Американский Научный Журнал HOLOGRAPHIC DEVICES FOR 3-D CONTROL OVER A COMPLEX SURFACE SHAPE (4-8)

The analysis of the shortcomings of non-destructive testing devices over the geometric characteristics of a part of a complex shape is given. It is shown that the design features of the control device correspond to the geometric model that will be used to calculate the shaping process. The description of the holographic control installation is given. The installation of holographic control is used to determine the geometric characteristics of a complex surface shape. Based on these characteristics, a three-dimensional geometric model is constructed surface and its micro-relief. A three-dimensional geometric model of a complex surface contains information about the curvature in the local area of the selected point. The three-dimensional geometric model of the surface is structured on the basis of a modular geometric approach. A brief concept of the modular-geometric approach that is used to describe the surface geometry and its micro-relief is given. Скачать в формате PDF
4 American Scientific Journal № (34) / 20 20
ТЕХНИЧЕСКИЕ НАУКИ

УДК 7822
ГРНТИ 59.45

ГОЛОГРАФИЧЕСКИЕ ПРИБ ОРЫ 3-D КОНТР ОЛЯ НАД ПОВЕРХНОСТЬЮ СЛОЖ НОЙ
ФОРМЫ
E A Б eлкин
1,
В Н П oярк oв 1,
O И Ma ркoв 2. 1 Болховский завод полупроводниковых приборов Болхов,
K . Ma ркс a, 17 Орловская обл., г. Болхов, 303140 Россия
2Кафедра экспериментальной и теоретической физики,
Физико -Матем атический факультет,
Орловский Государственный Университет им. И.С. Тургенева,
г.Орел , 302026 Россия

HOLOGRAPHIC DEVICES FOR 3-D CONTROL OVER A COMPLEX SURFACE S HAPE
E A Belkin
1,
V N Poyarkov 1,
O I Markov 2. 1 Bolhov Plant of semiconductor devices Bol hov,
17, K. Marksa str., Oryol region, city of Bolkhov, 303140 Russia
2 Department of Experimental and Theoretical Physics,
Faculty of Physics and Mathematics,
Oryol state University. I. S. Turgenev,
95, Komsomolskaya str., Orel 302026 Russia

Аннотация . Дан а нализ недостатков приборов неразрушающего контроля над геометрическими
характеристиками детали сложной формы. Показано, что конструктивные особенности прибора контроля
соответствуют геометрической модели, которая будет применяться для расчета процесса
форм ообра зования. Дано описание установки голографического контроля. Установка голографического
контроля применяется для определения геометрических характеристик поверхности сложной формы. На
основе этих характеристик происходит построение трехмерной геом етрической модели поверхности и ее
микрорельефа. Трехмерная геометрическая модель поверхности сложной формы содержит информацию о
кривизне в локальной области выбранной точки. Трехмерная геометрическая модель поверхности
структурируется на основе модульно -геоме трического подхода. Дано краткое понятие о модульно -
гео метрическом подходе, который применяется для описания геометрии поверхности и ее микрорельефа.
Abstract. The analysis of the shortcomings of non -destructive testing devices over the geometric
cha racte ristics of a part of a complex shape is given. It is shown that the design features of the control device
correspond to the geometric model that will be used to calculate the shaping process. The description of the
holographic control installation is given. The installation of holographic control is used to determine the geometric
characteristics of a complex surface shape. Based on these characteristics, a three -dimensional geometric model is
constructed surface and its micro -relief. A three -dimensional ge ometric model of a complex surface contains
information about the curvature in the local area of the selected point. The three -dimensional geometric model of
th e surface is structured on the basis of a modular geometric approach. A brief concept of th e modular-geometric
approach that is used to describe the surface geometry and its micro -relief is given.
Ключевые слова: Установка голографического контроля, микро рельеф, поверхность сложной
формы, геометрическая трехмерная модель.
Keywords: Installation of holographic control, micro -relief, surface of complex shape, geometric three -
dimensional model.

