Thermal Monitoring for Condition Based Maintenance of an X-ray Generator

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PoS(BPU11)270
Thermal Monitoring for Condition Based Maintenance
of an X-ray Generator
Plamen V. Petkov,𝑎,†Anton Zyapkov,𝑎,∗Nedislav Veselinov,𝑎Kaloyan Genkov,𝑎
Dimitar Todorov𝑏and Nikolay Zografov𝑎,𝑏
𝑎Faculty of Physics, Sofia University "St. Kliment Ohridski",
5 James Bourchier Blvd, 1164 Sofia, Bulgaria
𝑏Danlex EOOD Research center,
430 Tsar Boris III Blvd, 1619 Sofia, Bulgaria
E-mail: pvpetkov@phys.uni-sofia.bg,azjapkov@uni-sofia.bg,
nveselinov@phys.uni-sofia.bg,kgenkov@uni-sofia.bg,
dimitar.todorov@danlex.bg,nikolay.zografov@danlex.bg
The modern Non-Intrusive Inspection Systems (NIIS) are the backbone of air transportation
security. The commercial aviation is impossible without them. Real-time evaluation of the NIIS
technical condition is critical for the airport operators. Most of the operated worldwide NIIS
were designed before the Internet of Things (IoT) era, and they don’t have the options to provide
real-time monitoring of their operational status. The examined X-ray generator, one of the most
common types, is equipped with a stationary anode X-ray tube, mounted on an HS 100100V
(Smiths Heimann Gmbh). The X-ray tube is immersed in cooling oil bath and encapsulated in
stainless steel hull. The set of installed sensors consists of contact sensor arrays combined with a
distant infrared sensors system for mapping the outer surface X-ray generator temperature profile.
Real-live operational conditions were simulated to study steady-state thermal characteristics. Two
indicators for normal operation with sufficient conservatism were selected for suitable monitoring
of the operability of X-ray generator: the maximal allowed oil volume expansion and maximal
long-term temperature at the inner oil volume boundary. They were estimated by the reported in
this paper analytical 1-D thermal model after measurement of the outer hull’s surface temperature.
As a results, we distinguished four modes of X-ray generator operation: (1): ’normal operation;’
(2): ’slow degradation;’ (3): ’faster degradation;’ and (4): ’failure.’ The maximal temperatures
on the hull’s outer surface were estimated for each mode as follows: (1): 10 . . . 51◦𝐶, (2):
51 . . . 80◦𝐶, (3): 80 . . . 87◦𝐶. The failure can take place at temperatures above 87◦𝐶. We found
that the ’normal operation’ mode could be extended up to 60◦𝐶due to oil thermal expansion.
ArXiv ePrint:1234.5678
11th International Conference of the Balkan Physical Union (BPU11),
28 August - 1 September 2022
Belgrade, Serbia
∗Speaker
†Corresponding author
©Copyright owned by the author(s) under the terms of the Creative Commons
Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/

PoS(BPU11)270
Thermal Monitoring for Condition Based Maintenance of an X-ray Generator Anton Zyapkov
1. Introduction
The modern Non-Intrusive Inspection Systems (NIIS) are complicated machines that rely
on X-ray generation and provide detection capabilities, supported by state-of-the-art electronics,
electro-mechanics, software algorithms and solutions. They are the backbone of air transportation
security. Currently, the commercial aviation is impossible without NIIS. Thus, the adequate real-
time evaluation of the NIIS technical condition is critical for any airport smooth operation. However,
most of the NIIS operated worldwide are designed before the Internet of Things (IoT) era, and they
don’t have the capabilities to provide information in real-time about their technical status. A solution
for condition-based and predictive maintenance, developing recently (Predictive Maintenance Tool
for NIIS – PMT4NIIS), aims to provide an early warning for possible failures, based on predictive
algorithms using machine learning and Artificial Intelligence (AI) technologies [1]. That solution
relies strongly on the technical data collected from the NIIS itself, along with retrofitted sensors,
designed to monitor different physical and environmental parameters [2].
The X-ray generator is a major component in the NIIS system and is an all-electric system.
