CN109441793B - Method for obtaining p-V diagram of reciprocating compressor by measuring strain of piston rod - Google Patents
Method for obtaining p-V diagram of reciprocating compressor by measuring strain of piston rod Download PDFInfo
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Abstract
A method for obtaining a p-V diagram of a reciprocating compressor by measuring the strain of a piston rod comprises the steps of obtaining a rod load according to the measured strain of the piston rod, subtracting a reciprocating inertia force from the rod load to obtain a change curve of a resultant gas force, performing nonlinear regression on the resultant gas force curve in a Fourier series form to obtain a fitting function of the resultant gas force, expressing an axial side pressure function in a Fourier series form to obtain a cover side pressure function, solving an equation of the resultant gas force, which is the sum of the axial side gas force and the cover side gas force, to obtain various coefficients of the pressure function, obtaining an axial side and cover side pressure function (p-theta diagram), and obtaining the p-V diagram of the reciprocating compressor. On one hand, the invention does not need to punch on the compressor, thereby avoiding the problem of damaging the compressor body in the prior art. On the other hand, through data collection and calculation, the fitted curve can reflect the processes of air suction, air exhaust, expansion and compression, and fault diagnosis and running state monitoring can be carried out according to a p-V diagram of the reciprocating compressor.
Description
Technical Field
The invention belongs to the technical field of reciprocating compressors, and particularly relates to a method for obtaining a p-V diagram of a reciprocating compressor by measuring strain of a piston rod.
Background
The reciprocating compressor has wide application range, can compress all gases theoretically, can reach the required pressure no matter the flow size, has high volumetric efficiency, can adapt to the working conditions of oil and oil-free, is considered as the most efficient gas compression equipment and is widely applied to various fields of national economy such as refrigeration air conditioners, aerodynamic force, petrochemical industry, natural gas industry and the like. Once a reciprocating compressor fails, the whole process flow will be affected, with serious and even catastrophic consequences. In order to avoid accidents, the state monitoring and fault diagnosis of the compressor are very important.
The indication diagram, i.e. the p-V diagram, is the comprehensive reflection of the working performance and the running state of the compressor and is the most effective tool for diagnosing the fault of the compressor. The performance parameters such as suction and discharge pressure loss, indicated power, pressure ratio, volumetric efficiency and the like can be obtained through a p-V diagram in the working process of the compressor, and the leakage condition of a gas outlet valve, a piston ring, a stuffing and the like, the air pulsation condition of a pipeline, the heat exchange condition in the working process of the compressor and the like can be directly reflected through the shape of the p-V diagram.
The existing compressors manufactured according to the API618 standard are all provided with pressure measuring holes, most old compressors in service are not provided with the pressure measuring holes, the air cylinder needs to be processed for measuring the pressure change in the air cylinder, some process compressors for compressing special media do not allow the pressure measuring holes to be processed on the air cylinder, in addition, the strength of the air cylinder is influenced by holes formed in the wall of the air cylinder, and the potential threat exists, so that the invasive measuring and taking mode seriously limits the popularization and application of the p-V diagram diagnostic method.
In order to enable the p-V diagram method not to be limited to experimental research and be applied to actual production, the method which does not influence the structure and the strength of the cylinder needs to be adopted to obtain the monitoring of the pressure change in the cylinder.
Disclosure of Invention
In view of the problems in the prior art, it is an object of the present invention to provide a method for obtaining a p-V map of a reciprocating compressor by measuring the piston rod strain.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for obtaining a p-V map of a reciprocating compressor by measuring piston rod strain, comprising the steps of:
(1) installing a photoelectric sensor at the flywheel, determining an initial value 0 of a crank angle theta of the compressor through the obtained outer dead center signal, pasting a strain gauge on a piston rod, and measuring to obtain the crank angle theta of the compressor in one period of operation from [0, 2 pi ]]Rod load function F for each anglerod(θ)；
(2) To [0, 2 pi ]]Resultant force function F of gas force in cycleg(theta) performing nonlinear regression to obtain a fitting result with a period of [0, 2 pi ]]Function F'g(θ); wherein the gas force resultant force function Fg(θ)＝Frod(θ)-FI(θ)，Frod(theta) as a function of the rod load, FI(theta) is a reciprocating inertial force FI(θ)＝mprω2(cos θ + λ cos2 θ), where mpFor reciprocating inertial mass, r is the crank radius and omega is the compressorThe rotating speed, lambda is the crank radius connecting rod ratio, and theta is the crank angle;
(3) according to a period of [0, 2 π]Function F'g(theta), solving the axial pressure function pCE(theta) and head side pressure function pHE(theta) then at VCE(θ)/V0CEAnd VHE(θ)/V0HEAs abscissa, with pCE(θ)/psCEAnd with pHE(θ)/psHEAs a ordinate, the axial pressure p at a crank angle θ of 0 DEG is takenCE(0) For shaft side suction pressure psCETaking the cover side pressure p at a crank angle theta of 180 DEGHE(180) For cover side suction pressure psHEObtaining a p-V diagram of the reciprocating compressor; wherein, VCE(theta) is the axial working volume, VHE(theta) is the head-side working volume, V0CEIs the total axial volume, V0HEIs the total volume on the cover side; p is a radical ofCE(θ) is a function of the pressure on the shaft side, pHE(θ) is a head side pressure function.
