Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M
Models, methods, and algorithms for three-dimensional modeling of the screw winding of the Uragan-2M torsatron are considered. The application of the method of kinematic modeling is substantiated as the most acceptable for obtaining solid-state and surface models of elements of a magnetic system. Me...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2021 |
| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2021
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/195803 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M / S.O. Martynov, O.O. Luchaninov, V.P. Lukyanova, M.A. Khazhmuradov, S.I. Prokhorets // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 165-170. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-195803 |
|---|---|
| record_format |
dspace |
| spelling |
Martynov, S.O. Luchaninov, O.O. Lukyanova, V.P. Khazhmuradov, M.A. Prokhorets, S.I. 2023-12-07T10:35:46Z 2023-12-07T10:35:46Z 2021 Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M / S.O. Martynov, O.O. Luchaninov, V.P. Lukyanova, M.A. Khazhmuradov, S.I. Prokhorets // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 165-170. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.55.Hc; 52.65.Kj DOI: https://doi.org/10.46813/2021-136-165 https://nasplib.isofts.kiev.ua/handle/123456789/195803 Models, methods, and algorithms for three-dimensional modeling of the screw winding of the Uragan-2M torsatron are considered. The application of the method of kinematic modeling is substantiated as the most acceptable for obtaining solid-state and surface models of elements of a magnetic system. Methods for calculating the stresses and strains arising in the elements of the magnetic system of a screw winding under the influence of ponderomotive forces are presented, which makes it possible to determine the strength of the structural elements of the facility. Розглянуто моделі, методи і алгоритми тривимірного моделювання гвинтової обмотки торсатрона Ураган-2М. Обґрунтовано застосування методу кінематичного моделювання як найбільш прийнятного для отримання твердотільної і поверхневої моделей елементів магнітної системи. Наведено методи розрахунку напружень і деформацій, що виникають в елементах магнітної системи гвинтової обмотки під впливом пондеромоторних сил, що дає можливість визначити міцність елементів конструкції установки. Рассмотрены модели, методы и алгоритмы трехмерного моделирования винтовой обмотки торсатрона Ураган-2М. Обосновано применение метода кинематического моделирования как наиболее приемлемого для получения твердотельной и поверхностной моделей элементов магнитной системы. Приведены методы расчета напряжений и деформаций, возникающих в элементах магнитной системы винтовой обмотки под воздействием пондеромоторных сил, что дает возможность определить прочность элементов конструкции установки. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Experimental methods and processing of data Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M Моделі, методи і технології розрахунку характеристик фізичної установки Ураган-2М Модели, методы и технологии расчета характеристик физической установки Ураган-2М Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M |
| spellingShingle |
Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M Martynov, S.O. Luchaninov, O.O. Lukyanova, V.P. Khazhmuradov, M.A. Prokhorets, S.I. Experimental methods and processing of data |
| title_short |
Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M |
| title_full |
Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M |
| title_fullStr |
Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M |
| title_full_unstemmed |
Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M |
| title_sort |
models, methods, and technologies for calculation of characteristics of the physical facility uragan-2m |
| author |
Martynov, S.O. Luchaninov, O.O. Lukyanova, V.P. Khazhmuradov, M.A. Prokhorets, S.I. |
| author_facet |
Martynov, S.O. Luchaninov, O.O. Lukyanova, V.P. Khazhmuradov, M.A. Prokhorets, S.I. |
| topic |
Experimental methods and processing of data |
| topic_facet |
Experimental methods and processing of data |
| publishDate |
2021 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Моделі, методи і технології розрахунку характеристик фізичної установки Ураган-2М Модели, методы и технологии расчета характеристик физической установки Ураган-2М |
| description |
Models, methods, and algorithms for three-dimensional modeling of the screw winding of the Uragan-2M torsatron are considered. The application of the method of kinematic modeling is substantiated as the most acceptable for obtaining solid-state and surface models of elements of a magnetic system. Methods for calculating the stresses and strains arising in the elements of the magnetic system of a screw winding under the influence of ponderomotive forces are presented, which makes it possible to determine the strength of the structural elements of the facility.
