AN IMPROVED CAPACITIVE PRESSURE GAUGE TO MEASURE ARTILLERIES CHAMBER PRESSURES
Chandrika Ramesh
Abstract — An improved capacitive pressure gauge is proposed to measure artilleries chamber pressures. The gauge uses the circuit shell as its stationary anode and the gauge’s shell as its moveable cathode to induce pressure. Sapphire crystal end cap is used for communication and wireless charge which makes the gauge need not disassembling in working life. The principle of the gauge is introduced. The structure and the thermal effect are analyzed by ANSYS. The static and dynamic physical properties were tested. The simulation and test results show that the capacitance of the gauge is approximately linear to the loaded pressure. Its repeatability error is 1.5%. The measuring range of the gauge is 0~600MPa. Its volume is reduced to 18 mm3, it can be used to measure the chamber pressures of small caliber guns.
Index Terms — Capacitive Pressure Sensor, Chamber Pressure, Dynamic Testing, Wireless Charging
Introduction
HAMBER pressure is defined as the force per unit area that explosive gas acts upon the wall of the gun chamber when a gun is fired. It is important to test chamber pressure in research, development or produce acceptance of artillery systems [1], [2], [3], [4]. The Accurate and reliable chamber pressure data is the basic foundation to analyze the rationality of charge structure, the strength and stiffness design of gun carriage etc.
The main used test gauge [1] and[5]: 1) Internal copper crusher gauge (copper ball or copper cylinder), which is incapable of recording the dynamic change of the chamber pressure with time, only obtaining the maximum pressure by detecting distortion quantity of the copper ball or copper cylinder [6]. 2) Internal electronic pressure gauge (IEPG [1]), which can be merged in gun chamber bottom (as shown in Fig.1) to conveniently and accurately record pressure-time (p-t) curve without effect to the tested gun.
At present, the chamber pressures use mainly the third generation IEPG (as shown in Fig.2 [1]) made by Austrian HPI Company in 2000 to test.
The gauge volume is 22 cm3 and the measurement range is 0~600MPa [1]. IEPG produced in China, as shown in Fig.3, its volume is 22 cm3 and the measurement range is 0~600MPa. The capacitive pressure sensor (CPS) of adopting the shell as the elastic pressure-sensitive element has been researched since 2010, the CPS has higher sensitivity (0.0099 pF/MPa), lower temperature drift, and lower power consumption [7], [8], [9], [10].
However, the dielectric coefficient between two electrodes will be changed when end cover is exposed to air, and the size of IEPG can’t measure the chamber pressure under 60 mm diameter cannons.
Fig.1 Schematic of IEPG Application To Test Chamber Pressure
Fig.2 B251 IEPG Made By Austrian HPI Company
Fig.3 IEPG Made In China
For solving the above problems, an improved capacitive pressure gauge is realized. Different from the CPS structure, a new aluminosilicate glass top end cover is designed. The key technologies of the stabilization of capacitive dielectric coefficient and convenient operation are firstly introduced into this internal capacitive pressure gauge (ICPG) structure. More favorable volume is realized, which provides an overwhelming advantage of operating range over
50mm 24
mm
the previous IEPG.
ICPG Principle
The ICPG is mainly composed of sensor shell, circuit model, glass window, resonance coil and insulation pad, as shown in Fig.4. The circuit consists of a collection and storage model, a signal processing model, a power model, a photoelectric detector and an infrared communication interface, as shown in Fig.5. The clearance between the ICPG shell and the circuit shell form a capacitor [1] and [10], [11], [12]. The changes in clearance d0 lead to changes in capacitance, which is proportional to the pressure [13], [14], [15], [16]. The PS021 is the sensor capacitance conversion and acquisition module, the MSP430 is the control and storage part. The Infrared which replaces the UART interface in old circuit interface is used to communicate and transmit storage data to the computer. The charge mode uses wireless charge with resonance coil instead of normal plus way. The above improvement makes the ICPG need not disassembling in working life. PS021 based on TDC technology (Time-to-Digital Converter) is made by ACAM of Germany. It integrates capacitor discharge time measurement circuit for two channels. The sensitive capacitance and the reference capacitor are in series with discharge resistor, respectively. The time to discharge a sensor capacitor is proportional to its reference capacitance.
Fig. 4 ICPG Structure
Fig. 5 ICPG Circuitry Principle ICPG System Analysis
A. Theoretical analysis of elasticity of ICPG shell
The circuit outer radius is 6.75 mm, and the clearance of circuit shell and ICPG shell d0= 0.5 mm, so the inner radius of ICPG shell a =7.25 mm.