The performance of this system is relatively easily controlled by a few electrical parameters.
There is enough research, related to the aging of the elemental base to predict changes in its
condition. Therefore, our research activity is dedicated to the reliability of the entire system, which
is determined by the most critical component inside the generator: X-ray tube (Figure 1). The
tube is the main X-ray generating component that functions in severe thermal conditions under
which its structural materials are subjected to severe stresses. It is the failures of the X-ray tube
that are the most costly in the process of operating the equipment. Therefore, the efforts of the
current analysis are dedicated to monitoring of the X-ray generator normal operation conditions and
prediction the thermal status of its X-ray tube. Chapter two outlines specific issues, related to overall
X-ray generator design. The developed experimental approach and its practical implementation are
presented in chapter three. Here is given overall information about our thermal monitoring system,
which includes contact thermometers, attached to the X-ray generator surface as well as infrared
(IR) cameras (sensors), used for distant temperature monitoring. In the same chapter is reported
study on the IR sensors signal attenuation depending on the distance from the measured surface.
The experimental data and theoretical analysis are given in chapter four. The discussion of the
results is provided in chapter five and finally the conclusions, based on the current study are given
in chapter six.
2. X-ray generator working conditions and energy transfer paths
Figure 1 shows schematics of the X-ray tube, respectively. The electrons are generated by the
tungsten wire (cathode in Figure 1, called emitter or filament), which is heated to a temperature
above 2000◦𝐶, with the maximum permissible temperature being limited to 2700◦𝐶. If the voltage
between the cathode and the anode is 𝑈, Vand the current through the tube anode and cathode
is 𝐼, A, then each electron will reach the anode with a kinetic energy of 𝑈, eV. The total energy
deposited on the anode is 𝜔𝑈𝐼𝑡, where 𝜔is a wave weighting factor to account for the rms value of
the generator voltage, [3]. The weighting factor is related to the X-ray generation mode and takes
the values 0.71 for one and two-pulse generators, 0.96 for six-pulse generators and 0.99 for 9-pulse
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generators, respectively, [4]. Practically, this is all the energy generated by the electronic circuit
(X-ray generator) without taking into account the losses in the circuit itself. In the prototype, used
in current analysis, the X-ray tube is developed by Svetlana-Rentgen [5] type No. 0,32BPM 25-160,
design which is widely used.
Figure 1: General outline of a X-ray generator
In general, the resulting X-rays takes only 1% of the released energy. The remaining 99% is
released in the anode, made by pure copper after the electrons hit thetarget, a designated region,
called focal spot, made by the implanted tungsten in the anode (see Figure 1). The generated X-rays
depends mainly on the properties of the filament of the cathode, which in our case is made by
tungsten and have a peak at about 60 MeV. The peak is characteristic to this material, [3]. The
cathode potential difference (heating voltage) varies up to 4.2 V, and the heating current is up to
4.4 A DC. The electrons generated by the filament are accelerated under the action of a potential
difference varying for different devices. For HS 100100V (HI-SCAN 6040 aX/aTiX) type systems,
[6], it is around 160 kV. From the entire photon spectrum, only photons with energies from 50
to 70 keV are used for imaging, while the remaining ones are being absorbed by the biological
shielding of the generator, made by lead, tightened to the outer surface of the hull by five belts
(see Figure 3a). Since the photons carry a minimal amount of the released energy, it is not taken
into account and ignored in the current model. In this case, it is very important to account for the
heating of the focal spot target of the anode due to the deposited energy from the electron beam.
The key characteristic factor of the X-ray generator "lifetime" is the temperature of the anode target.
