CN101770540A - Method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model - Google Patents
Method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model Download PDFInfo
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Abstract
The invention discloses a method for dynamically optimizing the structure of a valve plate of an aviation plunger pump based on an instantaneous flow model. The method is established on the basis of the instantaneous flow model of the aviation plunger pump, and comprises the following steps of: selecting the radius r2 and the shift angle theta of a shock relief vent as the design variables for the dynamic structure optimization of the valve plate of the aviation plunger pump; randomly generating two groups of initial parameter vectors and substituting the initial parameter vectors into the instantaneous flow model of the aviation plunger pump to obtain instantaneous flow values of the aviation plunger pump under the two groups of parameter vectors; selecting the instantaneous flow pulse amplitude of the aviation plunger pump as a target function, comparing two target function values F(XL) and F(XH) and modifying structure parameters in real time through rotation transformation and contraction transformation to finally obtain the optimized structure parameters under the least instantaneous flow pulse amplitude. The invention provides more accurate instantaneous flow model of the aviation plunger pump for the dynamic structure optimization of the valve plate of the aviation plunger pump, evaluates the target function in real time, is a dynamic optimizing process and has very high efficiency and overall optimizing capability.
Description
Technical field
The invention belongs to aviation ram pump Study on Structure Optimizing field, be specifically related to a kind of method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model.
Background technology
Axial plunger pump since characteristics such as it is high-power, high-level efficiency and reliability be widely used in the hydraulic air pump source system.And because the structure of self and the factors such as compressibility of fluid, the aviation ram pump is certainly existing the instantaneous delivery pulsation, and flow pulsation is the basic origin cause of formation of ram pump flow noise and compression shock, this compression shock can make that system works is unstable even resonance takes place, to the serious destruction of member generation of system.The factor that influences the flow pulsation of aviation ram pump is a lot, and wherein the structural parameters of valve plate are topmost influence factors, especially vibration damping pore radius r
2With mispairing angle θ.Therefore, the structure of valve plate of aviation plunger pump is optimized design and has crucial meaning for the vibration and the noise that reduce plane hydraulic system.
To aspect the influence of plunger pumping flow pulsation, a lot of scholars study at port plate structure.The GaneshKumar Seeniraj of Purdue University etc. utilize the CASPAR software analysis port plate structure parameter influence of ram pump flow noise (is seen for details Ganesh Kumar Seeniraj, paper " the Impact of Valve Plate Design on Noise that Monika Ivantysynova delivered in the meeting " ASME 2006 International Mechanical Engineering Congress andExposition " that Chicago,U.S is held-10 days on the 5th November in 2006, VolumetricEfficiency and Control Effort in an Axial Piston Pump ", article is numbered: IMECE2006-15001); The Southwest Jiaotong University woods waits quietly the valve plate of different structure has been carried out the CFD simulation analysis, and provided and optimized suggestion (seeing Lin Jing for details, the paper " the axial plunger pump port plate structure is to the influence of flow pulsation " that Sun Mingzhi delivers on " Fluid Transmission and Control " the 3rd phase in 2007); The Ma Jien of Zhejiang University has set up the mathematical model of ram pump flow noise, and port plate structure has been carried out optimizing (seeing the Ma Jien of Zhejiang University PhD dissertation " Axial Piston Pump's Pulsant Flux and the research of valve plate optimal design " in 2009 for details); Those Cheng Lie of Gansu Polytechnical Univ etc. are by being optimized port plate structure, (it is strong to see that one-tenth for details to have designed the low noise port plate structure of asymmetric deflection, Yin Wenbo, the paper that spark green grass or young crops was delivered on 2002 " Gansu Polytechnical Univ's journal " the 28th the 4th phase of volume " axially ram pump valve plate design under the compressible fluid actuating medium situation ").Existing valve plate structure for plunger pump optimization method mostly is to utilize software or design variable is sampled and realized the static optimization of port plate structure be easy to be absorbed in local optimum, and efficient being very low.
Summary of the invention
The objective of the invention is: overcome the defective that local optimum is hanged down and be absorbed in easily to present valve plate structure for plunger pump static optimization efficient, a kind of method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model is provided.
