Numerical Simulation and Hydrodynamic Analysis of an Amphibious Spherical Robot

Yanlin He1, 2, 3, Liwei Shi1, 2, 3 *, Shuxiang Guo1, 2, 3, 4, Ping Guo1, 2, 3 , and Rui Xiao1, 2, 3

1The Institute of Advanced Biomedical Engineering System, School of Life Science, Beijing Institute of Technology, No.5, Zhongguancun South Street, Haidian District, Beijing, China

2Key Laboratory of Convergence Medical Engineering System and Healthcare Technology, the Ministry of Industry and Infor-mation Technology, Beijing Institute of Technology, No.5, Zhongguancun South Street, Haidian District, Beijing, China

3Key Laboratory of Biomimetic Robots and Systems, Ministry of Education, Beijing Institute of Technology, No.5, Zhongguan-cun South Street, Haidian District, Beijing, China

4Faculty of Engineering, Kagawa University, 2217-20 Hayashi-cho, Takamatsu, Kagawa, Japan panshaowu.hit@gmail.com, shiliwei@bit.edu.cn, guoshuxiang@bit.edu.cn,

*Corresponding author

Abstract - Considering that the necessity of amphibious op-eration in harsh environment, this paper firstly presents the structure of an amphibious spherical robot based on 3D printing technology, which can act as a carrier of reconnaissance equip-ment, weapons systems and communications systems, and per-form a variety of tasks near the sea and beaches. Since the struc-ture of the robot had features of amphibious characteristics and quadruped gaits. Inevitably, there are new problems in the process of kinetic mechanism analysis. It is hydrodynamic cha-racteristic that is a critical factor for underwater robot. This paper presents the investigation of hydrodynamic performance of concept structure design of an amphibious spherical robot based on 3D printing technology with three basic motion---horizontal forward motion, ascending motion and sinking down motion in vertical plane. Firstly, the structural configuration, principle of work and performance parameter of the amphibious spherical robot based on 3D printing technology were described. Then the ANSYS WORKBENCH software was employed to establish the 3D model and meshing result of the amphibious spherical robot as well as its flow fields. For the reason that the complex struc-ture of our amphibious spherical robot based on 3D printing technology will cause some limitations on hydrodynamic analysis, its 3D models was properly simplified and ANSYS FLUENT software was then used to analyze the impact of hydrodynamic factors according its three motion models, and compared the simulation results with the theoretical values. Finally, the pres-sure contours, velocity vectors and drag coefficient showed the detail of the flow field when the amphibious spherical robot is performing its three basic motion. Index Terms – Dynamic Models; 3D Printing Amphibious Spherical Robot; Hydrodynamic Characteristic Estimation; Com-putational Fluid Dynamics.

I. INTRODUCTION

With the evolution after millions of years, aquatic animals possess superb swimming skills and incredible efficiency, turtle is an outstanding one. And with the development of ma-chinery, materials and control theory, the development of bio-nic underwater robot imitating aquatic animals as turtle be-comes possible. Additionally, thanks to the good water pres-sure resistance of spherical objects, the spherical robot can perform a rotational motion with 0 turn radius. Many types of spherical underwater robots have been developed, for instance,

the robot ODIN-III have been developed at the University of Hawaii [1]. It had a metal shell with a diameter of 630mm and a weight of 150kg. This robot was used to monitor the envi-ronment and implement some underwater operations. There are also some other research institutes engaged in this field, such as Harbin Engineering University and Beijing University, which have developed their own underwater spherical robot [2-3]. The Kagawa University have developed a spherical un-derwater robot which is flexible and employed three vectored water-jet thrusters as its propulsion system [4-7]. Then we have adopted this concept of amphibious spherical robot and made some improvements on the basis of some related expe-riments. This newly amphibious spherical robot can not only walks with all sorts of posture on land, but also perform some different motion in underwater environment.

