=Paper=
{{Paper
|id=Vol-3027/paper119
|storemode=property
|title=Development of the Skin of the Surface of the Tunnel Part of the Ship's Hull
|pdfUrl=https://ceur-ws.org/Vol-3027/paper119.pdf
|volume=Vol-3027
|authors=Irina Shorkina,Sergey Novikov
}}
==Development of the Skin of the Surface of the Tunnel Part of the Ship's Hull==
https://ceur-ws.org/Vol-3027/paper119.pdf
Development of the Skin of the Surface of the Tunnel Part
of the Ship's Hull
Irina Shorkina 1,2 and Sergey Novikov 1,3
1
Volga State University of Water Transport, Nesterova st., 5, Nizhny Novgorod, 603951, Russia
2
Nizhegorodsky State Architectural and Civil Engineering University, Ilyinskaya st., 65, Nizhny Novgorod,
603950, Russia
3
Samara State Transport University, Svobody st., 28, Samara, 443066, Russia
Abstract
In modern shipbuilding, extremely high requirements are imposed on the speed of the vessel.
The material costs for ensuring the seaworthiness of modern transport vessels account for about
half of the constant operating costs. Experimental materials confirm that the geometry of the
surface of the tunnel part of the vessel's hull has a significant effect on its propulsive
coefficient. Improving the shape of the tunnel part allows you to change the hydrodynamic
pressure and reduce the negative effect of the flow formed when the vessel moves forward. At
the same time, the complex geometric shape of this part of the hull significantly complicates
the preparation of maps of its cutting and, as a result, its production, since it is a set of complex
surfaces of double curvature. This article describes a practical approach to solving the problem
of constructing a sheet cutting map. For modeling a three-dimensional model and controlling
the shape of the surface, the capabilities of the Rhinoceros 6 system are presented. The results
are presented as the deviation in the area of the deployable and non-deployable surfaces.
Keywords
Surfaces of double curvature, surface unfolding, surface cutting maps, surface quality,
curvature visualization, the shape of the aft end of the vessel
1. Introduction
In recent decades, the shipbuilding industry has been intensively searching for alternative
architectural forms of ship hulls. One of the priority studies in this direction is the design of tunnel-type
vessels [2, 3]. The main research is aimed at finding ways to improve the main geometric characteristics
of the hull with single-hull and multi-hull architecture of the vessel, optimizing the geometry of the
contours for specific operating conditions [4, 5]. However, in the vast majority of cases, one of the main
problems in this case is the construction of unrolling sheets of the shell of the vessel with a complex
shape of the stern contours and the subsequent construction of material cutting maps.
The purpose of this work is the practical construction of the unrolling of the sheets of the shell of
the tunnel part of the ship's hull. The geometric problem of constructing surface scans is the basic one
when forming material cutting maps. Numerous studies have been devoted to solving the problem of
unrolling surfaces of single and double curvature onto a flat region with minimal deviations in surface
area, see, for example, [7, 8].
F
GraphiCon 2021: 31st International Conference on Computer Graphics and Vision, September 27-30, 2021, Nizhny Novgorod, Russia
EMAIL: irenika77@gmail.com (I. Shorkina); novsp78@yandex.ru (S. Novikov)
ORCID: 0000-0002-0960-1801 (I. Shorkina); 0000-0002-3981-7873 (S. Novikov)
©️ 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
2. Description of the approach to solving the problem
In accordance with the point of view presented in [1], the problem of surface unrolling is divided
into two independent formulations, namely: the construction of an unstrained scan of ruled surfaces and
the construction of a mapping of non-deployable surfaces of double curvature to a flat area, which is
associated with some deformation of surface elements. A more detailed study of the problem shows
that from a geometric point of view, both formulations do not differ from each other and can be
considered as an isometric mapping of a surface to a flat area. As is known, the isometric mapping of a
surface is also equiareal and conformal due to the conservation of both the areas of the elementary parts
of the surface and the angles between an arbitrary pair of curves on the surface. The only difference is
that linear surfaces are displayed without distortion of linear elements, and surfaces of double curvature
can be mapped to a flat area only approximately.
In this work, the problem of forming the unrolling sheets of the tunnel shell of the hull of the
passenger ship – the floating restaurant "Zhemchuzhina" was solved. The passenger vessel was built by
reconstructing and re-equipping the hull of a self-propelled ferry with a lifting capacity of 60 tons. The
self-propelled ferry "Gidrolog" had a rounded stern and one water jet propulsion, intended for carrying
out various types of work on rivers. The hull of the passenger vessel was designed with a transom stern
and two tunnel formations in the stern to accommodate the propeller-steering complex.