In the case of the current NIIS investigation, the melting temperature of the tungsten focal spot is
3410◦𝐶. The entire system is placed in an oil bath, where the oil is designated to cool the system
during normal operation (Figure 1). Therefore, the produced amount of heat undergoes dissipation
in the oil bath in which the X-ray tube is immersed. This way, the X-ray tube is cooled. During the
normal operation of the equipment, the "focal spot" can reach values up to 2500◦𝐶. The maximum
permissible temperature of its heating without damage is 2757◦𝐶. The anode is made of copper
(which melting temperature is about 1336◦𝐶). Its temperature during the normal operation can
reach up to 1000◦𝐶. The energy, released in the focal spot is produced in the form of heat that further
is transported from the anode to the cooling radiator, where it is removed by the oil to the outer
surface of X-ray generator [8]. The X-ray generator is sealed, and no information could be obtained
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of its cooling status during the normal operation. Therefore, the physical and chemical properties
of the oil, used in X-ray generators should obey the strict requirements of several standards, listed
in Refs. [8,9,10]: It must contain no water, water-soluble acids, alkali and particulate matter.
The total acidity should be below 1.2 mgKOH/kg, [10]. The dielectric strength of this type of
oil depends on the electrons accelerating voltage operation range. In the currently investigated
machine, it is required to be within 40 kV to 65 kV, [8]. The temperature ranges of oil operation are
deduced from the analysis, made in Refs. [9,10]: Normally, the oil should be operated within the
range of 10 ◦Cto 80 ◦C, [6,10]. In the range from 80 ◦Cto 250 ◦C, for long term operation, stray
gases (such as ethane and hydrogen) formation could be observed and finally 300◦𝐶is defined as
operational limit, Ref. [10], which could vary depending of the dielectric oil boiling point.
This imaging system belongs to so called "fixed target X-ray generators" that are designed to
operate in a relatively low power mode due to the temperature limitations imposed on the materials
used, [7,4,3].
3. Experimental approach
In the present study, we propose a thermal monitoring approach as a new source of valuable
data for estimating the X-ray generator’s technical condition and input to the predictive models.
The study provides both analytical and experimental data. The proposed analytical model has
been extended with the experimental results, based on the large data-sets (big-data), collected by
appropriate sensors.
The thermal parameters of the x-ray generator were studied during numerous long tests run
series conducted on HS 100100V, located at the Danlex research center. This X-ray generator type
is widely implemented on similar X-ray security inspection systems for luggage and cargo. To reach
a steady state of the x-ray generator thermal status, most of the respective test runs have lasted more
than 24 hours of continuous workload (X-ray beaming), simulating real operating conditions.
The experimental setup consists of contact sensor arrays combined with a distant infrared
sensors system, in order to provide the temperature mapping of the hull’s entire outer surface of
the X-ray generator. These data are used for generation of boundary conditions for the thermal
analytical model.
3.1 Installation of contact thermometers
The contact measurement of the X-ray generator surface temperature is performed by 35 digital
temperature sensors of DS18B20 type (working in the range from −55 ◦to 125 ◦) with precision
of ±0.5◦𝐶. They were mounted in specially made wooden fixtures, whose purpose was to attach
them securely to certain points on the hull’s outer surface (see Figure 2a), [11]. The locations of
the sensor fixtures were aligned with the parts of the volume of the hull of greatest interest to the
research team. The distribution of sensors was performed as follows: Along the length of the X-ray
axis, nine sensors were placed in a row (line), Figure 3a. An exception is the area around X-ray
beam radiation flux shield: Because of the impossibility to place thermometers there, only five
sensors were considered. This way, four lines are formed (see Figure 2a). Each line is assigned one
letter of the Latin alphabet, starting from left to right. After the letter there is a number that indicates
the cross-sectional position of the sensor. All equal numbers are aligned to form a X-ray generator
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cross-section. During the mounting, there was avoided placing a sensor on the belts holding the
X-ray generator’s shield (see Figure 3a). The further measurement with IR sensors reveals that the
temperature drops at these zones due to the improved cooling, see Figure 7. Separately, seven more
(a) Crossectional distribution of contact thermometers
(b) Determination of IR sensors optimal position
Figure 2: Schematic presentation of IR and contact thermometers mounting schemes
sensors in a series, denoted as T1. . . T7, were installed in the NIIS volume at various points of
specific interest. They measure the temperature inside the body of the testing machine (HI-SCAN
6040 aX/aTiX). As a result, two sets of temperatures are formed in the NIIS housing, see Figure 3b:
(a) temperatures in the immediate vicinity of the X-ray generator, T1. . . T5; (b) ambient, inside
the machine temperatures, T6 and T7. Once the machine entered a stationary operating mode
(NO, Figure 6), the temperature values became very stable and no significant difference between
statistically measured temperatures by the two sets is detected. They exhibit little deviations in their
nominal values at different external environmental conditions, around NIIS. Generally, it was found
no significant variations in T1-T7 measurement (see Table 1) once the machine entered stationary
mode of operation.