The further improvement of the invention is that the specific process of the nonlinear regression in the step (2) is as follows: taking a nonlinear function prototype as a Fourier series form:theta is crank angle, n is number of expansion times, and a is used to ensure fitting accuracy0，a1，...，anAnd b1，...，bnAs a coefficient, fitting was performed to obtain a period of [0, 2 π]Function F'g(θ)。
In a further development of the invention, the number of expansions n is equal to or greater than 50.
A further development of the invention consists in solving the axial pressure function p in step (3)CE(theta) and head side pressure function pHE(θ), the specific process is as follows:
(a) obtaining the pressure function p on the shaft side in the form of Fourier series expansionCE(θ)：
Wherein: theta is the crank angle, n is the number of expansions, aCE0，aCE1，...，aCEnAnd bCE1，...，bCEnIs a coefficient;
(b) from the axial side pressure function pCE(theta) obtaining a head-side pressure function pHEExpression of (θ):
(c) solving the equation: f'g(θ)＝pCE(θ)×SCE-pHE(θ)×SHEWherein p isCE(θ) is a function of the pressure on the shaft side, pHE(θ) is a head side pressure function, SCEIs the axial side area of the piston, SHEArea of piston cap side, obtained aCE0，aCE1......aCEnum，bCE1，bCE2......bCEnumTo obtain the axial pressure function pCE(theta) and head side pressure function pHE(θ)。
The invention is further improved in that the shaft side working volume
Working volume on cover side
Total axial volume V0CE＝2SCEr, total cover side volume V0HE＝2SHEr, wherein: r is the crank radius, theta is the crank angle, and lambda is the crank link ratio.
Compared with the prior art, the invention has the following beneficial effects: the invention determines the initial value of the crank angle theta of the compressor to be 0 through the obtained outer dead point signal by installing the photoelectric sensor at the flywheel, and sticks the strain gauge on the piston rodMeasuring the crank angle theta of the compressor in one period of operation from 0, 2 pi]Rod load function F for each anglerod(θ); according to the rod load function Frod(theta) subtracting the reciprocating inertial force FI(theta) obtaining a variation function F of the resultant force of gas forcesg(theta), performing nonlinear regression in Fourier series form to obtain fitting result, and performing axial pressure function pCE(theta) and head side pressure function pHE(theta), and combining the working volumes of the pistons on the shaft side and the cover side and the total volume to obtain a p-V diagram of the reciprocating compressor. On one hand, the invention does not need to punch on the compressor, thereby avoiding the problem of damaging the compressor body in the prior art. On the other hand, through data collection and calculation, the fitted curve can reflect the processes of air suction, air exhaust, expansion and compression, and fault diagnosis and running state monitoring can be carried out according to a p-V diagram of the reciprocating compressor.