Розглянуто моделі, методи і алгоритми тривимірного моделювання гвинтової обмотки торсатрона Ураган-2М. Обґрунтовано застосування методу кінематичного моделювання як найбільш прийнятного для отримання твердотільної і поверхневої моделей елементів магнітної системи. Наведено методи розрахунку напружень і деформацій, що виникають в елементах магнітної системи гвинтової обмотки під впливом пондеромоторних сил, що дає можливість визначити міцність елементів конструкції установки.
Рассмотрены модели, методы и алгоритмы трехмерного моделирования винтовой обмотки торсатрона Ураган-2М. Обосновано применение метода кинематического моделирования как наиболее приемлемого для получения твердотельной и поверхностной моделей элементов магнитной системы. Приведены методы расчета напряжений и деформаций, возникающих в элементах магнитной системы винтовой обмотки под воздействием пондеромоторных сил, что дает возможность определить прочность элементов конструкции установки.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195803 |
| citation_txt |
Models, methods, and technologies for calculation of characteristics of the physical facility Uragan-2M / S.O. Martynov, O.O. Luchaninov, V.P. Lukyanova, M.A. Khazhmuradov, S.I. Prokhorets // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 165-170. — Бібліогр.: 5 назв. — англ. |
| work_keys_str_mv |
AT martynovso modelsmethodsandtechnologiesforcalculationofcharacteristicsofthephysicalfacilityuragan2m AT luchaninovoo modelsmethodsandtechnologiesforcalculationofcharacteristicsofthephysicalfacilityuragan2m AT lukyanovavp modelsmethodsandtechnologiesforcalculationofcharacteristicsofthephysicalfacilityuragan2m AT khazhmuradovma modelsmethodsandtechnologiesforcalculationofcharacteristicsofthephysicalfacilityuragan2m AT prokhoretssi modelsmethodsandtechnologiesforcalculationofcharacteristicsofthephysicalfacilityuragan2m AT martynovso modelímetodiítehnologíírozrahunkuharakteristikfízičnoíustanovkiuragan2m AT luchaninovoo modelímetodiítehnologíírozrahunkuharakteristikfízičnoíustanovkiuragan2m AT lukyanovavp modelímetodiítehnologíírozrahunkuharakteristikfízičnoíustanovkiuragan2m AT khazhmuradovma modelímetodiítehnologíírozrahunkuharakteristikfízičnoíustanovkiuragan2m AT prokhoretssi modelímetodiítehnologíírozrahunkuharakteristikfízičnoíustanovkiuragan2m AT martynovso modelimetodyitehnologiirasčetaharakteristikfizičeskoiustanovkiuragan2m AT luchaninovoo modelimetodyitehnologiirasčetaharakteristikfizičeskoiustanovkiuragan2m AT lukyanovavp modelimetodyitehnologiirasčetaharakteristikfizičeskoiustanovkiuragan2m AT khazhmuradovma modelimetodyitehnologiirasčetaharakteristikfizičeskoiustanovkiuragan2m AT prokhoretssi modelimetodyitehnologiirasčetaharakteristikfizičeskoiustanovkiuragan2m |
| first_indexed |
2025-11-24T16:51:22Z |
| last_indexed |
2025-11-24T16:51:22Z |
| _version_ |
1850489349658902528 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 165
https://doi.org/10.46813/2021-136-165
MODELS, METHODS, AND TECHNOLOGIES FOR CALCULATION
OF CHARACTERISTICS OF THE PHYSICAL FACILITY URAGAN-2M
S.O. Martynov, O.O. Luchaninov, V.P. Lukyanova, M.A. Khazhmuradov, S.I. Prokhorets
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: khazhm@kipt.kharkov.ua
Models, methods, and algorithms for three-dimensional modeling of the screw winding of the Uragan-2M
torsatron are considered. The application of the method of kinematic modeling is substantiated as the most accepta-
ble for obtaining solid-state and surface models of elements of a magnetic system. Methods for calculating the
stresses and strains arising in the elements of the magnetic system of a screw winding under the influence of
ponderomotive forces are presented, which makes it possible to determine the strength of the structural elements of
the facility.
