Research on the Application of Parametric Methods in Submarine

Conceptual Design

Jingda Li

1,a

, Fei Peng

, Wanjiang Qi

and Zhanzhi Wang

Ship and Ocean College, Naval University of Engineering, Wuhan, China

PLA 32123 Unit, Yantai, China

Keywords: Parameterized, Overall Submarine Design, Conceptual Design, Mathematical Model.

Abstract: Traditional submarine conceptual design relies on representation models established in the form of symbols

to describe the design scheme. However, the representation model cannot well cooperate with the computer-

aided design system to improve design efficiency. This article proposes to parameterize the submarine layout

in the conceptual design stage of the submarine based on the three levels of pressure hull, cabin, and

equipment layout, and based on this, build a mathematical model of the simple submarine layout in the

conceptual design stage. This mathematical model can be used as part of the digital design and construction

of submarines, and can be used in conjunction with computer-aided design technology to improve design

efficiency. At the same time, relying on this method will help scientific researchers understand the inherent

laws in the design of submarines and unmanned underwater vehicles and come up with the best design

solutions.

1 INTRODUCTION

Conceptual design is a plan demonstration design

carried out in the top-level design stage of

submarine. It is the overall conceptual activity in

the early stage of submarine design. It is the

materialization process from abstract thinking to

the determination of specific design plans. The

basic idea of current submarine conceptual design

is to use expression models in the form of symbols,

words, etc. to describe the complex behaviors and

implementation steps of submarine equipment

conceptual design. Then, by solving the expression

model, we can understand the design process and

reveal the overall function and structural attributes

of the submarine. The internal laws to obtain the

best design solution (Ma Yunyi, 2020).

With the development of science and

technology, computer technology is gradually

applied to all aspects of weapons and equipment

development (Chen Jianguo, Nie Yuqiang). In this

process, the expression model in the submarine

conceptual design did not match well with the

computer-aided design system (CAD). This

problem directly affects the efficiency of the

Male, master student. Main research direction: design

conceptual design stage of modern submarines (Bai

Tao - Zhou Nianfu).

In order to improve the efficiency of the

submarine conceptual design stage, domestic and

foreign experts conducted parametric design

research. Ki-Su Kim, Myung-Il Roh (Kim K-S,

Jung S-K) proposed a layout design study based on

expert systems based on parameterization.

Sebnem Helvacioglu and Mustafa Insel

(Helvacioglu S, Helvacıoğlu Ş) proposed research

on ship layout design based on reasoning. Jiang

Wenying and Lin Yan (Jiang Wenying, 2016)

conducted research on the layout design of the

main hull of ships based on parameterization. T.

Ray, R.P. Gokarn, O.P. Sha(Ray T, 1995)

established a global optimization model for ship

design, and treated the ship design optimization

problem as a multi-criteria constrained multi-

variable nonlinear optimization problem for

research. Yu Yanyun (Yu Yanyun, 2009) proposed a

design method for ships and offshore platforms

based on three-dimensional solid modeling

technology and parametric technology by

discussing the design principles and design

methods of the overall design of ships and offshore

platforms. In summary, establishing a submarine

and manufacturing of ships and marine structures.

Li, J., Peng, F., Qi, W. and Wang, Z.

Research on the Application of Parametric Methods in Submarine Conceptual Design.

DOI: 10.5220/0012281500003807

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 2nd International Seminar on Artiﬁcial Intelligence, Networking and Information Technology (ANIT 2023), pages 285-290

ISBN: 978-989-758-677-4

285

mathematical model based on parametric

expression is the key to improving design

efficiency (Roh M-I, 2007).

This paper mainly studies the problem of

parametric expression of submarine general

arrangement in the conceptual design stage.

Parametric expression is carried out at three levels:

pressure hull shape, compartment division, and

equipment layout. Based on this, the submarine's

general layout in the conceptual design stage is

expressed as a mathematical model that can be

calculated and analyzed. This method helps carry

out multi-disciplinary and multi-objective design

optimization of submarines, improves design

efficiency, and realizes parameter-driven

requirements for submarine design solutions.

2 PARAMETRIC EXPRESSION

METHOD FOR SUBMARINE

LAYOUT

2.1 Parametric Expression Method for

Pressure-Resistant Shells

At present, the pressure-resistant shell of

submarines is mainly a rotary body, which can be

described by the mathematical ship shape method.