3.2 Infrared sensors characterization
After performance of the positional analysis of the available space in the HS 100100V machine,
there were identified possible positions for mounting of IR sensors. We installed four tiny IR
cameras, MLX90640 — BA with silicon made lens and thermopile array sensors. Further in the
text, we designate to them numbers from S1 to S4. The 32 ×24 px. array sensor uses a 100 𝜇m
pixel technology. It offers very good performance for applications that do not require images with
high-resolution or a high rate of frames, which means that they cannot provide reliable results in
transient conditions. Silicon optics is operating in the 1.2𝜇mto 7𝜇mwavelength range. The
lenses are mounted such a way to guarantee Field of View (FOV) 55◦[12,13]. According to the
specification, their operational range is from −40 ◦Cto 200 ◦Cwith precision of ±2.0◦𝐶. The
resolution of their matrix is 32 ×24 px., [12]. Image detection angle varies from 32 ◦to 55 ◦
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and it is established according to the IR sensors characteristics and the X-ray machine capabilities
to support a suitable structure for sensors holding, [12]. The optimal distance for their position
is identified to lie between the points AB in Figure 2b. Using the software LibreCad, [14], an
analysis was performed for evaluation of the possible positions of the infrared sensors in which
the resolution angle of 55◦is ensured. Geometrically, there was found that optimal distance varies
between 𝑥𝑚𝑖𝑛 =64 mm and 𝑥𝑚𝑎𝑥 =140 mm.Figure 2b shows our preliminary geometric study to
determine the optimal position of the sensors. It can be seen that if placed 140 mm normally to
the surface of the generator at position B, (𝑥𝑚𝑎 𝑥 ), the infrared camera will cover a range from
140 mm to 176 mm due to the surface curvature. In the second position A, the distance to the
sensors will vary from 64 mm to 106 mm, see Figure 2b. If the IR camera (sensor) is very close to
the surface, it will cover a smaller part from the outer the X-ray generator hull’s surface and part
of the environment, which will lead to a potential degradation of the measurement accuracy, [12].
As the distance from the X-ray generator increases, the IR cameras resolution decreases and the
temperature readings may significantly deviate from the real values (see further in the text). After
IR sensors installed at the selected positions around X-ray generator, the emissivity was selected
also 0.95, according to the measured surface of X-ray generator and the vendor specifications. The
(a) Picture with contact thermometers distribution at
X-ray generator surface. In the picture are seen sensors
𝐶1. . . 𝐶 9and 𝐷4, 𝐷5, 𝐷1. . . 𝐷3.
(b) Positional placement of IR sensors. In the picture are
seen the sensors S2 and S4. The two others are positioned
symmetrically to them on the other side of X-ray generator
Figure 3: Schematic presentation of IR and contact thermometers installation.
assessment of the resolution of the IR sensors was carried out as follows: In laboratory conditions, a
hot-tip solder was placed in front of the camera at various fixed distances, see Figure 4 and Figure 5.
The obtained sequence of images is used further for determination of the spatial sensitivity of the
IR sensors. The results show a decrease of the camera resolution with an increase of the distance.
