CN113361060A - Friction torque optimization method for converting electromechanical indicator diagram into indicator diagram of pumping unit - Google Patents

Friction torque optimization method for converting electromechanical indicator diagram into indicator diagram of pumping unit Download PDF

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CN113361060A
CN113361060A CN202010149201.3A CN202010149201A CN113361060A CN 113361060 A CN113361060 A CN 113361060A CN 202010149201 A CN202010149201 A CN 202010149201A CN 113361060 A CN113361060 A CN 113361060A
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crank
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CN113361060B (en
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张立婷
李世超
郑东梁
曾鹏
石硕
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Shenyang Institute of Automation of CAS
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Abstract

The invention relates to the field of oil extraction engineering, in particular to a friction torque optimization method for converting an electric indicator diagram of an oil pumping unit into an indicator diagram. According to the invention, data are obtained through a sensor, friction torque and driving torque which are counted in friction are obtained through a stress balance equation of the crank, the connecting rod and the walking beam according to the data and the stress of the crank, the connecting rod and the walking beam, the friction torque and the driving torque are obtained after repeated iteration, an electric diagram is constructed and converted into an indicator diagram, and the working state of the pumping unit is monitored in real time. The method solves the problem of low conversion diagram precision caused by neglecting friction in the traditional method, improves the diagram conversion precision, and improves the oil well diagnosis and production metering accuracy based on the conversion diagram; through the optimization and improvement of the process of the traditional method for converting the indicator diagram into the indicator diagram, the accuracy and the timeliness of indicator diagram conversion are effectively improved, so that the indirect measurement mode of the indicator diagram is gradually realized, the working condition diagnosis and metering cost of an oil well is greatly reduced, and the low-cost Internet of things construction of the oil field based on the electric parameters is promoted.

Description

Friction torque optimization method for converting electromechanical indicator diagram into indicator diagram of pumping unit
Technical Field
The invention relates to the field of oil extraction engineering, in particular to a friction torque optimization method for converting an electric indicator diagram of an oil pumping unit into an indicator diagram.
Background
In recent years, indicator diagram analysis methods have become the main technical means for realizing oil well working condition diagnosis in various domestic oil fields, but indicator diagram measurement has the problems of high cost, poor real-time performance, low efficiency and the like, the working condition of ground equipment cannot be judged, and the requirements of oil field development digitization and intellectualization are difficult to meet. The electric diagram is convenient to measure, low in installation and maintenance cost, capable of comprehensively reflecting the working conditions of underground and ground equipment and capable of continuously monitoring for a long time. The inversion of the indicator diagram by using the electric parameters is to calculate the displacement and the load according to the measured electric parameters of the motor power and the like and the basic parameters of the pumping unit and the dynamics and the transmission relation of each mechanism of the pumping unit system. At present, the method for inverting the indicator diagram by using the electrical parameters has some defects, such as low conversion precision and efficiency, and if the method can be effectively optimized and improved, the method can be well applied to the engineering practical application in the oil field production field.
In the process of inverting the indicator diagram by using the indicator diagram, the solution of the friction torque is a key factor influencing the conversion efficiency and the conversion accuracy. Because a complex coupling relation exists between the counter force of the rotating pair and the required friction torque, in the process of solving the motion law of the crank by calculating the friction torque, a complex nine-element quadratic balance equation set needs to be solved, so that the time consumption of the whole work diagram inversion process is too long, the field actual requirement of real-time diagnosis is difficult to meet, friction is often ignored in a common conversion method, the difference between a simulation result and the real motion law is large, and the work diagram conversion precision is low.
The method for inverting the indicator diagram by the electric diagram is optimized and improved by adopting a combined solving algorithm of a balance equation, can overcome the defects and shortcomings of the method, greatly shortens the solving time while ensuring the conversion precision, effectively improves the calculation timeliness, has important significance for the practical application of the method for converting the electric diagram into the indicator diagram, and can greatly promote the construction of the low-cost Internet of things of the oil field based on the electric parameters.
