CN113987836A - Gear pump accelerated life coefficient calculation method based on rotating speed and pressure - Google Patents

Gear pump accelerated life coefficient calculation method based on rotating speed and pressure Download PDF

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CN113987836A
CN113987836A CN202111372636.5A CN202111372636A CN113987836A CN 113987836 A CN113987836 A CN 113987836A CN 202111372636 A CN202111372636 A CN 202111372636A CN 113987836 A CN113987836 A CN 113987836A
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gear pump
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obtaining
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刘菁
胡守信
高玉和
冯刚
李嘉璇
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China Aerospace Beijing Hangke Engine Control System Technology Co ltd
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Abstract

The application provides a gear pump accelerated life coefficient calculation method based on rotating speed and pressure, which comprises the following steps: obtaining a dimensionless quantity alpha based on the concentrated load, the elastic modulus of the bearing, the radius of the inner hole of the bearing and the radius of the gear journal which are borne by the gear journal of the gear pump to be accelerated; obtaining a contact half-angle sine value of the bearing and the gear shaft based on the elastic modulus ratio, the dimensionless quantity alpha, the bearing poisson ratio and the gear shaft poisson ratio; obtaining the maximum value of the normal contact stress of the bearing based on the unit average pressure of the inner hole of the bearing and the sine value of the contact half angle; determining the contact stress value of the whole contact surface of the bearing based on the maximum normal contact stress value; acquiring the maximum rotating speed and the maximum outlet pressure of a gear pump to be accelerated; obtaining the wear volume by the Archard theory; an accelerated life factor is calculated based on the wear volume.

Description

Gear pump accelerated life coefficient calculation method based on rotating speed and pressure
Technical Field
The application belongs to the technical field of accelerated life tests of gear pumps of fuel control devices, and particularly relates to a gear pump accelerated life coefficient calculation method based on rotating speed and pressure.
Background
Fuel control devices are a key part of the fuel supply system of aircraft engines, which supply fuel for the engine in accordance with commands from the engine electronic controller. The fuel control device of general common structure all adopts the gear pump as the pump head, because the gear pump is in operating condition all the time, its operational environment is the worst, in case the performance deviates, must lead to engine fuel to supply the problem to appear. It is common that the volumetric efficiency of the gear pump is reduced to cause the outlet flow to be reduced, so in order to find out the actual service life of the gear pump, related tests are often required to be carried out.
The conventional method is to carry out a 1:1 test according to a load spectrum, for example, if the design life of a gear pump is 1000 hours, then an actual test also needs to carry out a 1000-hour test, but the conventional method has the problems of high time and test cost and even influences on a design completion node, so an accelerated life test needs to be carried out.
In the relative technologies, the accelerated life test is started by increasing the test load, for example, adding pollutants into the fuel, increasing the outlet pressure of the gear pump, increasing the rotation speed of the gear pump, increasing the temperature, and the like, but the increase of the outlet pressure of the gear pump is the most common.
Disclosure of Invention
In order to solve the technical problem, the application provides a method for calculating an accelerated life coefficient of a gear pump based on rotating speed and pressure, which comprises the following steps:
obtaining a dimensionless quantity alpha based on the concentrated load, the elastic modulus of the bearing, the radius of the inner hole of the bearing and the radius of the gear journal which are borne by the gear journal of the gear pump to be accelerated;
obtaining a contact half-angle sine value of the bearing and the gear shaft based on the elastic modulus ratio, the dimensionless quantity alpha, the bearing poisson ratio and the gear shaft poisson ratio;
obtaining the maximum value of the normal contact stress of the bearing based on the unit average pressure of the inner hole of the bearing and the sine value of the contact half angle;
determining the contact stress value of the whole contact surface of the bearing based on the maximum normal contact stress value;
acquiring the maximum rotating speed and the maximum outlet pressure of a gear pump to be accelerated; the maximum rotating speed and the sliding distance of the gear pump to be accelerated are linearly related; the contact stress value of the whole contact surface of the bearing corresponds to the maximum outlet pressure in a nonlinear way;
obtaining the wear volume by the Archard theory; an accelerated life factor is calculated based on the wear volume.
