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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>OCEANS.</journal-title>
      </journal-title-group>
      <issn pub-type="ppub">0197-7385</issn>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1109/OCEANS.1991.606498</article-id>
      <title-group>
        <article-title>Mathematical MoDELING, CAD AND CFD ANALYSIS for ENHANCEd PERFORMANCE</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Silvio Javier Lázaro-Cárdenas</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>José Luis Ordóñez-Ávila</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alicia María Reyes-Duke</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Engineering,Universidad Tecnológica Centroamericana</institution>
          ,
          <addr-line>(Unitec)</addr-line>
          ,
          <country country="HN">Honduras</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Faculty of Engineering, Universidad Tecnológica Centroamericana, (Unitec)</institution>
          ,
          <addr-line>San Pedro Sula 21102</addr-line>
          ,
          <country country="HN">Honduras</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>1991</year>
      </pub-date>
      <volume>606498</volume>
      <issue>4</issue>
      <fpage>1414</fpage>
      <lpage>1420</lpage>
      <abstract>
        <p>Nowadays, robotics research is quickly expanding and developing, allowing increased opportunities to perform studies using advanced technologies such as models and design software. This project aims to design and build a 5-DOF ROV, beginning with mathematical modeling and moving to kinematic and dynamic models to understand its behavior undervarious circumstances. The ROV designed uses CAD and CFD tools to ensure that it can endure environmental conditions while remaining highly maneuverable, low-cost,and capable of performing user-defined tasks. The body of the ROV isprinted with an Ender 3 Pro 3D printer, the electrical system and data are driven by a Raspberry Pi 4, and the propulsion system is powered by six Blue-Robotics T200 Thruster turbines. Communication between the ROV and the land computer is performed via an umbilical cable with 8 pins. The project will facilitate research in the field of robotics, providing valuable insights into the design and operation of ROVs in challenging environments.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;DOF</kwd>
        <kwd>ROV</kwd>
        <kwd>CAD</kwd>
        <kwd>CFD</kwd>
        <kwd>mathematical modeling</kwd>
        <kwd>RaspberryPi 4</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>StrEAMLINING Sub-aquatic ROV FABRICATION through</p>
    </sec>
    <sec id="sec-2">
      <title>1. INTRoDUCTION</title>
      <p>
        Remotely operated vehicles (ROV) are underwater robots designed to accomplish tasks
underwater. They are frequently utilized in a variety of sectors, including oil and gas exploration,
marine research, and undersea exploration. Building a ROV requires detailed planning and
consideration of several elements, including the environment in which it will operate, the
activities it will do, and the materials and components utilized in its development [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
      <p>This paper will describe the design and development of a ROV by applying different techniques
to achieve an optimal design for any required needs. The robot should have a system capable
of maneuvering in conditions of high dynamic requirements. Computer-aided design (CAD)
and computational fluid dynamics (CFD) tools will be used to calculate the pressures to which
the robot will be subjected, as well as a better hydrodynamic design based on fluid dynamics
calculations. The manufacturing process for ROVs involves complex design requirements with
stringent performance and cost-effectiveness criteria. This can streamline the ROV fabrication
process and enhance performance while ensuring cost-effectiveness.</p>
      <p>
        Developing a mathematical model where the basic morphology of our robot will be studied,
as well as its kinematic model and dynamic model. For the electronic operation, the use of a
Raspberry Pi would satisfy the need for electronics communication, which will be responsible
for maintaining programming and communication with the various sensors and turbines to be
used in the design of the ROV. For the monitoring system, it would count with video modules in
a simple way. A Pix-hawk 2.4 controller for more accurate stability control, as well as real-time
telemetry monitoring of the ROV [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>This research will be key for the validation of the method based onCAD and CFD [6], as well
astheimprovementinthe developmentoftheserobotsforfutureresearch,reducingthetime
and cost of testing and the errors of mechanical designs that fail to meet demanding conditions
in environments unfavorable for ROVs. Achieving an advance in underwater research and
supplying the fundamental need on which this research is based, which is the constant and
high-quality monitoring of the coral reefs of Honduras [3]. Nowadays, with the continuous
development of low-cost technologies such as 3D printing and open-source hardware and
software, the cost of building an ROV has been further reduced. Autonomous underwater
vehicles have grown to be very popular for this purpose as a result of the increased use of
remotely operated vehicles around the world, but the cost of controlling these vehicles is
significantly higher than that of remotely operated vehicles [4]. This paper will present a
valuable resource for researchers and engineers involved in the manufacturing process of
ROVs andforanyone interested inexploringthe potential of advanced modelingandanalysis
techniques in underwater technology.</p>
    </sec>
    <sec id="sec-3">
      <title>2. Method AND Data</title>
      <sec id="sec-3-1">
        <title>2.1. MeCHANICAL DESIGN based ON CAD</title>
        <p>
          The proposed method attempts to define the required stages for designing a ROV capable of
meeting the requirements determined for monitoring corals and marine life off the coast of
Honduras. This research is based on a hierarchical method, which is quite useful for complex
engineering design models such as mathematical modeling. In high-throughput processes,
mathematical modeling and simulations are a fundamental part of achieving a high-quality
study [5]. In the case of mathematical modeling, each level represents an equation that is related
to the next level [
          <xref ref-type="bibr" rid="ref2">2, 5, 6</xref>
          ].
