Cathode protection data acquisition and processing system and measurement method
By designing a cathode protection data acquisition and processing system, using a micro-resistance acquisition module and a signal conditioning circuit module, the problems of inaccurate monitoring of cathode protection systems and large environmental dependence in the existing technology are solved, and real-time and accurate cathode protection systems are achieved. Data acquisition and analysis improves measurement accuracy and stability.
Patent Information
- Application Number
- CN202411371169.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-29
- Publication Date
- 2025-01-03
AI Technical Summary
The monitoring of existing cathode protection systems relies on manual inspection and regular maintenance, and lack of real-time data acquisition and analysis, resulting in inaccurate evaluation. In addition, traditional four-wire method and weightless method have problems such as poor output current accuracy and stability and high environmental dependence.
A cathode protection data acquisition and processing system is designed, using micro-resistance acquisition module, effective value detection module and signal conditioning circuit module, and using the current feedback mechanism to provide constant current source output. Combined with STM32 chip and 4G remote transmission module, real-time acquisition and analysis Data, calculate the corrosion rate.
Real-time data acquisition and accurate analysis of the cathode protection system is realized, measurement accuracy and stability are improved, and pipeline corrosion can be accurately evaluated in complex environments.
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Figure CN119243167A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of metal corrosion measurement, and in particular to a cathode protection data acquisition and processing system and a measurement method. Background Art
[0002] Metal corrosion is one of the main causes of metal structure failure, especially in pipelines, storage tanks and marine structures in the oil, natural gas, chemical and other industries, where the corrosion problem is particularly serious.
[0003] Traditional anti-corrosion methods include coatings and cathodic protection, among which cathodic protection technology is widely used due to its high efficiency and economy. At present, the monitoring of cathodic protection systems mainly relies on manual inspection and regular maintenance, lacking real-time data collection and analysis methods, resulting in inaccurate evaluation of cathodic protection effects. In addition, most cathodic protection monitoring systems only focus on data collection and ignore data analysis, and micro-resistance such as ER resistance and diffusion resistance is not incorporated.
[0004] The patent with publication number CN114959716A uses the weight loss method to measure the corrosion rate, but the measurement accuracy of the weight loss method will change due to factors such as the roughness of the sample surface, the oxide layer, etc., and the weight loss method has strict requirements on environmental conditions. The corrosion products produced by the sample will also affect the measurement results.
[0005] The document "Research and Design of Portable Intelligent DC Microresistance Tester Based on Four-wire Measurement Method" and the patent with publication number CN 111722137 A use the traditional four-wire method to measure DC microresistance, including: a constant current source and a differential amplifier circuit. For the constant current source, the output voltage range is limited, and the adaptability to load changes is poor, which makes it impossible to maintain the stability of the constant output current. When the output current changes, the error will also increase after passing through the differential amplifier circuit. Summary of the invention
[0006] In view of the shortcomings of the prior art, the present invention utilizes a current feedback mechanism to stabilize the output current of the constant current source, thereby solving the problems of poor output current accuracy and stability of the traditional four-wire method; and the problem that the existing weightlessness method for corrosion rate measurement is greatly affected by the environment.
[0007] The technical solution adopted by the present invention is: a cathodic protection data acquisition and processing system comprises:
[0008] The controller, micro-resistance acquisition module, effective value detection module and signal conditioning circuit module are all electrically connected to the controller; wherein,
[0009] The signal conditioning circuit module uses the on-off potential acquisition circuit to measure the DC voltage signal of the on-off potential of the cathodic protection polarization test piece; uses the AC current acquisition circuit to measure the AC current signal of the polarization test piece; uses the DC current acquisition circuit to measure the self-corrosion potential of the cathodic protection test piece; and uses the AC voltage acquisition circuit to measure the AC voltage signal of the polarization test piece;
[0010] The micro-resistance acquisition module is used to collect the micro-resistance value of the ER test piece and generate a constant current value;
[0011] The effective value detection module converts the AC signal in the AC current acquisition circuit and the AC voltage acquisition circuit into a DC signal;
[0012] The controller uses the micro-resistance value of the ER test piece to calculate the corrosion rate, thereby determining the extent of corrosion on the pipeline.