PACS: 52.55.Hc; 52.65.Kj
INTRODUCTION
The Uragan-2M (U-2M) stellarator toroidal magnetic
system is a complex technical object designed to contain
a high-temperature plasma with specially created magnet-
ic field. This system belongs to the type of magnetic traps
– torsatrons, a characteristic feature of which is the unidi-
rectional movement of currents along the conductors of
the poles of the screw winding (SW) 1. Experimental
studies of the magnetic configuration of the torsatron
identified a number of problems, the solution of which
depends on the calculations of the stressed-deformed state
of the elements of the magnetic system.
These tasks include:
– determination of the extreme values of the currents
in the conductors of the SW poles at which defor-
mations occur, leading to significant disturbances in the
magnetic configuration of the physical facility;
– calculation of the absolute values of the forces that
generate such deformations;
– determination of stresses in the elements of the
magnetic system, at which they reach the yield point.
Methods for calculating stresses and strains occuring
in the elements of the magnetic system of an SW under
the influence of ponderomotive forces are presented.
The basis of such calculations is a three-dimensional
geometric model of the U-2M magnetic system, built
using mathematical models, methods and technologies.
These include:
– object-oriented analysis for dividing the torsatron
into subsystems and connections between them;
– methods of analytical geometry and computational
mathematics for obtaining geometric models of objects
of complex spatial shape SW poles;
– the method of finite element analysis for the con-
struction of volumetric and SW surface models.
For the successful use of these methods, it is neces-
sary to take into account the design features of the
U-2M, which directly determine the system of re-
strictions on the controlled parameters.
1. STATEMENT OF THE PROBLEM
The magnetic system of a torsatron consists of a
number of windings, the most complex of which is the
SW. It is characterized as an object of complex spatial
shape and large overall dimensions – two-lead, provid-
ing four periods of the magnetic field. This means that
in a sector bounded by a right angle composed of
meridional sections of the torus, the SW geometry is
uniquely determined (Fig. 1). The number of conductors
in a SW pole is twenty.
The cross-section of the conductor has a trapezoidal
shape with dimensions 2024100 mm. The geomet-
rical characteristics of the SW are set by a set of
meridional sections of the torus every 0.5when going
around the main axis of the torus. The magnetic system
of the torsatron also includes a number of flat annular
windings, the planes of which are located perpendicular
to the main axis of the torus.
Fig. 1. The meridional section of the SW poles:
1 – conductor at the SW pole;
1 and 2 – the angles of the center of the pole
2. METHODS OF THE GEOMETRIC
MODELING OF SW
To obtain a mathematical model of the SW geome-
try, the kinematic modeling method [2, 3] was used. The
essence of the method is that the shaping of the surface
of the poles of the magnetic windings of the torsatron is
formed when a plane curve moves in space, the shape of
which either changes according to a known rule or re-
mains unchanged in the process of movement. Thus, to
specify the kinematic surface of the SW, it is necessary
to specify a family of plane curves and the law of varia-
tion of a plane curve in space.
Let )V(i – a family of plane curves depending on a
parameter U and belonging to a fixed plane
2
0R .
32
0i RR:T – family of maps of this plane in space. In
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 166
this case, the surface of the SW pole is given by the
composition of the mappings
)V(T)V,U( ii ,
where V,U – the curvilinear coordinates of the surface.
For a specific case of SW production, the contour of
plane curves defines a surface in the form of a set of
sections. In this case, the SW surface is represented as a
changing curve moving in space, by turns taking the
form of meridional sections. In this case, between the
sections, the surface is interpolated by linear segments
connecting the characteristic points of structural ele-
ments on adjacent sections.
Thus, the surface of the SW poles can be represented
in the form of a grid (raster) consisting of elements –
generating lines and segments connecting adjacent gen-
erating lines of the vertices of the conductors of the
poles of the magnetic windings. With such a representa-
tion of the modeled surface, the coordinates of the raster
vertices are uniquely determined in the selected coordi-
nate system. If it is necessary to determine the coordi-
nates of points on the modeled surface that are outside
the vertices of the raster, the Bezier splines are used [4].