Based on the measurements at different distances, an empirical relation was found for prediction of
the measured surface temperature with accounting the signal attenuation (Figure 5), as follows:
𝑇𝑚𝑎𝑥 =𝐴ln 𝑥+𝐵(1)
Where 𝐴and 𝐵are empirical constants, characterizing the particular temperature field. The
attenuation effect of the entire measurement channel follows logarithmic law. For temperatures up
to 110 ◦C, we obtained: 𝐴=−22.95 and 𝐵=152.73 where the distance is given in cm. Further
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Figure 4: Detected temperature by IR sensors at different distances, where 𝑑1. . . 𝑑8denote distances from
the hot-tip solder
investigation indicate that for lower temperatures, not using Equation 1 for surface temperature
restoring will bring little distortion of te measurement accuracy. At a distance greater than 20 cm,
Figure 5: Measured constant temperature by IR sensors at different distances (note that numbers in the figure
correspond to the numbers in Figure 4 )
the measured temperature is hardly distinguished from the background temperature. The optimal
measurement distance is determined to be about 14 cm from the observed object.
From Figure 3b is seen that due to the limited space, there cannot be installed IR cameras
pointing to the surface of the X-ray generator from the the X-ray machine outer edge (the side of
contact sensors 𝐶1. . . 𝐶9,Figure 3a). The X-ray beam and its shielding also divide the generator
housing in two distinguished parts suitable for optical observation, Figure 3. For these reasons, four
cameras were installed at the inner side of the generator to cover its surfaces pointing inside the
X-ray machine. Each IR camera is numbered. In Figure 3b, there are shown only IR cameras S2
and S4. The other two IR cameras are placed symmetrically on the other side of X-ray generator,
noted correspondingly S3 and S1. All IR sensors were mounted at 140 mm from generator surface
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to avoid distorted data from the pixels at the IR cameras edges, because of the lower precision
±3.0◦𝐶, as specified b the vendor, [12]. With calibration sets, developed for the purpose of the
analysis, we found that the distance between two pixels is v:h = 8:6 mm in average. Further, during
the measurement from S1 and S4 we could not obtain reliable data and it was found that only results
from S2 and S3 are sufficient to provide information about the temperature field at the inner X-ray
generator surface.
4. Analytical solution
During the operation of X-ray machine, the following three modes can be distinguished: start-
up procedure (SU), normal operation (NO) and shut-down (SD) modes, (see Figure 6). Two of the
regimes (SU and SD) are non-stationary and a change as a function of the time of the measured
temperature values is denoted. Since the most important for long term operation are stationary
modes (NO), the investigation is limited to study only of these regimes. In this case, the system
is fully loaded. Therefore, as the time independence of measured temperatures takes place, the
statistical approach is suitable for further data analysis. Figure 7 shows the typical loading scheme
of the testing machine at the Danlex research center, that imitates the real loading at the airport
operation. Two sets of regimes are shown: SU-1, NO-1, SD-1 which continues longer in the time
and shorter: SU-2, NO-2, SD-2. After the statistical analysis performance of all NO regimes, no
significant deviation in estimated outer hull’s (boundary) surface temperatures is obtained. It also
was found that these temperatures maintain the same stable average values at different environmental
condition. Note that in Figure 6 the maximal steady state values of outer surface temperature do
not exceed 49.8±5.5◦𝐶Although there could be developed analytically solvable theoretical model
in three dimensions involving heat conduction and convection heat transfer, practical problems,
related to the suitable description of the temperature field inside the generator for the purpose of
PMT4NIIS arise. Because of this, an one-dimensional model for heat conduction, for finding the
distribution of the temperature field inside the oil volume in two dimensions, was implemented
(see Equation 2). Such assumption is not entirely correct, because inside the volume not only
heat conduction but also convective heat transfer takes place, [15]. However, based on the results,
published in [16], the heat conduction model can be extended with an effective heat conduction
coefficient, 𝜆𝑒 𝑓 𝑓 which accounts not only the conductive but also the convective part of the heat
removal process, [17]. Further, we propose the usage two-layer model, where outer X-ray generator
stainless steel huff (outer shell) holds the inner oil volume, that fills the entire space, surrounding
X-ray tube. At the center of these cylinders is assumed an inner heated cylindrical surface, 𝑇𝑖, as
seen in Figure 8. For simplicity, we assume that the diameter of this surface is equal to the X-ray
tube outer diameter, because (as mentioned in section 2), it is considered to be the most critical
component for the X-ray generator operation.