Disclosure of Invention
The invention aims to solve the technical problems that the existing electric diagram inversion indicator diagram method is long in calculation time consumption and poor in conversion precision, and provides a combined solving algorithm of a balance equation aiming at the problems. The method greatly shortens the solving time while ensuring the conversion precision, and effectively improves the calculation timeliness.
The technical scheme adopted by the invention for solving the technical problems is as follows: a friction torque optimization method for converting an electric diagram of an oil pumping unit into an indicator diagram is characterized in that data are obtained through a sensor, friction torque and driving torque which are counted into friction are obtained through a stress balance equation of a crank, a connecting rod and a walking beam according to the data and stress of the crank, the connecting rod and the walking beam, the friction torque and the driving torque are obtained through repeated iteration, an electric diagram is constructed and converted into the indicator diagram, and the working state of the oil pumping unit is monitored in real time.
The optimized friction torque and driving torque are obtained through the following steps:
step 1: setting numerical values of an iteration error epsilon and a maximum iteration number N;
step 2: obtaining stress balance equations of the crank, the connecting rod and the walking beam according to the stress of the crank, the connecting rod and the walking beam, and establishing the balance equations simultaneously to obtain a balance equation set in a matrix form;
and step 3: combining partial equations according to a balance equation set in a matrix form to obtain an equation set under the condition of not counting friction and solving to obtain counter force of each revolute pair without counting friction and driving torque on a crankshaft;
and 4, step 4: obtaining friction torque of each revolute pair without friction through the counterforce of each revolute pair;
and 5: substituting the friction torque of each rotating pair without friction into a balance equation set in a matrix form to obtain the counter force of each rotating pair with the friction force initially counted and the driving torque on the crankshaft;
step 6: obtaining friction torque counted in friction according to the counter force of the friction-counted rotating pair and the driving torque on the crankshaft;
and 7: obtaining an iteration error;
and 8: when the iteration error is smaller than the set iteration error epsilon, the friction torque and the driving torque which are counted into friction at this time are taken as final results; and when the calculated iteration error is larger than the set iteration error epsilon, returning to the step 6 according to the obtained reaction force of the revolute pair and the driving torque on the crankshaft, and performing iteration circulation. And step 9: drawing an electric diagram and converting the electric diagram into an indicator diagram by acquiring the final counter force of the revolute pair and the driving torque on the crankshaft, and monitoring the working state of the pumping unit in real time by the indicator diagram obtained in real time;
the balance equation set in matrix form is as follows:
Figure BDA0002400841020000031
wherein R is the length of the crank, P is the length of the connecting rod, C is the length of the rear arm of the walking beam, A is the length of the front arm of the walking beam, and theta2At an angle theta from the base rod in the counterclockwise direction to the crank3Is the angle between the connecting rod and the base rod, theta4The included angle between the rear arm of the walking beam and the base rod is in the clockwise direction. Alpha is the angle between the base rod and the vertical direction, J1、J2、J3Is the moment of inertia m of crank, connecting rod and walking beam around the center of mass1、m2、m3The mass of the crank, connecting rod, walking beam, G1、G2、G3Is the gravity of a crank, a connecting rod and a walking beam,ε1、ε2、ε3angular acceleration of crank, connecting rod, walking beam centroid,/s1、ls2、ls3Is the distance between the crank, the connecting rod, the center of mass of the walking beam and the corresponding revolute pair, a2x、a2yIs the component of the acceleration of the connecting rod mass center in the x and y directions, omega1、ω3Angular velocity, P, of crank, walking beamAFor load at suspension point, F01x、F01yFor forces in the x and y directions of the crank-rotating shaft revolute pair, F21x、F21yFor forces in the x and y directions of the revolute pair between the crank and the connecting rod, F32x、F32yForce in the x and y directions of the revolute pair between the connecting rod and the walking beam, F30x、F30yStress of a revolute pair between a walking beam and a frame of the oil pumping unit in the x and y directions, MdIs the drive torque.
