CN114996917A - Single-disc crack rotor dynamic characteristic evaluation method based on similarity theory - Google Patents

Single-disc crack rotor dynamic characteristic evaluation method based on similarity theory Download PDF

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CN114996917A
CN114996917A CN202210536042.1A CN202210536042A CN114996917A CN 114996917 A CN114996917 A CN 114996917A CN 202210536042 A CN202210536042 A CN 202210536042A CN 114996917 A CN114996917 A CN 114996917A
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周文杰
金贤
付玉壮
高波
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Jiangsu University
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Abstract

The invention provides a single-disk crack rotor dynamic characteristic evaluation method based on a similar theory, which comprises the steps of firstly determining the sizes of all parts according to a single-disk crack rotor prototype; then, the similarity ratio kappa of the shaft diameter is determined by utilizing the similarity theory d Then, the axial length similarity ratio kappa is obtained in turn according to a formula derived from a similarity theory x Single disc diameter similarity ratio κ D Single disc thickness similarity ratio kappa H Similar to bearing stiffness ratio κ K Crack depth similarity ratio κ a1 Ratio of similarity to shaft diameter κ d The same; and determining the size of the similar model according to the similarity ratio, carrying out rotor dynamics analysis on the prototype and the similar model, and analyzing the critical rotating speed and the natural frequency of the prototype and the similar model. The invention is in phaseThe influence of cracks is considered in the similarity calculation, the dynamic characteristics of the prototype can be evaluated and predicted by using the similarity model, and the method has obvious engineering practical value.