The present invention is on the basis of setting up aviation ram pump instantaneous delivery nonlinear model, and the instantaneous delivery pulsation amplitude of choosing the aviation ram pump is as the optimization aim function, and employing rotating vector method is carried out the real-time online modification to the port plate structure parameter; And amended parameter is brought in the aviation ram pump instantaneous flow model resolve in real time, objective function is carried out Real-Time Evaluation, up to obtaining optimum structural parameters combination.
The idiographic flow of the method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model provided by the invention is as follows:
The first step, choose vibration damping pore radius r
2With the design variable of mispairing angle θ as dynamically optimizing structure of valve plate of aviation plunger pump, given design variable vibration damping pore radius r
2Span with mispairing angle θ.
Generally speaking, the vibration damping pore radius greater than 0 less than oil extraction window top arc radius r
3, the mispairing angular region is spent less than 90 greater than 0 degree; For concrete ram pump, can further dwindle this two design variable spans according to actual conditions, with the calculated amount of less optimizing process.
Second step, the vibration damping pore radius r that determines in the first step
2In the span of mispairing angle θ, produce two groups of initial parameter vector X at random
L=(θ, r
2)
TAnd X
H=(θ ', r
2')
T
The 3rd the step, with two groups of parameter vector X
HAnd X
LBe updated in the aviation ram pump instantaneous flow model, obtain the instantaneous delivery value of two groups of aviation ram pumps under the parameter vector.
The instantaneous delivery of aviation ram pump is the curve of periodicity near sinusoidal, and aviation ram pump instantaneous flow model is as follows in the one-period:
Wherein,
In the formula, p
dBe pump work pressure, p
1Be plunger cavity internal pressure, C
dBe the damping hole coefficient of flow, ρ is a fluid density.E is the elastic modulus of fluid, and A is the plunger sectional area, and ω is the angular velocity of ram pump, and β is a swashplate angle, and k is the leadage coefficient of plunger cavity, V
0Be in the original volume of upper dead center for plunger cavity; r
1Be the logical oil groove end of plunger arc radius, r
2Be vibration damping pore radius, r
3Be plunger oil extraction window end arc radius, R is a plunger distribution circle radius, and φ is the angle that plunger turns over;
θ
0, r
20Be respectively
θ, r
2One group of definite value in specific ram pump.
The 4th goes on foot, chooses aviation ram pump instantaneous delivery pulsation amplitude as objective function, relatively two target function value F (X
L) and F (X
H), i.e. aviation ram pump instantaneous delivery pulsation amplitude is if F is (X
L)>F (X
H), exchange parameter vector X then
LWith X
HValue, otherwise do not exchange.
The flow pulsation of aviation ram pump is the basic reason of initiation pressure impact and noise, reduces instantaneous delivery pulsation amplitude and has substantive meaning for the flow noise and the vibration that reduce the aviation ram pump.Therefore, choose the instantaneous delivery pulsation amplitude F=max (Q of aviation ram pump
s)-min (Q
s) as the objective function of port plate structure dynamic optimization, wherein Q
sIt is the instantaneous delivery of aviation ram pump.
The 5th step, compute vectors difference X=X
H-X
L, with phasor difference X around vector X
LTerminal point L rotation, rotational transform is followed formula X '=Xrotator and is obtained postrotational new vector X
TWith new vector X
TAssignment is given X
H, i.e. X
H=X
TWherein,
Be twiddle factor,
Be the anglec of rotation,
Generally get 120 degree.
If the 6th step was finished the tour rotation around a L, then turned to for the 7th step, otherwise turned to for the 3rd step.
If the 7th step ‖ X
H-X
L‖<ε, ε are given computational accuracy, and ε generally is chosen for 0.0001, majorized function global optimum then, and promptly minimum instantaneous delivery pulsation amplitude is F (X
Min), the optimization structure parameter is X
Min=X
L, optimizing process finishes; Otherwise to X
HDo contracted transformation, i.e. X
H=X
L+ contractor (X
H-X
L), contractor is a contraction factor, and its span is (0,1), gets golden section usually, and promptly contractor=0.618 turned to for the 3rd step.