The method for acquiring the counter force of each revolute pair without friction and the driving torque on the crankshaft comprises the following steps:
the following two equations are combined together and solved to obtain F32xAnd F32y；
Figure BDA0002400841020000041
F obtained by solving32xAnd F32ySubstituting the combined matrix form into a balance equation set to obtain F21xAnd F21y，F30xAnd F30y，F21xAnd F21y；
According to F21xAnd F21yTo obtain MdThe method of (3) is implemented by the following formula:
Figure BDA0002400841020000042
the solving method for solving the friction torque of each revolute pair without friction through the counter force of each revolute pair comprises the following steps:
Mf01the friction torque at the crankshaft is specifically as follows:
Figure BDA0002400841020000043
Mf21the friction torque of a revolute pair between the crank and the connecting rod is as follows:
Figure BDA0002400841020000044
Mf32the friction torque of a revolute pair between the connecting rod and the walking beam is as follows:
Figure BDA0002400841020000045
Mf30the friction torque of a revolute pair between a walking beam and a frame of the oil pumping unit is as follows:
Figure BDA0002400841020000051
wherein f is the friction coefficient, and r is the radius of the rotating auxiliary shaft neck;
the calculation of the friction-included revolute pair reaction force and the driving torque on the crankshaft specifically comprises the following steps:
will Mf01And Mf21Substituting into a crank dynamics equation:
Figure BDA0002400841020000052
will Mf21And Mf32Substituting a connecting rod kinetic equation:
Figure BDA0002400841020000053
will Mf30And Mf32Substituting into walking beamKinetic equation:
Figure BDA0002400841020000054
respectively obtain F32xAnd F32y(ii) a According to F32xAnd F32yCan obtain F21xAnd F21y、F30xAnd F30y、F30xAnd F30；
According to F21xAnd F21yTo obtain MdThe method of (3) is implemented by the following formula:
Figure BDA0002400841020000055
the iterative error calculation method in step 7 is as follows:
and the iteration error |, the friction torque calculation result of the last friction counting-the friction torque calculation result of the last friction counting.
The iterative loop specifically includes:
substituting the n-th calculated reaction force of the revolute pair and the driving torque on the crankshaft into a balance equation set in a matrix form to obtain the n + 1-th reaction force of the revolute pair and the driving torque on the crankshaft, wherein the friction force is counted;
obtaining friction torque and driving torque of the n +1 th counted friction force according to the revolute pair reaction force of the n +1 th counted friction force and the driving torque on the crankshaft;
and judging the ending or the iteration again by calculating the iteration error.
The data acquisition through the sensor specifically comprises the steps of acquiring an included angle alpha between a base rod and the vertical direction and an included angle theta between a walking beam rear arm and the base rod in the clockwise direction through an angle sensor arranged on the oil pumping unit4；
Angular velocity omega of crank and walking beam obtained by angular displacement sensor mounted on oil pumping unit1、ω3。
The revolute pair counter-forces include01x、F01yFor forces in the x and y directions of the crank-rotating shaft revolute pair, F21x、F21yFor forces in the x and y directions of the revolute pair between the crank and the connecting rod, F32x、F32yForce in the x and y directions of the revolute pair between the connecting rod and the walking beam, F30x、F30yThe rotating pair between the walking beam and the oil pumping machine frame is stressed in the x and y directions.
The invention has the following beneficial effects and advantages:
1. the method adopts a combined solving algorithm of a balance equation, greatly shortens the calculation time of the friction torque in the process of converting the electric diagram into the indicator diagram, thereby meeting the real-time requirement of oil well indicator diagram diagnosis and having great engineering application value.
2. The method solves the problem of low accuracy of the converted indicator diagram caused by neglecting friction in the traditional method, and improves the indicator diagram conversion accuracy, thereby improving the accuracy of oil well diagnosis and production metering based on the converted indicator diagram.
3. Through optimization and improvement of the solving process of the traditional method for converting the indicator diagram into the indicator diagram, the accuracy and timeliness of indicator diagram conversion are effectively improved, so that an indirect measurement mode of the indicator diagram is gradually realized, the working condition diagnosis and metering cost of an oil well is greatly reduced, and the low-cost Internet of things construction of the oil field based on the electric parameters is promoted.
