CN115077826B - Rotor system vibration response similar scaling experiment method considering coupling variable power number - Google Patents
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Abstract
The invention discloses a rotor system vibration response similar scaling experiment method considering coupling variable power numbers, relates to the technical field of similar scaling experiments, and provides a variable power number idea and a coupling influence rule considering similar parameters, so that the precision of distortion similar prediction is improved, the variable power numbers aiming at the rotor system vibration response are provided, and the prediction precision of the vibration response is improved. Considering the problem that a rotating shaft and a rotating disc are difficult to process due to the fact that a rotor system is completely similar to a scale, and the problem that the rigidity of a supporting structure is difficult to accurately meet completely similar conditions, the length of the rotating shaft and the supporting rigidity are simultaneously distorted in a scaling ratio, and aiming at the coupling influence among parameters, a variable power number considering the coupling influence is provided. The method gets rid of the limitation of a system control equation, greatly reduces the workload of formula derivation, and is suitable for similar model experiments of complex systems; and the vibration response of a prototype does not need to be obtained in advance, and the method is suitable for the scaling model experiment problem in the actual engineering.
Description
Technical Field
The invention relates to the technical field of rotor systems, in particular to a vibration response similar scaling experiment method of a rotor system considering coupling variable power numbers.
Background
Rotor systems are widely used in large rotating machines, such as aircraft engines and gas turbines. In terms of an aircraft engine, all vibration characteristics of a rotor system of the aircraft engine are not completely mastered, and theory and simulation analysis are difficult to accurately reflect the vibration characteristics of the rotor system, so experimental research is an essential link in the design and maintenance process of the aircraft engine, and a large amount of experimental verification is required for the design of a new model. However, since the aero-engine has a complex structure and a large axial span, the problem that the experimental study of the dynamic characteristics directly on a full-size prototype rotor system is long in experimental period, high in risk, high in cost and the like often exists. Aiming at the problem, an effective solution is to design a similar scale model by using a similar theory, and the vibration characteristic of the similar scale model can still reflect the real vibration characteristic of the engine, so that the experiment difficulty is reduced, the experiment period is shortened, the dynamic characteristic and parameter influence mechanism of a full-size prototype are revealed, and the similar theory is widely applied to the vibration experiment of a large-scale structure.
The length-diameter ratio of a rotating shaft of the rotor system of the aircraft engine is large, and the rotating disc is thin, so that the rotating shaft is too thin and the rotating disc is too thin due to the fact that the rotating shaft is reduced in size according to the complete similarity relation, and further the rotating shaft is difficult to machine. Therefore, the distortion similarity has stronger engineering applicability and practical significance.
In the existing distortion similarity method, a similarity method based on sensitivity analysis is to establish a similarity relation between a prototype and a model by utilizing a data-driven thought and based on a response and sensitivity analysis method of the model; the method does not need derivation of a control equation and a similar relation of the system, and compared with a similar method depending on the control equation of the system, the method greatly reduces the workload of derivation. And the method does not need to obtain the vibration response of a prototype in advance, can be applied to actual engineering compared with a similar method based on an optimization algorithm, and is suitable for distortion similarity of complex structures.
However, the influence of the simultaneous change of a plurality of system parameters on the system response is not equal to the accumulation of the changes of the parameters, and in the similar method based on the sensitivity analysis, as in the inventor's earlier published paper "design method and experimental research of distortion dynamics similar test model considering variable power", the parameter coupling influence is not considered, so that the similar prediction of the scaling of a single parameter can be only carried out, and the method is only suitable for the prediction of the critical rotating speed of the rotor system.
Disclosure of Invention
In view of the above, the invention provides a rotor system vibration response similar scaling experiment method considering coupling variable power, and a similar relation considering coupling influence among parameters is deduced based on a full differential theory, so that multiple parameters can be scaled according to different proportions at the same time, and the method is more suitable for actual engineering. Since the vibration response is sensitive to the parameter influence, similar prediction of the vibration response of the rotor system can be realized by considering the parameter coupling influence.