1.I ntroduction
Non -destructive testing devices for geometric
ch aracteristics of the part surface and its microrelief
used in industrial production do not allow determining
the numerical values of parameters for constructing the
topography of the microrelief. T herefore, among the
parts that have the same roughness, the topography of
the surface microrelief may be different within a wide range. During operation, this leads to a decrease in
service life, rapid wear, changes in functional
characteristics, and a dec rease in the efficiency of
components and assemblies [1] wh ere this part is
included as a component element.
The nondestructive testing devices used have a
number of significant drawbacks:

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- probe probes examine the object -part itself and
its surface whi le interacting with it. This leads to large
errors in metro logical measurements.
- optical devices that implement methods:
interferometry, holographic immersion, etc. provide
information on the basis of which you can build a not
sufficiently complete three -dimensional geometric
model of the part [2]. In particular , this applies to parts
that have Aerohydrodynamic surfaces.
- scanning devices allow you to get an idea of the
microrelief in the local area without taking into account
the curvature of its depres sions and peaks.
- devices that control defects in the sha pe of a part
are usually highly specialized. Some of them examine
the external geometry, others internal, and others
determine internal defects. Also, the devices differ in
the ability to control t he details of the round handicap,
having flat faces, having frame discrete -defined
surfaces. There is no universal device that would allow
metrological measurements regardless of the size and
shape of the part. The structural defects of devices of nondest ructive
control is to limit their functionality. As a rule, the
design of control devices allows you to measure
numerically one -dimensional estimated parameter -the
height of the micrometer in the study of surface
roughness and fix the surface profile in a flat section.
The consequence of this is that: The calcula tion of
the forming surface of the tool does not calculate the
topography of its microrelief. This is due to the lack of
sufficient information about the geometric structure of
the microrelief as a three -dimensional image, due to the
use of a one -dimension al estimation parameter. The use
of a one -dimensional estimation parameter -the height
of the micro -area -for geometric modeling of the shape
of the microrelief gives an idea of the microrelief as a
surface with numerical marks. The description of a
surface with numeric marks does not define the
curvature in the local neighborhood of this point.
Also, the uncertainty of the surface geometry
between sections makes it impossible to build a
complete geo metric image of the surface. Thus, the
problem is that no m odern nondestructive testing
device [3], due to its design features, can make
metrological measurements necessary to build a three -
dimensional geometric model of the surface of the part,
which is a superposition of the geometric image of the
surface and th e topography of its microrelief.
This problem is relevant in the manufacture of
parts for operational properties, which, in the tribo -
conjugations of contacting surfaces, have high
requirements. T his also applies to blade machines that
operate in aggressi ve gas and liquid environments. It is
known that wear resistance, fatigue strength, and other
performance properties in tribo -stresses, as well as
cavitation wear, are determined by the geometry of the
surface and the topography of its microrelief.
The so lution is to develop a new generation of
non- destructive testing devices.
These devices will make it possible to make
metrological measurements necessary for applying the
modular -geometric approac h in structuring a three -
dimensional geometric model of the surface. 2. Modular
-geometric approach to modeling a
complex surface shape
Extensive theoretical and experimental material
accumulated in the field of creating new types of
abrasive tools has ca used a new wave of development
of abrasive processing in pr oduction [4]. This allowed
us to get broader generalizations.
Shaping is the goal of the abrasive and blade
processing process.
The main objectives of the shaping theory are to
design the tool an d determine the kinematics of the
"part -tool" system based on the specified geometry of
the surface of the processed part. The inverse problem
of the theory is to calculate the forming surf ace of the
part based on the known geometry of the tool and the
kin ematics of the "part –tool" system.
The success of solving these complex problems
and the development of this area of research depend on
the applied mathematical methods [5].
Classification of complex -shaped surfaces cannot
be constructed. There are no co mmon features in the
surface structure. The surface of a complex shape is
structured on the basis of the modular principle. The
structuring approach is determined by the proble ms of
the theory of shaping. The modular -geometric
approach used to solve these problems is to
approximate the local area of the surface with a
contiguous paraboloid. The Riemann -Christoffel tensor
is a geometric characteristic for estimating the
curvature of a local section. The analytical definition of
a contiguous paraboloid as a s econd-order geometric
image of contact with a given local area of the surface
is determined from the Taylor series expansion. The
Taylor series defines the geometric images of a higher
order of contact: coboloid, quadronoid etc.
In technical applications, you should limit
yourself to approximating the local area with a
contiguous paraboloid. Since the curvature of the
surface at the point of contact is equal to the curvature
of the touching paraboloid.
Discretely defined surface of the workpiece, in
Gener al, can be approximated by a set of modules that
have a smooth "cross -linking". Each module is a
contiguous paraboloid of a certain type.
It is established that the modular pr inciple used to
describe the geometry of frame discrete -defined
surfaces can be taken as the basis for structuring the
surface microrelief.
When constructing a model that describes the
micro -relief of a surface, the modular principle of
structuring a comp lex-shaped surface is used to solve
the problems of smooth "cross -linking" of in dividual
modules. A system of criteria for quantifying the
topography of the microrelief is defined: k1, k2 – the
main curvature of the surface, Rz -the height of the
micro -irre gularity. Experimentally confirmed the
theoretically justified hypothesis about the information
completeness of the system of criteria for topography
of the microrelief. The geometric model of a microrelief is a set of
modules that have a smooth "cross -linking" -
contiguous paraboloids. Three -dimensional geometric
models of the micro relief of surfaces considered in the
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theory of shaping have been developed: flat, round
cylindrical, discrete -defined frame and irregular -
shaped bodies.
Developed a simulation model of microrelief flat
surface depending on the processing modes [6], for
ex ample, flat grinding, which takes into account the
changing topography of the surface microrelief of the
workpiece depending on the angular speed of rotation
of the circle, the speed of part motion, from the time of
processing and the depth of grinding.
T he proposed geometric model of abrasive
processing (the case of flat grinding) takes into account
the actual location and geometric shape of the abrasive
grains on the surface of the circle, the depth and width
of the groove from the grains, the overlap of the
grooves during grinding, as well as the real topography
of the microrelief of the surface planes of the part.
3. Devices for monitoring the characteristics of
the geometr y and topography of the surface
microrelief
