CN105550510A - Dual-pump confluence flow pulsation feature extraction method - Google Patents

Abstract

The invention relates to a dual-pump confluence flow pulsation feature extraction method, comprising the following steps of: 1) obtaining a single-pump flow function according to types of the pumps Q(Phi); 2) obtaining a dual-pump confluence flow function Q<confluence>(Phi, Phi<b>); according to the single-pump flow function and rotation angle phase difference between the pumps; 3) calculating a flow pulsation function Delta(Phi<b>):Delta(Phi<b>)=[Q<confluence max>(Phi<b>)-Q<confluence min>(Phi<b>)]/Q<confluence>(Phi<b>) average; 4) calculating a flow pulsation distribution function F(Delta) and a derivative thereof f(delta) according to the flow pulsation function Delta(Phi<b>), the f(Delta) refers to probability density when the flow pulsation is Delta, namely, the dual-pump confluence flow pulsation feature, and the value of the f(Delta) represents degree of possibility of occurrence of the flow pulsation Delta. As compared with the prior art, the method has the advantages, such as simple and convenient calculation and high accuracy, can be used for accurate calculation of flow pulsation of a hydraulic system supplying oil through dual-pump confluence, and provides a theoretical basis for building a design criteria for flow pulsation inhibition and model selection for components and parts of a dual-pump system.

Description

A kind of Dual-pump flow-converging flow pulsation feature extraction method

Technical field

The present invention relates to a kind of discharge characteristic extracting method, especially relate to a kind of Dual-pump flow-converging flow pulsation feature extraction method.

Background technology

In aviation and engineering machinery field, for meeting the demand of system large discharge, improve capacity usage ratio, hydraulic system often adopts double pump fuel feeding simultaneously.Aviation or engineering machinery have multiple hydraulic mechanism, and when some mechanism does not work, the direct oil return box of unnecessary hydraulic oil causes energy dissipation.Adopt double pump for oil form, the requirement of single pump specifications parameter can be reduced, the demand of system large discharge can be met again, fully improve capacity usage ratio.Dual-pump flow-converging flow equals the superposition of double pump instantaneous delivery, show the flow pulsation phenomenon different from single pump, find in practical application that Dual-pump flow-converging is conducive to improving flow pulsation, but accurate flow pulsation feature extraction method is not had, better basis cannot be provided for the application of double pump system, cannot evaluation system flow pulsation characteristic quality.

Summary of the invention

Object of the present invention be exactly in order to overcome above-mentioned prior art exist defect and a kind of easy, that accuracy is high Dual-pump flow-converging flow pulsation feature extraction method that calculates is provided, the accurate Calculation that the flow rate of hydraulic system that can be used for employing Dual-pump flow-converging fuel feeding is pulsed, sets up design criteria for double pump system flow pulsation suppression and components selection provides theoretical foundation.

Object of the present invention can be achieved through the following technical solutions:

A kind of Dual-pump flow-converging flow pulsation feature extraction method, comprises the following steps:

1) single-pump flow function is obtained according to the type of pump wherein for the anglec of rotation of pump;

2) Dual-pump flow-converging flow function is obtained according to the anglec of rotation phase differential between single-pump flow function and double pump

Wherein represent the anglec of rotation of first pump, represent the anglec of rotation phase differential between second pump and first pump;

3) calculated flow rate pulsatile function

Wherein with represent Dual-pump flow-converging flow function maximal value and minimum value respectively, represent the mean value of Dual-pump flow-converging flow function;

4) according to flow pulsation function probability density when calculated flow rate pulsation distribution function F (δ) and derivative f (δ), f (δ) represent that flow pulsation is δ, is Dual-pump flow-converging flow pulsation characteristic.

Described single-pump flow function with Dual-pump flow-converging flow function the cycle of being is the periodic function of T.

Described anglec of rotation phase differential and interval [0, T) upper probability is uniformly distributed.

Described step 4) in, flow pulsation distribution function F (δ) expression formula is:

$F\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}0,\mathrm{\&delta;}<{\mathrm{\&delta;}}_{min}\\ L\left(\mathrm{\&delta;}\right)/T,{\mathrm{\&delta;}}_{\min }\&le;\mathrm{\&delta;}\&le;{\mathrm{\&delta;}}_{max}\\ 1,\mathrm{\&delta;}>{\mathrm{\&delta;}}_{max}\end{array}\right.$

Wherein δ _minand δ _maxrepresent flow pulsation function respectively minimum value and maximal value, L (δ) represent meet 's corresponding burst length.