Therefore, the invention provides the following technical scheme:
the invention provides a rotor system vibration response similar scaling experiment method considering coupling variable power, which comprises the following steps:
s1, acquiring geometric dimension parameters and material parameters of a rotor system prototype;
s2, determining the scaling of the geometric dimension parameters according to the laboratory environment;
s3, establishing a similar relation between a prototype of the rotor system and a scaling model by using a coupling power-varying method, wherein the power is a function varying along with scaling; scaling a plurality of parameters in the similarity relationship of the rotor system simultaneously according to different proportions; the input parameter of the similarity relation is the scaling of the geometric dimension parameter, and the output parameter is the scaling of the vibration response;
s4, substituting the scaling of the geometric dimension parameters into the similarity relation to obtain the scaling of the vibration response;
and S5, carrying out a vibration experiment on the scaling model, and multiplying the obtained vibration response by the scaling of the vibration response to obtain the vibration response of the prototype.
Further, the rotor system is an aircraft engine rotor system.
Further, determining a scaling of the geometry parameter includes: the scaling of the spindle length is determined.
Further, establishing a similarity relation between the prototype of the rotor system and the scaling model by using a coupling variable power method, wherein the similarity relation comprises the following steps:
establishing a similar relation between a prototype of the rotor system and a scaling model;
determining coupling influence among a plurality of parameters in the similarity relation according to a full differential theory; the similarity relation comprises powers of the consideration coupling influence of each parameter;
and establishing a power function, and determining the power of each parameter in the similarity relation.
Further, the power function takes the right end point of the interval of the m similarity ratio intervals as an input parameter, and the output parameter is m powers expressed as:
wherein λ is (1) ,…,λ (k) ,…,λ (m) Is the right end point of the similarity ratio interval; a. b is the coefficient of a power function.
Further, the coefficients a and b are determined by:
taking the logarithm of the power function:
writing the above equation in matrix form:
B＝AP；
in the formula:
substituting the input parameters and the output parameters by using a least square method to obtain a coefficient matrix P:
P＝(A T A) -1 A T B；
the coefficients a and b are obtained.
Further, the m similarity ratio intervals are:
wherein the content of the first and second substances,
as a geometric parameter X i Is the left end point of the similarity ratio interval of the similarity ratio, and delta is the geometric parameter X i The similarity ratio of (a) is the difference between the right end point and the left end point of the similarity ratio interval.
The invention has the advantages and positive effects that:
1. the method deduces the similarity relation considering the coupling influence among the parameters based on the full differential theory, realizes the simultaneous scaling of a plurality of parameters according to different proportions, has stronger applicability to the actual engineering, and is particularly suitable for the similar prediction of the vibration response of a rotor system which has a complex structure and is sensitive to the parameter influence. In addition, the power is a key parameter of similar prediction, the power is considered as a function changing along with the scaling, the prediction result correction of different scaling can be realized, and the prediction precision of vibration response is improved.
2. Considering the problem that a rotating shaft and a rotating disc are difficult to process due to the fact that a rotor system is completely similar to a scale, and the problem that the rigidity of a supporting structure is difficult to accurately meet completely similar conditions, the length of the rotating shaft and the supporting rigidity are simultaneously distorted in a scaling ratio, and aiming at the coupling influence among parameters, a variable power number considering the coupling influence is provided.
3. The method gets rid of the limitation of a system control equation and is suitable for similar model experiments of complex systems; and the similar relation does not need to be deduced based on equation analysis, so that the workload of formula deduction is greatly reduced.