        </p>
        <p>Many designs often involve using software tools to create detailed 3D models of a mechanical
product or component. The design is created by defining various parameters and dimensions that
specify the shape, size, and material properties of the object. Experimentation with
computeraided models is an increasingly important problem-solving technique. The aim of this method
is to reduce costs by developing a customized robot that meets specific details and fits the needs
required in different environmental scenarios and that fits specific needs for special tasks, which
can be developed in CAD. This would mean considerable savings without the need to purchase
a robot in the first instance [7, 8]. This test involves mechanical displacement, Von Mises stress,
has flaws or can’t withstand the pressure at which it is meant to be submerged. The pressure
that the fluid applies to the structure is oneof the mostcrucial factors to be taken into account.
The parameters that the CAD model generates are displayed in Table. 1.</p>
      </sec>
      <sec id="sec-3-2">
        <title>2.2. HydroDINAMIC Study</title>
        <p>According to D’Alambert’s paradox, which states that no hydrodynamic force will act on a body
moving with constant velocity in a non-viscous fluid, frictional forces will be present when the
solid bodyis in a viscous fluid, such that the system is not conservative with respect to energy,
commonly referred to as interference drag [9, 10].</p>
        <p>When a vehicle or solid body is submerged, it is essential to achieve the best possible stability
to obtain better control of the vehicle. Sometimes external forces act on the ROV, which can
cause a reduction in stability. The longitudinal design of the ROV will be fundamental to
determining better stability [11]. The different drag coefficients according to its shape and
design are presented for the ROV, where (DC) stands for ”drag coefficient” and adopting a
particularity of ”double the speed, quadruple the drag,” this refers to the amount of flow through
which the ROV body goes and will increase its drag proportionally to the flow [10, 11].</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>3. Mathematical MoDELING</title>
      <sec id="sec-4-1">
        <title>3.1. KINEMATIC MoDELING</title>
        <p>When designing and manufacturing a ROV, mathematical development becomes a fundamental
part when trying to have control in an environment as dynamic as the ocean. Testing a robot is
time consuming and costly. Mathematical modeling is useful for simulation purposes and to
design control systems that take into account the dynamics of the system before building it [12].</p>
        <p>The mathematical model of a ROV requires two fundamental branches of study, these
being kinematics and dynamics, the kinematic model consists of various equations which are
where  = [ 1 2 ] ,  = [ 1 2] [14, 16].</p>
      </sec>
      <sec id="sec-4-2">
        <title>3.2. DYNAMIC MoDELING</title>
        <p>The dynamic model of an ROV brings together the equations of forces and motions acting on
the ROV. The Newton-Euler equations of motion to determine the dynamics of a submerged
body would be used to obtain part of a dynamic system of the ROV. These bodies are exposed
to different types of forces [17]. These are mainly inertial, hydrodynamic and restoring forces.
To get an idea of how a dynamic model can be started, a short equation is presented and shown
in (1).</p>
        <p>+  ( ) +  ( ) +  ( ) = 
(1)</p>
        <p>To explain the above equation, M is described by a 6 x 6 matrix relating the inertia matrix
and added masses in (2), C(v) is a 6 x 6 matrix relating the Coriolis matrix and its added masses
in (3), D(v) is described as a 6 x 6 matrix in (4) elaborated using the damping forces and g which
is represented by a 6 x 1 vector and elaborated using the restoring forces [18, 19]. Each of these
matrix are made up of different parameters wit h in ea ch vector and are rewritten in (5), (6), (7).</p>
        <p>When deriving the equations of motion of the rigid body by applying Newtonian formulation,
the mass ma8tr.4ix09of the rigid body is calculated as follows [20] in (8) and (9):
 (  ) ==  ( )++  ( )</p>
        <p>( ) =   ( ) +    ( )</p>
        <p>12162
( ) = ⎢
8.409
0</p>
        <p>0
8.409
0
0
0
⎢−8.409</p>
        <p>Applying hydrodynamic terms, the added mass matrix MA and Coriolis added masses can be
derived by applying an energy method based on Kirchhoff’s equations [20]. The added masses
of the ROV in a fluid are determined by the added mass matrix which is defined as follows:
  = − ⎢</p>
        <p>There are four main sources of hydrodynamic damping in ROV’s, these being potential
damping, damping due to waves, surface friction between the ROV and the fluid, and damping
due to vortexshedding. However,the effects of potential damping and dampingdue to waves
are not taken into account in ROV studies, that is why D(v) can be expressed as a linear damping
termDLcausedbyfrictionandaquadraticdampingtermDNL(v)duetovortices,thesecanbe
expressed in the following equations:</p>
        <p>= −    [  ,   ,   ,   ,   ,   ]
  ( ) = −
[ | || |, | || |,  | || |,  | || |,  | || |,  | || |]
(7)
(8)
(9)</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>4. FABRICATION</title>
      <p>The proposed design consists of a closed, hermetic design with a large interior capacity. Its
structure consists of a plastic shell, and with the help of Ultimaker Cura software, we were able