Burst length L (δ) obtains according to such as under type:

Judge Dual-pump flow-converging flow pulsation function whether one of meet the following conditions:

A, Dual-pump flow-converging flow pulsation function interval [0, T) monotone decreasing;

B, Dual-pump flow-converging flow pulsation function interval [0, T) monotone increasing;

If satisfy condition A, then meet 's corresponding burst length L (δ) is

L(δ)＝T-g ^-1(δ)

If satisfy condition B, then meet 's corresponding burst length L (δ) is

L(δ)＝g ^-1(δ)

Wherein g ^-1(δ) be flow pulsation function inverse function;

If condition A and B does not all meet, then establish there is p monotone decreasing interval [a ₀, a ₁), [a ₁, a ₂) ..., [a _p-1, a _p), q monotone increasing interval [b ₀, b ₁), [b ₁, b ₂) ..., [b _q-1, b _q), meet 's corresponding burst length L (δ) is

$L\left(\mathrm{\&delta;}\right)=\underset{i=1}{\overset{p}{\&Sigma;}}\&lsqb;a_i-h_i\left(\mathrm{\&delta;}\right)\&rsqb;+\underset{j=1}{\overset{q}{\&Sigma;}}\&lsqb;h_j\left(\mathrm{\&delta;}\right)-b_{j-1}\&rsqb;$

Wherein h _i(δ) be

$h_i\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}{\mathrm{\&alpha;}}_i,\mathrm{\&delta;}<\mathrm{\&delta;}\left({\mathrm{\&alpha;}}_i\right)\\ g_i^{-1}\left(\mathrm{\&delta;}\right),\mathrm{\&delta;}\left({\mathrm{\&alpha;}}_i\right)\&le;\mathrm{\&delta;}\&le;\mathrm{\&delta;}\left({\mathrm{\&alpha;}}_{i-1}\right)\\ {\mathrm{\&alpha;}}_{i-1},\mathrm{\&delta;}>\mathrm{\&delta;}\left({\mathrm{\&alpha;}}_{i-1}\right)\end{array}\right.$

H _j(δ) be

$h_j\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}{b}_{j-1},\mathrm{\&delta;}<\mathrm{\&delta;}\left(b_{j-1}\right)\\ g_j^{-1}\left(\mathrm{\&delta;}\right),\mathrm{\&delta;}\left(b_{j-1}\right)\&le;\mathrm{\&delta;}\&le;\mathrm{\&delta;}\left(b_j\right)\\ b_j,\mathrm{\&delta;}>\mathrm{\&delta;}\left(b_j\right)\end{array}\right.$

Wherein, represent at i-th monotone decreasing interval [a _i-1, a _i) flow pulsation function inverse function, represent at a jth monotone increasing interval [b _i-1, b _i) flow pulsation function inverse function.

Flow pulsation characteristic mentioned by present hydraulic system is only concerned about max min and the mean value of flow, and for the flow pulsation of Dual-pump flow-converging, due to its randomness, can not go to pass judgment on its flow pulsation situation with a numerical value simply.Existing flow pulsation method for expressing cannot represent its randomness characteristic.Compared with prior art, the present invention proposes the accurate extracting method of flow pulsation characteristic after Dual-pump flow-converging, draw the mathematical expression of Dual-pump flow-converging flow pulsation characteristic theoretically, calculate easy, accuracy is high; The present invention, by flow pulsation probability density function, have expressed the random character of its flow, has reference significance, also can be used as hydraulic pump selection ground for judgement double pump flow pulsation parameter quality.

Accompanying drawing explanation

Fig. 1 is schematic flow sheet of the present invention;

Fig. 2 is the Dual-pump flow-converging flow pulsation function schematic diagram that specific embodiment calculates;

Fig. 3 is the Dual-pump flow-converging flow pulsation distribution function schematic diagram that specific embodiment calculates;

Fig. 4 is the Dual-pump flow-converging flow pulsation probability density function schematic diagram that specific embodiment calculates.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment is implemented premised on technical solution of the present invention, give detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

The present embodiment provides a kind of Dual-pump flow-converging flow pulsation feature extraction method, and as shown in Figure 1, the method comprises the following steps:

1) single-pump flow function is obtained wherein for the anglec of rotation of pump, the periodic function of this function to be the cycle be T.