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Figure 6: Three modes differentiated during the operation of X-ray machine: startup (SU), normal opera-
tion(NO), shutdown (SD). The plot presents two full operations 1:SU-NO-SD, 2:SU-NO-SD. The obtained
data from IR sensors are compared with the nearest to them contact sensors: correspondingly D4 with S3
and D2 with S2
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(a) Obtained data from sensor S2. (b) Obtained data from sensor S3.
Figure 7: Three dimensional representation of measured temperature at the X-ray generator outer surface.
Note the temperature falls due to improved cooling at the holding shields belts
4.1 Formulation of the equations
Based on the assumptions, presented above, the equation for heat conduction for stationary
case is applicable as follows:
𝑟𝑑2𝑇
𝑑𝑟2+𝑑𝑇
𝑑𝑟
=0(2a)
1
𝑟
𝑑
𝑑𝑟 𝑟¯
𝜆𝑜(𝜙, 𝑟 )𝑑𝑇
𝑑𝑟 =0(2b)
where ¯
𝜆𝑜(𝜙, 𝑟 )≡𝜆𝑒 𝑓 𝑓 is the effective heat transfer coefficient that in general is not constant (𝜙and
𝑟are correspondingly angular and radial coordinates). However, for simplicity and due to the fact
that temperature gradient during normal operation are not very high, we can assume it constant and
denote further as 𝜆0. Therefore, Equation 2a describes stainless steel wall stationary heat transfer,
while Equation 2b represents the oil volume heat transfer.
4.2 Boundary conditions
The boundary conditions at the outer surface of the X-ray generator wall are defined as follows:
The first condition, Equation 3a describes the temperature at the surface, which is expected to be
measured by contact thermometers and IR sensors, while the second Equation 3b is estimating the
heat transfer governed by the temperature difference between the surface and the surrounding air.
𝑇𝑜𝑢𝑡 |𝑟𝑤−𝛿=𝑇𝑜𝑢𝑡 |𝑟𝑤+𝛿≡𝑓(𝑠)(3a)
−𝜆𝑤
𝑑𝑇
𝑑𝑟 𝑟𝑤−𝛿
=𝛼𝑜𝑢𝑡 (𝑇𝑜𝑢𝑡 −¯
𝑇𝑎𝑖𝑟 )=𝛼𝑜𝑢𝑡 (𝑓(𝑠) − ¯
𝑇𝑎𝑖𝑟 )(3b)
where 𝑇𝑜𝑢𝑡 =𝑓(𝑠)indicates the surface temperature, obtained by the measurement system. The
internal boundary conditions represent the temperature continuity at the oil/stainless steel boundary,
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Figure 8: Schematic presentation of the modelling zone crosseton, where 𝑟𝑖is the assumed outer radius of
X-ray tube, equal to the anode radius; 𝑟𝑜is the internal radius of stainless steel hull; 𝑟𝑤is the outer radius of
X-ray generator.
Equation 3b as well as the heat flux transfer, Equation 4b:
𝑇𝑜|𝑟𝑜−𝛿=𝑇𝑤|𝑟𝑜+𝛿(4a)
−𝜆𝑜
𝑑𝑇
𝑑𝑟 𝑟𝑜−𝛿
=−𝜆𝑤
𝑑𝑇
𝑑𝑟 𝑟𝑜−𝛿
(4b)
In order to calculate correctly the boundary conditions, it is necessary to know the coefficient
of heat transfer from the wall to the environmental air. Its determination is very difficult and is
based mostly on empirical relations. In our case, the most suitably is to use the Nusselt number:
𝑁𝑢 =2𝑟𝑤𝛼𝑜𝑢𝑡
𝜆𝑤, where 2𝑟𝑤is the outer diameter of the horizontal cylinder and the other quantities
are explained in Table 1. For horizontal cylinder, the following relation can be used in cases of
operation: 𝑁𝑢 =0.481 +0.172 ×exp −0.258𝑊
2𝑟𝑤×𝑅𝑎0.2, where W is the length of the horizontal
cylinder. The number 𝑅𝑎 =𝑔 𝛽 (𝑇𝑜𝑢𝑡 −𝑇𝑎𝑖𝑟 )8𝑟3
𝑤
𝜈2𝑃𝑟 is the Raleigh number. For the air are valid the
following data: compressibility is 𝛽=3.25 ×10−3, kinematic viscosity is 𝜈=16.5×10−6m2s−1,
𝑃𝑟 =0.7. [18][19]. During the normal operation (NO), the regime is very stable, then the applied
constant value for heat transfer coefficient is given in Table 1.