Hydrodynamic characteristics are significant factors in the research of underwater robot and the efficiency of its con-trol algorithm also depends on the results of these analysis. Therefore, many researches have studied hydrodynamic cha-racteristics on underwater robot. Ueno et al. have analyzed the Submersible Surface Ship, a new type of ship that can avoid rough seas by going underwater while maintaining residual buoyancy for safety [8]. They have carried out some experi-ments in a tank to analysis its hydrodynamic characteristics and illustrated the interaction effects due to some experiment results. Tezduyar et al. have adopted a method of computa-tional fluid mechanics and proposed two numerical procedures [9]. Cheng et al. have analyzed some hydrodynamic characte-ristics of a propeller with an end-plate effect and compared the results with those of a conventional one [10]. Chunfeng Yue, et al. have analyzed some hydrodynamic characteristics of a spherical underwater robot SUR-II. Some holes and fins are also considered in the analysis process and the results have showed that these holes had some important effect on the drag coefficient [11].In this paper, we employ the ANSYS FLU-ENT software to get some other important parameters, such as the water resistance, drag coefficient, velocity vector ，contours of pressure according to modeling and hydrodynamic analysis.

The present paper is organized as follows, Section II briefly introduces the structure of our amphibious spherical

robot based on 3D printing technology and some forces analy-sis under different motion states. Section III describes some different motion models and meshing results of this robot and hydrodynamic analysis are illustrated. In section IV, three different motion states of the robot are analyzed by using AN-SYS FLUENT and at the same time some related parameters are shown. Finally, the work is concluded with some remarks.

II. STRUCTURE AND STRESS ANALYSIS OF ROBOT

Appearances of this amphibious spherical robot based on the 3D printing technology are shown in Fig.1 [12].The robot is composed of a sealed transparent hemispheroid, two opena-ble transparent quarter spherical shells and four actuating units. The control circuits, batteries and some other sensors are installed in the sealed hemisphere shell, and two quarter spher-ical shells are controlled by two servo motors to implement opening and closing states. Each actuating unit is consisted of a water-jet propeller and two servo motors. Using these two servo motors that are mutually perpendicular in one actuating unit, each actuating unit can realize two degrees of freedom movement. As Fig.1 (left) shows that the robot performs walk-ing motion and then it remains opening state. The right one shows the robot performs underwater motion and in this movement it holds closed state. For the amphibious spherical robot made by this kind of 3-D printing technology, this as-sembly method could not only save space for hemispherical shell, but also make the waterproof performance of whole ro-bot more perfect.

Fig.1 3D printing technology based amphibious spherical robot

The amphibious spherical robot based on 3D printing technology mainly employs water-jet propellers of its four legs to implement different underwater motions. Each leg of the robot is mainly composed of a vertical motor, a horizontal motor and a water-jet motor. By changing the directions and propulsive forces of its four vectored propellers, the robot can not only move forward or backward, but also rotate clockwise or counter-clockwise, and such abilities as ascending or diving and float in the underwater environment. In the horizontal plane, the robot can adjust a pair of water-jet propellers in the same horizontal plane to implement forward or backward mo-tion [13-15], and Fig.2 illustrates the front view and bottom view of robot while implementing forward motion. Moreover, the robot can adjust its four water-jet propellers in the vertical plane to generate vertical propulsive forces so that it can im-plement ascending motion or sinking down motion，and Fig.3 shows the detail of its water-jet propellers for vertical motion and the arrow in picture on behalf of the direction of force. What’s more, Fig.4 shows some specific forces and moments

generated by the water-jet propellers in the movement of the robot.

III. 3D MODELS OF ROBOT AND FLOW FIELD

A. Physical models and meshing In order to reduce computation time and get more effec-

tive results, we firstly simplified the 3D model of amphibious spherical robot. The simplification standard is to reduce the amount of surfaces and parts as much as possible. Therefore, some unimportant parts and surfaces will be simplified, in-cluding some screws, wires, some tiny and complicated parts. Meanwhile, in order to analysis the hydrodynamic influence of amphibious spherical robot, we built a flow field based on the 3D model of amphibious spherical father robot. The size of flow field should be big enough to ensure that the wall of flow field cannot affect the results of hydrodynamic analysis. Gen-erally, the size and shape of flow field are largely decided by the robot, and the velocity of robot will also have a relatively high effect on the flow field [16-17].

Fig.2 Underwater forward motion (horizontal)

Fig.3 Underwater vertical motion

a. Horizontal movement

b. Vertical movement

Fig.4 Forces and moments analysis of motion

In the processing of our simulation analysis, three typical models of motion have been established, including forward

motion on the horizontal plane as well as ascending and sink-ing down motion in the vertical plane. Here the maximum speed of flow field is 0.3m/s and the spherical robot is set as a static wall, and the related velocity parameters are used in this paper according to some previous experiments. The domain of flow field is set as a cylindrical area with a radius of 0.5m and a length of 1m. The amphibious spherical robot is located in the central area of the cylindrical flow field. Finally, the gen-erated hydrodynamic analysis model is obtained, as is shown in Fig.5 [18].