2) Dual-pump flow-converging flow function is obtained according to the anglec of rotation phase differential between single-pump flow function and double pump

Wherein represent the anglec of rotation of first pump, represent the anglec of rotation phase differential of second pump and first pump, the periodic function of this function to be also the cycle be T, and interval [0, T) upper probability is uniformly distributed.

Dual-pump flow-converging flow function only consider interval [0, T) on expression formula, the interflow flow function cycle of remaining is the periodic function of T, and the randomness of Dual-pump flow-converging flow pulsation is embodied in parameter on, when reason is two pump startups, the phase differential of the anglec of rotation is different due to the difference of initial phase, and initial phase is random.

3) calculated flow rate pulsatile function

Wherein with represent Dual-pump flow-converging flow function maximal value and minimum value respectively, represent the mean value of Dual-pump flow-converging flow function.

4) according to flow pulsation function calculated flow rate pulsation distribution function F (δ) and derivative f (δ) thereof, probability density when f (δ) represents that flow pulsation is δ, be Dual-pump flow-converging flow pulsation characteristic, its value have expressed and occurs that flow pulsation is the possibility size of δ.Wherein, flow pulsation distribution function F (δ) is

$F\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}0,\mathrm{\&delta;}<{\mathrm{\&delta;}}_{min}\\ L\left(\mathrm{\&delta;}\right)/T,{\mathrm{\&delta;}}_{\min }\&le;\mathrm{\&delta;}\&le;{\mathrm{\&delta;}}_{max}\\ 1,\mathrm{\&delta;}>{\mathrm{\&delta;}}_{max}\end{array}\right.---\left(1\right)$

Wherein δ _minand δ _maxrepresent flow pulsation function respectively minimum value and maximal value, L (δ) represent meet 's corresponding burst length.

L (δ) obtains according to such as under type:

Judge Dual-pump flow-converging flow pulsation function whether one of meet the following conditions:

A, Dual-pump flow-converging flow pulsation function interval [0, T) monotone decreasing;

B, Dual-pump flow-converging flow pulsation function interval [0, T) monotone increasing;

If so, for condition A, meet 's corresponding burst length L (δ) is

L(δ)＝T-g ^-1(δ)(2)

For condition B, meet 's corresponding burst length L (δ) is

L(δ)＝g ^-1(δ)(3)

Wherein g ^-1(δ) be flow pulsation function inverse function.

If do not meet above-mentioned A, B condition, Dual-pump flow-converging flow pulsation function interval [0, T) there is multiple monotone increasing or interval of successively decreasing.If there is p monotone decreasing interval [a ₀, a ₁), [a ₁, a ₂) ..., [a _p-1, a _p), q monotone increasing interval [b ₀, b ₁), [b ₁, b ₂) ..., [b _q-1, b _q), then meet 's corresponding burst length L (δ) is

$L\left(\mathrm{\&delta;}\right)=\underset{i=1}{\overset{p}{\&Sigma;}}\&lsqb;{\mathrm{\&alpha;}}_i-h_i\left(\mathrm{\&delta;}\right)\&rsqb;+\underset{j=1}{\overset{q}{\&Sigma;}}\&lsqb;h_j\left(\mathrm{\&delta;}\right)-b_{j-1}\&rsqb;---\left(4\right)$

Wherein h _i(δ) be

$h_i\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}{\mathrm{\&alpha;}}_i,\mathrm{\&delta;}<\mathrm{\&delta;}\left({\mathrm{\&alpha;}}_i\right)\\ g_i^{-1}\left(\mathrm{\&delta;}\right),\mathrm{\&delta;}\left({\mathrm{\&alpha;}}_i\right)\&le;\mathrm{\&delta;}\&le;\mathrm{\&delta;}\left({\mathrm{\&alpha;}}_{i-1}\right)\\ {\mathrm{\&alpha;}}_{i-1},\mathrm{\&delta;}>\mathrm{\&delta;}\left({\mathrm{\&alpha;}}_{i-1}\right)\end{array}\right.---\left(5\right)$

H _j(δ) be

$h_j\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}{b}_{j-1},\mathrm{\&delta;}<\mathrm{\&delta;}\left(b_{j-1}\right)\\ g_j^{-1}\left(\mathrm{\&delta;}\right),\mathrm{\&delta;}\left(b_{j-1}\right)\&le;\mathrm{\&delta;}\&le;\mathrm{\&delta;}\left(b_j\right)\\ b_j,\mathrm{\&delta;}>\mathrm{\&delta;}\left(b_j\right)\end{array}\right.---\left(6\right)$

And represent at i-th monotone decreasing interval [a _i-1, a _i) flow pulsation function inverse function. represent at a jth monotone increasing interval [b _i-1, b _i) flow pulsation function inverse function.

