CN106354980B - External characteristics mathematical model construction method is pumped under a kind of rotating forward pump operating condition - Google Patents
External characteristics mathematical model construction method is pumped under a kind of rotating forward pump operating condition Download PDFInfo
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- CN106354980B CN106354980B CN201610888693.1A CN201610888693A CN106354980B CN 106354980 B CN106354980 B CN 106354980B CN 201610888693 A CN201610888693 A CN 201610888693A CN 106354980 B CN106354980 B CN 106354980B
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Abstract
The present invention relates to external characteristics mathematical model construction method is pumped under a kind of rotating forward pump operating condition.It gives a series of experiments point when full mold pump rotates forward pump operating condition, flow value interval when choosing experimental point is uniform, and lift, efficiency and axis torque value under corresponding discharge point are had recorded respectively, in order to obtain more intuitive external characteristic curve, obtained testing site lift, flow and axis torque are screened according to certain standard respectively, the test point value obtained after screening is brought into mathematical model, the mathematical model that coefficient uniquely determines is calculated, and then is used in theory analysis and actual moving process.Using the present invention can obtain the mathematical models being bonded with experimental data, relatively reliable prediction is carried out to the operating point that do not tested, foundation can also be provided to pump the determination of the operating point of optimum operation, and then prolong the service life and reach certain energy-saving effect.
Description
Technical field
The present invention relates to one kind for describing pump external characteristics mathematical model construction method, and in particular to a kind of rotating forward plugman
External characteristics mathematical model construction method is pumped under condition.
Background technique
Pump is a kind of universal machine being widely used in industry, and it is industrial that the electric power that annual pump class product consumes accounts for China
Electric ratio is very high, it is therefore necessary to pump testing data are carried out with the foundation and research of Related Mathematical Models, it is relatively preferable to select
Running operating point provide foundation, and then improve efficiency, prolong the service life with it is energy saving.
The characteristic curve of pump class product is generally referred to as the characteristic curve under normal operating conditions, and in certain special operatings
Under the conditions of, pump can be run in the case where lift, flow, torque and steering are negative.In view of the complexity flowed in pump, accurately
Characteristic curve can only by test make.But analysis is carried out to the data point of part actual experimental and mathematical model is built
It is vertical to make qualitatively analysis to the characteristic curve of pump, the optimal operating condition point pumped within the scope of certain flow can also be obtained.
For these reasons, the present inventor rotates forward the great number tested data of pump operating condition according to pump, in conjunction with hydrodynamics and
Mathematical principle proposes to pump external characteristics mathematical model construction method under a kind of rotating forward pump operating condition, and the model and pump rotate forward plugman
There is admirably correlation between condition characteristic curve, also have to the operating point that do not tested and more accurately predict, and can be with
The mathematical model homologous thread is extended to coordinate system adjacent quadrants, flows backwards damped condition and rotating forward positive stream damped condition to rotating forward
External characteristics predicted.The model is to pump the external characteristics of certain operating conditions using mathematical method research, determine its optimum operation work
Condition point provides necessary Fundamentals of Mathematics.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of outstanding mathematical models, and are used in a certain reality
In operation process, pump operating condition external characteristics is rotated forward to describe pump, is provided for further research, exploitation with operating relatively reliable
Ground Fundamentals of Mathematics.The present inventor rule of thumb obtains 14 groups of data with after the practical rejecting of engineering by 25 groups of test datas, in conjunction with stream
Mechanics and related mathematical principle have obtained a kind of mathematical model for meeting research and engine request, by multiple practice test,
The description that the mathematical model rotates forward pump operating condition external characteristics to pump is more accurate, and can carry out to other operating condition external characteristic curves
Prediction and offer rotate forward the optimal operating condition point of pump operating condition.
The technical scheme adopted by the invention is that:
External characteristics mathematical model construction method is pumped under a kind of rotating forward pump operating condition, is included the following steps:
Step S1: the first type of mathematical model is provided:
In formula:
a1, b1, c1, a2, b2, c2, a3, b3, c3, a4, b4, c4, a5, b5--- 1~coefficient of coefficient 14；
X --- x represents the flow Q, m when rotating forward pump operating condition always in the mathematical model3/s；
Y --- when describing variation of the lift H with flow Q, y represents corresponding practical lift H under the flow；
When describing axis torque M with flow Q variation, y represents axis torque M；
When description, which rotates forward pump operating condition efficiency eta, to be changed with flow Q, y represents efficiency eta；
Q --- the corresponding flow of each operating point, m when rotating forward pump operating condition3/h；
H --- the corresponding lift of each operating point, m when rotating forward pump operating condition；
M --- the corresponding axis torque of each operating point, Nm when rotating forward pump operating condition.