The material of the ICPG shell is 18Ni maraging steel, yield strengths=2100MPa. According to the formulas of the yield pressure and the outer radius of the ICPG shell [1] and [17], the outer radius of shell b is expressed with
1 1 3 e
s
b a
p
(1)
From the equation (1), while the load pressure pe
=600MPa then b =10.46 mm. For CPS safety and high sensitivity reasons, the factor of safety is 1.1, so the working limit pressure up to 660MPa, then the b =11 mm. The thickness of the top lid and bottom lid of the ICPG is respectively 7.5 mm and 4 mm. According to the height of the circuit shell, the height of sensor tube is taken as 35 mm, and the total height of ICPG L is 48 mm, therefore the total volume of the ICPG V =18 cm3. Thus, under the 600MPa pressure, the ICPG is still operating in the range of elastic deformation.
B. ANSYS simulation of the ICPG
The ICPG shell structure is shown in Fig. 6.
The thickness of the top lid h0 is 7.5 mm, the bottom lid h1 is 4 mm, the height L is 48 mm. The cone angle is 45°, and used to prevent the hot gas entering the tube by the high-pressure compressing the shell. The thicknesses h2 is 3.75 mm, inner radius a is 7.25 mm，outer radius b is 11 mm. The simplified axis-symmetric model established by ANSYS is used to analyze the intensity of the ICPG shell. The outer shell of the model is covered by the same pressure and the inner is unconstrained. The shell material parameters are shown in Tab. I.
Fig. 6 The Structural Model of ICPG Shell
Table I Shell Material Parameter
Fig.7 Von-Misses Stress at 660 MPA
The Von-misses stress contour at 660MPa pressure is shown in
Error! Reference source not found.
. The maxim stress of the shell center is 1940MPa which is smaller than the yield stress of 2100MPa. The maxim stress of the top lid center is 1200MPa which is smaller than the yield stress of 1250MPa. Hence, the shell is safe. The maxim variation of the inner radius of ICPG is 0.1mm at the center of shell while the pressure of 660MPa is loaded.C. Wireless Charging System
The basic structure of Wireless Charging System (WCS) is shown in Fig. 8. The WCS system contains the power management circuit and the charging controller of the secondary side. The power management circuit is used to control the power flow in the Inductive Power Transmission (IPT) system. The IPT system consists of a primary resonant power supply that generates an AC voltage to energize a primary coil [18]. The magnetic field generated by the energized primary coil is coupled to the secondary coil. The IPT technology can transfer the energy in a predefined distance via the alternating electromagnetic field without the direct electrical contact.
DC/
i AC
u u
1u
2u
3u
4u
oRecti
-fier filter DC/
DC
Cha- rger
Batt- ery
Fig. 8 The Structure of Wireless Charging System
IPT inductive circuit topology is shown in Fig. 9.
The series-parallel(SP) compensated topology is applied to improve the power transfer efficiency.
IP
LP
S
j MI
LS
p
j MI IS
M CP
CS RL Ui
IL
+─ +─
UO
+
─
+
─
Fig. 9 SP Compensated Topology of Mutual Inductance Model
The equivalent circuit equations are given by:
P P S
P
= 1
Ui I j L j MI
j C
(2)
S S L P
S
0 =I j L R 1 j MI
j C
P (3)
where the primary side and secondary side work at the same angular frequency given by:
S S 2
P P
S
1 1
=
L C M
L C
L
(4)
Combine equation (2), (3) and (4) to get
2 P = i2 S L
I U L
M R (5)
= P = S i
o L
S
L U U j MI R
j L M
(6)
2
IN 2
S
Z =M RL
L (7) According to equation (5), (6) and (7), the zero phase angle(ZPA) between the input voltage and current, the purely resistive input impedance and the constant voltage out for load when Ui, LS and M are given.
XKT- 408A
T5336 LP
CP
C1
+
12V
CS
T 3 1 6 8 D1 2A/60V
C2 R1
R3
L1
R2
R4
LS
10uF /25V
6.3kΩ 10kΩ 31kΩ
5kΩ 10uF
C3
-
M 4 0 5 6V4
+
- Fig.10 The Schematic Diagram of WCS
The schematic diagram of WCS is shown in Fig.10. XKT-408A and T5336 as inverter with
Symbol 18NI（350）
Managing steel
Alumino silicate glass Material model linear and
isotropic
linear and isotropic
Density ρ（kg/m3） 7800 2620
Modulus of elasticity E（GPa）
210 80
Poisson's ratio ì 0.3 0.17
Yield stress P（MPa） 2100 1250
switching devices that outputs 80kHz AC voltage.
The AC voltage is connected to transmit coils by the series compensating capacitor CP. The charging side of WCS consists of a receiver coil, its parallel compensating capacitor CS, a T3168 rectifier, the DC filtering capacitor, the charging IC M4054 and battery.
Fig.11 is the schematic of charging circuit. Fig.
12 shows the voltage and current signature as lithium-ion passes through the stages for trickle charge and charge termination. If the battery voltage is less than the threshold 2.9V, the M4054 enter trickle charge mode. In the mode, the M4054 supply charge current 7mA to the battery.