Above-mentioned L (δ) account form, its principle is: if Dual-pump flow-converging flow pulsation function in interval monotone decreasing, is easy to get satisfied 's span is cause so have length of an interval degree is L (δ)=T-g ^-1(δ).If Dual-pump flow-converging flow pulsation function in interval monotone increasing, is easy to get satisfied 's span is cause so have length of an interval degree is L (δ)=g ^-1(δ).When there is multiple increasing or decreasing and being interval, only need each monotony interval, meet the burst length required is obtained, cumulative.With at certain monotone decreasing interval [a _i-1, a _i) be example, if δ < δ is (a _i), minimum value δ (a on this interval is described _i) be all greater than δ, so meet the length required is 0, namely according to a _i-h _i(δ) result calculated is 0; If δ is (a _i)≤δ≤δ (a _i-1), so meet on this interval require value exists and a _ibetween, so length is exactly if δ > δ is (a _i-1), maximal value δ (a on this interval is described _i-1) be all less than δ, so meet the length required is a _i-a _i-1, namely whole burst length all meets the demands.

For 7 plunger axial plunger pump Dual-pump flow-convergings, the flow function of its single pump is:

Wherein K is the coefficient relevant with ram pump self structure and rotating speed; β is the half of adjacent two plunger angles, i.e. β=π/Z, Z is plunger number, equals 7 here; for the corner of ram pump.

Single-pump flow function cycle T=β, then Dual-pump flow-converging flow function is

Wherein represent the phase differential of second pump and first pump anglec of rotation, and

Calculate Dual-pump flow-converging flow pulsation function

Wherein because of Dual-pump flow-converging flow pulsation function about symmetry, calculates below and only considers this scope, and can not probability density function result of calculation be impacted, Fig. 2 is Dual-pump flow-converging flow pulsation function.

Finally calculate Dual-pump flow-converging flow pulsation probability density function, according to Fig. 2, Dual-pump flow-converging flow pulsation function in interval monotone decreasing, so has L (δ)=[β/2-g ^-1(δ)].Flow pulsation distribution function is

$F\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}0,\mathrm{\&delta;}<{\mathrm{\&delta;}}_{\min }\\ \frac{\frac{\mathrm{\&beta;}}{2}-g^{-1}\left(\mathrm{\&delta;}\right)}{\frac{\mathrm{\&beta;}}{2}}\\ 1,\mathrm{\&delta;}>{\mathrm{\&delta;}}_{\max }\end{array}\right.,{\mathrm{\&delta;}}_{min}\&le;\mathrm{\&delta;}\&le;{\mathrm{\&delta;}}_{max}$

Fig. 3 is flow pulsation distribution function.

To its differentiate, obtain flow pulsation probability density function

By computer programming, can show that Dual-pump flow-converging flow pulsation probability density function is as Fig. 4.This probability density function is Dual-pump flow-converging flow pulsation characteristic and expresses.Can find out, the interval probability density value of the low discharge pulsation probability density value more interval than large discharge pulsation is large, and namely the probability that occurs of low discharge pulsation is large, and this theory calculate being also Dual-pump flow-converging reduces flow pulsation proves.

The above, be only better embodiment of the present invention, can not with the scope of restriction the claims in the present invention.Namely all equalizations done according to the claims in the present invention change and modify, and will not lose the main idea place of invention, also not depart from spirit of the present invention and right, former capital should be considered as further status of implementation of the present invention.