Denominator cannot be zero always in the mathematical model.
Step S2: when the rotation direction that test pumps in the process is positive, the test data more than or equal to 25 groups, foundation are obtained
Experience and engineering is practical rejects wrong testing site, finally determines 14 groups of satisfactory testing sites；
Wherein, following both sides factor is considered as when obtaining test data:
A derives from full mold pump testing, the rotation pumped during test for the test data of 1~coefficient of design factor 14
Direction is forward direction, and the flow value interval of selected testing site is uniform；
B is obtained be more than or equal to 25 groups of test datas after, test data is screened, empirically with the practical rejecting of engineering
Wrong testing site.
Step S3: bringing obtained 14 groups of test datas after step S2 screening into equation (1), and coefficient 1~be is calculated
Number 14 is in the value range of 95% confidence interval and the optimum value of 1~coefficient of coefficient 14；
Actual flow value Q, practical lift H after screening is brought into mathematical model and solves 1~coefficient of coefficient 14 95%
Value range and optimum value when confidence interval obtain the mathematical modulo uniquely determined that description pump rotates forward pump operating condition external characteristics
Type；
The value range is as follows:
a1=(- 5.739e+006,5.739e+006), a2=(- 1.669e+006,1.669e+006), a3=(- 2.84e+
006,2.84e+006),
b1=(- 5.298e+006,5.298e+006), b2=(- 1.305e+006,1.305e+006), b3=(- 1.837e
+ 006,1.837e+006),
c1=(- 4.749e+006,4.749e+006), c2=(- 9.693e+005,9.693e+005), c3=(- 3.064e
+ 005,3.064e+005),
a4=(- 1.457e+006,1.457e+006), b4=(- 2.172e+006,2.172e+006), c4=(- 2.448e
+ 006,2.448e+006),
a5=(- 2.359e+005,2.359e+005), b5=(- 9.558e+005,9.558e+005).
Identified optimum value is as follows:
a1=0.06978, a2=-1.176, a3=0.9429,
b1=-0.6532, b2=1.243, b3=1.033,
c1=1.091, c2=2.179, c3=1.348,
a4=-0.8925, b4=1.587, c4=0.4237,
a5=0.1451, b5=0.5208, after obtaining the optimum value of each coefficient, that is, obtains and rotate forward under pump operating condition outside pump
Characteristic mathematical model.
The mathematical model that the present invention obtains are as follows:
In formula,
X --- x represents the flow Q, m when rotating forward pump operating condition always in the mathematical model3/s；
Y --- when describing variation of the lift H with flow Q, y represents corresponding practical lift H under the flow,
When describing axis torque M with flow Q variation, y represents axis torque M,
When description, which rotates forward pump operating condition efficiency eta, to be changed with flow Q, y represents efficiency eta；
Q --- flow when rotating forward pump operating condition, m3/h；
H --- the corresponding lift of each operating point, m when rotating forward pump operating condition；
M --- the corresponding axis torque of each operating point, Nm when rotating forward pump operating condition.
It, can be by it after the present invention obtains the mathematical model that the description pump that coefficient uniquely determines rotates forward pump operating condition external characteristics
In terms of being used in following two:
A prolongs the mathematical model of acquisition according to the shape of mathematical model homologous thread in x-y coordinate system to the second quadrant
Stretching can predict that pump rotates forward the external characteristics of positive stream damped condition；According to the shape of mathematical model homologous thread in x-y coordinate system
Extend to predict to pump to fourth quadrant and is rotating forward the external characteristics situation for flowing backwards damped condition；
B Q-H curve corresponding to the mathematical model of acquisition and Q- η curve are analyzed, and available full mold pump is best
The operating point of operation, and then be used in practical work process, improve efficiency and reach certain energy-saving effect.
The invention has the benefit that
The present invention obtains pumping external characteristics mathematical model construction method under a kind of rotating forward pump operating condition, which is according to being greater than
Equal to 25 groups test datas remaining 14 groups of test datas after certain standard is rejected, in conjunction with hydrodynamics and related mathematical principle
It establishes, the coefficient in model is that the real data calculating obtained using test is uniquely determined, this mathematics all made
Model can accurately describe pump and rotate forward the external characteristics of pump operating condition, while make the mathematical model corresponding bent in x-y coordinate system
The shape of line has more accurately prediction effect to the curve that adjacent quadrants extend, and the determination of optimal operating condition point is pumped for full mold
Reference frame is provided, filled up there is no to rotate forward at present to a certain extent pumps external characteristics mathematical model building side under pump operating condition
The blank of method provides to further use external characteristics mathematical model construction method under mathematical tool research pump rotating forward pump operating condition
Essential condition.