[0013] As a preferred embodiment of the present invention, the micro-resistance acquisition module includes: a reference voltage circuit, a constant current source circuit and an amplifier circuit. The reference voltage circuit is used to provide a stable reference voltage for measuring the external test strip resistance of the ER test strip, the constant current source circuit is used to provide a stable constant current value for measuring the external test strip resistance of the ER test strip, and the amplifier circuit is used to reduce the voltage interference in measuring the external test strip resistance.
[0014] As a preferred embodiment of the present invention, the micro-resistance acquisition module includes: a voltage reference chip U13, capacitors C38, C39, C2, resistors R8 to R15, operational amplifiers U2, U3, transistor Q1 and a precision operational amplifier U4; wherein the first pin of U13 is connected to one end of C39, the second pin of U13 is respectively connected to one end of C38, one end of R8 and the third pin of U2, the other end of R8 is connected to the first pin and the second pin of U3, the second pin of U2 is respectively connected to the first pin and the second pin of U3, and the second pin of U2 is respectively connected to the first pin and the second pin of U3. The first pin of U2 is connected to the base of R9 and Q1 in sequence, the emitter of Q1 is connected to one end of R10 and the common end of R12 and R13 respectively, the other common end of R12 and R13 is connected to the third pin of U3 and the third pin of U4 respectively, the second pin of U4 is connected to one end of R14 and R60 respectively, the other end of R60 is connected to the sixth pin of U4 and one end of R15 respectively, and the other end of R15 is connected to one end of C2 respectively.
[0015] As a preferred implementation of the present invention, the controller adopts an STM32 chip.
[0016] As a preferred embodiment of the present invention, it also includes: a display screen module, which is used to display the collected data values in real time.
[0017] As a preferred embodiment of the present invention, it also includes: a power supply module, which is used to provide voltage and current values.
[0018] As a preferred embodiment of the present invention, it also includes: a 4G remote transmission module, which is used to remotely transmit the collected various data to the host computer through 4G communication.
[0019] As a preferred embodiment of the present invention, it also includes: a host computer for analyzing the collected data, judging the interference degree of pipeline stray current and performing statistical analysis on the corrosion rate.
[0020] As a preferred embodiment of the present invention, it also includes: a relay circuit, which controls the on and off of the controller.
[0021] As a preferred embodiment of the present invention, a measurement method of a cathodic protection data acquisition and processing system includes:
[0022] Step 1: Use the micro-resistance acquisition module to collect the internal and external resistance values of the ER test piece;
[0023] Step 2: Measure the thickness of the external test piece at time t:
[0024] Step 3: According to the difference in thickness of the external test piece at two times, the corrosion rate is obtained, and the formula is:
[0025]
[0026] Among them, t2 and t1 are different moments, and dc is the thickness of the outer test piece.
[0027] Beneficial effects of the present invention:
[0028] 1. The micro-resistance acquisition module designed by the present invention uses a voltage following mechanism and a negative feedback mechanism to provide a stable constant current for measuring the micro-resistance value of the ER test piece, which is more stable than the existing four-wire method for measuring the micro-resistance value; and uses an amplification circuit to improve the accuracy of measuring the micro-resistance;
[0029] 2. By measuring the thickness of the external test piece at different times, the corrosion rate of the pipeline can be predicted more easily. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Figure 1 It is a logic block diagram of the cathodic protection data acquisition and processing system of the present invention;
[0031] Figure 2 is a circuit diagram of a controller of the present invention;
[0032] Figure 3 It is an on-off potential acquisition circuit of the signal conditioning circuit module of the present invention;
[0033] Figure 4It is an AC current acquisition circuit of the signal conditioning circuit module of the present invention;
[0034] Figure 5 It is a DC current acquisition circuit of the signal conditioning circuit module of the present invention;
[0035] Figure 6 It is an AC voltage acquisition circuit of the signal conditioning circuit module of the present invention;
[0036] Figure 7 It is the circuit diagram of the effective value detection module of the present invention;
[0037] Figure 8 It is the circuit diagram of the micro-resistance acquisition module of the present invention;
[0038] Fig. 9 It is a relay circuit diagram of the present invention;
[0039] Fig.10 It is a schematic diagram of the corrosion rate measurement method of the present invention. DETAILED DESCRIPTION
[0040] The present invention is further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, and therefore it only shows the components related to the present invention.
