CN106372445A - Construction method of full-characteristic mathematical model of mixed-flow pump - Google Patents

Abstract

The invention relates to a construction method of a full-characteristic mathematical model of a mixed-flow pump. Aiming at the mixed-flow pump, the invention discloses the mathematical model meeting research and engineering requirements; after accurate values of all coefficients included in the mathematical model are calculated through test data, the mathematical model with all known coefficients can be obtained and is used for describing an external characteristic of the mixed-flow pump under all conditions of full characteristics. The mathematical model provided by the invention is high in precision and high in correlation with the full characteristics of the mixed-flow pump, and can be well fitted with the test data and also accurately forecast the external characteristic of a working condition point without the test data. The mathematical model provided by the invention supplies an important mathematical basis to the research on the full characteristics of the mixed-flow pump by using a mathematical method.

Description

A kind of mixed-flow pump omnicharacteristic mathematical model construction method

Technical field

The present invention relates to a kind of mixed-flow pump external characteristics mathematical model construction method, particularly to a kind of mixed-flow pump omnicharacteristic number Learn model building method.

Background technology

Mixed-flow pump is a kind of universal machine being widely used in industry, and the electric power that annual pump class product consumes accounts for China's work Industry electricity consumption ratio is very high.In the middle of pump class product, the hydraulic characteristic(s) of mixed-flow pump between centrifugal pump and axial-flow pump, applicable situation With scope widely, therefore necessary mixed-flow pump of continuing to optimize designs so as to have higher reliability, efficiency and use Life-span.

The external characteristics of pump class product is its very important use characteristic, refers to pump product different flow, rotating speed, raises Corresponding relation between journey, axle moment of torsion.Designer need carry out the Hydraulic Design to pump according to actual needs it is ensured that product external characteristics Current demand can be fully met.In view of the importance of pump product external characteristics, there are multiple methods that it is studied, can pass through Substantial amounts of test data is studied it is also possible to be derived from principles of fluid mechanics, and above two method is to external characteristics Assurance respectively have pluses and minuses.

The present inventor according to great number tested data, in conjunction with hydrodynamics with mathematical principle it is proposed that a kind of mixed-flow pump is entirely special Property mathematical model construction method, the model of proposition is good with the external characteristics relatedness of each operating mode under mixed-flow pump omnicharacteristic, can not only Laminating test data well, and can accurately predict there is no the operating point of test data.Mathematics proposed by the present invention Model designs for mixed-flow pump and research work provides necessary Fundamentals of Mathematics.

Content of the invention

Present invention solves the technical problem that being to provide a kind of excellent mathematical model, for describing mixed-flow pump under omnicharacteristic External characteristics, for mixed-flow pump design and further research provide necessary Fundamentals of Mathematics.The present inventor is according to a number of examination Test data, in conjunction with hydrodynamics and mathematical principle it is proposed that a kind of mathematical model meeting research work and engine request, through by mistake Difference analysis and practice test, this model is more accurate to the description of external characteristics under mixed-flow pump omnicharacteristic.

The technical solution adopted in the present invention is:

Propose a kind of construction method of mixed-flow pump omnicharacteristic mathematical model, test data is substituted into the number that this patent proposes Learn model, obtain the coefficient in mathematical model and then obtain the math equation representing each operating mode external characteristics under omnicharacteristic, mathematics side Error between journey and test data can be judged by error analyses, if error size be unsatisfactory for require; pass through into One step screening solves the test data of mathematical model coefficient revising；

Mathematical model under step s1. proposition rotating forward operating mode, runaway speed, zero speed conditions, reversing damped condition:

The mathematical model that description mixed-flow pump rotates forward external characteristics under operating mode is:

$y=a_1*q^3+b_1*q+c_1+\frac{d_1*q^2+e_1*q+f_1}{g_1*q^3+k_1*q^2+l_1*q+p_1}---\left(1\right)$

Under description mixed-flow pump reversing damped condition, the mathematical model of external characteristics is:

$y=a_2*sin\frac{b_2*q^3+c_2*q^2+d_2*q+e_2}{f_2*q+g_2}+\frac{k_2*q^2+l_2*q+p_2}{r_2*q^2+s_2*q+t_2}---\left(2\right)$

Description mixed-flow pump mathematical model of external characteristics under runaway speed, zero speed conditions is:

Y=a₃*q³+b₃*q²+c₃*q+d₃(3)

Description mixed-flow pump mathematical model of external characteristics under zero speed conditions is:

Y=a₄*q³+b₄*q²+c₄*q+d₄(4)

In formula:

a_i、b_i、c_i、d_i、e_j、f_j、g_j、k_j、l_j、p_j、r₂、s₂、t₂Mathematical model coefficient, wherein i=1,2,3,4, j= 1,2；

The flow of q zero dimension, equal to q/q_n, dimensionless；

Y y when description lift h changes with flow q represents h, and when describing moment of torsion m and changing with flow q, y represents m, no Dimension；

The lift of h zero dimension, equal to h/h_n, dimensionless；

The moment of torsion of m zero dimension, equal to m/m_n, dimensionless；

Q flow, cube m/h；

q_nThe metered flow of mixed-flow pump, cube m/h；

H lift, rice；

h_nThe rated head of mixed-flow pump, rice；

M moment of torsion, cattle rice；

m_nThe nominal torque of mixed-flow pump, cattle rice；

Step s2. by rotate forward operating mode, reversing damped condition, runaway speed, zero speed conditions test data substitute into respectively above-mentioned Various (1)～(4) obtain following formula (5)～(8), can obtain the exact numerical values recited of coefficient contained by each mathematical model:

Working condition tests data substitution design factor will be rotated forward as follows:

$\left\{\begin{array}{c}{y}_{11}=a_1*q_{11}^3+b_1*q_{11}+c_1+\frac{d_1*q_{11}^2+e_1*q_{11}+f_1}{g_1*q_{11}^3+k_1*q_{11}^2+l_1*q_{11}+p_1}\\ y_{12}=a_1*q_{12}^3+b_1*q_{12}+c_1+\frac{d_1*q_{12}^2+e_1*q_{12}+f_1}{g_1*q_{12}^3+k_1*q_{12}^2+l_1*q_{12}+p_1}\\ ......\\ y_{110}=a_1*q_{110}^3+b_1*q_{110}+c_1+\frac{d_1*q_{110}^2+e_1*q_{110}+f_1}{g_1*q_{110}^3+k_1*q_{110}^2+l_1*q_{110}+p_1}\end{array}\right.---\left(5\right)$

Y in formula₁₁, y₁₂... ..., y₁₁₀, q₁₁, q₁₂... ..., q₁₁₀For 10 groups of test datas, obtain a₁、b₁、c₁、d₁、e₁、f₁、 g₁、k₁、l₁、p₁Exact numerical values recited can obtain describing the equation that this mixed-flow pump rotates forward external characteristics under operating mode；Draw: a₁=- 0.1775, b₁=-2.211, c₁=3.144, d₁=-32.77, e₁=-1.469, f₁=22.32, g₁=-8.765, k₁=- 0.4279, l₁=-10.49, p₁=-13.9.

Reversing damped condition test data is substituted into design factor as follows:

$\left\{\begin{array}{c}{y}_{21}=a_2*\sin \frac{b_2*q_{21}^3+c_2*q_{21}^2+d_2*q_{21}+e_2}{f_2*q_{21}+g_2}+\frac{k_2*q_{21}^2+l_2*q_{21}+p_2}{r_2*q_{21}^2+s_2*q_{21}+t_2}\\ y_{22}=a_2*\sin \frac{b_2*q_{22}^3+c_2*q_{22}^2+d_2*q_{22}+e_2}{f_2*q_{22}+g_2}+\frac{k_2*q_{22}^2+l_2*q_{22}+p_2}{r_2*q_{22}^2+s_2*q_{22}+t_2}\\ ......\\ y_{213}=a_2*\sin \frac{b_2*q_{213}^3+c_2*q_{213}^2+d_2*q_{213}+e_2}{f_2*q_{213}+g_2}+\frac{k_2*q_{213}^2+l_2*q_{213}+p_2}{r_2*q_{213}^2+s_2*q_{213}+t_2}\end{array}\right.---\left(6\right)$