Detailed description of the invention
Fig. 1 is to be constructed using mathematical model of the present invention to pump external characteristics mathematical model under a kind of rotating forward pump operating condition
The schematic diagram of model curve and testing site that the test of method and data are calculated.
Specific embodiment
The present invention is further described with reference to the accompanying drawings and detailed description.
The present invention is obtained final mathematical model by following steps and carries out the application of model:
1. pumping external characteristics mathematical model construction method, the mathematical model under a kind of rotating forward pump operating condition are as follows:
In formula, a1, b1, c1, a2, b2, c2, a3, b3, c3, a4, b4, c4, a5, b5Respectively 1~coefficient of coefficient 14, in the mathematics
X represents the true flow rate value Q that test obtains always in model；When describing variation of the lift H with flow Q, y represents test and obtains
Lift value H；Y represents axis torque M when description axis torque M changes with flow Q；Description rotates forward pump operating condition efficiency eta and becomes with flow Q
Y represents efficiency eta when change, and denominator is not zero always in equation.
2. should be noted that when obtaining test data following to accurately obtain the value of 1~coefficient of coefficient 14 in equation (1)
Two aspects:
(1) full mold pump is carried out rotating forward pump operating condition test, the rotation direction pumped during test is forward direction, that is, the stream pumped
Amount, lift, revolving speed and axis torque are positive value, and the flow value interval of selected testing site is uniform；
(2) after obtaining the test data more than or equal to 25 groups, test data is screened, it is empirically practical with engineering
Wrong testing site is rejected, the solution of coefficient in model is carried out with remaining 14 groups of test datas.
3. in order to obtain the optimum value of 1~coefficient of coefficient 14 in mathematical model and more intuitively reflect the mathematical model can
By property, brings obtain after screening 14 groups of test datas into mathematical model and calculates, specific processing method is as follows:
When calculating, x is always the actual flow value Q that test obtains in mathematical model, when drawing Q-H curve, model
In y be practical lift H；Q-M and Q- η curve is drawn, y is respectively actual axle torque M and efficiency value η.
4. in this embodiment, providing the calculating step of mathematical model Q-H curve: will empirically with engineering it is practical reject
14 groups of actual flow value Q and practical lift value H afterwards are brought into mathematical model, calculate the exact value of 1~coefficient of coefficient 14, are tied
Fruit is as follows:
a1=0.06978, a2=-1.176, a3=0.9429, b1=-0.6532, b2=1.243, b3=1.033, c1=
1.091
c2=2.179, c3=1.348, a4=-0.8925, a5=0.1451, b4=1.587, b5=0.5208, c4=
0.4237；
Coefficient 1 in the equation uniquely determined the above are final remaining 14 groups of actual flow value Q and practical lift value H~be
The exact value of number 14 obtains reliably pumping rotating forward pump operating condition external characteristics mathematical model.
5. the pump of acquisition is rotated forward the application of mathematical model of pump operating condition external characteristics in terms of following two:
(1) according to mathematical model, the shape of homologous thread can predict the pump to the extension of the second quadrant in x-y coordinate system
Rotate forward the external characteristics of positive stream damped condition；According to mathematical model, the shape of homologous thread is prolonged to fourth quadrant in x-y coordinate system
It stretches to predict to pump and is rotating forward the external characteristics situation for flowing backwards damped condition.
(2) the obtained corresponding Q-H curve of mathematical model and Q- η curve is analyzed, full mold pump optimum operation can be obtained
Operating point, and then be used in practical work process, improve efficiency and reach certain energy-saving effect.
Claims (6)
1. pumping external characteristics mathematical model construction method under a kind of rotating forward pump operating condition, characterized by the following steps:
Step S1: the first type of mathematical model is provided:
In formula
a1, b1, c1, a2, b2, c2, a3, b3, c3, a4, b4, c4, a5, b5Respectively 1~coefficient of coefficient 14；
X --- x represents the flow Q, m when rotating forward pump operating condition always in the mathematical model3/s；
Y --- when describing variation of the lift H with flow Q, y represents corresponding practical lift H under the flow,
When describing axis torque M with flow Q variation, y represents axis torque M,
When description, which rotates forward pump operating condition efficiency eta, to be changed with flow Q, y represents efficiency eta；
H --- the corresponding lift of each operating point, m when rotating forward pump operating condition；
M --- the corresponding axis torque of each operating point, Nm when rotating forward pump operating condition；
Denominator is not zero always in equation；
Step S2: when the rotation direction that test pumps in the process is positive, the test data more than or equal to 25 groups is obtained, empirically
Wrong testing site, finally determines 14 groups of satisfactory testing sites with the practical rejecting of engineering；
Step S3: the 14 groups of test datas obtained after step S2 screening are brought into equation (1), 1~coefficient of coefficient 14 is calculated
In the value range of 95% confidence interval and the optimum value of 1~coefficient of coefficient 14.
