Steering system pressure pulsation testing system and measuring method
By installing power components and pressure sensor components in the hydraulic steering system, and collecting pressure change data from the motor pump, muffler, and steering mechanism, combined with equivalent impedance calculation, the problem of inaccurate flow pulsation calculation in the hydraulic steering system is solved, and high-precision flow pulsation measurement is achieved.
Patent Information
- Application Number
- CN202511843702.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-09
- Publication Date
- 2026-02-13
AI Technical Summary
Existing methods for calculating flow pulsation in hydraulic steering systems have low accuracy, making it difficult to accurately measure and calculate flow pulsation data. Traditional methods are affected by factors such as half-wavelength degradation, boundary reflection, and mismatch between sound velocity and characteristic impedance, resulting in unstable results.
A steering system pressure pulsation testing system is adopted, including a power component and a pressure sensor component. Power is provided by a motor pump and a muffler. Multiple dynamic and steady-state pressure sensors are set up to collect pressure change data on the hydraulic pipeline. The flow pulsation is calculated by combining the equivalent impedance, so as to achieve reliable closed-loop calculation.
It improves the accuracy of flow pulsation calculation in hydraulic steering systems, provides accurate data support, and ensures the effective acquisition of pressure pulsation and accurate calculation of flow pulsation under experimental conditions of the steering system.
Smart Images
Figure CN121520274A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of steering gear performance testing technology, and in particular to a steering system pressure pulsation testing system and measurement method. Background Technology
[0002] The pressure and flow pulsations in a hydraulic steering system directly affect valve stability and steering feel. However, existing measurement and calculation methods are not ideal. Flowmeters typically have insufficient dynamic bandwidth, are sensitive to oil temperature and cavitation, and are intrusive in installation, making it difficult to capture high-frequency pulsations. Traditional pipeline models based on two-point pressure inversion are prone to amplitude and phase distortion and unstable results due to factors such as half-wavelength degradation, unknown boundary reflections, sound velocity and characteristic impedance mismatch, branch coupling, and asynchronous sampling. In engineering settings, sensor zero drift, temperature drift, and the difficulty in separating steady-state and dynamic states further complicate the process, making it difficult to form a reliable closed loop for pressure measurement and flow calculation. Therefore, it is challenging to accurately calculate the flow pulsation data of the hydraulic steering system. Summary of the Invention
[0003] The main purpose of this application is to provide a steering system pressure pulsation testing system and measurement method, which aims to solve the technical problem of low accuracy in existing hydraulic steering system flow pulsation calculation methods.
[0004] To achieve the above objectives, this application provides a steering system pressure pulsation testing system for testing a steering system. The steering system includes a steering mechanism, which is connected to a hydraulic station via two hydraulic lines. The testing system includes a power component and a pressure sensor component. The power component provides power to deliver hydraulic oil from the hydraulic station to the steering mechanism via the hydraulic lines. The power component includes a motor pump and a muffler simultaneously installed on the two hydraulic lines. The pressure sensor component is installed on the two hydraulic lines and is used to collect pressure change data between the motor pump and the muffler, and between the muffler and the steering mechanism, respectively.
[0005] Optionally, the pressure sensor assembly includes a first dynamic pressure sensor, a third dynamic pressure sensor, a fifth dynamic pressure sensor, and a first steady-state pressure sensor disposed on one of the hydraulic lines, and a second dynamic pressure sensor, a fourth dynamic pressure sensor, a sixth dynamic pressure sensor, and a second steady-state pressure sensor disposed on the other hydraulic line; wherein the first dynamic pressure sensor and the second dynamic pressure sensor are both located at the outlet end of the motor pump, the third dynamic pressure sensor, the fourth dynamic pressure sensor, the first steady-state pressure sensor, and the second steady-state pressure sensor are all located at the outlet end of the muffler, and the fifth dynamic pressure sensor and the sixth dynamic pressure sensor are both located at the inlet end of the steering mechanism.