[0041] like Figure 1 As shown, a cathodic protection data acquisition and processing system comprises:
[0042] The controller, micro-resistance acquisition module, effective value detection module and signal conditioning circuit module are all electrically connected to the controller; wherein,
[0043] The signal conditioning circuit module uses the on-off potential acquisition circuit to measure the DC voltage signal of the on-off potential of the cathodic protection polarization test piece; uses the AC current acquisition circuit to measure the AC current signal of the polarization test piece; uses the DC current acquisition circuit to measure the self-corrosion potential of the cathodic protection test piece; and uses the AC voltage acquisition circuit to measure the AC voltage signal of the ER test piece;
[0044] The micro-resistance acquisition module is used to collect the micro-resistance value of the ER test piece and to generate a constant current value;
[0045] The effective value detection module converts the AC signal in the AC current acquisition circuit and the AC voltage acquisition circuit into a DC signal;
[0046] The controller uses the micro-resistance value of the ER test piece to calculate the corrosion rate, thereby determining the extent of corrosion on the pipeline.
[0047] It also includes: a display screen module, which is used to display the collected data values in real time.
[0048] It also includes: a power supply module, which is used to provide stable and reliable voltage and current to ensure the normal operation of the controller and the circuit modules connected thereto.
[0049] It also includes: a 4G remote transmission module, which is used to remotely transmit the collected various data to the host computer through 4G communication.
[0050] It also includes: a host computer for analyzing the collected data, judging the interference degree of pipeline stray current and conducting statistical analysis on the corrosion rate.
[0051] like Figure 2 This is the circuit diagram of the controller U14. The present invention adopts an STM32 single-chip microcomputer, and the controller can also adopt an MCU controller and a microprocessor; the pins PB14 and PB15 of U14 are connected to the display screen module; the pins PA9 and PA10 are used to realize the communication with the host computer and transmit the collected data to the host computer.
[0052] like Figure 3 The on-off potential acquisition circuit includes: resistors R28, R29, R31 to R33, operational amplifiers U5 to U6 and capacitor C33, the DC_VOLTAGE pin is connected to the left end of R28, the right end of R28 is connected to the 3rd pin of R29 and U5 respectively, the lower end of R29 is grounded, the 2nd pin and the 1st pin of U5 are short-circuited, the 1st pin of U5 is also connected to one end of R31 and then connected to R32 and the 3rd pin of U6 respectively, the 2nd pin and the 1st pin of U6 are short-circuited 1 pin is short-circuited, the 1st pin of U6 is also connected to the left end of R33, the right end of R33 is connected to one end of C33 and then grounded, and the right end of R33 is also connected to the ADC_1 pin of U14; the signal DC_VOLTAGE to be collected is connected to the voltage follower U5 and then to the in-phase proportional amplifier U6. The U5 voltage follower has the characteristics of high input resistance and low output resistance, the input voltage and the output voltage are in phase, and the voltage amplification factor is constantly less than and close to 1, which can reduce the distortion of the signal.
[0053] like Figure 4It is an AC current collection circuit, including: resistors R37 to R40, R49 to R50, operational amplifiers U7 to U8 and capacitor C34, the AC_CURRENT pin is connected to the upper end of R40 and the third pin of U7, the right end of R34 is respectively connected to the second pin of U7 and the left end of R49, the right end of R49 is connected to the first pin of U7 and the left end of R37, the right end of R37 is connected to the third pin of U8, the second pin of U8 is respectively connected to the right end of R38 and the left end of R50, the right end of R50 is respectively connected to the The first pin is connected to the left end of R39, and the right end of R39 is respectively connected to the upper end of C34 and the ADC_2 pin of U14; the signal to be collected AC_CURRENT is connected to the in-phase proportional amplifier U7, and then connected to the in-phase proportional amplifier U8 after passing through R37. The in-phase proportional amplifier is used to amplify the amplitude of the input signal to the required value so that the signal to be collected meets the sampling range of the A / D conversion chip of U14; the AC_CURRENT pin is used to measure the AC current signal of the polarization test piece to detect whether the pipeline is affected by stray current AC interference.