4. The invention does not need to obtain the vibration response of a prototype in advance, and is suitable for the scaling model experiment problem in the actual engineering.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic illustration of a kinetic similarity prediction in an embodiment of the present invention;
FIG. 2 is a finite element model of a dual rotor system in an embodiment of the present invention;
FIG. 3 is a diagram illustrating a prototype and a model with the largest distortion according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating the vibration response prediction of a prototype under co-rotation in an embodiment of the present invention;
FIG. 5 is a diagram illustrating the vibration response prediction error of a prototype under co-rotation in an embodiment of the present invention;
FIG. 6 is a diagram illustrating the vibration response prediction of a prototype under reverse rotation in an embodiment of the present invention;
FIG. 7 is a diagram illustrating the vibration response prediction error of the prototype under the condition of reverse rotation according to the embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
When a large-scale rotor system vibration experiment is carried out, the problems of high experiment cost, long period, large risk and the like are caused due to the fact that a rotor system is too large. The invention aims to establish a distortion similarity relation aiming at the vibration response of a rotor system, predict the vibration response of a full-size prototype by using a similar scaling model and realize a similar model experiment of the rotor system, thereby reducing the experiment cost, the risk and the difficulty and shortening the experiment period. Aiming at the distortion similar condition of the rotor system, the problem that the rotating shaft and the rotating disc are difficult to process due to the fact that the rotor system is completely similar to a reduced scale is considered, and in addition, the rigidity of the supporting structure is difficult to accurately meet the completely similar condition, so that the invention only reduces the length of the rotating shaft and the supporting rigidity, other parameters are kept unchanged, the size reduction is realized, and the problem that the processing is difficult and the rigidity similar relation is difficult to meet is solved.
As shown in fig. 1, which shows a flow chart of dynamics similarity prediction, the prototype system takes the load as input and outputs a response; a similar model of dynamics, similar to the prototype system in terms of dynamic parameters, takes as its input the input (load) of the prototype system and outputs a response. Namely, the dynamic similarity model predicts the similar output (response) of the prototype system under the conditions of similar load and similar dynamic parameters.
In the similarity model of the rotor system, the similarity ratio is the ratio of the prototype parameter to the model parameter, and can be expressed as:
in the formula, X and Y represent geometric parameters and vibration response, respectively, and superscripts (p) and (m) represent a prototype and a model, respectively. Wherein, the geometric parameters comprise the length of the rotating shaft, the diameter of the rotating shaft, the thickness of the rotating disc and the like. In the embodiment of the invention, the diameter of the rotating shaft and the thickness of the rotating disc are not scaled when the length of the rotating shaft is scaled, so that the problem that the diameter of the rotating shaft and the thickness of the rotating disc are too small to process due to full scaling is avoided.
The similarity relationship can be expressed as:
wherein n is the number of similarity ratios,
at a power of the similarity factor.
Taking the logarithm of formula (3) can obtain:
according to the full differential theory, equation (4) can be converted into:
in the formula, o (ρ) is infinitesimal.
Order to
Ignoring the infinitesimal, the sum of powers considering the coupling effects is:
equation (6) can be written approximately as:
in the formula (I), the compound is shown in the specification,
and/or>
When all the similarity ratios are respectively->
And &>
The vibration response obtained.
Equation (7) can be further simplified to:
according to the sensitivity analysis, the power without considering the coupling effect is:
according to the central difference theory, equation (9) can be written as:
in the formula (I), the compound is shown in the specification,
and &>
Is when X i Respectively is->
And/or>
The vibration response obtained.
Therefore, the power to consider the coupling effect can be obtained by multiplying the sum of the powers by the ratio of the powers, i.e.:
in the conventional method, the power for the vibration response is constant, but in reality the power is a variable that varies with the similarity factor. In order to further improve the prediction accuracy, the invention provides a power variation thought aiming at the vibration response, and the following is a specific flow for establishing the power variation of the vibration response.
The similarity ratio interval between the formula (8) and the formula (10) is
Can be rewritten as>
Fixing the left end point of the interval, continuously expanding the right end point to->
Thus, m intervals of the similarity ratio can be obtained: />
For simplicity, the right end of the interval is denoted as λ (1) ,…,λ (k) ,…,λ (m) And serves as an input parameter. M power-numbers ^ obtained by m intervals and equation (8-11)>
As an output parameter, the method is used for constructing a power function, and the expression of the power function is as follows:
where a and b are coefficients to be determined in a power function.