Preferably, the sine value of the contact half angle is less than or equal to pi/9.
Preferably, before obtaining the sine value of the contact half angle between the bearing and the gear shaft based on the elastic modulus ratio, the dimensionless quantity alpha, the bearing poisson ratio and the gear shaft poisson ratio, the method further includes:
and obtaining the elastic modulus ratio based on the bearing elastic modulus of the gear pump to be accelerated and the gear shaft elastic modulus.
Preferably, before obtaining the maximum value of the normal contact stress of the bearing based on the unit average pressure of the inner bore of the bearing and the sine value of the contact half angle, the method further includes:
and obtaining the unit average pressure of the bearing inner hole based on the concentrated load and the diameter of the bearing inner hole.
Preferably, the deriving the wear volume using archer's theory comprises:
and calculating the wear volume based on the wear coefficient, the sliding distance, the material hardness and the contact stress value of the whole contact surface of the bearing.
Preferably, the contact stress value of the whole contact surface of the bearing is obtained based on flow field simulation.
Preferably, if the ratio of the accelerated outlet pressure to the non-accelerated outlet pressure is greater than 2, the accelerated life factor is corrected based on the flow field simulation.
Preferably, the correcting the accelerated life factor based on the flow field simulation includes:
and calculating the accelerated life coefficient based on the contact stress value of the whole contact surface of the bearing.
The application has the following technical effects:
according to the method, the acceleration ratio of the acceleration test or the reverse acceleration service life time can be rapidly calculated, and the technical problem that the acceleration ratio of the existing acceleration service life test is not easy to operate or the steps are complex is solved.
Drawings
FIG. 1 is a flow chart of a method for calculating an accelerated life factor of a gear pump based on rotation speed and pressure according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a simulation analysis result of stress distribution of an inner hole contact surface of a bearing of a gear pump provided in an embodiment of the present application;
FIG. 3 is a schematic diagram of a mesh model of a fluid domain in an inner hole of a bearing of a gear pump according to an embodiment of the present application.
Detailed Description
The method starts from the abrasion volume, and according to the Archard theory, the volume loss generated by the friction of two objects which are in relative motion friction has a relation with the sliding distance, the load and the material hardness, and the basic formula is as follows:
W＝K·S·Pσ/Pm (1)
in formula (1), W is the wear volume in m3, which is the unknown quantity to be solved; s is a sliding distance, the unit is m, the sliding distance is a known quantity and can be obtained according to design input; pσThe normal contact stress (radial force) unit of the corresponding contact surface is Pa and is an unknown quantity; pm is the hardness of the material, the unit is Brinell hardness, and the Pm is a known quantity and can be obtained by consulting a related material manual; k is a wear coefficient (in a certain proportional relation with the friction coefficient) and is a dimensionless quantity, and can be consulted from a mechanical design manual.
According to the formula 1, the main variables influencing the abrasion are the sliding distance S and the normal contact stress, and the two parameters are directly related to the gear pump rotating speed and the pressure after the pump respectively.
Wherein S is in linear relation with the rotating speed n in unit time, PσThe relationship with the pressure after the pump needs to be analyzed in detail, according to literature data, the pressure after the pump is increased, and the bearing stress is also increased, but the relationship is not linear.
Wherein, let 0 state be non-accelerated state, 1 state be accelerated state, k be acceleration coefficient, then obtain
Figure BDA0003360652590000031
As can be seen from the formula (2), the key to solving the acceleration coefficient is to obtain the normal contact stress.