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FIG. 1 is a flow chart of an optimization solution algorithm according to the present invention;
Detailed Description
The present invention is described in further detail below.
The method comprises the steps of obtaining an included angle alpha between a base rod and the vertical direction through an angle sensor arranged on an oil pumping unit and obtaining an included angle theta between a walking beam rear arm and the base rod in the clockwise direction through the sensor4(ii) a Angular velocity omega of crank and walking beam obtained by angular displacement sensor mounted on oil pumping unit1、ω3。
According to the Darbian principle, stress analysis is carried out on a crank, a connecting rod and a walking beam to obtain a stress balance equation of the crank, the connecting rod and the walking beam, the equations are combined, expressions on two sides of an equal sign are expressed in a matrix form, and a balance equation set in the matrix form can be obtained:
Figure BDA0002400841020000071
wherein R is the length of the crank, P is the length of the connecting rod, C is the length of the rear arm of the walking beam, A is the length of the front arm of the walking beam, and theta2At an angle theta from the base rod in the counterclockwise direction to the crank3Is the angle between the connecting rod and the base rod, theta4The included angle between the rear arm of the walking beam and the base rod is in the clockwise direction. Alpha is the angle between the base rod and the vertical direction, J1、J2、J3Is the moment of inertia m of crank, connecting rod and walking beam around the center of mass1、m2、m3The mass of the crank, connecting rod, walking beam, G1、G2、G3Is the gravity of crank, connecting rod and walking beam, epsilon1、ε2、ε3Angular acceleration of crank, connecting rod, walking beam centroid,/s1、ls2、ls3Is the distance between the crank, the connecting rod, the center of mass of the walking beam and the corresponding revolute pair, a2x、a2yIs the component of the acceleration of the connecting rod mass center in the x and y directions, omega1、ω3Angular velocity, P, of crank, walking beamAFor load at suspension point, F01x、F01yFor forces in the x and y directions of the crank-rotating shaft revolute pair, F21x、F21yFor forces in the x and y directions of the revolute pair between the crank and the connecting rod, F32x、F32yForce in the x and y directions of the revolute pair between the connecting rod and the walking beam, F30x、F30yStress of a revolute pair between a walking beam and a frame of the oil pumping unit in the x and y directions, MdIs the drive torque.
An optimization solving algorithm is adopted, and the solving process is as follows:
step 1: the iteration error epsilon and the maximum iteration number N are determined.
Step 2: based on the balance equation set in the form of the matrix listed by the stress analysis of each part of the pumping unit, the partial equations are combined as follows, and the listed equation set is solved under the condition of not counting friction.
The crank dynamics equation:
Figure BDA0002400841020000081
Figure BDA0002400841020000082
Figure BDA0002400841020000083
connecting rod kinetic equation:
-F21x+F32x＝m2a2x (4)
-F21y+F32y＝m2a2y+G2 (5)
Figure BDA0002400841020000084
walking beam kinetic equation:
Figure BDA0002400841020000085
Figure BDA0002400841020000086
Figure BDA0002400841020000087
under the condition of not counting friction, a coefficient matrix obtained by combining the balance equations is a 9 × 9 square matrix, and when the inverse of the matrix is likely to generate distortion, in order to ensure the accuracy of a solution result, a new combined solution method related to the balance equations is adopted, and a specific solution method is as follows:
(a) equations (6) and (9) contain only two unknowns F32xAnd F32yFirstly, the two equations are combined together, and a system of linear equations with two elements is solved to obtain F32xAnd F32y。
Figure BDA0002400841020000091
Figure BDA0002400841020000092
(b) F obtained by solving (a)32xAnd F32ySubstituting (4) and (5) to obtain F21xAnd F21y。
-F21x+F32x＝m2a2x (4)
-F21y+F32y＝m2a2y+G2 (5)