A Cartesian rectangular coordinate system is

constructed with the center point of the submarine's

rotary body axis at the pressure hull as the origin,

the direction of the origin toward the bow of the

ship as the X-axis, the ship's width direction as the

Y-axis, and its vertical direction as the Z-axis. The

spherical bodies at the bow and stern of a

submarine can be approximated by the following

formulas:

()

zrx R





−



==−



−







(1)

Among them:

is the maximum radius of the

submarine's rotating body;

is the starting point coordinate of the

spherical surface on the X axis;

is the coordinate of the end point of the

spherical surface on the X axis;

is the shape factor.

The middle part of the submarine pressure hull

can be considered as a cylinder with a constant

radius or a linear change in radius, that is,

()

zrx R==

() ( )

,zrx zxR==

(2)

The

()

obtained from formulas (1) and (2)

is the radius of the submarine pressure hull rotary

body. In formula (2),

()

,zxR

represents the

linear equation related to

and

2.2 Cabin Parameterization Expression

Method

Submarine equipment is numerous and the space is

small, so the pressure-resistant shell curved surface

needs to be taken into consideration when

designing the cabin layout.

1) Submarine cabin classification

In order to achieve an accurate parametric

expression of the submarine cabin, the submarine

cabin can be divided into 16 basic shapes as shown

in Table 1 according to the different constituent

elements (the figures in the figure are for

demonstration only, and the dimensions of each

cabin type are not necessarily Proportion):

Table 1. Classification of cabin composition.

No. Cabin composition Appearance diagram

1 bulkhead and hull curved

surface

2 bulkheads and hull curved

surfaces

3 bulkheads and hull curved

surfaces

4 bulkheads and hull curved

surfaces

5 bulkheads and hull curved

surfaces

6 6 bulkheads

Several bulkheads and

several hull curved surfaces

——

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286

2) Parametric expression method of submarine

cabin

It can be seen from "Submarine cabin

classification" that submarine cabins can be

basically divided into 6 categories and 16 types

according to different constituent elements, of

which 5 categories and 15 types are related to the

main hull surface. For these 15 types of cabins, the

curve characteristics of the submarine pressure hull

need to be. The parametric implementation of the

cabin provides the basis.

According to the parametric approximate

expression of the submarine's main hull surface,

combined with the classification of submarine

cabins, under the same coordinate system, the

position parameters of each bulkhead in the

submarine cabin are combined with the

submarine's main hull surface to realize the

classification of submarine cabins. Parametric

expression, such as formula (3) to formula (8).

()

i i li li

C x x y z zrx y yrx z

−−−−

Ⅰ-i

(3)

()

i i li li

C x x y z zrx y yrx z

−−−−

Ⅱ-i

(4)

()

i i li li

Cxxyzzrxyyrxz

−−−−

-iⅢ

(5)

()

iilili

C x x y z zrx y yrx z

−−−−

Ⅳ-i

(6)

()

i i li li

C x x y z zrx y yrx z

−−−−

Ⅴ-i

(7)

()

121 212iii iii

Cxxyyzz

−−− −−−

Ⅵ-i

(8)

Among them,

Ⅰ-i

Ⅱ-i

Ⅲ-i

Ⅳ-i

Ⅴ-i

, and

Ⅵ-i

represent the six types of

submarine compartments in Table 1;

1 i

−

2 i

−

represent the head and tail position

coordinates of the submarine cabin on the X-axis.

1 i

−

2 i

−

represent the head and tail position

coordinates of the submarine cabin on the Y-axis.

1 i

−

2 i

−

represent the head and tail position

coordinates of the submarine cabin on the Z-axis.

−

represents the limited range of the

submarine cabin on the Y-axis of the coordinate

axis.

−

represents the limited range of the

submarine cabin on the Z-axis of the coordinate

axis.

()

,zrx y

represents the expression formula

of the Z coordinate of the hull surface and the

()

and Y coordinates of the radius of rotation in the

submarine cabin;

()

,yrx z

represents the expression formula

of the Y coordinate of the hull surface and the

()

and Z coordinates of the radius of rotation in the

submarine cabin;

The details are shown in Figure 1.

Figure 1: Concept diagram of parameterized expression of

submarine cabin.