When the voltage at the BAT pin rises above the threshold 2.9V, the M4054 enters the Constant-Current mode. During the Constant-Current mode, the 50mA charge current is supplied to the battery. When the battery voltage reaches 3.9V, Constant-Voltage 4.2V charging begins. The charge cycle is terminated when the average charge current diminishes below 2mA.
Fig.11 Schematic of Charge Circuit
Time Battery Voltage
Charge Current
Constant Voltage Constant
Current
S0 S1 S2
4.2 Voltage
/V Current
/mA 50
7 2
2.9 3.9
S3 Trickle Done
0 0
Fig. 12 Charge Stage of Lithium-ion
D. ICPG thermal effect
The ICPG is placed in the high-temperature gas.
The thermal deformation will produce a measurement error. The thermal barrier coating (TBC) is added to protect the shell against its thermal deformity TBC is a double-layer structure, with the heat-insulating ceramics as its surface layer, the anti-gasified tack coat between alloy and the outer shell. The surface layer is usually 250~300 μm, the middle is approximately 120~150 μm, and the total thickness is approximately 450 μm. The heat-insulating coefficient is about 0.05 m2·K/W.
Supposing that the initial temperature is 20°C, the explosion pressure duration time is about 25 ms, and the maxim gas temperature is up to 3000°C, using the first boundary condition of the temperature field, the temperature characteristics of the shell with TBC are analyzed through ANSYS, as shown in Fig.
13
, Fig.14
, Fig.15
and Fig.
16
.Fig. 13 Temperature Distribution On The Shell at 3000°C at 25 MS
Fig. 14 Enlarged Temperature Distribution Of Part Nodes Of Tube Body
a) Node 3873 (The Outer Part of Thermal Coating)
b) Node 99 (The Border Point Of Tube Body and TBC)
Fig. 15 Temperature - Time Chart
As shown in Fig.
16
, the temperature of the shell wall under the TBC shelter basically maintains about 20°C.Fig. 16 Temperature along The Wall Thickness Direction at 25 ms
During the period from the fire to the pressure gauge taken out of the chamber (about 20 s), the temperature distribution of the shell is shown in Fig.
17
, the outside temperature is much higher, reaching above 100°C, the inner temperature remains at normal temperature, which will not affect the normal operation of the recording circuit.The above analysis indicates that the instantaneous high temperature influence on the shell is negligible.
Fig. 17 Temperature distribution of the shell at 20 s
E. Dynamic characteristics of ICPG
The dynamic characteristics of the elastic sensitive component and the hysteresis during transformation are related to sensor inherent frequency. The high frequency is expected. The ANSYS model is built on the axis-symmetric full expansion, and the material parameter settings are shown in Tab. I. The different order models of ICPG shell simulated by ANSYS are shown in
Tab. II.
The 7th frequency order of shell modal is radial vibration, which is the first-order vibration mode.
The inherent frequency of the ICPG as the sensitive component is 28.425 kHz, as shown in Fig.
18
, which is much higher than 2 kHz chamber pressure frequency. The 8th frequency order is first-order flexural vibration, as shown in Fig.19
. The 9th frequency order is first-order tensional vibration as shown in Fig.20
. Therefore, compared to the cylinder, the chamber pressure can be seen as the quasi-static load. Under the chamber pressure, the ICPG shell will tend to distort inward.Table Ii Natural Different Order Model Of The Shell
Fig. 18 The 7th Frequency Order Vibration Model
Fig. 19 The 8th Frequency Order Vibration Mode
Fig. 20 The 9th Frequency Order Vibration Mode
Test Results and Analysis
In order to avoid the influence of the post-processed circuit on the mechanical characteristics and the stability of the sensor, static and dynamic tests were respectively done and analyzed.
A. Static Test
The 1000 MPA hydraulic calibration machine produced by Xi’an No.204 Research Institute was used to generate the pressure, and E4980A precision LCR meter produced by Agilent was used to test capacitance. The capacitance-pressure curve by the least Square is shown in Fig.22. The result shows that the sensitivity is 0.0217pF/MPA, the capacitance is approximately linear with the pressure, and the liner fitting degree is up to 0.9959. The sensor average output corresponding to load, least square fitting value and error is shown in Frequency
order
Frequency (HZ)
Vibration model
Frequency order
Frequency (HZ)
Vibration model
1 0 rigid motion 9 36205 torsional
vibration
2 0 rigid motion 10 36212 radial
vibration
3 0 rigid motion 11 36668 radial
vibration 4 1.09×10-2 rigid motion 12 46434 axial
vibration 5 1.54×10-2 rigid motion 13 46448 flexural
vibration 6 2.60×10-2 rigid motion 14 48325 flexural
vibration
7 28425 radial
vibration
15 48331 radial vibration 8 28635 flexural
vibration
16 48638 axial vibration
Tab.III.