From the above formula F21xAnd F21yCalculating the formula:
F21x＝F32x-m2a2x
F21y＝F32y-m2a2y-G2
(c) f obtained by solving (a)32xAnd F32ySubstituting (7) and (8) to obtain F30xAnd F30y。
Figure BDA0002400841020000093
Figure BDA0002400841020000094
From the above formula F30xAnd F30yCalculating the formula:
Figure BDA0002400841020000095
Figure BDA0002400841020000096
(d) f obtained by solving (b)21xAnd F21ySubstituting (3) to obtain Md。
Figure BDA0002400841020000097
From the above formula can MdCalculating the formula:
Figure BDA0002400841020000098
and step 3: the friction torque of each revolute pair is obtained from the revolute pair reaction force (the friction coefficient f is 0.15, and the friction radius r is 0.03m), and the specific method is as follows:
Mf01the unit is the friction torque at the crankshaft, which is N.m, and the calculation formula is as follows:
Figure BDA0002400841020000099
Mf21the unit is N.m, the friction torque of a rotating pair between the crank and the connecting rod is calculated by the following formula:
Figure BDA0002400841020000101
Mf32the unit is N.m, the friction torque of a revolute pair between the connecting rod and the walking beam is calculated by the following formula:
Figure BDA0002400841020000102
Mf30the unit is N.m, the friction torque of a revolute pair between a walking beam and a frame of the oil pumping unit, and the calculation formula is as follows:
Figure BDA0002400841020000103
and 4, step 4: substituting the solved friction torque into an equation set, and solving each counter force and driving torque under the friction condition by adopting a combined equation solving method as before, wherein the specific method comprises the following steps:
based on the equation set in the form of the matrix listed by the stress analysis of each part of the pumping unit, the partial equations are combined as follows, and the listed equation set is solved under the condition of accounting for friction.
The crank dynamics equation:
Figure BDA0002400841020000104
Figure BDA0002400841020000105
Figure BDA0002400841020000106
connecting rod kinetic equation:
-F21x+F32x＝m2a2x (4)
-F21y+F32y＝m2a2y+G2 (5)
Figure BDA0002400841020000107
walking beam kinetic equation:
Figure BDA0002400841020000108
Figure BDA0002400841020000111
Figure BDA0002400841020000112
(a) equations (6) and (9) contain only two unknowns F32xAnd F32yFirstly, the two equations are combined together, and a system of linear equations with two elements is solved to obtain F32xAnd F32y。
Figure BDA0002400841020000113
Figure BDA0002400841020000114
(b) F obtained by solving (a)32xAnd F32ySubstituting (4) and (5) to obtain F21xAnd F21y。
-F21x+F32x＝m2a2x (4)
-F21y+F32y＝m2a2y+G2 (5)
From the above formula F21xAnd F21yCalculating the formula:
F21x＝F32x-m2a2x
F21y＝F32y-m2a2y-G2
(c) f obtained by solving (a)32xAnd F32ySubstituting (7) and (8) to obtain F30xAnd F30y。
Figure BDA0002400841020000115
Figure BDA0002400841020000116
From the above formula F30xAnd F30yCalculating the formula:
Figure BDA0002400841020000117
Figure BDA0002400841020000118
(d) f obtained by solving (b)21xAnd F21ySubstituting (3) to obtain Md。
Figure BDA0002400841020000119
From the above formula can MdCalculating the formula:
Figure BDA0002400841020000121
and 5: and calculating friction torque according to the counter force of the revolute pair with friction, and subtracting the solving results of the friction torque twice to obtain the iteration error.
The iterative error |, the calculation result of the friction torque without the friction being counted at this time-the calculation result of the friction torque without the friction being counted at this time |
Step 6: and (5) repeating the step (4) and the step (5) until the iteration error is less than epsilon or the iteration times are equal to N, and obtaining the final results of the friction torque and the driving torque.
And drawing an electric function diagram and converting the electric function diagram into an indicator diagram by acquiring the final counter force of the revolute pair and the driving torque on the crankshaft, and monitoring the working state of the pumping unit in real time by the indicator diagram obtained in real time.