[0054] like Figure 5 It is a DC current collection circuit, including: resistors R54 to R59, R44 to R45, R33, operational amplifiers U9, U11, U12 and capacitor C37, the DC_CURRENT pin is connected to the upper end of R33 and the third pin of U9, the second pin of U9 is connected to one end of R55 and R54 respectively, the right end of R54 is connected to the first pin of U9 and the left end of R44 respectively, the right end of R44 is connected to the upper end of R56 and the third pin of U11 respectively, and the second pin of U11 is connected to the left end of R54 and the first pin of U9 respectively. The pins are respectively connected to the 1st pin of U11 and the left end of R57, the right end of R57 is respectively connected to the upper end of R58 and the 3rd pin of U12, the 2nd pin of U12 is respectively connected to the 1st pin of U12 and the left end of R59, the right end of R59 is respectively connected to the upper end of C37 and the ADC_3 pin of U14; the DC_CURRENT pin is used to measure the self-corrosion potential of the cathodic protection specimen, and the degree of self-corrosion of the cathodic protection specimen in the current environment can be reflected by detecting the high and low self-corrosion voltage.
[0055] like Figure 6It is an AC voltage acquisition circuit, including: resistors R51 to R53, R45 to R46, R48 and capacitor C36, the AC_VOLTEAGE pin is connected to the left end of R46, the right end of R46 is respectively connected to the upper end of R45 and the left end of R51, the right end of R51 is connected to the third pin of U10, the second pin of U10 is respectively connected to the right end of R53 and the left end of R52, the right end of R52 is respectively connected to the first pin of U10 and the left end of R48, the right end of R48 is respectively connected to the upper end of C36 and the ADC_4 pin of U14; the AC_VOLTEAGE pin is used to measure the AC voltage signal of the polarization test piece to detect whether the pipeline is affected by stray current AC interference.
[0056] like Figure 7 It is an effective value detection module, including: a voltage reference chip U1, a capacitor C1, and resistors R1 to R4. The left end of C1 is an input pin, which is connected to the AC_VOLTAGE pin of an AC voltage acquisition circuit or the AC_CURRENT pin of an AC current acquisition circuit. The right end of C1 is connected to the second pin of U1. The third pin of U1 is respectively connected to the common ends of R1 and R2. The left end of R1 is connected to VDD. The fourth pin of U1 is connected to the common ends of R3 and R4. The fifth pin of U1 is an output, which is connected to the third pin of U8 of an AC current acquisition circuit or the third pin of U10 of an AC voltage acquisition circuit. The LTC1966HMS8 chip is used to form an effective value detector to convert an AC signal into a DC signal.
[0057] like Figure 8 It is a micro-resistance acquisition module, including: voltage reference chip U13, capacitors C38, C39, C2, resistors R8 to R15, operational amplifiers U2, U3, transistor Q1, precision operational amplifier U4, the first pin of U13 is connected to VCC and the upper end of C39, the second pin of U13 is connected to the upper end of C38, the upper end of R8 and the third pin of U2 respectively, the lower end of R8 is connected to the first pin and the second pin of U3, the second pin of U2 is connected to the common end of R10 and R11 respectively, and the first pin of U2 is connected to the common end of R10 and R11 respectively. It is connected to R9 and the base of Q1, the collector of Q1 is connected to 5V, the emitter of Q1 is connected to the upper end of R10 and the common end of R12 and R13 respectively, the other common ends of R12 and R13 are connected to the 3rd pin of U3 and the 3rd pin of U4 respectively, the 2nd pin of U4 is connected to one end of R14 and R60 respectively, the other end of R14 is grounded, the other end of R60 is connected to the 6th pin of U4 and one end of R15 respectively, the other end of R15 is connected to the upper end of C2 and the ADC_5 pin of U14 respectively.
[0058] The third pin of U4 is connected to the external test piece resistance signal Rc of the input ER test piece, that is, Rc is connected between the output end of the constant current source circuit and the third pin of U4; the four-wire method uses four wires to measure micro-resistance, two of which are used to apply current and the other two are used to measure voltage; Figure 8 It includes: high-precision constant current source U13 and its auxiliary circuits; the constant current source circuit is U2, U3, Q1 and its auxiliary circuits; U4 and its auxiliary circuits are amplifier circuits.