Y in formula₂₁, y₂₂... ..., y₂₁₃, q₂₁, q₂₂... ..., q₂₁₃For 13 groups of test datas, obtain a₂、b₂、c₂、d₂、e₂、f₂、 g₂、k₂、l₂、p₂、r₂、s₂、t₂Exact numerical values recited can obtain describing the equation of external characteristics under this mixed-flow pump reversing damped condition；Draw: a₂ =0.118, b₂=0.3645, c₂=0.6884, d₂=0.8754, e₂=0.4924, f₂=1.328, g₂=0.3693, k₂=- 0.02948, l₂=-1.335, p₂=0.1719, r₂=-1.139, s₂=-0.831, t₂=1.95.

Runaway speed test data is substituted into design factor as follows:

$\left\{\begin{array}{c}{y}_{31}=a_3*q_{31}^3+b_3*q_{31}^2+c_3*q_{31}+d_3\\ y_{32}=a_3*q_{32}^3+b_3*q_{32}^2+c_3*q_{32}+d_3\\ y_{33}=a_3*q_{33}^3+b_3*q_{33}^2+c_3*q_{33}+d_3\\ y_{34}=a_3*q_{34}^3+b_3*q_{34}^2+c_3*q_{34}+d_3\end{array}\right.---\left(7\right)$

Y in formula₃₁, y₃₂,y₃₃, y₃₄, q₃₁, q₃₂, q₃₃, q₃₄For 4 groups of test datas, obtain a₃、b₃、c₃、d₃Exact numerical values recited be Can obtain describing the equation of external characteristics under this mixed-flow pump runaway speed；Draw a₃=-0.5187, b₃=0.3785, c₃=- 0.1963, d₃=0.005922.

Zero-turn speed working condition tests data is substituted into design factor as follows:

$\left\{\begin{array}{c}{y}_{41}=a_4*q_{41}^3+b_4*q_{41}^2+c_4*q_{41}+d_4\\ y_{42}=a_4*q_{42}^3+b_4*q_{42}^2+c_4*q_{42}+d_4\\ y_{43}=a_4*q_{43}^3+b_4*q_{43}^2+c_4*q_{43}+d_4\\ y_{44}=a_4*q_{44}^3+b_4*q_{44}^2+c_4*q_{44}+d_4\end{array}\right.---\left(8\right)$

Y in formula₄₁, y₄₂,y₄₃, y₄₄, q₄₁, q₄₂, q₄₃, q₄₄For 4 groups of test datas, obtain a₄、b₄、c₄、d₄Exact numerical values recited be Can obtain describing the equation of external characteristics under this mixed-flow pump zero speed conditions, draw a₄=-1.651, b₄=-0.05852, c₄=- 0.2906, d₄=-0.001703.

After step s3. obtains the coefficient of external characteristics mathematical model under each operating mode, error need be carried out to each mathematical model Whether analysis is reasonable with the error size determining mathematical model, and step is as follows:

(1) numerical value of zero dimension flow q is substituted into the size that mathematical model obtains y, i.e. zero dimension lift h or nothing The size of dimension moment of torsion m, then error delta size under this q value for the mathematical model be:

$\mathrm{\δ}=\frac{y}{y^{\′}}-1---\left(9\right)$

In formula, y ' represents the value of result of the test corresponding zero dimension lift h or zero dimension moment of torsion m under this q value；

(2) set up q- δ coordinate system, axis of abscissas is zero dimension flow q, and axis of ordinates is error delta, by step (1) In all error delta of obtaining its q value corresponding under this coordinate system mark, obtain several points and be referred to as error dot, using Ai Er meter All errors are smoothly connected and obtain a curve and be referred to as error distribution curve by special interpolation method, and point curve is in the horizontal seat of q- δ coordinate system Fluctuate near parameter, error distribution curve deviates the error size representing mathematical model under this q apart from size of axis of abscissas.