A kind of method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model of the present invention is compared with the valve plate structure for plunger pump optimization method of present existence, and its advantage is:
(1) changes by the area of passage in the labor aviation ram pump oil extraction process, consider the compressibility of fluid and the leakage of ram pump simultaneously, for dynamically optimizing structure of valve plate of aviation plunger pump provides accurate more aviation ram pump instantaneous flow model;
(2) the instantaneous delivery pulsation amplitude of choosing the aviation ram pump is as the optimization aim function, and this objective function can fundamentally reflect ram pump compression shock and noise condition, and is more rationally effective for structure of valve plate of aviation plunger pump optimization;
(3) this optimization method carries out the real-time online modification to the port plate structure parameter, and amended parameter is brought in the aviation ram pump instantaneous flow model resolve in real time, objective function is carried out Real-Time Evaluation, is a dynamic optimization process, has the efficient of better global optimum's property and Geng Gao.
Description of drawings
Fig. 1: the method for dynamically optimizing structure of valve plate of aviation plunger pump schematic flow sheet that the present invention is based on instantaneous flow model;
Fig. 2: structure of valve plate of aviation plunger pump sketch;
Fig. 3: vector rotation synoptic diagram;
Fig. 4: the area of passage in the aviation ram pump oil extraction process changes;
Fig. 5: certain type aviation ram pump instantaneous delivery curve;
Fig. 6: certain type structure of valve plate of aviation plunger pump parameter dynamic optimization process;
Fig. 7: around optimized parameter, choose the instantaneous delivery correlation curve that any 4 groups of parameters obtain.
Embodiment
Below in conjunction with drawings and Examples the method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model of the present invention is elaborated.
As shown in Figure 1, it is as follows to the present invention is based on the method for dynamically optimizing structure of valve plate of aviation plunger pump flow process of instantaneous flow model:
The first step, choose vibration damping pore radius r
2With the design variable of mispairing angle θ, because vibration damping pore radius r as dynamically optimizing structure of valve plate of aviation plunger pump
2With mispairing angle θ is to influence the main factor that aviation ram pump instantaneous delivery is pulsed; Given design variable vibration damping pore radius r
2Span with mispairing angle θ.
Generally speaking, vibration damping pore radius r
2Greater than 0 less than oil extraction window top arc radius r
3, 0 °<θ of mispairing angle θ scope<90 °; For concrete ram pump, can further dwindle this two design variable spans according to actual conditions, to reduce the calculated amount of optimizing process.
Second step, the vibration damping pore radius r that determines in the first step
2In the span of mispairing angle θ, produce two groups of initial parameter vector X at random
L=(θ, r
2)
TAnd X
H=(θ ', r
2')
T
The 3rd the step, with two groups of parameter vector X
HAnd X
LBe updated in the aviation ram pump instantaneous flow model, obtain the instantaneous delivery value of two groups of aviation ram pumps under the parameter vector.
It is as follows that aviation ram pump instantaneous flow model is set up derivation:
The instantaneous delivery of aviation ram pump is that periodically as shown in Figure 2, in one-period, the area of passage that is formed by vibration damping hole 1, plunger oil through 2 and oil extraction window 3 has following four change procedures, as shown in Figure 4:
Process 1: the oil through 2 of plunger forwards the process that just contacts vibration damping hole 1 to from initial position, and this process corner is
Process 2: to the process of surrounding vibration damping hole 1 fully, this process corner is the oil through 2 of plunger from contact vibration damping hole 1
Process 3: the oil through 2 of plunger is from surrounding vibration damping hole 1 fully to the process that rigidly connects bank oil window 3, and this process corner is
Process 4: the oil through 2 of plunger is raised to the process of pump discharge pressure from rigidly connecting bank oil window 3 to pressure, and this process corner is
More than in four processes, the area of passage formula is as follows:
Wherein,
In the formula, r
1Be the logical oil groove end of plunger arc radius, r
2Be vibration damping pore radius, r
3Be plunger oil extraction window end arc radius, R is a plunger distribution circle radius, and φ is the angle that plunger turns over.
With the mispairing angle θ and the vibration damping pore radius r2 of ram pump confidential relation is arranged, as shown in the formula:
By the aperture flow formula, the flow that can change damping hole is:
In the formula (4), p
dBe pump work pressure, p
1Be plunger cavity internal pressure, C
dBe the damping hole coefficient of flow, ρ is a fluid density.