[0059] The reference voltage circuit includes U13, which provides a high-precision reference voltage. U13 is a reference voltage source, and the chip model is REF3025AIDBZ. U13 is used to ensure that the circuit can still provide a stable measurement reference voltage when the power supply voltage fluctuates or other environmental changes occur (such as interference).
[0060] The constant current source circuit always controls the output current at a constant value through the negative feedback mechanism of Q1. Compared with the traditional constant current source circuit, U2 is used to enhance the negative feedback of Q1 to play the role of isolating the output; U3 plays the role of voltage following and isolation. When the output voltage of U13 fluctuates by using the voltage following of U3, the output voltage of U13 is self-regulated by using U3 and Q1; R12 and R13 can provide a stable measurement current to ensure that the current of Rc is constant, that is, the current input to the third pin of U4 is constant, thereby improving the accuracy of the measurement. The output current value of the resistor to be measured connected to the constant current source is: VREF is the reference voltage of U13.
[0061] The amplifier circuit uses the OPA197ID precision operational amplifier, which has high input impedance and low output impedance characteristics, making the voltage measurement part almost unaffected by external interference, and has low bias current, low noise and common mode consistency characteristics, which increases the accuracy of micro-resistance acquisition. After Rc is connected to the amplifier circuit, the current I output by the constant current source circuit 恒定 A voltage difference is generated when it flows through Rc. The A / D conversion chip in U14 collects the corresponding voltage value as ADC_5. After conversion, the resistance value of Rc is:
[0062] It can be seen that the current and voltage measurement channels of the micro-resistance acquisition module are completely independent, that is, they are divided into a constant current source circuit part and an amplifier circuit part. U2 plays an amplifying role, and U3 plays an isolating output role, so that the measured voltage will not be affected by the change of current; in micro-resistance acquisition, any additional resistance through which the current flows will affect the final measurement accuracy. The present invention greatly improves the measurement accuracy; and a multi-stage filter is used to effectively filter out noise and enhance the anti-interference ability of the system.
[0063] Compared with other four-wire measurement methods, the micro-resistance acquisition module of the present invention not only maintains the high-precision characteristics of the four-wire method itself, but also further improves the anti-interference ability of the system and the stability of measurement through measures such as operational amplifiers, filtering, setting independent channels and reference voltage sources, so that it can work stably and accurately in various complex environments.
[0064] like Fig. 9 It is a relay circuit, which is connected to the on-off potential collection circuit, and the on-off of the controller is controlled by the switch of the relay; the relay circuit includes: relay K1, diode D1 and transistor Q2, the base of Q2 is connected to the SEL pin of U14, the emitter of Q2 is grounded, the collector of Q2 is connected to the 8th pin of K1 and the positive electrode of diode D1 respectively, the negative electrode of D1 is connected to the 1st pin of K1 and the 5V voltage, the 2nd and 3rd pins of K1 are DC_VOLTEAGE and DC_VOLTEAGE_INPUT pins respectively, the DC_VOLTEAGE_INPUT pin receives the DC voltage signal for collecting the cathode protection on-off potential of the polarization test piece, the DC_VOLTEAGE pin is connected to the DC_VOLTEAGE pin of the on-off potential collection circuit, and the power-on or power-off potential is collected by controlling U14 through the power on and off of K1.
[0065] The measurement method based on the cathodic protection data acquisition and processing system includes:
[0066] Step 1: Use the micro-resistance acquisition module to collect the internal and external resistance values of the ER test piece;
[0067] Step 2: The ER test piece is composed of an outer test piece c and an inner test piece r. The initial thickness of the outer test piece c is dc (t=0), and t is the time. The resistance of the inner test piece is measured to be Rr, and the resistance of the outer test piece is Rc. After the pipeline is corroded for t time, the thickness of the outer test piece at time t is measured to be:
[0068] Step 3: According to the difference in thickness of the external test piece at two times, the corrosion rate is obtained, and the formula is:
[0069]
[0070] Among them, t2 and t1 are different moments, and dc is the thickness of the outer test piece.