In the formula (2), n1And n0Respectively representing the rotation speed in the non-accelerated state and the rotation speed in the accelerated state. The normal contact stress is calculated according to the formulas (3) to (8), and is respectively:
Figure BDA0003360652590000032
Figure BDA0003360652590000033
Figure BDA0003360652590000041
Figure BDA0003360652590000042
Figure BDA0003360652590000043
Figure BDA0003360652590000044
in the formulas (3) to (8), α is a dimensionless parameter; f is the concentrated load to which the gear journal is subjected, in units of N; e1 and E2 are respectively elastic modulus of the bearing and the gear shaft, and the unit is Pa; psi is the elastic modulus ratio, dimensionless; mu.s1、μ2The bearing and gear shaft Poisson ratio is zero dimensional quantity; r1 and R2 are respectively the radius and the tooth of the inner hole of the bearingThe radius of the axle journal, R1 between the two is approximately equal to R2, and the unit is m; r is the average value of R1 and R2 and the unit is m; ε is the difference between R1 and R2, representing half of the journal and bearing clearance, R1-R2, in m;
Figure BDA0003360652590000045
is the unit mean pressure in Pa; sigmarmaxThe maximum value of the normal contact stress is expressed in Pa;
Figure BDA0003360652590000046
the contact half angle, i.e., the angle corresponding to the arc length of the contact surface, is generally expressed in radians.
It should be noted that when
Figure BDA0003360652590000047
When, σrmaxAnd
Figure BDA0003360652590000048
the relationship is determined according to equation (8), otherwise according to equation (7).
Generally speaking, the gear pumps of the fuel system all meet the formula (8), and the working conditions corresponding to the formula (7) are rare.
When in use
Figure BDA0003360652590000049
Then, the above formula is derived to obtain
Figure BDA00033606525900000410
Let 0 state be non-accelerated state and 1 state be accelerated state
Figure BDA00033606525900000411
Wherein, the control of the clearance between the bearing and the gear journal is strict, for example, the clearance between a certain bearing and the gear journal is controlled within the range of 0.058-0.0063 mm, therefore, the normal working condition can be consideredTime epsilon1≈ε2And the load F borne by the gear journal is in direct proportion to the differential pressure delta P between the inlet and the outlet of the gear pump, namely F is in proportion to delta P, the general outlet pressure is in a range of P out/P in > 1 relative to the inlet pressure, and delta P is approximately equal to P out, namely approximately satisfied. By combining the above information, equation 11 can be simplified to
Figure BDA0003360652590000051
Wherein, P1For gear pump outlet pressure in accelerated state, P0Gear pump outlet pressure in the non-accelerated state.
In addition, according to the calculation of the actual working condition, the contact theory of the bearing and the gear journal is approximately in line contact (
Figure BDA0003360652590000052
Small in value), indicating that the maximum normal contact stress ratio can be considered to be approximately equal to the normal contact stress ratio of the entire contact surface, i.e.
Figure BDA0003360652590000053
The formula (2) may be changed to
Figure BDA0003360652590000054
Equation (13) illustrates the specific relationship between the acceleration factor and the rotation speed and the outlet pressure, and provides a method for rapidly solving the acceleration factor.
The application mainly comprises the following steps:
step S1: the method comprises the steps of obtaining the rotating speed and the outlet pressure of the conventional gear pump before acceleration according to design input, firstly obtaining a parameter S in a formula (1), then consulting a mechanical design manual and a material manual to obtain a value of a parameter K, Pm, but the value of P sigma is not known at present, but only the ratio of P sigma before and after an acceleration test needs to be obtained according to a formula (13) considering that only an acceleration ratio is obtained and the value of P sigma is not required to be directly obtained;
step S2: the ratio of the P sigma before and after the acceleration test needs to be obtained through the outlet pressure obtained in the step S1, the relation between the P sigma and the outlet pressure needs to be found, the process needs to be deduced according to the formulas (3) to (10), and the derivation shows that the ratio of the normal maximum contact stress between the contact of the bearing inner hole and the gear shaft before and after the acceleration test is equal to the evolution of the product ratio of the concentrated load borne by the gear journal and the product of the journal and the bearing gap;
step S3: continuing with the derivation at step S2, since the gear journal clearance variation is small and almost constant, the relevant ratio before and after the acceleration test is approximately considered to be about 1, and by the formula (11), the normal maximum contact stress ratio between the bearing inner bore and the gear shaft contact before and after the acceleration test can be approximately equal to the square of the outlet pressure ratio before and after the acceleration test;
step S4: since the contact half angle is small and nearly flat, the maximum normal contact stress ratio can be regarded as being approximately equal to the normal contact stress ratio of the whole contact surface, so that the formula (12) can be obtained, and then the formula (13) can be obtained by derivation (taking the outlet pressure before acceleration and the rotating speed as the reference);
step S4: if the ratio of the outlet pressure to be accelerated to the non-accelerated outlet pressure is greater than 2, the error should be corrected, see the detailed implementation steps.