Drawings
FIG. 1 is a graph of rod load, resultant gas force, reciprocating inertial force;
FIG. 2 is a gas force resultant force actual curve and a fitting curve;
FIG. 3 shows the results of fitting a curve to a p-theta diagram;
FIG. 4 shows the results of fitting a curve to a p-V diagram of a reciprocating compressor.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
The invention relates to a method for obtaining a p-V diagram of a reciprocating compressor by measuring the strain of a piston rod, which comprises the following steps:
(1) installing a photoelectric sensor at the flywheel, determining an initial value 0 of a crank angle theta of the compressor through the obtained outer dead center signal, pasting a strain gauge on a piston rod, and measuring to obtain the crank angle theta of the compressor in one period of operation from [0, 2 pi ]]Rod load function F for each anglerod(θ)；
(2) Calculating the resultant force function F of gas forceg(θ); the specific process is as follows:
(2a) calculating the reciprocating inertia force FI(θ)＝mprω2(cos θ + λ cos2 θ), where mpTo reciprocateInertia mass, r is a crank radius, omega is a compressor rotating speed, lambda is a crank radius connecting rod ratio, and theta is a crank angle;
(2b) gas-taking resultant force function Fg(θ)＝Frod(θ)-FI(θ), FIG. 1;
(3) for [0, 2 π ] in step (2)]Resultant force function F of gas force in cycleg(theta) performing nonlinear regression, and taking a nonlinear function prototype as a Fourier series form:
theta is crank angle, n is expansion times, n is greater than or equal to 50, preferably n is 50, a is0，a1，...，anAnd b1，...，bnAs a coefficient, fitting was performed to obtain a period of [0, 2 π]Function F'g(θ), FIG. 2;
(4) solving the axial pressure function pCE(theta) and head side pressure function pHE(θ), the specific process is as follows:
(4a) obtaining the pressure function p on the shaft side in the form of Fourier series expansionCE(θ)：
Wherein: theta is crank angle, n is expansion times, n is greater than or equal to 50, preferably n is 50, a isCE0，aCE1，...，aCEnAnd bCE1，...，bCEnIs a coefficient;
(4b) from the axial side pressure function pCE(theta) obtaining a head-side pressure function pHEExpression of (θ):
(4c) solving the equation: f'g(θ)＝pCE(θ)×SCE-pHE(θ)×SHEWherein p isCE(θ) is a function of the pressure on the shaft side, pHE(theta) is a head-side pressureFunction, SCEIs the axial side area of the piston, SHEArea of piston cap side, obtained aCE0，aCE1......aCEnum，bCE1，bCE2......bCEnumTo obtain the axial pressure function pCE(theta) and head side pressure function pHE(θ), as in FIG. 3;
(5) obtaining a p-theta diagram and a p-V diagram of the reciprocating compressor, wherein the specific process is as follows:
(5a) calculating side working volume of shaft
And cover side working volume
Calculating the total axial volume V0CE＝2SCEr and total cover side volume V0HE＝2SHEr, wherein: r is the crank radius, theta is the crank angle, and lambda is the crank link ratio;
(5b) using crank angle theta as abscissa and pCE(θ)/psCEAnd with pCE(θ)/psHEIs the ordinate in which pCE(theta) is the axial side pressure, pHE(theta) is a cover side pressure, and a shaft side pressure p at a crank angle theta of 0 DEG is takenCE(0) For shaft side suction pressure psCETaking the cover side pressure p at a crank angle theta of 180 DEGHE(180) For cover side suction pressure psHEObtaining a p-theta diagram, as shown in FIG. 4;
(5c) with VCE(θ)/V0CEAnd VHE(θ)/V0HEAs abscissa, with pCE(θ)/psCEAnd with pHE(θ)/psHEAs a ordinate, the axial pressure p at a crank angle θ of 0 DEG is takenCE(0) For shaft side suction pressure psCETaking the cover side pressure p at a crank angle theta of 180 DEGHE(180) For cover side suction pressure psHEAnd obtaining a p-V diagram of the reciprocating compressor, as shown in figure 4.
