CN110362858B - Reliability evaluation method for high-pressure internal gear pump gear pair - Google Patents
Reliability evaluation method for high-pressure internal gear pump gear pair Download PDFInfo
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Abstract
The invention discloses a reliability evaluation method for a high-pressure internal gear pump gear pair. Firstly, defining multiple failure modes of a gear pair of a high-pressure internal gear pump, and establishing a reliability function of each failure mode; secondly, calculating the failure probability of each failure form by adopting a saddle point approximation method based on a high-order moment; then, constructing an importance measurement model of each failure mode of the high-pressure internal gear pump gear pair; and finally, establishing a multi-target multi-constraint reliability optimization model of the high-pressure internal gear pump gear pair with multi-performance indexes. The method not only considers the influence of various failure modes of the gear pair of the high-pressure internal gear pump on the reliability of the system, but also considers a plurality of performance indexes which need to be simultaneously met by the high-pressure internal gear pump, so that the working performance of the high-pressure internal gear pump is improved while the gear pair obtained by the method meets the reliability requirement.
Description
Technical Field
The invention relates to the technical field of internal gear pumps, in particular to a reliability evaluation method for a gear pair of a high-pressure internal gear pump.
Background
The internal gear pump has the characteristics of simple and compact structure, small flow and pressure pulsation, high power-weight ratio and low noise, and is widely applied to the industrial fields of walking machinery, combined machine tools and the like. The internal gear pump has the advantages of small high-pressure cavity, perfect sealing structure, high volumetric efficiency and total efficiency and no oil trapping phenomenon of the external gear pump. Compared with a vane pump and a plunger pump, the internal gear pump has the characteristics of small flow pulsation, stable operation and low noise, and can be used for replacing the vane pump and the plunger pump for a hydraulic system with high control precision requirement. However, advances in industrial technology and improvements in host and system performance levels place higher demands on the load capacity, noise level, and volumetric efficiency of the gerotor pump.
Pressure is the most important performance parameter of internal gear pumps. Foreign products achieve higher working pressure, but have complex structure, high manufacturing cost and high price. In contrast, the highest pressure of domestic high-pressure internal gear pumps is mostly lower than 30 MPa. At present, domestic enterprises lack basic research on the aspects of parameter design, performance evaluation and the like of the high-pressure internal gear pump, and most of structural parameters and specifications directly imitate foreign similar products, so that the product design and manufacturing technology is lagged behind.
Meanwhile, the operating principle of the gear pump determines that the internal gear pump also has the problem of unbalanced hydraulic pressure. Along with the increase of the working pressure, the radial hydraulic pressure and the abrasion suffered by the gear pair of the internal gear pump are increased. In the long-term operation process, the performance of the high-pressure internal gear pump gear pair is rapidly degraded, so that the internal gear pump gear pair has unstable quality, high early failure rate and poor reliability. At present, although domestic enterprises have the production capacity of the high-pressure internal gear pump, the domestic high-pressure internal gear pump has a large gap with foreign products in the aspects of volumetric efficiency, noise, reliability, service life and the like.
How to improve the working performance of the internal gear pump while ensuring the reliability of the gear pair of the internal gear pump under high pressure is a difficult point of the design of the high pressure internal gear pump. The invention is expected to construct a multi-objective multi-constraint reliability design model of the high-pressure internal gear pump by combining an importance measure model and a multi-objective optimization design method from the viewpoint of reliability design, so as to realize the reliability design of the gear pair of the high-pressure internal gear pump.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a reliability evaluation method of a gear pair of a high-pressure internal gear pump by fully utilizing the approximation precision of a saddle point approximation method based on high-order moment and a reliability optimization design method based on importance measure, thereby realizing the structure optimization design of the gear pair of the internal gear pump under high pressure and improving the reliability of the internal gear pump under the working condition of high pressure and large flow.
In order to achieve the purpose, the invention adopts the technical scheme that:
a reliability assessment method for a high-pressure internal gear pump gear pair, the method comprising the steps of:
step 1: defining multiple failure modes of a gear pair of the high-pressure internal gear pump, and establishing reliability function functions of different failure modes;
step 2: adopting a saddle point approximation method based on high-order moment to approximate the probability distribution function of each reliability function, and calculating the corresponding failure probability;
and step 3: establishing importance measurement models of different failure modes of the gear pair of the high-pressure internal gear pump, and analyzing the influence degree of the different failure modes on the reliability of the gear pump;
and 4, step 4: and establishing a multi-target multi-constraint reliability optimization model of the high-pressure internal gear pump, and optimizing random parameters of a gear pair of the high-pressure internal gear pump by adopting an optimization method.