Claims (10)

1. A friction torque optimization method for converting an electric diagram of an oil pumping unit into an indicator diagram is characterized in that data are obtained through a sensor, friction torque and driving torque which are counted into friction are obtained through a stress balance equation of a crank, a connecting rod and a walking beam according to the data and stress of the crank, the connecting rod and the walking beam, the friction torque and the driving torque are obtained through repeated iteration, an electric diagram is constructed and converted into the indicator diagram, and the working state of the oil pumping unit is monitored in real time.
2. The method for optimizing the friction torque of the electric power diagram and the indicator diagram of the oil pumping unit as claimed in claim 1, wherein the optimized friction torque and driving torque are obtained by the following steps:
step 1: setting numerical values of an iteration error epsilon and a maximum iteration number N;
step 2: obtaining stress balance equations of the crank, the connecting rod and the walking beam according to the stress of the crank, the connecting rod and the walking beam, and establishing the balance equations simultaneously to obtain a balance equation set in a matrix form;
and step 3: combining partial equations according to a balance equation set in a matrix form to obtain an equation set under the condition of not counting friction and solving to obtain counter force of each revolute pair without counting friction and driving torque on a crankshaft;
and 4, step 4: obtaining friction torque of each revolute pair without friction through the counterforce of each revolute pair;
and 5: substituting the friction torque of each rotating pair without friction into a balance equation set in a matrix form to obtain the counter force of each rotating pair with the friction force initially counted and the driving torque on the crankshaft;
step 6: obtaining friction torque counted in friction according to the counter force of the friction-counted rotating pair and the driving torque on the crankshaft;
and 7: obtaining an iteration error;
and 8: when the iteration error is smaller than the set iteration error epsilon, the friction torque and the driving torque which are counted into friction at this time are taken as final results; when the calculated iteration error is larger than the set iteration error epsilon, returning to the step 6 according to the obtained reaction force of the revolute pair and the driving torque on the crankshaft, and performing iteration circulation;
and step 9: and drawing an electric function diagram and converting the electric function diagram into an indicator diagram by acquiring the final counter force of the revolute pair and the driving torque on the crankshaft, and monitoring the working state of the pumping unit in real time by the indicator diagram obtained in real time.
3. The method for optimizing friction torque of the electric indicator diagram of the oil pumping unit according to claim 2, wherein the balance equation set in the form of a matrix is as follows:
Figure FDA0002400841010000021
wherein R is the length of the crank, P is the length of the connecting rod, C is the length of the rear arm of the walking beam, A is the length of the front arm of the walking beam, and theta2At an angle theta from the base rod in the counterclockwise direction to the crank3Is the angle between the connecting rod and the base rod, theta4An included angle between the rear arm of the walking beam and the base rod in the clockwise direction, alpha is an included angle between the base rod and the vertical direction, J1、J2、J3Is the moment of inertia m of crank, connecting rod and walking beam around the center of mass1、m2、m3The mass of the crank, connecting rod, walking beam, G1、G2、G3Is the gravity of crank, connecting rod and walking beam, epsilon1、ε2、ε3Angular acceleration of crank, connecting rod, walking beam centroid,/s1、ls2、ls3Is the distance between the crank, the connecting rod, the center of mass of the walking beam and the corresponding revolute pair, a2x、a2yIs the component of the acceleration of the connecting rod mass center in the x and y directions, omega1、ω3Angular velocity, P, of crank, walking beamAFor load at suspension point, F01x、F01yFor forces in the x and y directions of the crank-rotating shaft revolute pair, F21x、F21yFor forces in the x and y directions of the revolute pair between the crank and the connecting rod, F32x、F32yIs a connecting rod and a gameForce in the x and y directions of the revolute pair between the beams, F30x、F30yStress of a revolute pair between a walking beam and a frame of the oil pumping unit in the x and y directions, MdIs the drive torque.