Consider the fluid compressibility, then the plunger cavity internal pressure satisfies the following differential equation:
In the formula (5), E is the elastic modulus of fluid, and A is the plunger sectional area, and ω is the angular velocity of ram pump, and β is a swashplate angle, and k is the leadage coefficient of plunger cavity, V
0Be in the original volume of upper dead center for plunger cavity.
The theoretical delivery formula of ram pump:
In the formula, α=π/Z, Z are the plunger number.
Simultaneous formula (1), (2), (3), (4), (5) and (6) obtain aviation ram pump instantaneous flow model:
The 4th goes on foot, chooses aviation ram pump instantaneous delivery pulsation amplitude as objective function, relatively two target function value F (X
L) and F (X
H), i.e. aviation ram pump instantaneous delivery pulsation amplitude is if F is (X
L)>F (X
H), then exchange X
LWith X
HValue, otherwise do not exchange.
The flow pulsation of aviation ram pump is the basic reason of initiation pressure impact and noise, reduces instantaneous delivery pulsation amplitude and has substantive meaning for the flow noise and the vibration that reduce the aviation ram pump.Therefore, choose the instantaneous delivery pulsation amplitude F=max (Q of aviation ram pump
s)-min (Q
s) as the objective function of port plate structure dynamic optimization, wherein Q
sIt is the instantaneous delivery of aviation ram pump.
The 5th step, compute vectors difference X=X
H-X
L, as shown in Figure 3, with phasor difference X around vector X
LTerminal point L rotation, rotational transform is followed formula X '=Xrotator and is obtained postrotational new vector X
TWith vector X
TAssignment is given X
H, i.e. X
H=X
TWherein,
Be twiddle factor,
Be the anglec of rotation,
Generally get 120 degree.
If the 6th step phasor difference X finishes the tour rotation around a L, then turned to for the 7th step, otherwise turned to for the 3rd step.
If the 7th step ‖ X
H-X
L‖<ε, ε are given computational accuracy, and ε generally is chosen for 0.0001, majorized function global optimum then, and promptly minimum instantaneous delivery pulsation amplitude is F (X
Min), the optimization structure parameter is X
Min=X
L, optimizing process finishes; Otherwise to X
HDo contracted transformation, i.e. X
H=X
L+ contractor (X
H-X
L), contractor is a contraction factor, and its span is (0,1), gets golden section usually, and promptly contractor=0.618 turned to for the 3rd step.
Embodiment
Utilization is carried out dynamic optimization based on the method for dynamically optimizing structure of valve plate of aviation plunger pump of instantaneous flow model to certain type structure of valve plate of aviation plunger pump.The structural parameters and the running parameter of this aviation ram pump are as follows: plunger distribution circle radius R=40mm, plunger is counted Z=9, revolution speed n=3000r/min, plunger radius r=10mm, swashplate angle β=18, fluid density p=900kg/m
3, fluid bulk modulus E=1000MPa, oil-discharging cavity pressure P
d=28MPa, plunger cavity initial volume V
0=18143mm
3, the flow coefficient C of damping hole
d=0.6, leadage coefficient k=0.95, mispairing angle θ
0=14 °, vibration damping pore radius r
20=1.5mm, plunger leads to oil groove end arc radius r
1=5mm, plunger oil extraction window top arc radius r
3=5mm, four angles
Specific embodiments is as follows:
The first step, choose vibration damping pore radius r
2With the design variable of mispairing angle θ, at this type aviation ram pump, vibration damping pore radius r as dynamically optimizing structure of valve plate of aviation plunger pump
2Span is that (0,5mm), mispairing angle θ span is (0,19 degree).
Second step, the vibration damping pore radius r that determines in the first step
2In the span of mispairing angle θ, produce two groups of initial parameter vector X at random
L=(θ, r
2)
TAnd X
H=(θ ', r
2')
T
The 3rd the step, with X
HAnd X
LBe updated in this type aviation ram pump instantaneous flow model, obtain the instantaneous delivery value of two groups of aviation ram pumps under the parameter vector, draw the instantaneous delivery curve according to this flow value, as shown in Figure 5.