Taking the logarithm of equation (12) yields:
writing equation (13) in matrix form:
B＝AP (14)
in the formula:
the input parameters and the output parameters are brought into equation (14) by the least square method, and a coefficient matrix P can be obtained:
P＝(A T A) -1 A T B (15)
therefore, the coefficients a and b can be obtained, and the coefficients a and b are substituted into the formula (3) to obtain the similar relationship.
In order to prove the advantages and effects of the invention, the dual-rotor system is selected for verification of vibration response prediction. The method does not need derivation of a control equation and a similar relation of a system, and compared with a similar method depending on the control equation of the system, the method greatly reduces the workload of derivation. And the vibration response of a prototype does not need to be obtained in advance, and compared with a similar method based on an optimization algorithm, the method can be applied to actual engineering and is suitable for distortion similarity of complex structures. Compared with a similar method depending on a system control equation and a similar method based on an optimization algorithm, the method has obvious advantages, and the two methods are difficult to apply to the similar prediction of the double-rotor system in the actual engineering. The method deduces the similarity relation considering the coupling influence among the parameters based on the full differential theory, realizes the simultaneous scaling of a plurality of parameters according to different proportions, has stronger applicability to the actual engineering compared with a similar method based on sensitivity analysis not considering the coupling influence among the parameters, and is particularly suitable for the similar prediction of the vibration response of a rotor system which has a complex structure and is sensitive to the parameter influence. In addition, the power is a key parameter of similar prediction, the power is considered as a function changing along with the scaling, the prediction result correction of different scaling can be realized, and the prediction precision of vibration response is improved. Specifically, the present invention is compared with a similar method based on sensitivity analysis (reference 1 (Scaling law associated from a sensitive analysis and applied to a in vivo simulation structures DOI:10.1016/j. Ymssp.2018.03.032), reference 2 (Scaling law of geometrical displaced models of a cantiler plate DOI: 10.1061/(ASCE) EM.1943-7889.0001028)), in which reference 1 obtains a sheet similarity relationship based on only local sensitivity analysis, does not consider a coupling effect of parameters, and does not consider a change in power number. Document 2 uses a regression fitting method to obtain the similarity relationship of the thin plate, and does not consider the parameter coupling effect and the variable power. In addition, both the documents 1 and 2 are similar methods for thin plates, and are only suitable for objects with simple structures, but for a more complicated rotor system, both the methods cannot meet the precision requirement of the vibration response of the rotor system, and are not suitable for the rotor system.
A double-rotor system is modeled by a finite element method, and a schematic diagram of a model section is shown in FIG. 2. According to the structural form and the working condition characteristics of the double-rotor system, in order to comprehensively verify the advantages and the effects of the double-rotor system, two working conditions of homodromous rotation and reverse rotation of the high-pressure rotor and the low-pressure rotor are selected for verification.
The similarity ratio of the length of the rotating shaft, the bearing rigidity and the vibration response is lambda l ，λ k And λ x . In order to fully prove the advantages and effects of the invention, the vibration response prediction is carried out on 13 prototypes by utilizing a scaling model, wherein the supporting rigidity similarity ratio (lambda) of the 13 prototypes k ) Is 2, the axial length similarity ratio (lambda) l ) Are respectively [0.95,1,1.05,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2]. It can be seen that the 13 prototypes have increasing degrees of scale and distortion, with the prototype with the greatest degree of distortion (λ) l ＝λ k = 2) and model are shown in fig. 3.
And selecting a vibration response of 3000r/min for similar prediction. The similarity relationship of the vibration response of the dual rotor system can be expressed as
Similar relations are established between the method of the invention and the methods of the documents 1 and 2, and the powers of the vibration response of the double-rotor system under different working conditions are shown in table 1.