To restore the surface according to Bezier, in each
cell of the SW raster, it is necessary to add twelve more
points to the existing four raster points so that each cell
has sixteen reference nodes. These sixteen nodes are
used to construct an approximating Bezier surface for
the cell. The advantage of the kinematic method of de-
fining the surface in comparison with other methods
using tightening of the corset of the surface created by
generating lines and guiding lines is that in this case, to
describe a surface of a complex shape (in our case, the
surface of the SW), a significantly smaller number of
intermediate sections is required due to additional con-
trol capabilities of the section plane. In this case, the
method takes into account many factors necessary in the
design process, in particular, simplicity of description,
storage and editing costs, presentation efficiency for a
specific SW, stages of technological equipment, intui-
tive ideas of developers, etc.
3. METHOD OF FINITE ELEMENT
ANALYSIS
The finite element method (FEM) [5] occupies a lead-
ing position in solving problems of solid mechanics due
to the possibility of modeling a wide range of objects and
phenomena. Popular alternative methods the finite dif-
ference method and the boundary element method
(boundary integral equations) now occupy rather narrow
niches, limited to research or special problems.
When constructing the geometry of the U-2M mag-
netic system the FEM is based on the discretization of
the SW volume in order to solve the equations of con-
tinuum mechanics under the assumption that the rela-
tions are fulfilled within each of the elementary regions.
Such elements correspond to the real part of the SW
space (Figs. 2-4).
Designations in the figures: ,, – element local
coordinate system; Z,Y,X – SW global coordinate sys-
tem; w,v,u – displacements in the local coordinate
system for the shell element; ,, – angles of ro-
tation relative to local axes at the node and in the global
coordinate system W,V,U .
Within the FE VO, the properties of the object are
assigned – the characteristics of the rigidity and strength
of the material (copper conductors of the SW poles) and
the fields of the quantities of interest – displacements,
deformations and stresses – are described.
Fig. 2. Volumetric linear finite element
Fig. 3. Volumetric parabolic finite element
Fig. 4. Parabolic finite element of the surface
Displacements, deformations and stresses are as-
signed at the nodes of the element, and then interpola-
tion functions are introduced, with the help of which the
corresponding valuescan be calculated at any point
within the SW element or at its boundary. The mathe-
matical description of an element is reduced to linking
the factors acting at the nodes: displacements and forc-
es. Such a sequence of actions in describing the dis-
placements and forces arising in the U-2M magnetic
system is sequentially implemented.
The problem is solved by the direct search method
under the assumption of a linear problem statement:
1. The displacement field within the SW element
(for a volumetric problem
T]w,v,u[ ) by means of
interpolation functions forming a matrix ]N[ is expressed
in terms of angular displacements }{ . The use of inter-
polation functions provides displacement values at any
point of the SW element, depending on the coordinates
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 167
and displacement values at the nodes. In matrix form,
the relations have the form
}Δ{N ,
where T
kkk222111 ]w,v,u,,w,v,u,w,v,u[}{ – for
the volumetric problem of modeling the SW poles of the
U-2M torsatron, k – is the number of nodes of the fi-
nite element.
2. The deformation field ε is expressed in terms of
the degrees of freedom {}
by deforming the displace-
ment field according to the relationships forming the
matrix [D]
and connecting deformations with SW dis-
placements = [D]{}.
3. Taking into account the equations of state, which
are based on Hooke's law and whose coefficients form a
matrix [E], a relation is established first between the
stress field and the deformation field ]E[ , and
then between the states of freedom at the FE nodes into
which the volume of the poles of the magnetic winding
of the torsatron is divided }{]D[]E[ .
4. Expressions are formed for the forces }F{ acting
at the vertices of the element, depending on the stress
field , for which the matrix of transformation of stress-
es into nodal forces ]A[ is used }{]A[}F{ .
5. The relations between the nodal forces and dis-
placements in the nodes of the torsatron SW are found
}{]k[}F{ , where ]D[]E[]A[]k[ – the stiffness
matrix of the finite element.
6. To give the matrix ]k[ the property of symmetry,
we replace the stiffness transformation matrix with the
matrix transformed to the displacement-to-deformation
transformation matrix [D]. Then ]D[]E[]D[]k[ T .