[0006] Optionally, it also includes an overflow valve located in the main oil circuit of the hydraulic station; wherein the main oil circuit connects two hydraulic lines.
[0007] Optionally, it also includes a housing, in which the steering mechanism, power components and pressure sensor components are all integrated.
[0008] Optionally, it also includes a vibration damping platform, on which the housing is mounted.
[0009] Optionally, it also includes a pressure gauge and a temperature sensor installed on the hydraulic line.
[0010] Optionally, the pressure sensor assembly, pressure gauge, and temperature sensor are all electrically connected to a data acquisition card.
[0011] Optionally, the motor pump is electrically connected to an electrical control cabinet, which is also electrically connected to a data acquisition card.
[0012] To achieve the above objectives, this application also provides a measurement method based on the aforementioned steering system pressure pulsation testing system, comprising the following steps: Obtain the position of the two hydraulic lines respectively x Flow rate at the measurement point Q x ; Obtain the position of the two hydraulic lines respectively x Pressure pulsation at the measurement point P ; Obtain the position of the two hydraulic lines respectively x Equivalent impedance at the measurement point Z x ;in, Z x = Z 0- Z L , Z 0 represents the pipe resistance of the hydraulic pipeline, and Z 0= / A, ρ Let B be the density of the fluid in the pipe, B be the effective bulk modulus of the fluid in the pipe, and A be the flow area of the pipe. Z L Let be the equivalent termination impedance of all pipes located after the measurement point, and Z L = P l / Q l ，P l The pressure is measured by a pressure sensor located after the measurement point. Q l This represents the flow rate at the pressure sensor located one step after the measurement point. Based on traffic Q xPressure pulsation P and equivalent impedance Z x The positions of the two hydraulic lines were obtained respectively. x Flow pulsation at the measurement point Q ;in, Q = Q x + P / Z x ; Get two traffic pulses Q The difference is returned to obtain the position of the two hydraulic lines respectively. x Flow rate at the measurement point Q x Iterate to two flow pulses Q The two flow pulsations with the smallest difference are selected. Q The average value output is the final flow pulsation value.
[0013] Optionally, Q x and P The expressions are as follows:
[0014]
[0015] In the formula, r For the pipe radius, P 0 represents the pressure measured by the pressure sensor located before the measurement point. Q 0 represents the flow rate at the pressure sensor preceding the measurement point. ρ L For the reflection characteristics of the pipe, where ρ L =( Z L - Z 0) / ( Z L + Z 0), l The distance between the two pressure sensors located before and after the measurement point.
[0016] The beneficial effects that this application can achieve are as follows: This application includes a power assembly and a pressure sensor assembly. The power assembly provides power to deliver hydraulic oil from the hydraulic station to the steering mechanism through hydraulic pipelines. The power assembly includes a motor pump and a muffler simultaneously installed on two hydraulic pipelines. The pressure sensor assembly is installed on both hydraulic pipelines and is used to collect pressure change data between the motor pump and the muffler, and between the muffler and the steering mechanism. This application can capture the fluid pressure fluctuations of the motor pump and the muffler by separately collecting pressure change data between the motor pump and the muffler, and between the muffler and the steering mechanism. This allows for the separate reflection of the motor pump's performance and fluid pulsation characteristics, and monitoring of the muffler's noise attenuation effect, providing accurate data support for subsequent flow pulsation calculations and improving calculation accuracy. In summary, this application can provide robust experimental conditions for the acquisition of steering system pressure pulsations and can effectively and accurately calculate the flow pulsations at any point in the steering system and its pipelines. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.
[0018] Figure 1 This is a schematic diagram of the frame structure of a steering system pressure pulsation testing system according to an embodiment of this application; Figure 2 This is a schematic diagram illustrating the installation principle of the pressure sensor assembly in an embodiment of this application; Figure 3 This is a schematic diagram of the hardware structure of a steering system pressure pulsation testing system according to an embodiment of this application.