Step s4. judges the excellent degree of this mathematical model according to the error distribution curve that step s3 obtains, full when simultaneously Can consider during sufficient following two condition that this mathematical model preferably describes the external characteristics of mixed-flow pump:

δ≤0.11 (10)

δ_80%≤0.08 (11)

In formula:

δ_80%The error distribution curve axis of abscissas always error on interval 80% region；

If step s5. can not meet two conditions in step s4 according to the mathematical model that step s1 is determined, can To exclude the larger test data of error and then to filter out exact test data, again solve coefficient contained by this mathematical model, until Till this mathematical model disclosure satisfy that two conditions in step s4.

By above-mentioned steps, a kind of mixed-flow pump omnicharacteristic mathematical model construction method can be obtained, this mathematical model is root According to great number tested data, set up in conjunction with hydrodynamics and mathematical principle, the unknowm coefficient in model can be using test gained Truthful data is obtained.

The invention has the benefit that

The mathematical model that this patent proposes can describe the external characteristics under mixed-flow pump omnicharacteristic well, has filled up at present still The blank of no mixed-flow pump omnicharacteristic mathematical model, important for being provided using mathematical tool research mixed-flow pump omnicharacteristic further Essential condition.

Brief description

The present invention is further described with reference to the accompanying drawings and detailed description.

Fig. 1 is a kind of error distribution curve of mixed-flow pump omnicharacteristic mathematical model construction method.

Fig. 2 is a kind of test data fitting figure of mixed-flow pump omnicharacteristic mathematical model construction method.

Specific embodiment

The present invention combines Figure of description and embodiment, and the specific embodiment of the present invention is described in further detail:

Using the mixed-flow pump omnicharacteristic mathematical model that this patent proposes, the omnicharacteristic of one mixed-flow pump is modeled:

The mathematical model that description mixed-flow pump rotates forward external characteristics under operating mode is:

$y=a_1*q^3+b_1*q+c_1+\frac{d_1*q^2+e_1*q+f_1}{g_1*q^3+k_1*q^2+l_1*q+p_1}---\left(1\right)$

Under description mixed-flow pump reversing damped condition, the mathematical model of external characteristics is:

$y=a_2*sin\frac{b_2*q^3+c_2*q^2+d_2*q+e_2}{f_2*q+g_2}+\frac{k_2*q^2+l_2*q+p_2}{r_2*q^2+s_2*q+t_2}---\left(2\right)$

Description mixed-flow pump mathematical model of external characteristics under runaway speed, zero speed conditions is:

Y=a₃*q³+b₃*q²+c₃*q+d₃(3)

Description mixed-flow pump mathematical model of external characteristics under zero speed conditions is:

Y=a₄*q³+b₄*q²+c₄*q+d₄(4)

Then the data obtaining the test of this mixed-flow pump omnicharacteristic substitutes into the above-mentioned various definite number that can obtain each coefficient Value:

Working condition tests data substitution design factor will be rotated forward as follows:

$\left\{\begin{array}{c}-1.9531=a_1*{2.06}^3+b_1*2.06+c_1+\frac{d_1*{2.06}^2+e_1*2.06+f_1}{g_1*{2.06}^3+k_1*{2.06}^2+l_1*2.06+p_1}\\ -0.86199=a_1*{1.811}^3+b_1*1.811+c_1+\frac{d_1*{1.811}^2+e_1*1.811+f_1}{g_1*{1.811}^3+k_1*{1.811}^2+l_1*1.811+p_1}\\ ......\\ 5.825=a_1*{\left(-1.6\right)}^3+b_1*\left(-1.6\right)+c_1+\frac{d_1*{\left(-1.6\right)}^2+e_1*q_{110}+f_1}{g_1*{\left(-1.6\right)}^3+k_1*{\left(-1.6\right)}^2+l_1*\left(-1.6\right)+p_1}\end{array}\right.---\left(5\right)$