The given dependences allow, knowing the dis-
placements in the SW nodes, to obtain the values of the
forces, as well as to solve the inverse problem – to find
displacements by forces. The direct formulation is used
to obtain the FE stiffness matrices, as well as to describe
the heat transfer process in the conductors of the SW of
the U-2M torsatron.
To obtain the stiffness matrices of the spatial ele-
ments of the SW poles, variational principles are used,
in particular, the principle of the minimum potential
energy. The stiffness matrix obtained in this way is cal-
culated by the relation
.dxdydz]D][E[]D[]k[
V
T
The problem of integration over the volume of a body
of complex shape or, in the case of a shell element, over
curved surfaces, is solved due to the fact that expressions
are written in the local coordinate system associated with
the element ,, , and the coordinates change in the
interval ]1,1[ . In this case, the expressions for the ele-
mentary volume of the SW pole take the form
dddJdxdydz ,
where J
is the determinant of the Jacobi matrix, then
1
1
1
1
1
1
]det[]][[][][ dddJDEDk T .
Analytical calculation of integrals in the expression
for the stiffness matrix isimpossible for triangular FE
with curved sides. Therefore, numerical integration is
used. Its essence lies in the fact that the integration is
replaced by the summation of the products of the inte-
grands calculated in a certain system of points. This
process is accompanied by the calculation of the
Jacobian determinant. A negative value is a conse-
quence of the degeneracy of this finite element.
Using the method of kinematic modeling, considered
in detail in the article, three-dimensional models of the
geometry of the magnetic system of the SW of the
U-2M torsatron were obtained. The calculation and
simulation results are shown in Figs. 5 and 6.
Fig. 5. Three-dimensional model of U-2M SW
on the field period
Fig. 6. Three-dimensional model of U-2M SW
4. MATHEMATICAL MODELS
FOR CALCULATING FORCES
The nature of the origin of ponderomotive forces is
based on two experimentally established facts a mag-
netic field acts on moving charges and moving charges
create a magnetic field.
These two facts underlie the law of Ampere and Bio-
Savard, which are used to obtain mathematical models
for calculating forces in the structural elements of the
U-2M magnetic system [5].
The force Fm acting on a moving charge q in the
magnetic field of the facility is expressed by the formula
,
c
q
m υBF
where Β is the vector of the magnetic field strength in
which the charge q moves. The force Fm
is perpendicular
to both the electron velocity υ and the vector Β, and the
magnitude of the force Fm
is proportional to the sine of the
angle between the vectors Β and υ. The value of the con-
stant c determines the system of units of measurement.
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 168
For practical assessments of the forces arising in the
structural elements of the torsatron, it is important to
take into account the electric currents in the poles of the
windings. In this case, the current created by moving
electrons with charge e and concentration n is described
by the relation υj ne .
The number of particles in the volume dV will be
VnddN , and the force Fd acting in a magnetic field
on an element of volume dV will be
.dV
c
ne
dN
c
e
d υΒυBF
After transformations
.dV
c
1
d jBF
For the calculations of the stress-strain states of the
facility, quantitative estimates of the forces are im-
portant for both volumetric (vector Vjd ) and linear ljd
current elements. If lj IddV , then
.d
c
1
d lBF (1)
Here the direction of the vector ld coincides with
the direction of the current I (Fig. 7).
Fig. 7. Vector representation of the calculation
of the forces acting on the current element
The force acting in the magnetic field of the
torsatron on the linear element of the conductor is de-
termined by integration over the entire length of the
conductor
lBF d
c
I
. (2)
The magnitude of the vector Β in relation (2) is de-
fined as
.dV
r
j
c
l
d
3
r
Β (3)
Formula (3) is valid for a volumetric current lement.
For line element
3r
d
c
I
d
lr
Β . (4)
The total field is determined by integrating expres-
sions (3) and (4) over all values of the currents
dV
r
][
c
l
3
jr
B (5)
or
.
r
]d[
c
I
3
lr
Β (6)
Relations (5) and (6) are valid for the case when di-
rect currents flow in the conductors, which is imple-
mented in the design of the U-2M torsatron.
Within the framework of the developed model, the
coordinates of the geometric centers of the four half-
poles of the screw winding are determined.
These data are used in calculating the
ponderomotive forces acting on the helical winding in
the model consideration of currents concentrated in four
current filaments corresponding to the half-poles.