Fig.5 3D model of amphibious spherical robot in the flow field

In above processing as well, the mesh of robot and flow field is another important factor, and the overall amount of mesh decides the performance of hydrodynamic analysis and the computational complexity. With regard to the meshing of robot, the size is relatively small. However, the meshing size of the cylinder flow field can be large. This method will en-sure the accuracy of the numerical calculation, and at the same time avoid the powerful computation [19]. The meshing re-sults of 3D model of robot and flow field are illustrated in Fig.6. In order to greatly reduce the number of meshing and improve the quality and accuracy of meshing, we converted the unstructured mesh into the polyhedral mesh, and the trans-formed meshing results are shown in Fig.7. The total number of units is 367178, and the total number of nodes is 70441. It can accelerate the operation speed of the processing and com-puting, proved by experiments, to rearrange the mesh of com-puting domain. Therefore, the value of Bandwidth Reduction in the Domain command stream must be set less than or equal to 1.In Fig.8, the value of Bandwidth Reduction in the com-mand stream of Domain is 1.

Fig.6 Finite element model of meshing

Fig.7 Polyhedral meshing result

Fig.8 Solving set of command stream

B. Mathematical models and calculation methods Generally speaking, while the spherical underwater robot

is implementing underwater movement, secondary drag force and linear damping force are two fundamental forces that must be taken into consideration. In this paper, the spherical under-water robot is designed for low-speed underwater work. Therefore, it is assumed that the rate of fluid field area is low and here can be considered as stationary. Thus we only consi-dered the second drag force of spherical underwater robot and it can be exposed as the following equation.

)1(****21 2

ed SVRCF ρ=

Cd: the drag coefficient. Re: the Reynolds number. ρ : the density of the fluid. V: the relative velocity of robot to the fluid. S: the cross-sectional area. F: thrust forces also equivalent to water resistance.

When the spherical underwater robot moves in under-water environment for horizontal and vertical plane, at this time S=pi*r*r=0.049m2, and r=0.125m is the radius of spheri-cal underwater robot. ρ =1000kg/m2 is the density of flow field and the maximum velocity of spherical underwater robot is 0.3m/s. The drag coefficient of spherical underwater robot is decided by Reynolds Re=105 and greater than 103, and it in-dicates that the flow field of water moving through the spheri-cal underwater robot is turbulent. According to some previous experimental results of the actuating system with this spherical underwater robot, while the spherical underwater robot is moving in horizontal plane under water, the propulsion forces of spherical underwater robot is actuated by two horizontal water-jet propellers and it is approximately 3.46N. The actuat-ing forces of spherical underwater robot while implementing

ascending motion and sinking down motion are 6.93N and 1.061N respectively. Finally, from the formula (1), we can obtain that the drag coefficients of three basic motion states above mentioned are 0.579, 1.2257 and 0.0416.

IV. HYDRODYNAMIC ANALYSIS OF ROBOT

A. Horizontal Motion After executing meshing operation of the spherical un-

derwater robot and flow field, three meshing results files were imported into ANSYS FLUENT. In the material and boundary condition setting, the inlet of flow field is set as velocity-inlet and the outlet of flow field is set as out-flow. In this research, according to Reynolds number criterion, k-ε model is selected to describe the flow field situation, while turbulence occurs in all cases. Experience has shown that, by considering the sim-plicity of method and easiness of achievement---they in this research are assumed that the flow field moves at a speed of 0.3m/s, the spherical underwater robot is considered as static wall and the convergence criterion in this simulation calcula-tion is 0.0001, the calculating curve of convergence criterion are illustrated in Fig.9 [20].

Fig.9 The curve of convergence criterion

From preliminary research results, while the spherical underwater robot is moving in the horizontal plane under wa-ter, by adjusting one pair of water-jet propellers in the same direction, the robot can complete forward motion. After carry-ing out some relevant operations, the drag coefficient of robot implementing horizontal forward motion is shown in Fig.10, and Fig.11 illustrates how the velocity of spherical underwater robot was affected by the flow field, particularly, the effect of the holes was not obvious. Fig.12 presents that a cutaway view of pressure was affected by the spherical underwater robot. By means of formula (1) as well, the drag coefficient of spherical underwater robot moving in horizontal plane is 0.61. In AN-SYS FLUENT software, after operating 1000 steps, the drag coefficient for horizontal motion converges to a constant Cd=0.579, which indicates there exists a 5% error compared with the calculated value. Consequently, the results of ANSYS FLUET analysis are acceptable.