Description

Single-disc crack rotor dynamic characteristic evaluation method based on similar theory
Technical Field
The invention relates to a single-disc crack rotor dynamic characteristic evaluation method based on a similar theory, and belongs to the field of rotating machinery.
Background
Crack failure is one of the common failures of rotating machinery. The cause of the crack is mainly the fatigue crack generated due to the defect of the rotor material itself or the long-term operation. The rotor-bearing system is used as a core component of the rotary machine, and the dynamic characteristics of the rotor-bearing system are directly related to the working performance and the structural safety of the whole rotary machine. Therefore, the dynamic characteristic research of the crack rotor-supporting system has important academic value and engineering practical value. In real life, for a large and complex rotor system, if the prototype thereof is directly tested, huge test cost is brought and test risk is increased. If the rotor system is properly scaled by using a similar theory, the cost can be greatly saved and the experiment difficulty can be reduced. For research on similar theories, certain achievements exist. There are many gaps in similar calculations for a cracked rotor-bearing system. Therefore, it is important to develop a single-disk crack rotor dynamic characteristic evaluation method based on similar theory.
Disclosure of Invention
The patent develops a calculation method for similarity transformation of dynamic characteristics of a single-disc crack rotor by starting from a similar theory and combining rotor dynamics and a crack rotor aiming at the blank of a single-disc crack rotor-supporting system in the similar theory. The invention considers the similarity conversion of the cracks, and keeps the characteristics of the natural frequency of the rotor and the like unchanged in the conversion process. The method can reduce the experiment difficulty of the crack rotor, greatly save the experiment cost and improve the safety and the reliability of the experiment.
In order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows:
a single-disc crack rotor dynamic characteristic evaluation method based on a similar theory is characterized by comprising the following steps:
the method comprises the steps of firstly, dividing a single-disc crack rotor prototype into a rotating shaft, a rotating disc and cracks, and determining the sizes of all parts of the single-disc crack rotor prototype;
secondly, according to the requirement of similarity conversion, the similarity ratio kappa of the shaft diameter is firstly determined d Then, the axial length similarity ratio kappa is obtained in turn according to a formula derived from a similarity theory x Diameter similarity ratio of rotating disks kappa D Thickness similarity ratio of turntable kappa H Similar to bearing stiffness ratio κ K (ii) a Crack depth similarity ratio
Figure BDA0003647904350000011
Ratio of similarity to shaft diameter κ d The same;
thirdly, obtaining a similar model according to the size of the single-disc crack rotor prototype and the conversion of the similarity ratio of each part;
and fourthly, carrying out rotor dynamics analysis on the prototype and the similar model, and analyzing the critical rotating speed and the natural frequency of the prototype and the similar model.
Further, the dimensions of each part of the single-disc cracked rotor prototype determined in the first step include the length of the rotating shaft, the diameter of the rotating shaft, the thickness of the rotating disc, the outer diameter and the inner diameter of the rotating disc, and the depth of the crack.
Further, a similarity theory is adopted to carry out similarity theory transformation on the single-disc crack rotor, and the method comprises the following specific steps:
1) according to the vibration equation of the rotor system, the following can be known:
Figure BDA0003647904350000021
m is the mass of the rotor per unit length; e is the elastic modulus of the rotating shaft; i is the section distance of the rotating shaft; a is the moment of inertia of the mass per unit length of the turntable relative to the axis of rotation; p is the rotor imbalance force; p ═ me 1 f 2 Where f is the natural frequency of the rotor, e 1 An unbalance curve is formed; x is the length of the rotating shaft; y is the synthetic deflection of the rotating shaft; t is time; i is an imaginary unit;
introducing the inclination angle alpha and normal stress sigma of the elastic curve of the rotating shaft to perfect the dynamic state of the rotor system, namely:
Figure BDA0003647904350000022
wherein M is * As bending moment, M * Gx, G is gravity; w is bending-resistant section coefficient, W ═ pi d 3 D is the diameter of the rotating shaft;
according to the formulas (1) and (2), an integral simulation method is used for establishing a similarity relation to obtain a similar pi group, and according to the pi theorem, in order to meet the requirement that the dynamics of a prototype rotor system and a model rotor system are similar, the corresponding pi values are equal:
Figure BDA0003647904350000023
subscript c represents a similar model, subscript n represents a prototype;
the following factors are introduced to simplify the formula (3), and corresponding variables in the pi group are replaced to be simplified only by omega, d, rho, g and x
Univariate representation:
Figure BDA0003647904350000031
g is the gravity of the rotating shaft; j. the design is a square p Is the rotational inertia of the turntable; rho is the density of the rotating shaft material; d is the diameter of the rotating shaft; omega is the rotation speed of the system; taking E, d, x and rho of the rotating shaft as design parameters, and obtaining the similarity ratio of the rotating shaft as follows:
Figure BDA0003647904350000032
when the material is unchanged before and after the similarity conversion, κ ρ ＝κ E ＝κ g 1, obtaining the formula:
Figure BDA0003647904350000033
2) according to the rotational inertia and the mass formula of the turntable, the similarity relation of the turntable can be obtained:
Figure BDA0003647904350000034
Figure BDA0003647904350000041
wherein b is the ratio of the inner diameter and the outer diameter of the turntable of the single-disc crack rotor prototype, and D is the outer diameter of the turntable; d is the inner diameter of the turntable, which is the same as the diameter of the rotating shaft; h is the thickness of the turntable; ρ' is the density of the turntable; j. the design is a square p Is the moment of inertia; kappa type Jp The rotating inertia of the rotating disc is similar to that of the rotating disc; kappa m' The mass similarity ratio of the rotating disc is; c represents a similar model and n represents a prototype. m' is the mass of the turntable;