The step 1 specifically comprises the following steps:
the failure modes of the high-pressure internal gear pump gear pair refer to three failure modes of internal gear tooth surface contact strength failure, internal gear tooth root bending strength failure and internal gear tooth root bending strength failure;
and respectively establishing a reliability function aiming at the three failure modes, wherein,
reliability function g for failure of tooth surface contact strength of inner gear ring1(X1) Comprises the following steps:
g1(X1)＝σ′Hlim-σH，
reliability function g of internal gear tooth root bending strength failure2(X2) Comprises the following steps:
g2(X2)＝σ′Flim-σF
reliability function g for failure of bending strength of tooth root of inner gear ring3(X3) Comprises the following steps:
g3(X3)＝σ′Flim-σF
in the formula, σHThe contact stress of a gear pair of the high-pressure internal gear pump is shown;
σ′Hlimthe contact fatigue strength of a gear pair of the high-pressure internal gear pump;
σFthe bending stress of the gear pair of the high-pressure internal gear pump;
σ′Flimthe bending fatigue strength of the gear pair of the high-pressure internal gear pump;
X1，X2and X3Respectively random parameter vectors of the reliability function under different failure modes.
The step 2 specifically comprises the following steps:
the saddle point approximation method based on high-order moment is adopted to calculate the failure probability in the form of,
wherein, PfRepresents the probability of failure, phi represents the cumulative probability distribution function of a standard normal distribution variable,
and
is a parameter of the saddle point approximation function, y is a normalized variable of a state variable of the reliability function, KYsA cumulative quantity mother function representing a normalized variable y in the form of
KYs (2)The second derivative of the mother function of the cumulative quantity representing the normalized variable y, in the form of
Wherein, thetaYsAnd ηYsRespectively representing the skewness and kurtosis of the state variables of the reliability function.
t represents a saddle point value and can be calculated by establishing a saddle point equation in the following form
Wherein beta is a second-order reliability index of the function, and a parameter a of the saddle point equation1，a2，a3And b is calculated as follows
The step 3 specifically comprises the following steps:
the established importance measurement model of the failure mode of the gear pair of the high-pressure internal gear pump is
Where m represents the number of failure modes of the gear pair,
the influence of the ith failure form on the failure probability of the system is shown and calculated by the following formula
Wherein, PfsIndicating the probability of system failure, P, of a high-pressure gerotor gear pairfjThe resulting probability of system failure is calculated after the i-th failure form is discarded.
The step 4 specifically comprises the following steps:
the established high-pressure internal gear pump multi-target multi-constraint reliability optimization model is
max f(d)＝ω1S+ω2κ+ω3η+ω4/α+ω5/ζ+ω6/ν
dL≤d≤dU
Wherein, S represents the pressure of the high-pressure internal gear pump;
κ represents volumetric efficiency;
η represents the total efficiency;
α represents a pressure pulsation value;
zeta represents noise, and the performance index functions are all constructed by a response surface method;
v represents a two-norm of importance measure of the failure form of the gear pair of the high-pressure internal gear pump;
ωi(i 1.., 6) represents a weighting coefficient of each optimization target;
n represents the number of reliability function functions;
dLand dURespectively, the upper and lower bounds of the design variable vector d.
Due to the adoption of the technical scheme, the invention at least has the following beneficial effects:
(1) aiming at various failure modes of the high-pressure internal gear pump gear pair, the method can establish a reasonable reliability function, accurately approaches probability distribution functions under various failure modes, and improves the accuracy of failure probability estimation;
(2) the method fully considers the influence of different failure modes of the high-pressure internal gear pump gear pair on the system reliability, establishes an importance measurement model of the failure modes, and realizes the importance ranking of the failure modes;
(3) from the perspective of reliability design, the invention can meet the reliability design requirement of the gear pair and also can meet the requirement of a plurality of performance indexes of the high-pressure internal gear pump by establishing the multi-target multi-constraint reliability optimization model of the high-pressure internal gear pump, so that the pressure, the volume efficiency and the total efficiency of the optimized high-pressure internal gear pump are improved, and the pressure pulsation value and the noise are reduced.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a structural view of a high-pressure internal gear pump gear pair in the embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings and examples.
As shown in fig. 1, the method for designing the reliability of the gear pair of the high-pressure internal gear pump according to the present invention includes the following steps:
step 1: defining failure types of a gear pair of the high-pressure internal gear pump as three failure types including tooth surface contact strength failure of an inner gear ring, tooth root bending strength failure of the inner gear ring and tooth root bending strength failure of the inner gear ring, and establishing reliability function functions under different failure types;
step 2: aiming at the reliability function of the three failure types, calculating a fourth moment of each reliability function, approximating a probability distribution function of each reliability function by adopting a saddle point approximation method based on a high-order moment, and calculating corresponding failure probability;
and step 3: establishing an importance measurement model of each failure mode of the high-pressure internal gear pump gear pair, and realizing importance sequencing of influence degrees of different failure modes on system reliability;
and 4, step 4: and establishing a multi-target multi-constraint reliability optimization model of the high-pressure internal gear pump, and optimizing random parameters of a gear pair of the high-pressure internal gear pump to obtain optimal parameters of the gear pair of the high-pressure internal gear pump, which meet reliability constraint and working performance optimization targets.