TABLE 1
The results of the vibration response prediction for the prototype with the largest degree of distortion in the case of the same-direction rotation are shown in fig. 4, and the vibration response prediction errors for the 13 prototypes are shown in fig. 5. The prediction results of documents 1 and 2 are also plotted in fig. 4 and 5 for comparison. It can be seen that the prediction results of the present invention are closer to those of the prototype and the prediction error is significantly reduced compared to documents 1 and 2. The advantages and effects of the invention become more and more obvious as the distortion degree of the prototype increases. Therefore, the invention obviously improves the prediction accuracy of the vibration response of the rotor system.
The reverse rotation indicates that the rotation directions of the inner rotor and the outer rotor of the double-rotor system are opposite, and the vibration response prediction result and the prediction error under the working condition are respectively shown in fig. 6 and fig. 7. It can be seen that the prediction accuracy of the invention is much higher than that of the documents 1 and 2, and the invention greatly improves the prediction accuracy of the vibration response of the rotor system, so that the advantages and effects of the invention are proved.
In the embodiments provided in the present invention, it should be understood that the disclosed technical contents can be implemented in other manners. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units may be a logical division, and in actual implementation, there may be another division, for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, units or modules, and may be in an electrical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on a plurality of units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic disk, or an optical disk, and various media capable of storing program codes.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A method for performing a similar scaling experiment on vibration response of a rotor system by considering coupling variable power is characterized by comprising the following steps of:
s1, acquiring geometric dimension parameters and material parameters of a rotor system prototype;
s2, determining the scaling of the geometric dimension parameters according to the laboratory environment;
s3, establishing a similar relation between a prototype of the rotor system and a scaling model by using a coupling power-varying method, wherein the power is a function varying along with scaling; scaling a plurality of parameters in the similarity relationship of the rotor system simultaneously according to different proportions; the input parameter of the similarity relation is the scaling of the geometric dimension parameter, and the output parameter is the scaling of the vibration response;
s4, substituting the scaling of the geometric dimension parameters into the similarity relation to obtain the scaling of the vibration response;
s5, performing a vibration experiment on the scaling model, and multiplying the obtained vibration response by the scaling of the vibration response to obtain the vibration response of the prototype;
the method for establishing the similarity relation between the prototype of the rotor system and the scaling model by using the coupling variable power method comprises the following steps:
establishing a similar relation between a prototype of the rotor system and a scaling model;
determining coupling influence among a plurality of parameters in the similarity relation according to a full differential theory; the similarity relation comprises powers of the consideration coupling influence of each parameter;
and establishing a power function, and determining the power of each parameter in the similarity relation.
2. The method for the rotor system vibration response similarity scaling experiment considering the coupling variable power number is characterized in that the rotor system is an aircraft engine rotor system.
3. The method for the rotor system vibration response similar scaling experiment considering the coupling variable power number as claimed in claim 2, wherein the step of determining the scaling of the geometric dimension parameter comprises the following steps: the scaling of the spindle length is determined.
4. The method for the rotor system vibration response similarity scaling experiment considering the coupling variable power numbers as claimed in claim 1, wherein the power function takes the right end point of the interval of m similarity ratio intervals as an input parameter, and the output parameter is m power numbers and is expressed as:
wherein λ is (1) ,…,λ (k) ,…,λ (m) Is the right end point of the similarity ratio interval; a. b is the coefficient of the power function.
5. The method for the rotor system vibration response similar scaling experiment considering the coupling variable power number is characterized in that the coefficients a and b are determined by the following modes:
taking the logarithm of the power function:
writing the above equation in matrix form:
B＝AP；
in the formula:
substituting the input parameters and the output parameters by using a least square method to obtain a coefficient matrix P:
P＝(A T A) -1 A T B；
the coefficients a and b are obtained.
6. The method for the rotor system vibration response similar scaling experiment considering the coupling variable power number as claimed in claim 4, wherein the m similar ratio intervals are as follows:
wherein the content of the first and second substances,
as a geometric parameter X i Is the left end point of the similarity ratio interval of the similarity ratio, and delta is the geometric parameter X i The similarity ratio of (a) is the difference between the right end point and the left end point of the similarity ratio interval. />
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