline can also realize the fast dynamic simulation for such long mining pipeline compared to the conventional finite element model of pipeline.
(2) A new 3D coupled dynamic model of the total deep ocean mining system is established by integrating the upper and lower ends of the 3D multi-body discrete element dynamic model of the pipeline to the kinematics model of the surface mining ship and the 3D single-body dynamic model of the seafloor miner respectively, which can realize the fast dynamic simulation of the total coupled deep ocean mining system compared to traditional dynamic model.
(3) The 3D coupled dynamic simulations of two newly proposed operation modes for the total system show that during the whole operation processes, the motion states of all the subsystems are stable and within designed permissible areas, the synchronized motion of the total system can be kept well, so further prove the feasibility and efficiency of the two new mining operation modes.

Figure 1
Figure 1 Schematic diagram of a 1000 m deep ocean mining system configuration

Figure 2
Figure 2 Single-body model structure of tracked vehicle Fig. 2 illustrates the 3D single-body model structure of the tracked vehicle, l, b and h are the total length, width and height of the vehicle, l 1 is the track-terrain contact length, d is the track width, b 1 is the centerline distance of the tracks, l 2 , b 2 and h 2 represent the mass center location of the vehicle.

Figure 3 Figure 4
Figure 3 Track-terrain interaction dynamics model

Figure 5
Figure 5 Photograph of tracked test vehicle and its measurement control system architecture

Figure 9
Figure 9 Buoyancy modulus configuration on flexible hose 4 Kinematics model of mining ship

Figure 11
Figure 11 3D integrated dynamic simulation model of total deep ocean mining system in MSC.ADAMS environment

XFigure 12
Designs of new mining operation modes for total system (a) Mining operation mode I (b) Mining operation mode II Figure 13 Motion trajectories simulations of subsystems (a) Mining operation I (b) Mining operation mode II Figure 14 Forces acting on miner by flexible hose

Fig.
Fig.15shows the deflection angles of the rigid lifting pipeline relative to its initial vertical states, which is an important index for evaluating the transmission safety and performance of the pipeline.

Figure 15
Figure 15 Deflection Angles of lift pipeline relative to initial vertical state

Table 1
Principal parameters of the miner

Table 2
Mechanics parameters of the seafloor sediment