Calculations of electrodynamic forces and their
components were performed on the MathCad14 plat-
form in the form shown in Fig. 8 coordinate system and
are shown in Figs. 9-14.
Fig. 8. Coordinate system. M – point belonging to the screw conductor
Fig. 9. Dependence of the component rF
on the number of the discrete element of each SW half-pole
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 169
Fig. 10. Dependence of the component F
on the number of the discrete element of each SW half-pole
Fig. 11. Dependence of the component F
on the number of the discrete element of each SW half-pole
Fig. 12. Dependence of the component zF
on the number of the discrete element of each SW half-pole
Fig. 13. Dependence of the modulus of the electrodynamic force on the number of the discrete element
of each SW half-pole
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 170
Fig. 14. Dependence of the modulus of the magnetic field induction vector on the number of the discrete element
of each SW half-pole
CONCLUSIONS
The paper presents mathematical models, methods
and algorithms for three-dimensional modeling of the
screw winding of the U-2M torsatron. The use of the
kinematic modeling method is substantiated as a basic
method of geometric modeling. To obtain the SW three-
dimensional model, a set of meridional sections of the
SW located on the torus was used as a drawing curve,
followed by the formation of a raster and the restoration
of coordinates on the simulated surface using a Bezier
spline.
Models and methods for calculating stresses and
strains arising in the elements of the magnetic system of
a screw winding under the influence of ponderomotive
forces are presented. The calculation is carried out on
the basis of the theory of electromagnetic interactions.
The performed calculations make it possible to deter-
mine the strength of the structural elements of the U-2M
installation.
REFERENCES
1. E.D. Volkov, V.A. Suprunenko, A.A. Shishkin. Stel-
larator. Kiev: “Naukova Dumka”, 1983, 310 p. (in
Russian).
2. V.M. Chernen'kiy. Imitatsionnoye modelirovaniye.
M.: “Vyssh. shk.”, 1990 (in Russian).
3. R. Gallager. Metod konechnykh elementov. Osnovy.
M.: “Mir”, 1984 (in Russian).
4. M.B. Shubin. Kompleks program formirovaniya
poverkhnostey. M.: “VTS AN SSSR”, 1979, 102 p.
(in Russian).
5. I.Ye. Irodov. Osnovnyye zakony elektro-
magnetizma. M.: “Vyssh. shk.”, 1991 (in Russian).
Article received 31.05.2021
МОДЕЛИ, МЕТОДЫ И ТЕХНОЛОГИИ РАСЧЕТА ХАРАКТЕРИСТИК ФИЗИЧЕСКОЙ
УСТАНОВКИ УРАГАН-2М
С.А. Мартынов, А.А. Лучанинов, В.П. Лукьянова, М.А. Хажмурадов, C.И. Прохорец
Рассмотрены модели, методы и алгоритмы трехмерного моделирования винтовой обмотки торсатрона
Ураган-2М. Обосновано применение метода кинематического моделирования как наиболее приемлемого
для получения твердотельной и поверхностной моделей элементов магнитной системы. Приведены методы
расчета напряжений и деформаций, возникающих в элементах магнитной системы винтовой обмотки под
воздействием пондеромоторных сил, что дает возможность определить прочность элементов конструкции
установки.
МОДЕЛІ, МЕТОДИ І ТЕХНОЛОГІЇ РОЗРАХУНКУ ХАРАКТЕРИСТИК ФІЗИЧНОЇ
УСТАНОВКИ УРАГАН-2М
С.О. Мартинов, О.О. Лучанінов, В.П. Лук'янова, М.А. Хажмурадов, С.І. Прохорець
Розглянуто моделі, методи і алгоритми тривимірного моделювання гвинтової обмотки торсатрона Ура-
ган-2М. Обґрунтовано застосування методу кінематичного моделювання як найбільш прийнятного для
отримання твердотільної і поверхневої моделей елементів магнітної системи. Наведено методи розрахунку
напружень і деформацій, що виникають в елементах магнітної системи гвинтової обмотки під впливом пон-
деромоторних сил, що дає можливість визначити міцність елементів конструкції установки.
|