Obtain a₁、b₁、c₁、d₁、e₁、f₁、g₁、k₁、l₁、p₁Exact numerical values recited can obtain describing this mixed-flow pump and rotate forward operating mode The equation of lower external characteristics is:

$\begin{array}{c}h=\left(-0.1775\right)*q^2+\left(-2.211\right)*q+3.144\\ +\frac{-32.77*q^2+(-1.469)*q+22.32}{-8.765*q^3+(-0.4279)*q^2+(-10.49)*q+(-13.9)}\end{array}$

Reversing damped condition test data is substituted into design factor as follows:

$\left\{\begin{array}{c}1.718438=a_2*\sin \frac{b_2*{\left(-1.3186\right)}^3+c_2*{\left(-1.3186\right)}^2+d_2*\left(-1.3186\right)+e_2}{f_2*\left(-1.3186\right)+g_2}+\frac{k_2*{\left(-1.3186\right)}^2+l_2*\left(-1.3186\right)+p_2}{r_2*{\left(-1.3186\right)}^2+s_2*\left(-1.3186\right)+t_2}\\ 1.5376=a_2*\sin \frac{b_2*{\left(-1.25\right)}^3+c_2*{\left(-1.25\right)}^2+d_2*\left(-1.25\right)+e_2}{f_2*\left(-1.25\right)+g_2}+\frac{k_2*{\left(-1.25\right)}^2+l_2*\left(-1.25\right)+p_2}{r_2*{\left(-1.25\right)}^2+s_2*\left(-1.25\right)+t_2}\\ ......\\ -1.0566=a_2*\sin \frac{b_2*{0.7468}^3+c_2*{0.7468}^2+d_2*0.7468+e_2}{f_2*0.7468+g_2}+\frac{k_2*{0.7468}^2+l_2*0.7468+p_2}{r_2*{0.7468}^2+s_2*0.7468+t_2}\end{array}\right.---\left(6\right)$

Obtain a₂、b₂、c₂、d₂、e₂、f₂、g₂、k₂、l₂、p₂、r₂、s₂、t₂Exact numerical values recited can obtain describing this mixed-flow pump Under reversing damped condition, the equation of external characteristics is:

$\begin{array}{c}h=0.118*\sin \frac{0.3645*q^3+0.6884*q^2+0.8754*q+0.4924}{1.328*q+0.3693}\\ +\frac{-0.02948*q^2+\left(-1.335\right)*q+0.1719}{-1.139*q^2+\left(-0.831\right)*q+1.956}\end{array}$

Runaway speed test data is substituted into design factor as follows:

$\left\{\begin{array}{c}0.94=a_3*{\left(-0.92\right)}^3+b_3*{\left(-0.92\right)}^2+c_3*\left(-0.92\right)+d_3\\ 0.2558=a_3*{\left(-0.469\right)}^3+b_3*{\left(-0.469\right)}^2+c_3*\left(-0.469\right)+d_3\\ -0.335=a_3*{0.99}^3+b_3*{0.99}^2+c_3*0.99+d_3\\ -0.066=a_3*{0.4996}^3+b_3*{0.4996}^2+c_3*0.4996+d_3\end{array}\right.---\left(7\right)$

Obtain a₃、b₃、c₃、d₃Exact numerical values recited can obtain describing the equation of external characteristics under this mixed-flow pump runaway speed and be:

H=-0.5187*q³+0.3785*q²+(-0.1963)*q+0.005922

Zero-turn speed working condition tests data is substituted into design factor as follows:

$\left\{\begin{array}{c}0.7999=a_4*{\left(-0.72\right)}^3+b_4*{\left(-0.72\right)}^2+c_4*\left(-0.72\right)+d_4\\ 0.04=a_4*{\left(-0.22\right)}^3+b_4*{\left(-0.22\right)}^2+c_4*\left(-0.22\right)+d_4\\ -0.078=a_4*\left(-0.264\right)9^3+b_4*{\left(-0.264\right)}^2+c_4*\left(-0.264\right)+d_4\\ -0.812=a_4*{0.705}^3+b_4*{0.705}^2+c_4*0.705+d_4\end{array}\right.---\left(8\right)$