As initial information, the customer provided a theoretical drawing (in DXF format) of the tunnel of
the updated passenger ship hull (fig. 1). To form the surface, the initial data can be represented as a
certain cloud of points in the coordinate system "Theoretical frames – Theoretical Waterlines", or can
be represented as lines of a theoretical drawing (wire model), or both together.
Figure 1: Theoretical drawing of the tunnel
Modeling of the tunnel surface and the formation of skin scans was performed using the capabilities
of the Rhinoceros 6 graphics package [9].
The Rhinoceros 6 graphics package has a set of tools that allows you to create, edit, analyze,
visualize and transform NURBS curves, surfaces, solids, point clouds and polygon networks with high
accuracy. The complexity of the surface or the size of the object do not impose boundary conditions for
the formation of smooth models, deprivation can arise only from the computer technology used.
To solve this problem, an algorithm for constructing a cutting map was formulated:
1. Formation of a three-dimensional model of the tunnel surface.
The model was created based on a network of curves using the Surface Curve Network command.
The set of curves in the first direction was set by the contours of the tunnel frames, and in the second
direction – by the contour of the zero waterline and the zero buttock-line of the tunnel. Between the
surface of the tunnel and the bottom there is a zygomatic rounding with a radius of 50 mm, which was
created by the Fillet Surface team. The resulting model is shown in figure 2.
Figure 2: Model of the tunnel surface based on a network of curves using the Surface Curve Network
command
2. Analysis of the curvature of the surface.
To form the cutting maps, the curvature of the tunnel surface was analyzed. Currently, several
methods of quality control are used for ship surfaces. Quality control methods make it possible to see
the change in the geometry of the surface sections, allow you to identify the kinks of the curve and
monitor the transition areas of curved contours to flat ones. The methods allow us to find the best surface
that is close to the original data with minimal deviation, so that the surface satisfies the conditions of
smoothness and monotony. The use of control methods gives a real representation of the form, which
will meet the quality criterion as much as possible.
The Rhinoceros 6 graphics package has tools that allow you to control the quality of the shape of
the simulated surface by visualizing the Gaussian curvature of the surface and the curvature of curves
and sections:
- visualization of Gaussian curvature. The method clearly reflects the quality of the surface due
to the color transition. A sharp change in color contrast indicates problems with the smoothness of the
surface in the area under consideration;
- visualization of the curvature of curves, sections and surfaces. Curvature visualization allows
you to check the most difficult sections of curves. If the curvature plot is continuous and changes
smoothly, then the characteristics are desirable for the curve and the curve is smoothed. Jumps in the
curvature plot indicate kinks.
The Gaussian curvature toolkit shows the colors on the surface, based on the average curvature at
each point (figure 3). The color here is not as important as the shape that creates the color. When
Figure 3: Visualization of the Gaussian curvature of the surface. The Gaussian curvature tool
the color progressions are gradual, the surface shows an acceptable degree of smoothing. Analyzing the
surface, areas were identified that require additional testing for smoothness.
To clarify the display of changes in the curvature of curves on some parts of the surface, graphs of
the curvature of sections were constructed. The curvature plot showed the characteristics required for
the curve. The plot changed smoothly, there were no jumps in the curvature plot, therefore, the curve
satisfies the conditions. Figure 4 shows a plot of one cross-sectional curve, where the smoothness of
the curve is clearly visible.
Figure 4: Analysis of the curvature of the cross-section line
3. Formation of unfolding sheets of tunnel skin.
To form the unfolding of the skin sheets, the simulated surface was divided into nine parts (fig. 5)
with planes parallel to the plane of the midship frame and offset 100 mm aft from the elements of the
transverse tunnel set.
Figure 5: Splitting the tunnel surface into parts
Seven parts of the tunnel surface were defined as ruled surfaces and the construction of the skin
sheets was reduced to the construction of an unstressed sweep of single curvature. The two parts of the
tunnel surface are surfaces of double curvature. These fragments of the skin were further divided into
parts in order to minimize the deviation of the sweep area from the area of the original surface.