2. pumping external characteristics mathematical model construction method under a kind of rotating forward pump operating condition according to claim 1, feature exists
In: in step S2, in terms of should be noted that following two when obtaining test data:
(1) test data for the value of 1~coefficient of design factor 14 derives from full mold pump testing, and what is pumped during test turns
Dynamic direction is forward direction, and the flow value interval of selected testing site is uniform；
(2) obtain more than or equal to after 25 groups of test data, test data screened, empirically with the practical rejecting of engineering
Wrong testing site finally determines 14 groups of satisfactory testing sites.
3. pumping external characteristics mathematical model construction method under a kind of rotating forward pump operating condition according to claim 1, feature exists
In: in step S3, actual flow value Q, the practical lift H after screening are brought into mathematical model, are calculated in mathematical model
Each coefficient is as follows in the value range of 95% confidence interval:
a1=(- 5.739e+006,5.739e+006), a2=(- 1.669e+006,1.669e+006), a3=(- 2.84e+006,
2.84e+006),
b1=(- 5.298e+006,5.298e+006), b2=(- 1.305e+006,1.305e+006), b3=(- 1.837e+
006,1.837e+006),
c1=(- 4.749e+006,4.749e+006), c2=(- 9.693e+005,9.693e+005), c3=(- 3.064e+
005,3.064e+005),
a4=(- 1.457e+006,1.457e+006), b4=(- 2.172e+006,2.172e+006), c4=(- 2.448e+
006,2.448e+006),
a5=(- 2.359e+005,2.359e+005), b5=(- 9.558e+005,9.558e+005)；
Identified optimum value is as follows:
a1=0.06978, a2=-1.176, a3=0.9429,
b1=-0.6532, b2=1.243, b3=1.033,
c1=1.091, c2=2.179, c3=1.348,
a4=-0.8925, b4=1.587, c4=0.4237,
a5=0.1451, b5=0.5208, after obtaining the optimum value of each coefficient, that is, obtains and pump external characteristics under rotating forward pump operating condition
Mathematical model.
4. a kind of application rotates forward the method for pumping external characteristics mathematical model under pump operating condition, it is characterised in that: the mathematical model is
It is obtained by construction method according to any one of claims 1 to 3, the mathematical model are as follows:
In formula,
X --- x represents the flow Q, m when rotating forward pump operating condition always in the mathematical model3/s；
Y --- when describing variation of the lift H with flow Q, y represents corresponding practical lift H under the flow,
When describing axis torque M with flow Q variation, y represents axis torque M,
When description, which rotates forward pump operating condition efficiency eta, to be changed with flow Q, y represents efficiency eta；
H --- the corresponding lift of each operating point, m when rotating forward pump operating condition；
M --- the corresponding axis torque of each operating point, Nm when rotating forward pump operating condition.
5. a kind of application according to claim 4 rotates forward the method for pumping external characteristics mathematical model under pump operating condition, feature
It is: the mathematical model that the pump rotates forward pump operating condition external characteristics is used to predict that pump to rotate forward the external characteristics of positive stream damped condition
The external characteristics situation for flowing backwards damped condition is being rotated forward with pump, specifically:
It, can to the extension of the second quadrant according to the shape of mathematical model homologous thread in x-y coordinate system to the mathematical model of acquisition
To predict to pump the external characteristics for rotating forward positive stream damped condition；According to the shape of mathematical model homologous thread in x-y coordinate system to
Four-quadrant, which extends to predict to pump, is rotating forward the external characteristics situation for flowing backwards damped condition.
6. a kind of application according to claim 4 rotates forward the method for pumping external characteristics mathematical model under pump operating condition, feature
It is: the mathematical model that the pump rotates forward pump operating condition external characteristics is used to analyze the operating point of full mold pump optimum operation, tool
Body are as follows:
Q-H curve corresponding to the mathematical model of acquisition and Q- η curve are analyzed, and can analyze to obtain full mold pump most good speed
Capable operating point.
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| CN106960129B (en) * | 2017-04-01 | 2019-04-23 | 中工武大设计研究有限公司 | A kind of rotation flow partition method |
| CN109033527B (en) * | 2018-06-28 | 2023-02-10 | 江苏国泉泵业制造有限公司 | Mathematical model for describing external characteristics of centrifugal pump |
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