As described in further detail below, to verify the correctness of equation (13), a relevant simulation analysis work is performed based on Pumplinx.
In the embodiment of the application, taking a certain type of gear pump as an example, the gear pump has the 100% rotating speed of 8000r/min, the outlet pressure of 5MPa, the working medium of No. 3 jet fuel and the oil film thickness of 3 microns under normal load. And (4) supposing that the rotating speed is kept unchanged, increasing the pressure behind the pump to 7MPa due to the limitation of a safety valve, and carrying out simulation analysis on the change rule of the normal contact stress of the bearing.
Fig. 3 is a grid model generated based on the binary tree cartesian grid principle, the total grid number is 778707, the total node number is 1371473, and the second-order windward format is selected for the turbulence model.
In the working condition selection, five working conditions of 5MPa, 5.5MPa, 6MPa, 6.5MPa and 7MPa are sequentially selected by taking the outlet pressure as a reference, and the following simplifying measures are taken in the concrete simulation analysis:
(a) the simulation model is simplified, theoretically, the whole gear pump structure such as a driving gear, a driven gear, a fixed bearing, a floating bearing and the like should be considered in addition to an oil film for simulation, but analysis finds that the simulation can be approximated by the boundary condition of given pressure or flow, so that the simplification is performed for improving the analysis efficiency;
(b) temperature rise is not considered, because the viscosity of the working medium is reduced due to the temperature rise, the lubricating performance of an oil film is reduced, but the performance attenuation is relatively limited on the whole, and the key elements which influence the normal contact stress are not considered, so that the temperature rise is ignored;
(c) as can be seen from fig. 2, the contact surface pressure distribution is complex and variable, and cannot be measured by a single normal contact stress value, but the normal bearing force of the entire contact surface can be obtained by integration, so that the normal contact stress is obtained indirectly and converted into the normal bearing force, that is, equation 12 is converted into
Figure BDA0003360652590000061
After simplification, the results of the five working conditions are detailed in table 1, and it can be seen that the basic trends of the square root of the outlet pressure ratio and the normal force ratio are consistent, and although a certain error exists, the basic rule can be reflected and approximately meets the formula (13).
TABLE 1
Figure BDA0003360652590000071
It should be noted that the literature also discloses that the relationship between the outlet pressure and the normal force (radial force) is obtained by simulation while keeping the rotation speed constant, and the details are shown in table 2
TABLE 2
Figure BDA0003360652590000072
Comparing tables 1 and 2, it can be seen that the error in table 2 is significantly larger, because the outlet pressure span in table 2 is larger, and the accumulated error is larger, for example, if the outlet pressure is selected to be 3.97MPa, the error will be significantly reduced; on the other hand, the results in Table 2 take into account the temperature effect, and the error is therefore relatively large in combination with the above factors.
When the gear pump actually works, under the condition of normal load at 100% rotating speed, the opening pressure of the safety valve is generally 1.5 times of the maximum pump back pressure, so that the condition that the span reaches 5 times like table 2 is not a real working condition, and the correctness of the optimized design trend of the bearing is only verified in the document 1, so that the reason can be considered to be in a certain range, and the correctness of the formula (13) is credible.