Claims (5)

1. a Dual-pump flow-converging flow pulsation feature extraction method, is characterized in that, comprise the following steps:

1) single-pump flow function is obtained according to the type of pump wherein for the anglec of rotation of pump;

2) Dual-pump flow-converging flow function is obtained according to the anglec of rotation phase differential between single-pump flow function and double pump

Wherein represent the anglec of rotation of first pump, represent the anglec of rotation phase differential between second pump and first pump;

3) calculated flow rate pulsatile function

Wherein with represent Dual-pump flow-converging flow function maximal value and minimum value respectively, represent the mean value of Dual-pump flow-converging flow function;

4) according to flow pulsation function probability density when calculated flow rate pulsation distribution function F (δ) and derivative f (δ), f (δ) represent that flow pulsation is δ, is Dual-pump flow-converging flow pulsation characteristic.

2. Dual-pump flow-converging flow pulsation feature extraction method according to claim 1, is characterized in that, described single-pump flow function with Dual-pump flow-converging flow function the periodic function of to be all cycles be T.

3. Dual-pump flow-converging flow pulsation feature extraction method according to claim 2, is characterized in that, described anglec of rotation phase differential and interval [0, T) upper probability is uniformly distributed.

4. Dual-pump flow-converging flow pulsation feature extraction method according to claim 3, is characterized in that, described step 4) in, flow pulsation distribution function F (δ) expression formula is:

$F\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}0,\mathrm{\&delta;}<{\mathrm{\&delta;}}_{min}\\ L\left(\mathrm{\&delta;}\right)/T,{\mathrm{\&delta;}}_{\min }\&le;\mathrm{\&delta;}\&le;{\mathrm{\&delta;}}_{max}\\ 1,\mathrm{\&delta;}>{\mathrm{\&delta;}}_{max}\end{array}\right.$

Wherein δ _minand δ _maxrepresent flow pulsation function respectively minimum value and maximal value, L (δ) represent meet 's corresponding burst length.

5. Dual-pump flow-converging flow pulsation feature extraction method according to claim 4, is characterized in that, burst length L (δ) obtains according to such as under type:

Judge Dual-pump flow-converging flow pulsation function whether one of meet the following conditions:

A, Dual-pump flow-converging flow pulsation function interval [0, T) monotone decreasing;

B, Dual-pump flow-converging flow pulsation function interval [0, T) monotone increasing;

If satisfy condition A, then meet 's corresponding burst length L (δ) is

L(δ)＝T-g ^-1(δ)

If satisfy condition B, then meet 's corresponding burst length L (δ) is

L(δ)＝g ^-1(δ)

Wherein g ^-1(δ) be flow pulsation function inverse function;

If condition A and B does not all meet, then establish there is p monotone decreasing interval [a ₀, a ₁), [a ₁, a ₂) ..., [a _p-1, a _p), q monotone increasing interval [b ₀, b ₁), [b ₁, b ₂) ..., [b _q-1, b _q), meet 's corresponding burst length L (δ) is

$L\left(\mathrm{\&delta;}\right)=\underset{i=1}{\overset{p}{\&Sigma;}}\&lsqb;a_i-h_i\left(\mathrm{\&delta;}\right)\&rsqb;+\underset{j=1}{\overset{q}{\&Sigma;}}\&lsqb;h_j\left(\mathrm{\&delta;}\right)-b_{j-1}\&rsqb;$

Wherein h _i(δ) be

$h_i\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}{a}_i,\mathrm{\&delta;}<\mathrm{\&delta;}\left(a_i\right)\\ g_i^{-1}\left(\mathrm{\&delta;}\right),\mathrm{\&delta;}\left(a_i\right)\&le;\mathrm{\&delta;}\&le;\mathrm{\&delta;}\left(a_{i-1}\right)\\ a_{i-1},\mathrm{\&delta;}>\mathrm{\&delta;}\left(a_{i-1}\right)\end{array}\right.$

H _j(δ) be

$h_j\left(\mathrm{\&delta;}\right)=\left\{\begin{array}{c}{b}_{j-1},\mathrm{\&delta;}<\mathrm{\&delta;}\left(b_{j-1}\right)\\ g_i^{-1}\left(\mathrm{\&delta;}\right),\mathrm{\&delta;}\left(b_{j-1}\right)\&le;\mathrm{\&delta;}\&le;\mathrm{\&delta;}\left(b_j\right)\\ b_j,\mathrm{\&delta;}>\mathrm{\&delta;}\left(b_j\right)\end{array}\right.$

Wherein, represent at i-th monotone decreasing interval [a _i-1, a _i) flow pulsation function inverse function, represent at a jth monotone increasing interval [b _i-1, b _i) flow pulsation function inverse function.