Fig.10 Drag coefficient of forward motion

Fig.11 Velocity vectors of spherical robot (forward motion)

Fig.12 Contours of static pressure with forward motion

B. Vertical Motion The spherical underwater robot complementing ascending motion in vertical plane underwater could adjust the angle of its four water-jet propellers in vertical plane and produce some forces. From the formula (1), the forces generated by the wa-ter-jet propellers is 6.93N, some related mechanism of forces are illustrated in Fig.3 and Fig.4. Similar to the simulation process above mentioned, some simulation results are as fol-lowing. The drag coefficient of vertical ascending motion is depicted in Fig.13. Simultaneously, it is presented from Fig.14-Fig.15 how the cross-section of vector velocity and pressure were affected by the flow field. The velocity vectors of ascending motion is shown in Fig.14 and the cutaway view of contours static pressure with ascending motion is shown in Fig.15.

Fig.13 Drag coefficient of ascending motion

Fig.14 Velocity vectors of ascending motion

Fig.15 Contours of static pressure with upward motion

On the contrary, while the spherical underwater robot is complementing sinking motion in vertical plane under water, it also could adjust the angle of its four water-jet propellers in vertical plane. Similar to the simulation process above men-tioned, the drag coefficient of vertical sinking motion is de-picted in Fig.16, the velocity vectors of ascending motion is shown in Fig.17 and the cutaway view of contours static pres-sure with sinking motion is shown in Fig.18. With respect to the simulation calculation method, the drag coefficient of ver-tical ascending motion and sinking down motion converge to constant 1.2257 and 0.0347 respectively. However, the drag coefficient of vertical ascending motion and sinking down motion obtained from formula (1) are 1.346 and 0.332 respec-tively. By calculating, the maximum error of vertical motion is

6% compared with the theoretical calculation value. Conse-quently, the results of ANSYS FLUET analysis of different vertical motion are also acceptable.

Fig.16 Drag coefficient of sinking motion

Fig.17 Velocity vectors of sinking motion

Fig.18 Contours of static pressure with sinking motion

V. CONCLUSION AND FUTURE WORK

In this paper, the hydrodynamic characteristic studied on an amphibious spherical robot based on 3D printing technolo-gy was conducted experimentally to determine the effect of various parameters such as the drag coefficient, propulsion

force, water pressure, and propulsion efficiency generated by the servo motor.

By virtue of robot hydrodynamics scheme, this spherical underwater robot was described in detail and the three most important motions were selected for hydrodynamic analysis. Based on some preliminary propulsive forces studied with this spherical underwater robot, some related hydrodynamic para-meters were set up in ANSYS FLUENT software to obtain more accurate results. Finally, for this spherical underwater robot, three fundamental motions were analyzed to demon-strate some related parameters estimation. The drag coefficient converges to 0.579 for the horizontal forward motion and 1.346 for the vertical ascending motion as well as 0.0332 for the vertical sinking down motion. Simultaneously, the maxi-mum error of these three basic motion is 6% compared with the theoretical calculation value obtained from the formula (1). Therefore, the drag coefficients of ANSYS FLUET analysis are acceptable and successful. In addition, the velocity vector and pressure contours have proved the hydrodynamic features and provided important evidence to conform the assumptions made during the hydrodynamic parameter estimation. More importantly, these simulation analysis results can be used to improve the control accuracy of amphibious spherical robot in underwater environment.

In future work, we will apply this hydrodynamic simula-tion analysis results to optimize the prototype of this amphi-bious spherical robot, for the sake of reducing the error be-tween theoretical value and simulation results. Furthermore, we will evaluate the simulation results of spherical robot with the practical data while the robot is operating in the real under water environment.

ACKNOWLEDGEMENTS

This work was supported by the Excellent Young Scho-lars Research Fund of Beijing Institute of Technology (No. 3160012331522) and the Basic Research Fund of the Beijing Institute of Technology (No.3160012211405). This research project was also partly supported by National Natural Science Foundation of China (61375094), Key Research Program of the Natural Science Foundation of Tian-jin (13JCZDJC26200) and National High Tech. Research and Development Program of China (No.2015AA043202).

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