One of the factors affecting the transport efficiency of the vessel is the approach to constructing the
surface scans of single and double curvature on a flat area. The solution of questions concerning
geometric methods for constructing optimal surface scans is proposed in [6, 7, 11]. The construction of
an unstressed scan of ruled surfaces and the construction of a mapping of non-deployable surfaces of
double curvature to a flat area is associated with some deformation of the surface elements. From a
geometric point of view, the construction of both scans is considered as an isometric mapping of the
surface to a flat area. As described in [10], the isometric mapping of a surface is equiareal and conformal
due to the conservation of both the areas of the elementary parts of the surface and the angles between
an arbitrary pair of curves on the surface. According to this statement, when performing a sweep on a
plane, it is necessary to meet the requirements for preserving the lengths of the sides and minimize the
difference in the areas of the original surface with the sweep area.
The scan of the received fragments of the surface of single curvature was performed by the Unroll
Developable Surface team. In order to unfold a surface with this tool, the surfaces must be linear in one
direction. The Gaussian curvature of each fragment is almost zero at each point of the surface. This tool
is best suited for building an unstressed scan.
Construction of scans of fragments of the double curvature skin is not an easy task. To solve this
problem, many schemes have been developed in Rhinoceros 6 that claim to transfer complex
computational geometry to the physical world. To form the cut, two forward fragments were
conditionally unrolled using the Smash Double-Curved Surface command. The most forward fragment
of the skin was further divided into two parts in order to minimize the deviation of the sweep area from
the area of the original surface (figure 6).
Figure 6: Scanning the tunnel skin onto a flat area
3. Results
As a result of the performed operations, a 1:1 scale cutting map of the skin sheets of the tunnel part
in DXF format was formed (figure 7). The file was transferred to the customer for cutting steel sheets
on a CNC machine.
Figure 7: The tunnel part cutting map
The analysis of the results of the construction of scans, both of linear deployable surfaces and of
surfaces of double curvature, showed that the maximum deviation in area was less than 1% (Table 1).
It should be noted that the surface was scanned without taking into account the thickness of the steel
shell, which is 5 mm.
Table 1
Results of building scans
Surface area, Scan area, Area difference, Area difference,
mm2 mm2 mm2 %
Deployable
1252589,880 1248312,400 4277,480 0,341490864
surface
Non-deployable
809004,412 806480,075 2524,337 0,312030066
surface
The adopted design solutions turned out to be mostly correct and fully meet the customer's
requirements. The formation of the shell and its installation to the elements of the ship's hull set did not
cause difficulties for the shipyard workers.
4. References
[1] A.V. Pogorelov, Differential Geometry, 6th ed., Moscow, Nauka, 1974.
[2] A. Pylaev, Tunnel type ship, 2019. URL: http://unionexpert.su/korabl-tunnelnogo-tipa/
[3] Yu. Makarov, A. Mozgovoy, In Search of New Solutions, 2017. URL:
https://oborona.ru/includes/periodics/navy/2017/0725/104321914/detail.shtml
[4] A.B. Petrov, Efficiency of oversized propellers on ships with a tunnel stern bypass, Master’ thesis,
Leningrad, USSR, 1985.
[5] V.P. Lang, V.F. Belonenko, K.A. Smirnov, Displacement Semi-Trimaran Corps, 2014. Patent No.
RU2014100993A, Filed January 15, 2014, Issued July 20. URL:
https://patents.google.com/patent/RU2014100993A/ru
[6] E.V. Popov, Construction of sweeps of surfaces of single and double curvature, Descriptive
geometry, engineering and computer graphics: International interuniversity collection, works of
the departments of graphic disciplines, N. Novgorod: NGASU, 2000, Issue 5, pp. 272–276.
[7] V.N. Shalimov, K. Shalimova, Algorithm for constructing cutting maps for awning fabric
structures, volume 27 Collection of scientific papers Sworld, No. 1, Ivanovo: Scientific world,
2010, pp. 37-40.
[8] A. Kuznetsov, Yu. Platonov, A. Ryabokon, Specialized CAD tools for shipbuilding by "CSoft -
Bureau ESG" based on Autodesk products, CAD & Graphics magazine, volume 6, 2012. URL:
https://sapr.ru/article/23075
[9] New features in Rhino 6, 2021. URL: https://www.rhino-3d.ru/rhinoceros/new-in-rhino-
6/features/
[10] I. Kh. Sabitov, Isometric transformations of a surface that generate its conformal mappings onto
itself, volume 189, Mat. sb., 1998, No. 1, pp. 119-132. doi: https://doi.org/10.4213/sm297
[11] M. Stavrić, M. Manahl, A. Wiltsche, Discretization of double curved surface, Challenging Glass 4
& COST Action TU0905 Final Conference – Louter, Bos & Belis (Eds), Taylor & Francis Group,
London, 2014, pp. 133-140. doi:10.1201/b16499-23