In the structural parameters and the following formula of running parameter substitution with this type aviation ram pump, obtain the instantaneous flow model of this type aviation ram pump:
Wherein,
The 4th goes on foot, chooses aviation ram pump instantaneous delivery pulsation amplitude as objective function, relatively two objective function F (X
L) and F (X
H), i.e. aviation ram pump instantaneous delivery pulsation amplitude is if F is (X
L)>F (X
H), then exchange X
LWith X
HValue, otherwise do not exchange.
The flow pulsation of aviation ram pump is the basic reason of initiation pressure impact and noise, reduces instantaneous delivery pulsation amplitude and has substantive meaning for the flow noise and the vibration that reduce the aviation ram pump.Therefore, choose the instantaneous delivery pulsation amplitude F=max (Q of aviation ram pump
s)-min (Q
s) as the objective function of port plate structure dynamic optimization, wherein Q
sIt is the instantaneous delivery of aviation ram pump.
The 5th step, compute vectors difference X=X
H-X
L, with phasor difference X around vector X
LTerminal point L rotation, rotational transform is followed formula X '=Xrotator and is obtained postrotational new vector X
TWith new vector X
TAssignment is given X
H, i.e. X
H=X
TWherein, choose the anglec of rotation
Twiddle factor then
If the 6th step phasor difference X finishes the tour rotation around a L, then turned to for the 7th step, otherwise turned to for the 3rd step;
If the 7th step ‖ X
T-X
L‖<ε, ε=0.0001, majorized function global optimum then, promptly minimum instantaneous delivery pulsation amplitude is F (X
Min), the optimization structure parameter is X
Min=X
L, optimizing process finishes; Otherwise to X
TDo contracted transformation, i.e. X
T=X
L+ contractor (X
T-X
L), contraction factor contractor=0.618 turned to for the 3rd step.
Through after the above-mentioned flow process, obtaining this type aviation ram pump instantaneous delivery pulsation amplitude minimum is 0.784 * 10
-3m
3/ s, this moment, optimum port plate structure parameter combinations was: mispairing angle θ=10 °, vibration damping pore radius r
2=0.9mm.Whole dynamic optimization process is only through 8 second time, and as shown in Figure 6, corresponding minimum instantaneous delivery pulsation amplitude had proved that the method for dynamically optimizing structure of valve plate of aviation plunger pump that the present invention is based on instantaneous flow model has very high efficient when the optimizing time was 8s.
Choose 4 groups of parameters arbitrarily near the optimized parameter combination, in the instantaneous flow model of substitution aviation ram pump, the optimized parameter that comprises that obtains as shown in Figure 7 is combined in the instantaneous delivery curve under 5 groups of interior parameters.Table 1 has provided under these 5 groups of parameters, the contrast of the instantaneous delivery of this aviation ram pump pulsation amplitude.By Fig. 7 and table 1 as can be seen, mispairing angle θ=10 ° and vibration damping pore radius r
2During=0.9mm, flow pulsation amplitude minimum has verified that the method for dynamically optimizing structure of valve plate of aviation plunger pump that the present invention is based on instantaneous flow model has good global optimizing.