In practical application, if the post-pump pressure after acceleration is two times greater than the post-pump pressure without acceleration, the error is corrected by referring to the table 1 and the table 2, so that the related parameters after acceleration are more accurate.
One of the preconditions of the accelerated life test is to maintain the outlet flow constant
The method can quickly calculate the acceleration ratio of the acceleration test or reversely deduct the acceleration life time, avoids the defects of poor operation or complex steps of the acceleration ratio of the existing acceleration life test, obtains the method and the analysis basis from various case summaries, improves or modifies the method on the basis of not deviating from the invention, and belongs to the protection range of the invention.

Claims (8)

1. A gear pump accelerated life coefficient calculation method based on rotation speed and pressure is characterized by comprising the following steps:
obtaining a dimensionless quantity alpha based on the concentrated load, the elastic modulus of the bearing, the radius of the inner hole of the bearing and the radius of the gear journal which are borne by the gear journal of the gear pump to be accelerated;
obtaining a contact half-angle sine value of the bearing and the gear shaft based on the elastic modulus ratio, the dimensionless quantity alpha, the bearing poisson ratio and the gear shaft poisson ratio;
obtaining the maximum value of the normal contact stress of the bearing based on the unit average pressure of the inner hole of the bearing and the sine value of the contact half angle;
determining the contact stress value of the whole contact surface of the bearing based on the maximum normal contact stress value;
acquiring the maximum rotating speed and the maximum outlet pressure of a gear pump to be accelerated; the maximum rotating speed and the sliding distance of the gear pump to be accelerated are linearly related; the contact stress value of the whole contact surface of the bearing corresponds to the maximum outlet pressure in a nonlinear way;
obtaining the wear volume by the Archard theory; an accelerated life factor is calculated based on the wear volume.
2. A method of calculating an accelerated life factor of a gear pump according to claim 1, wherein the sine of the contact half angle is less than or equal to pi/9.
3. The method for calculating the accelerated life factor of the gear pump based on the rotating speed and the pressure as claimed in claim 2, wherein before obtaining the sine value of the contact half angle between the bearing and the gear shaft based on the elastic modulus ratio, the dimensionless quantity alpha, the bearing poisson ratio and the gear shaft poisson ratio, the method further comprises:
and obtaining the elastic modulus ratio based on the bearing elastic modulus of the gear pump to be accelerated and the gear shaft elastic modulus.
4. A method for calculating an accelerated life factor of a gear pump according to claim 3, wherein before obtaining the maximum normal contact stress of the bearing based on the unit mean pressure of the inner bore of the bearing and the sine value of the contact half angle, the method further comprises:
and obtaining the unit average pressure of the bearing inner hole based on the concentrated load and the diameter of the bearing inner hole.
5. A method for calculating an accelerated life factor of a gear pump based on rotation speed and pressure according to claim 4, wherein the obtaining of the wear volume by using Archard theory comprises:
and calculating the wear volume based on the wear coefficient, the sliding distance, the material hardness and the contact stress value of the whole contact surface of the bearing.
6. The method for calculating the accelerated life coefficient of the gear pump based on the rotating speed and the pressure as claimed in claim 1, wherein the contact stress value of the whole contact surface of the bearing is obtained based on flow field simulation.
7. The method of claim 6 wherein the accelerated life factor is corrected based on the flow field simulation if the ratio of the accelerated outlet pressure to the un-accelerated outlet pressure is greater than 2.
8. The method for calculating the accelerated life factor of the gear pump based on the rotating speed and the pressure as claimed in claim 7, wherein the correcting the accelerated life factor based on the flow field simulation comprises:
and calculating the accelerated life coefficient based on the contact stress value of the whole contact surface of the bearing.
CN202111372636.5A 2021-11-18 2021-11-18 Gear pump accelerated life coefficient calculation method based on rotating speed and pressure Pending CN113987836A (en)

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