Obtain a₄、b₄、c₄、d₄Exact numerical values recited can obtain describing the equation of external characteristics under this mixed-flow pump zero speed conditions For:

H=-1.651*q³+(-0.05852)*q²+(-0.2906)*q+(-0.001703)

Obtain under each operating mode external characteristics mathematical model really after butt journey, error analyses need be carried out to each mathematical model Whether rationally to determine error size, step is as follows:

(1) numerical value of zero dimension flow q is substituted into mathematical model and obtain zero dimension lift h size, then mathematical model Error delta size under this q value is:

$\mathrm{\δ}=\frac{h}{h^{\′}}-1---\left(9\right)$

In formula, h ' represents the value of result of the test corresponding zero dimension lift under this q value；

(2) set up q- δ coordinate system, axis of abscissas is zero dimension flow q, axis of ordinates is error delta, will obtain in (1) To all error delta under this coordinate system its q value corresponding mark, obtain several points and be referred to as error dot, slotting using Hermite All error dot are smoothly connected and obtain a curve and be referred to as error distribution curve by value method, and curve is in q- δ coordinate system axis of abscissas Nearby fluctuate, error distribution curve deviates the error size representing mathematical model under this q apart from size of axis of abscissas.

Error distribution to each math equation above-mentioned is analyzed finding, 4 more than obtaining mathematical model all can Meet condition:

δ≤0.11 (10)

δ_80%≤0.08 (11)

It can be considered that above-mentioned 4 mathematical modeies preferably describe the omnicharacteristic of this mixed-flow pump.

It will be seen from figure 1 that error distribution meets under rotating forward operating mode, runaway speed, zero speed conditions, reversing damped condition simultaneously δ≤0.11, δ_80%≤0.08.

Figure it is seen that the test data evidence under rotating forward operating mode, runaway speed, zero speed conditions, reversing damped condition meets Mathematical model.

The above, be only one embodiment of the present of invention, not make any limit to the technical scope of the present invention System, requires any modification, equivalent variations and the modification that above-described embodiment is made, all still falls within this according to the invention of the present invention The scope of bright technical scheme.

Claims (3)

1. a kind of mixed-flow pump omnicharacteristic mathematical model construction method is it is characterised in that comprise the steps:

Mathematical model under step s1. proposition rotating forward operating mode, runaway speed, zero speed conditions, reversing damped condition:

The mathematical model that description mixed-flow pump rotates forward external characteristics under operating mode is:

$y=a_1*q^3+b_1*q+c_1+\frac{d_1*q^2+e_1*q+f_1}{g_1*q^3+k_1*q^2+l_1*q+p_1}---\left(1\right)$

Under description mixed-flow pump reversing damped condition, the mathematical model of external characteristics is:

$y=a_2*sin\frac{b_2*q^3+c_2*q^2+d_2*q+e_2}{f_2*q+g_2}+\frac{k_2*q^2+l_2*q+p_2}{r_2*q^2+s_2*q+t_2}---\left(2\right)$

Description mixed-flow pump mathematical model of external characteristics under runaway speed, zero speed conditions is:

Y=a₃*q³+b₃*q²+c₃*q+d₃(3)

Description mixed-flow pump mathematical model of external characteristics under zero speed conditions is:

Y=a₄*q³+b₄*q²+c₄*q+d₄(4)

In formula:

a_i、b_i、c_i、d_i、e_j、f_j、g_j、k_j、l_j、p_j、r₂、s₂、t₂Mathematical model coefficient, wherein i=1,2,3,4, j=1,2；

The flow of q zero dimension, equal to q/q_n, dimensionless；

Y y when description lift h changes with flow q represents h, and when describing moment of torsion m and changing with flow q, y represents m, immeasurable Guiding principle；