Claims (5)
1. A method for obtaining a p-V map of a reciprocating compressor by measuring the piston rod strain, characterized in that it comprises the following steps:
(1) installing a photoelectric sensor at the flywheel, determining an initial value 0 of a crank angle theta of the compressor through the obtained outer dead center signal, pasting a strain gauge on a piston rod, and measuring to obtain the crank angle theta of the compressor in one period of operation from [0, 2 pi ]]Rod load function F for each anglerod(θ)；
(2) To [0, 2 pi ]]Resultant force function F of gas force in cycleg(theta) performing nonlinear regression to obtain a fitting result with a period of [0, 2 pi ]]Function F'g(θ); wherein the gas force resultant force function Fg(θ)＝Frod(θ)-FI(θ)，Frod(theta) as a function of the rod load, FI(theta) is a reciprocating inertial force FI(θ)＝mprω2(cos θ + λ cos2 θ), where mpThe reciprocating inertia mass is represented by r, the radius of a crank, omega, the rotating speed of the compressor, lambda, the connecting rod ratio of the radius of the crank and theta, and the crank angle;
(3) according to a period of [0, 2 π]Function F'g(theta), solving the axial pressure function pCE(theta) and head side pressure function pHE(theta) then at VCE(θ)/V0CEAnd VHE(θ)/V0HEAs abscissa, with pCE(θ)/psCEAnd with pHE(θ)/psHEAs a ordinate, the axial pressure p at a crank angle θ of 0 DEG is takenCE(0) For shaft side suction pressure psCETaking the cover side pressure p at a crank angle theta of 180 DEGHE(180) For cover side suction pressure psHEObtaining a p-V diagram of the reciprocating compressor; wherein, VCE(theta) is the axial working volume, VHE(theta) is the head-side working volume, V0CEIs the total axial volume, V0HEIs the total volume on the cover side; p is a radical ofCE(θ) is a function of the pressure on the shaft side, pHE(θ) is a head side pressure function.
2. The method for obtaining p-V map of reciprocating compressor by measuring strain of piston rod as claimed in claim 1, wherein the specific process of non-linear regression in step (2) is: taking a nonlinear function prototype as a Fourier series form:
theta is crank angle, n is number of expansion times, and a is used to ensure fitting accuracy0，a1，...，anAnd b1，...，bnAs a coefficient, fitting was performed to obtain a period of [0, 2 π]Function F'g(θ)。
3. A method for obtaining a p-V map of a reciprocating compressor by measuring the piston rod strain according to claim 2, characterized in that the number of expansions n is equal to or greater than 50.
4. Method for obtaining a p-V map of a reciprocating compressor by measuring piston rod strain according to claim 1, characterized in that in step (3) the shaft side pressure function p is solvedCE(theta) and head side pressure function pHE(θ), the specific process is as follows:
(a) obtaining the pressure function p on the shaft side in the form of Fourier series expansionCE(θ)：
Wherein: theta is the crank angle, n is the number of expansions, aCE0，aCE1，...，aCEnAnd bCE1，...，bCEnIs a coefficient;
(b) from the axial side pressure function pCE(theta) obtaining a head-side pressure function pHEExpression of (θ):
(c) solving the equation: f'g(θ)＝pCE(θ)×SCE-pHE(θ)×SHEWherein p isCE(θ) is a function of the pressure on the shaft side, pHE(θ) is a head side pressure function, SCEIs the axial side area of the piston, SHEThe area of the side of the piston cover,to obtain aCE0，aCE1......aCEnum，bCE1，bCE2......bCEnumTo obtain the axial pressure function pCE(theta) and head side pressure function pHE(θ)。
5. Method for obtaining a p-V map of a reciprocating compressor by measuring piston rod strain according to claim 1, characterized in that the shaft side working volume
Working volume on cover side
Total axial volume V0CE＝2rSCETotal volume V of the cover side0HE＝2rSHEWherein: r is crank radius, theta is crank angle, lambda is crank radius to link ratio, SCEIs the axial side area of the piston, SHEIs the piston cap side area.
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| CN110145462B (en) * | 2019-05-30 | 2020-10-27 | 西安交通大学 | Structure and method for measuring annular gap pressure of piston ring of micro oil-free compressor |
| CN113700639B (en) * | 2021-09-09 | 2022-07-12 | 西安交通大学 | Nondestructive fault diagnosis system and method for reciprocating compressor |
| CN114320827B (en) * | 2021-11-19 | 2022-10-25 | 西安交通大学 | Nondestructive monitoring device and method for indicator diagram of liquid-driven piston compressor |
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| CN85108763A (en) * | 1985-11-21 | 1987-03-25 | 西安交通大学 | High speed reciprocating mechanical pressure indicating graph measuring device |
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Effective date of registration: 20210126 Address after: 712000 room 505, 5 / F, building 14, West Yungu phase I, Fengxi new town, Xixian New District, Xi'an City, Shaanxi Province Patentee after: Shaanxi Kangpu Intelligent Technology Co.,Ltd. Address before: Beilin District Xianning West Road 710049, Shaanxi city of Xi'an province No. 28 Patentee before: XI'AN JIAOTONG University |