Instantaneous delivery pulsation amplitude contrast under table 1 different parameters
Mispairing angle θ (°) | The damping hole radius r 2??(mm) | Instantaneous delivery maximal value (L/s) | Instantaneous delivery minimum value (L/s) | Instantaneous delivery pulsation amplitude (L/s) |
??14 | ??1.5 | ??3.950 | ??2.600 | ??1.350 |
??12 | ??1.2 | ??4.013 | ??2.967 | ??1.046 |
??10 | ??0.9 | ??3.847 | ??3.063 | ??0.784 |
??9 | ??0.8 | ??3.785 | ??2.910 | ??0.875 |
??7 | ??0.5 | ??3.760 | ??2.765 | ??0.995 |
Claims (7)
1. based on the method for dynamically optimizing structure of valve plate of aviation plunger pump of instantaneous flow model, it is characterized in that:
The first step, choose vibration damping pore radius r
2With the design variable of mispairing angle θ as dynamically optimizing structure of valve plate of aviation plunger pump, given design variable vibration damping pore radius r
2Span with mispairing angle θ;
Second step, the vibration damping pore radius r that determines in the first step
2In the span of mispairing angle θ, produce two groups of initial parameter vector X at random
L=(θ, r
2)
TAnd X
H=(θ ', r
2')
T
The 3rd the step, with two groups of parameter vector X
HAnd X
LBe updated in the aviation ram pump instantaneous flow model, obtain the instantaneous delivery value of two groups of aviation ram pumps under the parameter vector;
The 4th goes on foot, chooses aviation ram pump instantaneous delivery pulsation amplitude as objective function, relatively two target function value F (X
L) and F (X
H), if F is (X
L)>F (X
H), then exchange X
LWith X
HValue, otherwise do not exchange;
Described objective function is the instantaneous delivery pulsation amplitude F=max (Q of aviation ram pump
s)-min (Q
s), Q wherein
sIt is the instantaneous delivery of aviation ram pump;
The 5th step, compute vectors difference X=X
H-X
L, with phasor difference X around vector X
LTerminal point L rotation, rotational transform is followed formula X '=Xrotator and is obtained postrotational new vector X
TWith new vector X
TAssignment is given XH, i.e. X
H=X
TWherein,
Be twiddle factor,
Be the anglec of rotation;
If the 6th step phasor difference X finishes the tour rotation around a L, then turned to for the 7th step, otherwise turned to for the 3rd step;
If the 7th step || X
H-X
L||<ε, ε are given computational accuracy, and then minimum instantaneous delivery pulsation amplitude is F (X
Min), the optimization structure parameter is X
Min=X
L, optimizing process finishes; Otherwise to X
HDo contracted transformation, i.e. X
H=X
L+ contractor (X
H-X
L), contractor is a contraction factor, turns to for the 3rd step.
2. the method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model according to claim 1 is characterized in that: the span in the first step is meant, described vibration damping pore radius r
2Satisfy 0<r
2<r
3, r
3Be oil extraction window top arc radius, described mispairing angle θ scope satisfies 0<θ<90 °.
3. the method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model according to claim 1, it is characterized in that: in the 3rd step, the instantaneous delivery of aviation ram pump is the curve of periodicity near sinusoidal, and aviation ram pump instantaneous flow model is as follows in the one-period:
Wherein,
In the formula, p
dBe pump work pressure, p
1Be plunger cavity internal pressure, C
dBe the damping hole coefficient of flow, ρ is a fluid density.E is the elastic modulus of fluid, and A is the plunger sectional area, and ω is the angular velocity of ram pump, and β is a swashplate angle, and k is the leadage coefficient of plunger cavity, V
0Be in the original volume of upper dead center for plunger cavity; r
1Be the logical oil groove end of plunger arc radius, r
2Be vibration damping pore radius, r
3Be plunger oil extraction window end arc radius, R is a plunger distribution circle radius, and φ is the angle that plunger turns over;
θ
0, r
20Be respectively
, θ, r
2One group of definite value in specific ram pump.
4. the method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model according to claim 1 is characterized in that: the anglec of rotation described in the 5th step
Be 120 degree.
5. the method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model according to claim 1 is characterized in that: the computational accuracy ε described in the 7th step is chosen for 0.0001.
6. the method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model according to claim 1 is characterized in that: the contraction factor contractor span described in the 7th step is (0,1).
7. according to claim 1 or 6 described method for dynamically optimizing structure of valve plate of aviation plunger pump based on instantaneous flow model, it is characterized in that: described contraction factor contractor gets golden section value, i.e. contractor=0.618.
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Cited By (3)
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CN103164583A (en) * | 2013-03-26 | 2013-06-19 | 中北大学 | Optimized design method of axial piston pump valve plate based on particle swarm optimization method |
CN103164583B (en) * | 2013-03-26 | 2015-05-20 | 中北大学 | Optimized design method of axial piston pump valve plate based on particle swarm optimization method |
CN104358657A (en) * | 2014-11-03 | 2015-02-18 | 安徽理工大学 | Two-side driving balance type low-speed large-torque axial plunger motor |
CN113032928A (en) * | 2021-03-30 | 2021-06-25 | 北京航空航天大学 | Plunger pump and follow-up piston control system integrated model establishing method and system |
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