The lift of h zero dimension, equal to h/h_n, dimensionless；

The moment of torsion of m zero dimension, equal to m/m_n, dimensionless；

Q flow, cube m/h；

q_nThe metered flow of mixed-flow pump, cube m/h；

H lift, rice；

h_nThe rated head of mixed-flow pump, rice；

M moment of torsion, cattle rice；

m_nThe nominal torque of mixed-flow pump, cattle rice；

Step s2. by rotate forward operating mode, reversing damped condition, runaway speed, zero speed conditions test data substitute into respectively above-mentioned various (1)～(4) obtain following formula (5)～(8), can obtain the exact numerical values recited of coefficient contained by each mathematical model:

Working condition tests data substitution design factor will be rotated forward as follows:

$\left\{\begin{array}{c}{y}_{11}=a_1*q_{11}^3+b_1*q_{11}+c_1+\frac{d_1*q_{11}^2+e_1*q_{11}+f_1}{g_1*q_{11}^3+k_1*q_{11}^2+l_1*q_{11}+p_1}\\ y_{12}=a_1*q_{12}^3+b_1*q_{12}+c_1+\frac{d_1*q_{12}^2+e_1*q_{12}+f_1}{g_1*q_{12}^3+k_1*q_{12}^2+l_1*q_{12}+p_1}\\ \mathrm{......}\\ y_{110}=a_1*q_{110}^3+b_1*q_{110}+c_1+\frac{d_1*q_{110}^2+e_1*q_{110}+f_1}{g_1*q_{110}^3+k_1*q_{110}^2+l_1*q_{110}+p_1}\end{array}\right.---\left(5\right)$

Y in formula₁₁, y₁₂... ..., y₁₁₀, q₁₁, q₁₂... ..., q₁₁₀For 10 groups of test datas, obtain a₁、b₁、c₁、d₁、e₁、f₁、g₁、 k₁、l₁、p₁Exact numerical values recited can obtain describing the equation that this mixed-flow pump rotates forward external characteristics under operating mode；

Reversing damped condition test data is substituted into design factor as follows:

$\left\{\begin{array}{c}{y}_{21}=a_2*\sin \frac{b_2*q_{21}^3+c_2*q_{21}^2+d_2*q_{21}+e_2}{f_2*q_{21}+g_2}+\frac{k_2*q_{21}^2+l_2*q_{21}+p_2}{r_2*q_{21}^2+s_2*q_{21}+t_2}\\ y_{22}=a_2*\sin \frac{b_2*q_{22}^3+c_2*q_{22}^2+d_2*q_{22}+e_2}{f_2*q_{22}+g_2}+\frac{k_2*q_{22}^2+l_2*q_{22}+p_2}{r_2*q_{22}^2+s_2*q_{22}+t_2}\\ \mathrm{......}\\ y_{213}=a_2*\sin \frac{b_2*q_{213}^3+c_2*q_{213}^2+d_2*q_{213}+e_2}{f_2*q_{213}+g_2}+\frac{k_2*q_{213}^2+l_2*q_{213}+p_2}{r_2*q_{213}^2+s_2*q_{213}+t_2}\end{array}\right.---\left(6\right)$

Y in formula₂₁, y₂₂... ..., y₂₁₃, q₂₁, q₂₂... ..., q₂₁₃For 13 groups of test datas, obtain a₂、b₂、c₂、d₂、e₂、f₂、g₂、 k₂、l₂、p₂、r₂、s₂、t₂Exact numerical values recited can obtain describing the equation of external characteristics under this mixed-flow pump reversing damped condition；

Runaway speed test data is substituted into design factor as follows:

$\left\{\begin{array}{c}{y}_{31}=a_3*q_{31}^3+b_3*q_{31}^2+c_3*q_{31}+d_3\\ y_{32}=a_3*q_{32}^3+b_3*q_{32}^2+c_3*q_{32}+d_3\\ y_{33}=a_3*q_{33}^3+b_3*q_{33}^2+c_3*q_{33}+d_3\\ y_{34}=a_3*q_{34}^3+b_3*q_{34}^2+c_3*q_{34}+d_3\end{array}\right.---\left(7\right)$