[0019] Figure label: 1-Power assembly, 1.1-Motor pump, 1.2-Muffler, 2-Pressure sensor assembly, 2.1-First dynamic pressure sensor, 2.2-Second dynamic pressure sensor, 2.3-Third dynamic pressure sensor, 2.4-First steady-state pressure sensor, 2.5-Fourth dynamic pressure sensor, 2.6-Second steady-state pressure sensor, 2.7-Fifth dynamic pressure sensor, 2.8-Sixth dynamic pressure sensor, 3-Relief valve, 4-Housing, 5-Vibration damping stand, 6-Pressure gauge, 7-Temperature sensor, 8-Data acquisition card, 9-Electrical control cabinet, 10-Steering mechanism, 11-Hydraulic pipeline, 12-Hydraulic station.
[0020] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation
[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0022] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of this application are only used to explain the relative positional relationship and movement of each component in a specific posture. If the specific posture changes, the directional indication will also change accordingly.
[0023] In this application, unless otherwise expressly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral part; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal communication of two components or the interaction between two components, unless otherwise expressly limited. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.
[0024] Furthermore, if the embodiments of this application involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the meaning of "and / or" throughout the text includes three parallel solutions; for example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied simultaneously. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed in this application.
[0025] Example 1 Reference Figures 1-3This embodiment provides a steering system pressure pulsation testing system for testing a steering system. The steering system includes a steering mechanism 10, which is connected to a hydraulic station 12 via two hydraulic lines 11. The testing system includes a power component 1 and a pressure sensor component 2. The power component 1 provides power to deliver hydraulic oil from the hydraulic station 12 to the steering mechanism 10 via the hydraulic lines 11. The power component 1 includes a motor pump 1.1 and a muffler 1.2 simultaneously installed on the two hydraulic lines 11. The pressure sensor component 2 is installed on the two hydraulic lines 11 and is used to collect pressure change data between the motor pump 1.1 and the muffler 1.2, and between the muffler 1.2 and the steering mechanism 10, respectively.
[0026] In this embodiment, pressure change data between the motor pump 1.1 and the muffler 1.2, and between the muffler 1.2 and the steering mechanism 10, can be collected by the pressure sensor assembly 2. This captures the fluid pressure fluctuations of the motor pump 1.1 and the muffler 1.2, reflecting the performance and fluid pulsation characteristics of the motor pump 1.1 and monitoring the noise attenuation effect of the muffler 1.2. This provides accurate data support for subsequent flow pulsation calculations and improves calculation accuracy. In summary, this embodiment provides strong experimental conditions for the acquisition of steering system data and effectively collects the pressure pulsation of the steering system. It can also effectively and accurately calculate the flow pulsation at any point in the steering system and its pipelines.
[0027] It should be noted that the hydraulic line 11 is also equipped with components such as adapters, flange clamps, flow meters, pilot-operated relief valves, and filters.
[0028] As an optional implementation, the pressure sensor assembly 2 includes a first dynamic pressure sensor 2.1, a third dynamic pressure sensor 2.3, a fifth dynamic pressure sensor 2.7, and a first steady-state pressure sensor 2.4 disposed on one of the hydraulic lines 11, and a second dynamic pressure sensor 2.2, a fourth dynamic pressure sensor 2.5, a sixth dynamic pressure sensor 2.8, and a second steady-state pressure sensor 2.6 disposed on the other hydraulic line 11; wherein the first dynamic pressure sensor 2.1 and the second dynamic pressure sensor 2.2 are both located at the outlet end of the motor pump 1.1, the third dynamic pressure sensor 2.3, the fourth dynamic pressure sensor 2.5, the first steady-state pressure sensor 2.4, and the second steady-state pressure sensor 2.6 are all located at the outlet end of the muffler 1.2, and the fifth dynamic pressure sensor 2.7 and the sixth dynamic pressure sensor 2.8 are both located at the inlet end of the steering mechanism 10.