4. The method for optimizing and solving the friction torque of the electric diagram-rotating indicator diagram of the oil pumping unit as claimed in claim 2 or 3, wherein the method for obtaining the counter force of each rotating pair and the driving torque on the crankshaft without friction comprises the following steps:
the following two equations are combined together and solved to obtain F32xAnd F32y；
Figure FDA0002400841010000031
Figure FDA0002400841010000032
F obtained by solving32xAnd F32ySubstituting the combined matrix form into a balance equation set to obtain F21xAnd F21y，F30xAnd F30y，F21xAnd F21y；
According to F21xAnd F21yTo obtain MdThe method of (3) is implemented by the following formula:
Figure FDA0002400841010000033
5. the method for optimizing friction torque of the electromechanical power diagram to the indicator diagram of the oil pumping unit according to claim 2 or 4, wherein the solution method for solving the counter force of each rotating pair to the friction torque without friction of each rotating pair comprises the following steps:
Mf01the friction torque at the crankshaft is specifically as follows:
Figure FDA0002400841010000034
Mf21the friction torque of a revolute pair between the crank and the connecting rod is as follows:
Figure FDA0002400841010000035
Mf32the friction torque of a revolute pair between the connecting rod and the walking beam is as follows:
Figure FDA0002400841010000036
Mf30the friction torque of a revolute pair between a walking beam and a frame of the oil pumping unit is as follows:
Figure FDA0002400841010000041
where f is the coefficient of friction and r is the radius of the rotating secondary journal.
6. The method for optimizing friction torque of an electric power diagram of an oil pumping unit according to claim 2 or 5, wherein the calculating includes calculating a counter force of a revolute pair and a driving torque on a crankshaft, which are calculated by:
will Mf01And Mf21Substituting into a crank dynamics equation:
Figure FDA0002400841010000042
will Mf21And Mf32Substituting a connecting rod kinetic equation:
Figure FDA0002400841010000043
will Mf30And Mf32Substituting into a walking beam dynamics equation:
Figure FDA0002400841010000044
respectively obtain F32xAnd F32y(ii) a According to F32xAnd F32yCan obtain F21xAnd F21y、F30xAnd F30y、F30xAnd F30；
According to F21xAnd F21yTo obtain MdThe method of (3) is implemented by the following formula:
Figure FDA0002400841010000045
7. the method for optimizing friction torque of an electrical indicator diagram of an oil pumping unit according to claim 2, wherein the iterative error in step 7 is calculated by the following formula:
and the iteration error |, the friction torque calculation result of the last friction counting-the friction torque calculation result of the last friction counting.
8. The method for optimizing the friction torque of the electric indicator diagram of the oil pumping unit according to claim 2, wherein the iterative loop specifically comprises:
substituting the n-th calculated reaction force of the revolute pair and the driving torque on the crankshaft into a balance equation set in a matrix form to obtain the n + 1-th reaction force of the revolute pair and the driving torque on the crankshaft, wherein the friction force is counted;
obtaining friction torque and driving torque of the n +1 th counted friction force according to the revolute pair reaction force of the n +1 th counted friction force and the driving torque on the crankshaft;
and judging the ending or the iteration again by calculating the iteration error.
9. The method for optimizing and solving friction torque of the electromechanical indicator diagram of the pumping unit according to claim 2, wherein the data obtained by the sensor is specifically an included angle α between a base rod and a vertical direction and an included angle θ between a rear arm of the walking beam and the base rod in a clockwise direction obtained by an angle sensor installed on the pumping unit4(ii) a Angular velocity omega of crank and walking beam obtained by angular displacement sensor mounted on oil pumping unit1、ω3。
10. The method for solving the friction torque optimization of the electromechanical indicator diagram of the pumping unit according to claim 2, wherein the counter force of the revolute pair comprises F01x、F01yFor forces in the x and y directions of the crank-rotating shaft revolute pair, F21x、F21yFor forces in the x and y directions of the revolute pair between the crank and the connecting rod, F32x、F32yForce in the x and y directions of the revolute pair between the connecting rod and the walking beam, F30x、F30yThe rotating pair between the walking beam and the oil pumping machine frame is stressed in the x and y directions.
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