# 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:

ASJ (2) / 2020

American Scientifi c Journal № ( 34) / 2 0 20 5

- 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

ASJ (2) / 2020

6 American Scientific Journal № (34) / 20 20

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;

ASJ (2) / 2020

American Scientifi c Journal № ( 34) / 2 0 20 7

- 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.

ASJ (2) / 2020

8 American Scientific Journal № (34) / 20 20

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.

References

[1] Saccocio E J 1967 Application of the dynamic

theory of X -ray diffraction to holography J. Appl. Phys.

38(10) 3994

[2] Kogelnik H 1969 Coupled wave theory of

thick hologram gratings Bell Syst. Techn. J. 48(9) 2909

[3] Liu H K et al 1976 Evaluation of a Composite

Mobile Holographic Nondestructive Test System BER

Rep. No 204 –74 (Univ. of Alabama) [4]

Liu H K and Owen R B 1979 Opt. Eng. 18

[5] Koenders L et al 2003 WGDM – 7:

Preliminary Comparison on Nanometrology Accordin g

to the rules of CCL key comparisons NANO 2 Step

height Standards

[6] Motamedi M E 2005 MOEMS: Micro – opto

– electro – mechanical systems

(Bellingham,Washington, US: SPIE Press) p 614

[7] Lyavshuk I A and Lyalikov A M 2006 Doubte

– exposure variable sh ear holographic interferometry

with controlled sensitivity Optics and Spectroscopy

101(6) 962 –6

[8] Sevrygin A A, Korotkov V I, Pulkin S A,

Venediktov V Yn and Volkov O V 2014 Digital

holographic Michelson interferometer for

nanometrology Proc. SPIE vol 9 271 (Beijing, China:

SPIE) 927118 [9] Sevrygin A A, Pulkin S A, Tursunov I M,

Venediktov D V and Venediktov V Y 2015 Digital

holographic interferometer with correction of

distortions Proc. SPIE vol 10799 (St. -Petersburg,

Russia: SPIE) 107990A

[10] Belkin E A, Poyarkov V N and

Stepanov Y S 2016 Installation of holographic control

over the process of microrelief formation Proc. Int.

Conf. Modern high -performance technologies and

equipment in mechanical engineering, MTET -2016 (St.

Petersburg, Russia)

[11] Stepanov Yu S, Belkin E A and

Barsukov G V Pat. RF No. 2215317. Profilograph /

Appied: 08.01.2002. Published:27.10.2003. Bull. 30.

[12] Belkin E A, Poyarkov V N and

Markov O I 2018 Holographic image of the surface

layer for 3D modeling. New method of non -dest ructive

testing (Saarbrücken, Germany: LAP Lambert

Academic Publishing) p 61

[13] Belkin E A, Poyarkov V N and

Markov O I 2018 Holography of the surface layer in the

visible range of electromagnetic radiation for its

geometric modeling International journa l of science,

technology and society 6(5) 72 -7

[14] Belkin E A, Poyarkov V N and

Markov O I 2019 New technologies of surface

treatment of complex shape and control over its

Geometry and topography of the microrelief

International journal of innovative stud ies and

engineering technology 5(4) 9 -16

ASJ (2) / 2020

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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American Scientifi c Journal № ( 34) / 2 0 20 7

- 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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