[0029] In this embodiment, a first dynamic pressure sensor 2.1 and a second dynamic pressure sensor 2.2 (corresponding to) are respectively arranged at the outlet of the motor pump 1.1. Figure 2(Y1 and Y2), the pressure sensors here can capture the fluid pressure fluctuations of the motor pump 1.1 in real time. By collecting the pressure changes at the outlet, the performance of the motor pump 1.1 and the fluid pulsation characteristics can be reflected, thus providing accurate data for the dynamic response analysis of the system. A third dynamic pressure sensor 2.3 (corresponding to...) is arranged at the outlet of the silencer 1.2. Figure 2 Y3), the fourth dynamic pressure sensor 2.5 (corresponding to) Figure 2 Y4), the first steady-state pressure sensor 2.4 (corresponding to Figure 2 W1) and the second steady-state pressure sensor 2.6 (corresponding to Figure 2 The arrangement (W2) can capture pressure changes within the muffler 1.2, ensuring effective monitoring of its noise attenuation effect and providing accurate data support for subsequent flow pulsation calculations. Pressure fluctuations in the muffler 1.2 directly affect the flow characteristics of the steering system; therefore, the pressure data at the muffler 1.2 outlet is crucial. This is achieved by arranging a fifth dynamic pressure sensor 2.7 and a sixth dynamic pressure sensor 2.8 (corresponding to...) at the inlet of the steering mechanism 10 cylinder. Figure 2 (Y5 and Y6 in the middle). This arrangement can effectively monitor the pressure pulsation at the cylinder inlet, reflecting the dynamic characteristics of the steering system and the cylinder's response to fluid pressure fluctuations, directly providing data support for the calculation of flow pulsation. By monitoring the inlet pressure, the relationship between flow rate changes and steering control can be indirectly determined, further optimizing the working efficiency of the steering system.
[0030] As an optional implementation, a relief valve 3 is also included in the main oil circuit of the hydraulic station 12; wherein the main oil circuit connects two hydraulic lines 11. The relief valve 3 can control the pressure and flow rate to stabilize the pressure fluctuations of the hydraulic system during the test process and ensure that the test system operates stably under different pressures.
[0031] As an optional implementation, it also includes a housing 4, in which the steering mechanism 10, power assembly 1 and pressure sensor assembly 2 are all integrated. This high degree of integration avoids the problem of messy wiring caused by a large number of sensors.
[0032] As an optional implementation, it also includes a vibration damping platform 5, on which the housing 4 is disposed.
[0033] In this embodiment, the vibration damping test stand 5 can effectively attenuate the transmission of vibration through the combination design of rubber vibration isolators and aluminum alloy supports, ensuring that the steering system is not disturbed by external vibration during the test. The rubber vibration isolators can be accurately selected to ensure that the steering system can effectively suppress the transmission of vibration during the test.
[0034] As an optional implementation, a pressure gauge 6 and a temperature sensor 7 are also provided on the hydraulic line 11 to display pressure data and temperature data at corresponding locations on the hydraulic line 11, respectively, for easy and intuitive viewing.
[0035] As an optional implementation, the pressure sensor assembly 2, pressure gauge 6, and temperature sensor 7 are all electrically connected to a data acquisition card 8. The data acquisition card 8 can be a 12-channel high-sampling-rate high-speed data acquisition card, which can be used to acquire pressure pulsation signals and convert them into editable data for data analysis and processing.
[0036] As an optional implementation, the motor pump 1.1 is electrically connected to an electrical control cabinet 9, which is also electrically connected to a data acquisition card 8. The electrical control cabinet 9 can control the start and stop, pressure adjustment, and speed adjustment of the motor pump 1.1. The electrical control cabinet 9 can be equipped with a data acquisition system to receive data transmitted from the data acquisition card 8 for subsequent data analysis.