3.1. Probe control devices
In prob e control devices (profilographs,
profilometers), a needle is used as a probe that is driven
in translational motion in the plane selected for
determining the microrelief profi le. The needle axis is
oriented normal to the surface [8]. The mechanical
vibrat ions of the needle are converted into electrical
vibrations. The profilogram is displayed as a curve.
Disadvantages of probe control devices:
1. The probe -diamond needle inte racts with the
studied surface, i.e. it deforms its microrelief. This is
usually true for parts made of plastic materials. When
the needle interacts with the micro -relief of the surface,
the surface of the needle itself changes, which leads to
an increase in electronic noise.
2. The needle usually has a radius of 2 microns.
The final size of the needle allows you to accurately
determine the profile of the microrelief for sufficiently
far -spaced micro -surfaces or slightly wavy surfaces.
3. The resolution o f the probe devices depends on
the radius of the needle rounding and the nature of the
surface topography, i.e. on the geometric
characteristics of the sensor examining the surface
microrelief and the geometric characteristics of the
object under study -the microrelief.
4. Low accuracy of measurements along the micro
furrows of the sur face layer of the part.
5. A large time interval to remove the maps
necessary for structuring the topography of the
microrelief in the framework of a modular geometric
approach .
3.2. Optical control devices
In interferometers (Twyman -green, Fizo,
Nomarsk y, etc.), the quality of surface treatment is
analyzed on the basis of the obtained interference
pattern [9].
Disadvantages of optical control devices:
1. The multibeam inter ferometer of bands of equal
chromatic order gives a relief picture averaged over
sites with a linear size of about 2 microns.
2. The optical heterodyne Profiler has an
insufficient horizontal resolution of about 2 microns. 3. A two
-beam polarizing interf erometer that
implements the differential interference contrast
method does not allow quantitative measurements
without digital signal processing.
4. The geometric characteristics of the surface
recorded by the interferometer depend significantly on
the o ptical properties of the object: its absorption
coefficient, reflection, etc.
5 . None of the currently used interferometers
provides complete information on the geometric
characteristics of the surface, which is necessary for
structuring the topography of its microrelief.
3.3. Electronic and probing microscopes
The principle of ope ration of a transmission or
raster electron microscope is similar to that of an optical
microscope. The difference is that instead of a stream
of electromagnetic waves in the visible frequency range
falling on the object under study, an electron
microscope uses a stream of electrons [10]. The design
of an electron microscope for controlling the electron
beam includes magnetic lenses, and for receiving the
electron beam - a cathode -a tungsten filament or a
pointed crystal of lanthanum hex aboride.
Disadvanta ges of the electron microscope:
1. An electronic microscope is a device for
monitoring the micro -relief of local areas. Despite the
high resolution, the electron microscope is not suitable
for evaluating the microrelief of a complex sh ape
surface in the r ange of 1 – 0.001 microns for the entire
internal and external geometry of the part.
2. The maximum frame size does not exceed
100x100mkm, which is not enough to make a part.
3. The electron microscope does not provide
information on the geometric charac teristics of the
surface necessary for structuring the topography of its
microrelief.
In scanning probe microscopes, the micro -relief of
the surface and its local properties are studied using
special probes. The working part of such probes is
about 10 nm in size. The distance between the probe
and the sample surface in order of magnitude i s 0.1-10
nm. Probe microscopes are based on various types of
interaction between the probe and the surface. Thus, the
operation of a tunnel microscope is based on the
phe nomenon of a tunnel current flowing between a
metal needle and a conductive sample. Va rious types of
force interaction are the basis for the operation of
atomic force, magnetic force, and electro -force
microscopes.
The disadvantages of scanning probe
mic roscopes are the same as those of an electron
microscope. To this list, it should be a dded that the
recorded characteristics depend on the electromagnetic
properties of the test sample [11].
3.4. Installation of 3D holographic control
Installation of 3D h olographic size control of
complex mechanical engineering parts (hereinafter
referred to as UGC) provides:
- state -of -the -art control of dimensions of
machine -building parts of complex shapes and profiles;
- displaying the actual configuration of the part
(visualization); - preparing data for archiving
measurement results;
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- possibility of layer -by -layer "penetration" into
the material of the part (Assembly) with control of the
size of hidden elements, cavities (subdetals and
subassemblies). UGC solves the following tasks for
enterprises:
- creating a methodological, scientific, technical
a nd technological base for high -precision automated
size control of complex machine parts;
- creation tool for high -precision automated
control of the dimensions of geomet rically
- complex parts of mechanical engineering.
- providing conditions for mass pro duction of
high -precision mechanical engineering products with
import substitution of components;
- ensuring technological and technical priority;
- development of innova tive industrial
technologies for creating promising types of weapons,
military and spe cial equipment;
- creating a pilot prototype, ready to scale in the
enterprises of mechanical engineering.
UGC is a complex of systems that include laser,
optical, Elec tromechanical and microprocessor
subsystems. The operation of these systems under the
control of the controller allows for high -precision
holographic 3D control of complex profile parts up to
2000 mm×500 mm×1000 mm with an error of no more
than 800 nanomet ers when working in the visible range
(Fig.1) and an error of no more than 50 nanomete rs
when working in the x -ray range.
UGC implements technological processes that
have a scientific and technological novelty, allowing to
find a market application and en sure the creation or manufacture of products with a new quality and a high
level of ef ficiency.
The development of the UGC is based on
theoretical and experimentally based methods of
modular -geometric modeling of the formation of the
surface microrelief [ 12], allowing them to develop and
manufacture devices for non -destructive testing of t he
surface microrelief of parts with errors specified in the
nano -range. Such devices are an optical Profiler for
passive control and an x -ray Profiler for active control .
The first device allows you to create maps with a
holographic image of an object in the optical frequency
range of electromagnetic waves for structuring a
modular geometric model (MGM) of an object [13],
such as the pen of a gas turbine blade and the
to pography of its microrelief, before and after
processing. The three -dimensional model of the blade
pen is a smooth cross -linking of contiguous paraboloids
of various types. A model of the topography of the
blade's microrelief (Fig.2) is also constructed ba sed on
the modular -geometric approach. The blade pen model
and the topography model of its microrelief represent a
superposition: a microrelief model is located on the top
of the pen.
The second device -allows you to control the
characteristics, for exampl e, the geometry of the blade
pen and the topography of its microrelief during
processi ng [14]. This device can be included in a
feedback control system that allows you to change the
parameters of the tool installation to obtain the desired
characteristics.