4.3 Solution of the equations
The provided Equation 2 can be solved analytically for the given boundary conditions. There-
fore, the solution is obtained for the solid wall region:
𝑇=𝑟𝑜𝛼𝑜𝑢𝑡
𝜆𝑤𝑓(𝑠)−¯
𝑇𝑎𝑖𝑟 ln 𝑟𝑜
𝑟+𝑓(𝑠)(5)
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Parameter Description Value
𝜆𝑜,[W m−1K−1]Oil heat transfer coefficient 0.3714
𝜆𝑤,[W m−1K−1]Wall heat transfer coefficient 52.0000
¯
𝑇𝑎𝑖𝑟 ,[𝐾(◦𝐶) ] Air bulk temperature 318(45)
𝑟𝑤,[mm]Internal wall radius 95.00
𝑟𝑜𝑢𝑡 ,[mm]Outer wall radius 105.00
𝑟𝑖,[mm]Equivalent X-ray tube outer radius (anode) 10.00
𝑎𝑜𝑢𝑡 ,[W m−2K−1]wall outer air heat transfer coefficient 7.9000
Table 1: The main parameters description and the assigned values used in calculations
The solution for the equation in the oil region is:
𝑇=𝑟𝑜𝛼𝑜𝑢𝑡
𝜆𝑜𝑓(𝑠)−¯
𝑇𝑎𝑖𝑟 ln 𝑟𝑤
𝑟+𝑟𝑜𝛼𝑜𝑢𝑡
𝜆𝑤𝑓(𝑠)−¯
𝑇𝑎𝑖𝑟 ln 𝑟𝑜
𝑟𝑤
+𝑓(𝑠)(6)
Equation 5 and Equation 6, are suitable for the finding of the temperature field at the desired X-ray
generator crossection. The heating source is at the inner boundary with radius 𝑟𝑖, with value defined
in Table 1. It is assumed to be equal to the radius of X-ray tube anode (see Figure 8).
5. Data analysis and discussion
Although the analytical solution was obtained, the following problems arose, related to the
practical implementation: (1) The IR cameras can not capture the full temperature field of the outer
surface. This happened due to the limited space available in the test machine that we used (this
possibly could be a general problem). (2) Contact thermometers are quite limited in number. In
this particular case interpolation of the resulting values is necessary in order to be generated the
temperature field at the surface. Given these two factors, the proposed two-layer one dimensional
analytical model, applied along axial direction to each cross-section, proved itself to be suitable
tool for thermal analysis of X-ray generator body.
The steady-state equation was defined in a cylindrical geometry, because the generator itself is
a horizontal cylinder (Figure 3a), where the oil volume forms an annulus with heated inner surface,
Figure 8. Two characteristics can be indicators for operational conditions of X-ray generator: the
internal oil temperature in the vicinity of the X-ray tube and the oil density. As a result from
theoretical analysis, two possible safety margins are identified: the temperature at the inner oil
volume contacting X-ray tube surface and the oil volume thermal expansion. Figure 9a shows
a diagram, obtained after the solution of Equation 5 and Equation 6 for the temperature field of
the X-ray generator. Here, on the x-axis is positioned the X-ray generator surface temperature
values as independent variable. Values obtained by the measurements (and further interpolation)
can be selected there. After solution of Equation 2 with appropriate boundary temperature range
40 ◦Cto 130 ◦Cand linear dependence is found (marked in red in Figure 9a. In this figure, the
corresponding temperature at the inner oil boundary (or the outer boundary of the X-ray tube) is
found at the y-axis along the known line and obtained from solution of Equation 2). Based on
the review, presented in section 2, four modes of operation of X-ray generator are distinguished:
12

PoS(BPU11)270
Thermal Monitoring for Condition Based Maintenance of an X-ray Generator Anton Zyapkov
(a) Temperature profile on the outer X-ray tube wall
and the average oil volume temperature related to the
outer hull’s surface temperature
(b) The volume of oil change, depending on the outer
hull’s surface temperature (the curve represents the
average oil volume temperature)
Figure 9: Thermal characterization of X-ray generator operational steady-state condition.