Examples
In order to more fully understand the characteristics and engineering applicability of the invention, the invention is designed for the reliability of the high-pressure internal gear pump gear pair structure shown in figure 2.
Three failure types of the gear pair are defined as follows: the tooth surface contact strength of the inner gear ring fails, the tooth root bending strength of the inner gear ring fails and the tooth root bending strength of the inner gear ring fails. According to the theory of stress-intensity interference, the reliability function of three failure types is respectively established, namely
g1(X1)＝σ′Hlim-σH
g2(X2)＝σ′Flim-σF
g3(X3)＝σ′Flim-σF
According to X1，X2And X3Respectively calculating the probability information of each random parameterBy fourth order moments of functional sexual functions, in particular
μg1＝15.83,σg1＝6.07,θg1＝-0.1876,ηg1＝3.207
μg2＝8.35,σg2＝3.63,θg2＝-0.0125,ηg2＝3.0077
μg3＝7.53,σg2＝3.21,θg3＝-0.0131,ηg3＝3.0104
Respectively calculating the failure probability of each failure mode to be respectively
Pfg1＝7.74×10-3，Pfg2＝1.093×10-2，Pfg3＝1.127×10-2
And respectively calculating the importance of each failure form to the failure probability of the system by adopting the failure form importance measurement model, wherein the importance measurement model comprises the following steps:
δ1＝0.743，δ2＝0.575，δ3＝0.548
wherein, delta1Representing the importance of the failure of the tooth-surface contact strength of the inner gear ring, delta2Indicating the importance of failure of the bending strength of the internal gear tooth root, delta3Indicating the importance of the ring gear tooth root bending strength failure.
Then, with the pressure, the volume efficiency, the total efficiency of the high-pressure internal gear pump are maximum, the pressure pulsation value and the noise are minimum, and the two-norm minimum of the importance measure of each failure form is taken as an optimization target, a reliability optimization design model containing a plurality of performance indexes of the gear pair of the high-pressure internal gear pump is established, and the reliability optimization design model specifically comprises the following steps:
max f(d)＝ω1S+ω2κ+ω3η+ω4/α+ω5/ζ+ω6/ν
dL≤d≤dU
taking the design variable as d0＝[mmn,z1,b]TWherein m ismnRepresenting the normal modulus of the mid-point of the gear pair, z1The number of teeth of the internal gear is indicated, and b the working tooth width. Taking the design initial value as d0＝[2.74,21,30]TThe optimized parameters can be obtained through a particle swarm algorithm and are as follows: d*＝[2.56,19.3,33.45]T。
The performance index pair table of the high-pressure ring gear pump before and after optimization is shown in table 1.
TABLE 1 Performance index comparison of high-pressure internal gear pumps before and after optimization
In summary, the invention provides a reliability evaluation method for a high-pressure internal gear pump gear pair. Firstly, defining three failure types of a gear pair of a high-pressure internal gear pump, and establishing reliability function functions of different failure types; secondly, approximating the probability distribution function of each reliability function by adopting a saddle point approximation method based on high-order moment, and calculating corresponding failure probability; then, an importance measurement model of the failure modes of the high-pressure internal gear pump is established, and the importance of different failure modes on the failure probability of the high-pressure internal gear pump is calculated; and finally, the requirements of the high-pressure internal gear pump on various performance indexes are fully considered, and a multi-target multi-constraint reliability optimization design model of the high-pressure internal gear pump gear pair is established. The reliability requirement can be met by optimizing the obtained gear pair random parameters, and meanwhile, the overall performance of the high-pressure internal gear pump is improved.
Parts of the invention not described in detail are well known to the skilled person.