Y in formula₃₁, y₃₂,y₃₃, y₃₄, q₃₁, q₃₂, q₃₃, q₃₄For 4 groups of test datas, obtain a₃、b₃、c₃、d₃Exact numerical values recited To the equation describing external characteristics under this mixed-flow pump runaway speed；

Zero-turn speed working condition tests data is substituted into design factor as follows:

$\left\{\begin{array}{c}{y}_{41}=a_4*q_{41}^3+b_4*q_{41}^2+c_4*q_{41}+d_4\\ y_{42}=a_4*q_{42}^3+b_4*q_{42}^2+c_4*q_{42}+d_4\\ y_{43}=a_4*q_{43}^3+b_4*q_{43}^2+c_4*q_{43}+d_4\\ y_{44}=a_4*q_{44}^3+b_4*q_{44}^2+c_4*q_{44}+d_4\end{array}\right.---\left(8\right)$

Y in formula₄₁, y₄₂,y₄₃, y₄₄, q₄₁, q₄₂, q₄₃, q₄₄For 4 groups of test datas, obtain a₄、b₄、c₄、d₄Exact numerical values recited To the equation describing external characteristics under this mixed-flow pump zero speed conditions.

2. a kind of mixed-flow pump omnicharacteristic mathematical model construction method according to claim 1 is it is characterised in that obtained Each coefficient value is:

a₁=-0.1775, b₁=-2.211, c₁=3.144, d₁=-32.77, e₁=-1.469, f₁=22.32, g₁=-8.765, k₁=-0.4279, l₁=-10.49, p₁=-13.9；

a₂=0.118, b₂=0.3645, c₂=0.6884, d₂=0.8754, e₂=0.4924, f₂=1.328, g₂=0.3693, k₂=-0.02948, l₂=-1.335, p₂=0.1719, r₂=-1.139, s₂=-0.831, t₂=1.95；

a₃=-0.5187, b₃=0.3785, c₃=-0.1963, d₃=0.005922；

a₄=-1.651, b₄=-0.05852, c₄=-0.2906, d₄=-0.001703.

3. a kind of mixed-flow pump omnicharacteristic mathematical model construction method according to claim 1 is it is characterised in that also include walking Rapid s3, step s4 and step s5, particularly as follows:

After step s3. obtains the coefficient of external characteristics mathematical model under each operating mode, error analyses need be carried out to each mathematical model With the error size of determination mathematical model rationally whether, step is as follows:

(1) numerical value of zero dimension flow q is substituted into the size that mathematical model obtains y, i.e. zero dimension lift h or zero dimension Change the size of moment of torsion m, then error delta size under this q value for the mathematical model is:

$\mathrm{\δ}=\frac{y}{y^{\′}}-1---\left(9\right)$

In formula, y ' represents the value of result of the test corresponding zero dimension lift h or zero dimension moment of torsion m under this q value；

(2) set up q- δ coordinate system, axis of abscissas is zero dimension flow q, axis of ordinates is error delta, will obtain in step (1) To all error delta under this coordinate system its q value corresponding mark, obtain several points and be referred to as error dot, slotting using Hermite All errors are smoothly connected and obtain a curve and be referred to as error distribution curve by value method, and point curve is in q- δ coordinate system axis of abscissas Nearby fluctuate, error distribution curve deviates the error size representing mathematical model under this q apart from size of axis of abscissas；

Step s4. judges the excellent degree of this mathematical model according to the error distribution curve that step s3 obtains, under meeting simultaneously Can consider during two conditions in face that this mathematical model preferably describes the external characteristics of mixed-flow pump:

δ≤0.11 (10)

δ_80%≤0.08 (11)

In formula:

δ_80%The error distribution curve axis of abscissas always error on interval 80% region；

If step s5. can not meet two conditions in step s4 according to the mathematical model that step s1 is determined, can arrange Except the larger test data of error and then filter out exact test data, again solve coefficient contained by this mathematical model, until this number Till model disclosure satisfy that two conditions in step s4.