tomodifytheparametersoftheprint,whichisprintedinpoly-lacticacid(PLA)atarateof100
percentinfillanda0.2mmheightbetweenprintinglayers,sealedwithepoxyresintosealany
type of opening between the filament [21].</p>
      <p>The design consists of 4 thrusters located horizontally and vectored at 45 degrees and 2
vertically, with this configuration the ROV obtain 5 DOF [22]. Although the shape of the robot
plays a significant role in its hydrodynamics, the number of degrees of freedom it will have
is unaffected. According to [23], an underwater robot’s degrees of freedom depend on the
quantity and placement of its thrusters. To achieve all degrees of freedom, some designs employ
reconfigured vector thrusters (RVT) or a significant number of fixed thrusters. An RVT is
described in [23] as a thruster connected to a servomotor inside the underwater vehicle that
rotates to adjust the thruster’s orientation and force.</p>
      <p>The design with the lowest drag coefficient is presented as a streamlined body, which hasa
drop shape [8], hydro-dynamically more efficient than the other suggested bodies due to its
front face when breaking the fluid. It is also observed that the streamlined half body obtains a
much lower drag coefficient than the other design types; both designs share many similarities,
affected by the angle of attack with which they pass through the fluid and affected by the drag
suffered by the half body due to its curvature, which is very similar to a wing, despite this being
a design not widely used in ROVs.</p>
      <p>The rov’s primary role is to navigate in different directions underwater, but this is not an
impediment to not taking into account the buoyancy of the ROV. If buoyancy is not taken into
consideration, the ROV may end up with a very heavy design that will not be able to operate in
a good wayor a too-light robot that will not be able to submerge,andthe designwill fail [8, 24].</p>
    </sec>
    <sec id="sec-6">
      <title>5. Results</title>
      <p>The research done in CAD and CFD allowed us to create a hydrodynamic design that can
function under challenging conditions. The ROV’s design was enhanced to move through water
with the least amount of drag and the greatest amount of maneuverability. The results of the
simulation indicated that the best performance would come from a streamlined shape with six
symmetrical thrusters.</p>
      <p>The six thruster configuration helps the robot gain good underwater movement. By making
use of the data provided by solid works and performing fluid dynamics, we can describe all the
possible movements and velocities that the ROV could operate under different circumstances.
As shown in Figure. 2, the displacement of the ROV through the Z, Y, and X axis, was tested at
2.5 m/s against water currents.</p>
      <p>Various stress tests werecarried outthrough CAd and CFD calculations obtained in solidworks,
tests where performed in multiple depths to ensure the ROV’s safety and reliability. The stress
studyof the first test involved submerging the ROV to depths of 10 meters, 50 meters, and100
meters. All tests perform with a good rating and a FOS above 1.44. However, at 100 meters
depth, the safety factor was equal to 1, the deformation was greater than in the earlier tests.
Therefore, in order to guarantee the ROV structure’s security, a maximum depth of 100 meters
was set.</p>
      <p>The decision to use carbon fiber [25], was to add strength to the PLA (poly-lactic acid), the
material used to 3D print the ROV, by doing so, the structure could increase the structural
rigidity and strength the ROV needs and allow deeper operations by combining a cured carbon
fiber layer over the PLA.</p>
    </sec>
    <sec id="sec-7">
      <title>6. CONCLUSIONS</title>
      <p>ROVs have become an essential component of sub-aquatic activities in a variety of sectors,
including oil and gas research, marine antiquities, oceanography, and military uses. Advanced
mathematical modeling, computer-aided design (CAD), and computational fluid dynamics (CFD)
research have greatly improved the performance and cost-effectiveness of subaquatic ROVs. A
complex process involving design, manufacturing, and testing is needed to create an underwater
robot using 3D printing. However, the use of 3D printing technology has many benefits, such
as the ability to precisely create custom designs with complex geometries. The robot can
withstand the harsh underwater environment thanks to the use of water-resistant materials and
waterproofing features. More people and organizations will be able to explore the ocean’s depths
as 3D printing technology advances and makes it easier and more affordable to manufacture
underwater robots, as shown in Figure. 3.</p>
      <p>CFD research is critical in the construction of ROVs. CFD analysis can forecast the movement
of water and pressure on the ROV’s surface by modeling the fluid dynamics that the ROV
will encounter. This data can be used to improve the ROV’s construction, decreasing drag
while increasing speed and maneuverability. CFD analysis can also help improve the structural
construction of the ROV, such as its buoyancy and stability, both of which are critical in
subaquatic activities. The ability to maximize design and manufacturing processes reduces
material and labor costs considerably, and the elimination of the need for tangible samples
lowers total production costs.
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    </sec>
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