Fig.1 - Holographic image micro -relief's. Fig.2 - 3D model of the micro -relief.
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4. Conclusion
Devices of the developed series belong to the
devices of the new generation. Their device implements
one of the ways to expand the functionality of
moni toring de vices and use the information obtained
with their help to build three -dimensional models -the
study of a holographic image, rather than the physical
object itself. Develop non -destructive testing devices
have the best performance compared to the pr ototypes.
They allow us to evaluate the geometry and micro -
relief of the surface on the basis of three -dimensional
geometric models with errors specified in the specified
nanointervals.
The passive control Profiler in the optical
frequency range of electr omagnetic waves allows you
to take maps from a holographic image of an object to
structure the modular geometric model of the blade pen
and the topography of its microrelief, before and after
processing. The three -dimensional model of the blade
pen is a sm ooth cross-linking of contiguous paraboloids
of various types. The topography model of the blade's
microrelief is also based on a modular geometric
approach. The blade pen model and the topography
model of its microrelief represent a superposition: a
micro relief mo del is located on the surface of the pen.
X -ray active control allows you to control the
characteristics of the blade pen geometry and
topography of the microrelief during processing. This
device can be included in a feedback control system
that allows you to change the parameters of the tool
inst allation to obtain the desired characteristics.
High -precision control of complex profile parts is
required in the implementation of industrial production
of modern mechanical engineering products: preci sion
mechanics, dies, spindles, ballscrews, lunettes , carbide
tools in machine tools; animating parts, cumulative
craters of warheads, gyroscopes, rudders, etc. in the
production of projectiles and missiles; turbine blades in
pumps, turbopump units, and ot her similar elements.
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