[0037] Example 2 Reference Figures 1-3 To achieve the above objectives, this embodiment also provides a measurement method based on a steering system pressure pulsation testing system described in the above embodiment, comprising the following steps: Obtain the positions of the two hydraulic lines 11 respectively. x Flow rate at the measurement point Q x ; Obtain the positions of the two hydraulic lines 11 respectively. x Pressure pulsation at the measurement point P ; Obtain the positions of the two hydraulic lines 11 respectively. x Equivalent impedance at the measurement point Z x ;in, Z x = Z 0- Z L , Z 0 represents the pipe resistance of hydraulic line 11, and Z 0= / A, ρ Let B be the fluid density in the pipe (i.e., the pipe of hydraulic line 11), B be the effective bulk modulus of the fluid in the pipe, and A be the flow area of the pipe. Z L Let be the equivalent termination impedance of all pipes located after the measurement point, and Z L = P l / Q l ，P lThe pressure is measured by a pressure sensor located after the measurement point. Q l This represents the flow rate at the pressure sensor located one step after the measurement point. Based on traffic Q x Pressure pulsation P and equivalent impedance Z x The positions of the two hydraulic lines were obtained respectively. x Flow pulsation at the measurement point Q ;in, Q = Q x + P / Z x ; Get two traffic pulses Q The difference is returned to obtain the position of the two hydraulic lines respectively. x Flow rate at the measurement point Q x Iterate to two flow pulses Q The two flow pulsations with the smallest difference are selected. Q The average value output is the final flow pulsation value.
[0038] In this embodiment, multiple dynamic pressure sensors are arranged at two hydraulic lines 11 and synchronously acquire data at high speed. Dual-baseline weighting is used to avoid half-wavelength degradation. Combined with boundary impedance matching and valve port equivalent modeling, instantaneous flow pulsation is accurately and in real-time inverted from pressure pulsation. Therefore, the flow pulsation here... Q The calculation integrates flow Q x Pressure pulsation P and equivalent impedance Z x Key parameters such as pressure measurement and flow calculation are used to achieve a reliable closed loop, thus balancing arbitrability, accuracy, and robustness. This is achieved by controlling the flow pulsation of the hydraulic lines in both branches. Q Perform mutual verification (i.e., difference comparison). The smallest difference indicates that the calculated data is more reliable. At this point, the two flow pulses with the smallest difference are selected. Q The average value is output as the final flow pulsation value, and high-precision flow pulsation data is finally calculated.
[0039] As an optional implementation method, calculate the flow. Q x and pressure pulsation P At that time, based on the propagation characteristics of pressure fluctuations within the pipeline, we can obtain:
[0040] In the above formula, P x For hydraulic line 11 in position x The pressure at the measurement point, where cosh( x )=( e x +e -x ) / 2, sinh( x )=( e x -e -x The flow rate can be calculated by dividing the result by 2. Q x The expression is: And the pressure pulsation was calculated. P for:
[0041] In the formula, r For the pipe radius, P 0 represents the pressure measured by the pressure sensor located before the measurement point. Q 0 represents the flow rate at the pressure sensor preceding the measurement point. ρ L For the reflection characteristics of the pipe, where ρ L =( Z L - Z 0) / ( Z L + Z 0), l The distance between the two pressure sensors located before and after the measurement point.
[0042] In the above formula, the spacing between adjacent pressure sensors l This can be used to guide the calculation of flow pulsations at the installation points of pressure sensors, assuming the distance between the first dynamic pressure sensor 2.1 and the third dynamic pressure sensor 2.3 is... l 1. The distance between the third dynamic pressure sensor 2.3 and the fifth dynamic pressure sensor 2.7 is... l 2. The distance between the second dynamic pressure sensor 2.2 and the fourth dynamic pressure sensor 2.5 is... l 3. The spacing between the fourth dynamic pressure sensor 2.5 and the sixth dynamic pressure sensor 2.8 is... l 4. The above spacing data can be processed separately. l 1- l 4. Substitute into the above formula to fully verify the reliability of the calculated data.
[0043] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.
Claims
1. A steering system pressure pulsation testing system, characterized by, The utility model relates to a kind of test steering system, steering system includes steering mechanism, steering mechanism is connected with hydraulic station by two hydraulic lines, and test system includes: Power assembly is used to provide power to deliver hydraulic oil of hydraulic station to steering mechanism by hydraulic line, and power assembly includes motor pump and muffler arranged simultaneously on two hydraulic lines; Pressure sensor assembly is arranged on two hydraulic lines, and pressure sensor assembly is used to respectively collect the pressure change data between motor pump and muffler, between muffler and steering mechanism.