Fig. 21 Relation Between △C and P
Table III Fitting Offset Load yn(pF) yn/(pF) YL n,
96 1.62 1.3001 0.3199
185 3.06 3.2314 -0.1714 246 4.36 4.5551 -0.1951 296 5.59 5.6401 -0.0501 389 7.56 7.6582 -0.0982
433 8.71 8.613 0.097
487 9.98 9.7848 0.1952
The fitting offset of testing data is:
/
, 1, 2, 6
L n n n
Y y y n
( ) (6)
where,ynis the average output of sensor n, yn/ is the fitting value of sensor n, YL n, is the fitting error of sensor n.
The linearity is:
, 100%
L maX L
FS
Y
Y (7)
where, YL,maxis max offset error, YFSis the full scale.
The max fitting offset YL,max is 0.3199 pF, the linearity is ±3.21% from (7).
The repeatability error is:
max 100%
R
FS
kS
Y (8)
where, k =2 while confidence coefficient is 95%, Smaxis the maximum standard deviation of every loads.
Smax= 0.07485, so the repeatability error Ris 1.5%.
B. Dynamic Test
The simulation gun pressure generator developed by the North University of China was used to simulate cannon chamber pressure in dynamic test [2], as shown in Fig. 22. In the experiment, the kittler 6215 with BK level was installed in the base of the simulation artillery chamber pressure generator. The elementary error of each standard pressure measurement system is not more than 0.5% FS. The data acquisition system is 14-Bit and sampling frequency is 125 kHz. The ICPG is placed at the end of chamber pressure generator which closes to standard pressure sensors.
(a). Structure Schematic
(b). Photo
Fig. 22 Simulation Gun Pressure Generator
Pressure relief diaphragm and air scoop are installed on the other end of the empty cavity. The pressure limiting diaphragm diameter is 18mm and the material is steel C45E4. The propellant is 5/7 single-base granule of the bullets used for anti-aircraft.
Table IV Correlation Coefficient Comparison
The experiment results are shown in Tab. IV. The maximum relative error value is -1.131%. The minimum correlation coefficient of pressure rising stage value is 0.9994. The pressure curves of the standardized sensor and the ICPG in an experiment are shown in Fig.23, the solid line is the ICPG response curve, the dashed line is the standardized sensor response curve. Two pressure curves have the same changing rate from zero to peak. However, the pressure curve of ICPG is changing faster than standardized sensor at the unloading pressure stage.
Fig.23 Comparison of Standardized Sensor And The ICPG Pressure Response Curve
Conclusions
The ICPG are presented. Its WCS principle is introduced. The structure and the thermal effect are analyzed by ANSYS. The ICPG is fabricated.
The static and dynamic tests of ICPG are done.
The simulation and test results show that the gauge can bear the high pressure of 600 MPa, its inherent frequency up to 28.425 kHz can meet the requirements of the chamber pressure tested, its capacitance is approximately linear with the pressure at the static experiment, and the peak value relative error is less than 2% at dynamic testing. The ICPG has the advantages of small structure of 18 mm3, stable property, low cost that the ICPG makes full use of the self shell to achieve the capacitive sensor, reduces the cost of IEPG using Kistler 6215, and un-disassembling that can be conveniently used
to test the chamber pressures of large, middle, and small caliber artilleries.
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Number
Pressure Peak Of Standard PIEZO-Sensor
(MPA)
Pressure Peak Of The Capacity Pressure Sensor(MPA)
Relative Error(%)
Correlation Coefficient Of Pressure Rising Stage
1 398.80 395.23 0.895 0.9997
2 363.48 367.59 -1.131 0.9996
3 408.15 404.38 0.924 0.9997
4 428.71 431.67 -0.690 0.9995
5 430.90 428.89 0.466 0.9994
6 589.40 591.65 -0.382 0.9995
Wen-bin YOU received the Ph.D. Degree in Instrument Science and Technology from the North University of China in 2014.
He is currently an Assistant Professor with the Computer Science and Control Engineering Department, North University of China. His research interests include the dynamic testing, calibration technology and sensors.
Yong-hong DING received the Ph.D. Degree in Instrument Science and Technology from the North University of China in 2014.
Her research interests include the measurement technology and instruments, wireless communication.
Tie-Hua MA received his Ph.D. Degree in precision instrument and machinery from Harbin Institute of Technology in 1996 and postdoctoral at Beijing Institute of Technology in1999.
His research interests include the dynamic test and measurement, accelerometer technology.
Xi-hui MU received the Ph.D. Degree in Mechanical engineering from Tianjin University in 2003. He was a senior visiting scholar at Purdue University in 2014.
His research interest includes the life information assessment and extension technology.