Claims (3)
1. A reliability assessment method for a high-pressure internal gear pump gear pair is characterized by comprising the following steps:
step 1: defining multiple failure modes of a gear pair of the high-pressure internal gear pump, and establishing reliability function functions of different failure modes;
step 2: adopting a saddle point approximation method based on high-order moment to approximate the probability distribution function of each reliability function, and calculating the corresponding failure probability;
and step 3: establishing importance measurement models of different failure modes of the gear pair of the high-pressure internal gear pump, and analyzing the influence degree of the different failure modes on the reliability of the gear pump;
and 4, step 4: establishing a multi-target multi-constraint reliability optimization model of the high-pressure internal gear pump, and optimizing random parameters of a gear pair of the high-pressure internal gear pump by adopting an optimization method;
the established importance measurement model of the failure mode of the gear pair of the high-pressure internal gear pump is
Wherein m represents the number of failure modes of the gear pair,
representing the effect of the ith failure mode on the probability of system failure, is calculated by:
wherein, PfsIndicating the probability of system failure, P, of a high-pressure gerotor gear pairfjCalculating the failure probability of the system after the ith failure form is omitted;
the step 4 specifically comprises the following steps:
the established high-pressure internal gear pump multi-target multi-constraint reliability optimization model is
max f(d)＝ω1S+ω2κ+ω3η+ω4/α+ω5/ζ+ω6/ν
dL≤d≤dU
Wherein, S represents the pressure of the high-pressure internal gear pump;
κ represents volumetric efficiency;
η represents the total efficiency;
α represents a pressure pulsation value;
zeta represents noise, and the performance index functions are all constructed by a response surface method;
v represents a two-norm of importance measure of the failure form of the gear pair of the high-pressure internal gear pump;
ωi(i 1.., 6) represents a weighting coefficient of each optimization target;
n represents the number of reliability function functions;
dLand dURespectively, the upper and lower bounds of the design variable vector d.
2. The reliability evaluation method of the high-pressure internal gear pump gear pair according to claim 1, wherein the step 1 is specifically:
the failure modes of the high-pressure internal gear pump gear pair refer to three failure modes of internal gear tooth surface contact strength failure, internal gear tooth root bending strength failure and internal gear tooth root bending strength failure;
and respectively establishing a reliability function aiming at the three failure modes, wherein,
reliability function g for failure of tooth surface contact strength of inner gear ring1(X1) Comprises the following steps:
g1(X1)＝σ′Hlim-σH，
reliability function g of internal gear tooth root bending strength failure2(X2) Comprises the following steps:
g2(X2)＝σ′Flim-σF
reliability function g for failure of bending strength of tooth root of inner gear ring3(X3) Comprises the following steps:
g3(X3)＝σ′Flim-σF
in the formula, σHThe contact stress of a gear pair of the high-pressure internal gear pump is shown;
σ′Hlimthe contact fatigue strength of a gear pair of the high-pressure internal gear pump;
σFthe bending stress of the gear pair of the high-pressure internal gear pump;
σ′Flimthe bending fatigue strength of the gear pair of the high-pressure internal gear pump;
X1，X2and X3Respectively random parameter vectors of the reliability function under different failure modes.
3. The reliability evaluation method of the high-pressure internal gear pump gear pair according to claim 1, wherein the step 2 is specifically:
the saddle point approximation method based on high-order moment is adopted to calculate the failure probability in the form of,
wherein, PfRepresents the probability of failure, phi represents the cumulative probability distribution function of a standard normal distribution variable,
and
is a parameter of the saddle point approximation function, y is a normalized variable of a state variable of the reliability function, KYsA cumulative quantity mother function representing a normalized variable y, of the form:
KYs (2)the second derivative of the mother function of the cumulative quantity representing the normalized variable y is of the form:
wherein, thetaYsAnd ηYsRespectively representing the skewness and kurtosis of the state variable of the reliability function;
t represents a saddle point value, which can be calculated by establishing a saddle point equation in the form:
wherein beta is a second-order reliability index of the function, and a parameter a of the saddle point equation1，a2，a3And b is calculated as follows:
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| PCT/CN2020/080090 WO2020244277A1 (en) | 2019-06-05 | 2020-03-19 | Method for assessing reliability of gear pair of high-pressure inner meshing gear pump |
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| CN110362858B (en) * | 2019-06-05 | 2021-10-22 | 徐州圣邦机械有限公司 | Reliability evaluation method for high-pressure internal gear pump gear pair |
| CN111581835B (en) * | 2020-05-14 | 2023-07-18 | 内蒙古工业大学 | Safety information acquisition method of mechanical structure |
| CN112528511B (en) * | 2020-12-17 | 2023-12-12 | 中国矿业大学 | Method for evaluating abrasion reliability of chain wheel of scraper conveyor |
| CN113010975B (en) * | 2021-01-21 | 2022-09-13 | 北京航空航天大学 | Gear clearance optimization design method comprehensively considering machining cost and motion stability |
| CN113255084B (en) * | 2021-07-07 | 2022-05-06 | 盛瑞传动股份有限公司 | Rapid optimization method of gear noise radiation based on response surface method |
| CN113408082B (en) * | 2021-08-20 | 2022-06-28 | 宁波东力传动设备有限公司 | Method for calculating dynamic meshing force of external-meshing straight-tooth cylindrical gear pair |
| CN114491832B (en) * | 2021-12-27 | 2023-12-01 | 徐州圣邦机械有限公司 | Reliability improving method of high-pressure internal gear pump |
| CN115906571B (en) * | 2022-11-24 | 2023-10-31 | 武汉科技大学 | Axial plunger pump plunger pair series combination seal reliability assessment method |
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