2.3 Equipment Layout Parameterized

Expression Method

There are a large number of equipment arranged in

the submarine pressure hull, and each belongs to

different systems/subsystems. The quality of

submarine equipment layout directly affects the

overall performance of the submarine, the use of

combat personnel and the convenience of

subsequent maintenance of the submarine.

Submarine equipment layout parameterization

mainly consists of the following two aspects:

(1) Parametric expression of device appearance.

(2) Parametric expression of equipment layout

location.

There are many devices involved in submarines,

with different shapes and sizes, and most of them

are irregular shapes. In order to realize the

parametric expression of the equipment, the

appearance of the submarine equipment should be

simplified accordingly. The boundary method is

used to simplify the model of each equipment into

a cuboid according to its size, and the equipment

position is expressed through the center of the

cuboid, as shown in Figure 2.

Figure 2: Simplified schematic diagram of submarine

equipment.

Research on the Application of Parametric Methods in Submarine Conceptual Design

287

Therefore, the arrangement of equipment in the

submarine is as shown in equation (9).

() () () ()

()

,,arrangement i location i shape i weight i=

(9)

Formula (9) respectively represents the center

position of the equipment, the simplified cuboid

size of the equipment, and the weight of the

equipment.

Among them:

() ( )

iii

location i x y z=

(10)

() ( )

ii i

hape i length width heigth=

(11)

iii

are the positions of the equipment

center in the Cartesian coordinate system

constructed in 2.1.

ii i

length width heigth

respectively represent

the length, width, and height of the device after it

is simplified into a rectangular parallelepiped.

3 EXAMPLES

"Agosta" is a conventional submarine designed by

the French Navy. The hull design adopts a double-

hull design and the pressure-resistant hull is round.

The power system is equipped with two diesel

generator sets, two sets of lead-acid batteries, a

main propulsion motor and an economical

navigation motor, and has good navigation

capabilities. In terms of weapons, it is equipped

with four torpedo launch tubes, which can prepare

16 torpedoes. The detection capability is also

equipped with a sonar, which can work in an active

and passive manner.

As a conventional submarine, the "Agosta"

basically includes all the elements of a modern

submarine and has room for modification. From

this, the design of the "Agosta" submarine can be

expressed parametrically to achieve subsequent

research.

Since the "Agosta" submarine is a double-hull

submarine, its inner shell, the pressure-resistant

shell, can be considered to be an elongated oval.

According to the existing drawings and data,

combined with the expression in 2.1, and in

accordance with relevant requirements, a Cartesian

submarine that meets the usage requirements is

constructed. The coordinate system can be

expressed parametrically in the following form:

()

0.3

0.25

1.1665 1 31, 30

0.1267 4.9665 30, 22.5

0.0458 3.1478 22.5, 10.5

2.6665 10.5,25.5

0.1111 5.4998 25.5,30

2.1665 1 30,31

zrx





−−





−∈−−









+∈−−



+∈−−





∈−



−+ ∈





−





−∈











(12)

The parameterized expression of the main

compartments in the submarine can also refer to the

description in "parametric expression method of

submarine cabin", as shown in Table 2 below:

Table 2: Parameterized representation list of submarine

main compartments.

Cabin Name NO. Parametric Expression

Torpedo

roo

()()() ()

( )

22 22

31 16 2.665, 2.665 2.665, 2.665C z rx y y rx z=− − =−=−

Ⅰ-1

Command

module

()()() ()

(

)

22 22

16 10.5 2.665, 2.665 0.15, 2.665Czrxyyrxz=− − − = − = −

Ⅲ-2

Front battery

compartment

()()() ()

(

)

22 22

16 7.75 2.661, 2.661 0.15,2.665Czrxyyrxz=− − =−=−

Ⅲ-3

Rear battery

compartment

()()() ()

(

)

22 22

4 3.5 2.661,2.661 0.15,2.665Czrxyyrxz=−− − =−=−

Ⅲ-4

Auxiliary

engine roo

()()() ()

(

)

22 22

7.75 3.5 2.661,2.661 0.15,2.665C z rx y y rx z=−− − =−=−

Ⅲ-5

Motor

compartment

()()() ()

(

)

22 22

3.5 10.5 2.661, 2.661 0.15,2.665Czrxyyrxz=− − − − = − = −

Ⅲ-6

Main cabin 7

()()() ()

(

)

22 22

10.5 31 2.665,2.665 2.665, 2.665Czrxyyrxz=− − − − = − = −

Ⅰ-7

The main equipment in the submarine can be

preliminarily parametrically arranged as described

in 1.3. For the convenience of explanation, the

equipment that has a greater impact on the

submarine layout and power is selected for

expression. The details are shown in Table 3:

Table 3: Parametric representation list of submarine main

equipment.