2. A pressure pulsation testing system for a steering system as claimed in claim 1, wherein Pressure sensor assembly includes first dynamic pressure sensor, third dynamic pressure sensor, fifth dynamic pressure sensor and first steady pressure sensor arranged on one of hydraulic lines, and second dynamic pressure sensor, fourth dynamic pressure sensor, sixth dynamic pressure sensor and second steady pressure sensor arranged on another hydraulic line;Wherein, first dynamic pressure sensor and second dynamic pressure sensor are located at the outlet end of motor pump, third dynamic pressure sensor, fourth dynamic pressure sensor, first steady pressure sensor and second steady pressure sensor are located at the outlet end of muffler, and fifth dynamic pressure sensor and sixth dynamic pressure sensor are located at the inlet end of steering mechanism.
3. A pressure pulsation testing system for a steering system as claimed in claim 1 or 2, characterized in that It further includes overflow valve arranged on main oil circuit of hydraulic station;Wherein, main oil circuit communicates two hydraulic lines.
4. A pressure pulsation testing system for a steering system as claimed in claim 1 or 2, wherein It further includes shell, and steering mechanism, power assembly and pressure sensor assembly are integratedly arranged in shell.
5. A pressure pulsation testing system for a steering system as claimed in claim 4, wherein, It further includes damping rack, and shell is arranged on damping rack.
6. A pressure pulsation testing system for a steering system as claimed in claim 1 or 2, wherein It further includes pressure gauge and temperature sensor arranged on hydraulic line.
7. A pressure pulsation testing system for a steering system as claimed in claim 6, wherein, Pressure sensor assembly, pressure gauge and temperature sensor are electrically connected with acquisition card simultaneously.
8. A pressure pulsation testing system for a steering system as claimed in claim 7, wherein, Motor pump is electrically connected with electric control cabinet, and electric control cabinet is also electrically connected with acquisition card.
9. A method of measurement, characterized by, Based on the pressure pulsation test system of the steering system as claimed in claim 2, comprising the following steps: The flow rates of the measuring points of the two hydraulic lines at positions x are acquired respectively Q x ; The pressure fluctuations of the measuring points of the two hydraulic lines at positions x are acquired respectively P ; The equivalent impedance of the measurement points of the two hydraulic lines at position x are acquired respectively Z x ; wherein, Z x = Z 0- Z L , Z 0 is the pipe impedance of the hydraulic line, and Z 0= / A, ρ is the fluid density in the pipe, B is the effective bulk modulus of the fluid in the pipe, and A is the flow area of the pipe, Z L is the equivalent terminal impedance of all lines after the measurement point, and Z L = P l / Q l ，P l is the pressure measured by a pressure sensor after the measurement point, Q l is the flow at the pressure sensor after the measurement point; According to the flow rate Q x , the pressure pulsation P and the equivalent impedance Z x , the flow rate pulsation Q of the measuring points of the two hydraulic pipelines at positions x is obtained respectively; wherein, Q = Q x + P / Z x ; Get two traffic pulses Q The difference is returned to obtain the position of the two hydraulic lines respectively. x Flow rate at the measurement point Q x Iterate to two flow pulses Q The two flow pulsations with the smallest difference are selected. Q The average value output is the final flow pulsation value.
10. A method of measuring as claimed in claim 9, characterized in that, Q x and P The expressions of the above are respectively: wherein r R is the pipe radius, P P0 is the pressure measured at the previous pressure sensor before the measurement point, Q Q0 is the flow at the previous pressure sensor before the measurement point, ρ L R is the pipe reflection characteristic, wherein ρ L = Z L - Z P0) / (Q0), Z L + Z P0), l is the distance between the two pressure sensors before and after the measurement point.