[0071] like Fig.10, the corrosion rate is obtained by collecting the resistance change of the ER test piece and fitting the wall thickness based on the measurement calculation, that is, through step 2, the change data of dc(t) with time t can be obtained, the change of the thickness of the external test piece in several time intervals is calculated, and then a linear fit is performed, and the slope obtained is the corrosion rate; it can be seen from the figure that the fluctuation of the fitted corrosion rate becomes smaller with the extension of time, and the fluctuation amplitude of the curve decreases from 0.1 month on the horizontal axis, and the corrosion rate calculated by difference gradually approaches stability. When it becomes stable, the accurate corrosion rate can be obtained. Fig.10 It can be seen that the corrosion rate has stabilized at 6.48um / a since February.
[0072] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.
Claims
1. A cathodic protection data acquisition and processing system, characterized in that: include: The controller, micro-resistance acquisition module, effective value detection module and signal conditioning circuit module are all electrically connected to the controller; wherein, The signal conditioning circuit module uses the on-off potential acquisition circuit to measure the DC voltage signal of the on-off potential of the cathodic protection polarization test piece; uses the AC current acquisition circuit to measure the AC current signal of the polarization test piece; uses the DC current acquisition circuit to measure the self-corrosion potential of the cathodic protection test piece; and uses the AC voltage acquisition circuit to measure the AC voltage signal of the polarization test piece; The micro-resistance acquisition module is used to collect the micro-resistance value of the ER test piece and generate a constant current value; The effective value detection module converts the AC signal in the AC current acquisition circuit and the AC voltage acquisition circuit into a DC signal; The controller uses the micro-resistance value of the ER test piece to calculate the corrosion rate, thereby determining the extent of corrosion on the pipeline.
2. The cathodic protection data acquisition and processing system according to claim 1, characterized in that: The micro-resistance acquisition module includes: a reference voltage circuit, a constant current source circuit and an amplifier circuit. The reference voltage circuit is used to provide a reference voltage for measuring the external test piece resistance, the constant current source circuit is used to provide a constant current value for measuring the external test piece resistance, and the amplifier circuit is used to reduce the voltage interference of measuring the external test piece resistance.
3. The cathodic protection data acquisition and processing system according to claim 2, characterized in that: The micro-resistance acquisition module includes: a voltage reference chip U13, capacitors C38, C39, C2, resistors R8 to R15, operational amplifiers U2, U3, transistor Q1 and precision operational amplifier U4; wherein, the first pin of U13 is connected to one end of C39, the second pin of U13 is respectively connected to one end of C38, one end of R8 and the third pin of U2, the other end of R8 is respectively connected to the first pin and the second pin of U3, the second pin of U2 is respectively connected to R10 and R The common end of R12 and R13 is connected to the common end of U3 and U4, the common end of R14 and R60 is connected, the other end of R60 is connected to the 6th pin of U4 and one end of R15, and the other end of R15 is connected to one end of C2.
4. The cathodic protection data acquisition and processing system according to claim 1, characterized in that: The controller uses STM32 chip.
5. The cathodic protection data acquisition and processing system according to claim 1, characterized in that: Also includes: Display screen module, used to display the collected data values in real time.
6. The cathodic protection data acquisition and processing system according to claim 1, characterized in that: Also includes: Power module, used to provide voltage and current values.
7. The cathodic protection data acquisition and processing system according to claim 1, characterized in that: Also includes: The 4G remote transmission module is used to remotely transmit the collected data to the host computer through 4G communication.
8. The cathodic protection data acquisition and processing system according to claim 1, characterized in that: Also includes: The host computer is used to analyze the collected data, determine the degree of interference of pipeline stray current and conduct statistical analysis of corrosion rate.
9. The cathodic protection data acquisition and processing system according to claim 1, characterized in that: Also includes: A relay circuit is used to control the on and off of the controller.
10. A measurement method for a cathodic protection data acquisition and processing system, characterized in that: The steps include: Step 1: Use the micro-resistance acquisition module to collect the internal and external resistance values of the ER test piece; Step 2: Measure the thickness of the external test piece at time t: Step 3: According to the difference in thickness of the external test piece at two times, the corrosion rate is obtained, and the formula is: Among them, t2 and t1 are different moments, and dc is the thickness of the outer test piece.