Mode Operational regime Defined temperature range at
X-ray tube cooling radiator
Measurable hull’s outer sur-
face temperature
1 Normal operation 10◦𝐶≤𝑇𝑖<80◦𝐶10◦𝐶≤𝑇𝑜𝑢𝑡 <51◦𝐶
2 Slow degradation 80◦𝐶≤𝑇𝑖<250◦𝐶51◦𝐶≤𝑇𝑜𝑢𝑡 <80◦𝐶
3 Faster degradation 250◦𝐶≤𝑇𝑖<300◦𝐶80◦𝐶≤𝑇𝑜𝑢𝑡 <87◦𝐶
4 Failure 𝑇𝑖>300◦𝐶 𝑇𝑜𝑢𝑡 >87◦𝐶
Table 2: Relation between operational modes and temperatures
(1): ’normal operation;’ (2): ’slow degradation;’ (3): ’faster degradation;’ and (4): ’failure.’ The
corresponding temperature ranges at the hottest surface of X-ray tube and calculated by Equation 2
possible values measured on the hull’s outer surface are given in Table 2. The maximal temperature
around the X-ray tube of 300◦𝐶corresponds to a temperature of 87◦𝐶on the outer surface of the
hull’s wall.
Similarly, the blue line in Figure 9a represents the average oil temperature, that further can be
used for analysis of the oil expansion. Data obtained from [20] is used in the further analysis to
obtain the volume change Δ𝑉regarding STP conditions:
Δ𝑉=𝑉0𝛽Δ𝑇(7)
where 𝑉0is the initial volume (at 20◦𝐶), 𝛽is the compressibility of the oil, defined by 𝛽=
5×10−07𝑇+0.0007 for a given temperature T, K; Δ𝑇is the temperature difference. It is known that
the oil volume is expanded and the expanded fluid goes into the X-ray generator expansion cuff. It
takes normally about 300–500 ml. oil, which in normal operation corresponds up to about 60◦𝐶at
the outer hull’ wall that slightly exceeds the limit for normal operation in Table 2.
13

PoS(BPU11)270
Thermal Monitoring for Condition Based Maintenance of an X-ray Generator Anton Zyapkov
6. Summary and Conclusions
The complete outer surface temperature profile of the X-ray generator was obtained using a
combination of installed contact thermometers and distant infrared (IR) sensors. The measurements
by infrared sensors were successfully verified with data from contact thermometers.
The obtained data from all measurements were used for generation of boundary conditions
for the analytical model, reported in this paper. As a solution of Equation 5 and Equation 6, we
obtained the temperature at the outer surface of X-ray tube cooling radiator, see Figure 1.
The solution of Equation 5 and Equation 6 reveals two major indicators of X-ray generator
failures: the cooling oil density and the temperature at the inner surface of the oil volume annulus
(outer surface of X-ray tube). The obtained results for normal operation by the two indicators
fully agree, where the hull’s outer surface temperature could be extended to 60◦𝐶, see Equation 7,
because of the oil thermal expansion. However, with the increasing of the temperature beyond the
normal operation, slow chemical degradation of oil, straw gases production and worsening of heat
removal could take place. Reaching the temperature of oil boiling at the outer X-ray tube indicates
failure of the system which should take place at the hull’s outer temperature of 87◦𝐶, see Table 2.
Acknowledgements
This research is financed by the Bulgarian National Innovation Fund under a financing agree-
ment №11-IF-02-25/11.12.2020.
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