Cabin Name No. Parametric Expression

Main motor 1

() ( )( )

()

1 21.5,0, 0.8 , 7, 2.75,4.5 ,32arrangement =− −

No. 1 diesel

engine

() ( )( )

()

2 13.5,0.9, 0.8 , 4.75,1.3,2 ,7arrangement =− −

No. 2 diesel

engine

() ( )( )

()

3 13.5, 0.9, 0.8 , 4.75,1.3,2 ,7arrangement =− − −

Air

conditioning

unit no. 1

() ( )( )

()

4 6.5,0.5, 1.1 , 4,1.5,1.75 ,1.5arrangement =− −

Air

conditioning

unit no. 2

() ( )( )

()

5 6.5, 2, 1.1 , 4,1.5,1.75 ,1.5arrangement =− −

No. 1 battery

ack

() ( )( )

()

6 0.5,0, 1.1 , 7.5,3.6,1.9 ,0.5arrangement =−

No. 2

attery

ack

() ( )( )

()

7 7.5,0, 1.1 , 7.5,3.6,1.9 ,0.5arrangement =−

Torpedo tube 8

() ( )( )

()

8 29,0,0 , 8.25,2.5, 2.5 ,1.5arrangement =

Left torpedo

mount

() ( )( )

()

9 20,1.25, 0.5 , 6.5,2,3.5 ,0.3arrangement =

Right torpedo

mount

() ( )( )

()

10 20, 1.25,0.5 , 6.5,2,3.5 , 0.3arrangement =−

The three-dimensional model of the submarine

pressure hull is generated in the software according

to Equation (12), and compared with the submarine

pressure hull constructed in CAD based on the data,

ANIT 2023 - The International Seminar on Artiﬁcial Intelligence, Networking and Information Technology

288

as shown in Figure 3. At the same time, the

pressure-resistant shell volume can be calculated

according to equation (12) to be 1986

, a n d

according to the data, the pressure-resistant shell

volume of the agosta submarine is 1983

, with

an error of 0.2%. Considering that the middle part

of the pressure-resistant shell is a streamlined

rotary body with a longitudinal section of multiple

straight lines, the error after mathematical

expression of this part is small. The bow and stern

of the pressure-resistant shell are both streamlined

rotary bodies with elliptical longitudinal sections.

After this part is expressed mathematically, the

mathematical expression method can only be

modeled theoretically, so there may be large errors.

Calculated from the current pressure-resistant shell

volume, the error is only 0.2%, which is within the

allowable range.

Figure 3: CAD construction of submarine pressure hull and

parametric method to generate submarine pressure hull

comparison diagram.

In the software, a three-dimensional model of

the submarine pressure-resistant shell can be

generated according to Equation (12). The

constructed three-dimensional model of the main

motor and the simplified model of the main motor

are put into the submarine three-dimensional model

for comparison, as shown in Figure 4.

Figure 4: Comparison diagram between a 3D model of

submarine main motor and a simplified model of submarine

main motor.

It can be seen from the figure 4: It can be

considered that in the conceptual design stage of

the overall submarine design, after the equipment

is parameterized and simplified, it will not have an

impact on the design effect of this stage, and at the

same time, it can meet the design requirements of

researchers at the data calculation level.

4 CONCLUSION

This article studies the application of parametric

methods in the overall design of submarines. In

order to realize the combined use of computer-

aided design systems and the overall design of

submarines, this article conducts the overall layout

of the submarine in terms of pressure hull shape,

cabin division, equipment layout, etc. Parametric

expression is used to establish a mathematical

model of the general layout of the submarine in the

conceptual design stage. Based on this, the

"Agosta" submarine was used as the object for

practical verification. The verification results show

that the parametric expression method proposed in

this article can realize the combined application of

computer-aided design system and overall

submarine design, help carry out multi-disciplinary

multi-objective optimization design of submarines,

and realize parameter-driven submarine design

solutions.

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