when the rotor-support system is similar, the ratio of the mass of the turntable to the moment of inertia to the ratio of the mass of the shaft to the moment of inertia is the same, and the thickness of the turntable kappa can be obtained without changing the material before and after the conversion H And the diameter of the turntable kappa D The similarity ratio of (A):
Figure BDA0003647904350000042
3) because the requirement of similar dynamics is met, the acting force proportion in the rotor system and the bearing system is the same; according to the formula of rigidity, k is m 1 f 2 And the formula of the bearing mass similarity ratio
Figure BDA0003647904350000046
Formula of similarity ratio with natural frequency
Figure BDA0003647904350000043
The bearing rigidity similarity ratio can be obtained:
Figure BDA0003647904350000044
4) based on a simple straight crack growing on the rotating shaft, the crack depth a 1 And the width b of the front end of the crack 1 Describing that the crack unit adopts a blocking method, the crack (7 section divides the crack area into a crack module I8, a crack module II9, a crack module III 10 and a crack module IV 11 from the two sides, the interfaces of the crack module I8 and the crack module II9 are mutually attached and do not existIn the gap, but displacement can occur, so as to simulate cracks; the crack module I8, the crack module II9, the crack module III 10 and the crack module IV 11, and the crack module III 10 and the crack module IV 11 are all in a connection state and cannot be displaced; simulating the mutual connection of the rest parts except the cracks and the rotating shaft; because the four modules are mutually connected with the rest shaft sections and no gap exists between the surfaces, when the similar transformation is carried out on the cracks, the similar transformation is carried out on the modules where the cracks are located; depth of crack a 1 The same similarity transformation, i.e. the ratio of similarity of crack depths, is performed as part of the shaft diameter
Figure BDA0003647904350000048
Ratio of similarity to shaft diameter κ d The same is that:
Figure BDA0003647904350000047
further, in the formula (6), the shaft diameter similarity ratio κ is first determined d And obtaining the shaft length similarity ratio kappa according to the natural frequency before and after the shaft similarity transformation x The formula used is:
Figure BDA0003647904350000045
the technical scheme of the invention can bring the following beneficial effects and effects:
according to the method, the real dynamic characteristic calculation of the large single-disc crack rotor can be converted into the acceptable dynamic characteristic calculation of a similar model by performing similar theoretical conversion on the single-disc crack rotor system. The technical scheme of the invention can ensure that the inherent frequency, the critical rotating speed and other dynamic characteristics of the prototype rotor and the model crack rotor are the same. The method greatly reduces the risk and the experiment cost of the crack rotor experiment, brings a new research method for the dynamic characteristic calculation of the crack rotor system in engineering, and widens the application of a similar theory in the field of rotating machinery.
According to the method, the real dynamic characteristic calculation of the large single-disc crack rotor can be converted into the acceptable dynamic characteristic calculation of a similar model by performing similar theoretical conversion on the single-disc crack rotor system. By using the technical scheme of the invention, the inherent frequencies of the prototype rotor and the model crack rotor can be ensured to be the same, and the error of the calculated result can be ensured to be within 5 percent, which is beneficial to modal experimental research. Because of the limitation of factors such as geometric dimension, physical space and experiment cost, and the like, a lot of difficulties exist in directly carrying out experiments on the prototype rotor system, so that the risk and the experiment cost of the crack rotor experiment can be greatly reduced by carrying out similarity transformation on the large-scale single-disc crack rotor through the technical scheme of the invention. In the technical scheme of the invention, the straight cracks are simplified and subjected to similarity conversion, so that the workload in the research process is greatly simplified, a new research method is brought to the dynamic characteristic calculation of a crack rotor system in engineering, and the application of a similarity theory in the field of rotating machinery is widened.
Drawings
FIG. 1 is a schematic structural diagram of a single-disk crack rotor according to the present invention
FIG. 2 is a structural schematic of a cross-section of a shaft at which a crack is located.
FIG. 3 is a schematic illustration of blocking the area around the crack.
FIG. 4 is a single disc crack rotor prototype modal diagram.
FIG. 5 is a single disc crack rotor similar model mode diagram.
In the figure:
1. the rotating shaft module I, 2, the rotating shaft module II, 3, the rotating shaft module III, 4, the rotating disc, 5, the rotating shaft module IV, 6, the rotating shaft module V, 7, the crack, 8 and the crack module I. And 9, cracking the module II. 10, crack module III, 11, crack module IV.
Detailed Description
In order to make the technical means, creation features and achievement functions of the invention easy to understand, the invention is further described with reference to the following embodiments and the accompanying drawings.
The invention relates to a single-disk crack rotor dynamic characteristic evaluation method based on a similar theory, and figure 1 shows a typical single-disk crack rotor structure which mainly comprises a rotating shaft and a rotating disk, wherein the rotating disk is positioned in the middle of a rotating shaft system, and cracks are arranged on the rotating shaft on one side of the rotating disk. The crack only takes depth into consideration, and fig. 2 is a schematic diagram of the crack structure.
The invention relates to a single-disk crack rotor dynamic characteristic evaluation method based on a similar theory, which comprises the following steps of:
firstly, dividing a single-disc crack rotor prototype into a rotating shaft, a rotating disc and cracks according to the structure of the single-disc rotor shown in FIG. 1, and determining the sizes of all parts of the single-disc crack rotor; including the length of the rotating shaft, the diameter of the rotating shaft, the thickness of the rotating disc, the outer diameter and the inner diameter of the rotating disc and the depth of cracks.
Secondly, according to the requirement of similarity conversion, firstly determining the similarity ratio kappa of the shaft diameter d Then, the axial length similarity ratio kappa is obtained in turn according to a formula derived from a similarity theory x Single disc diameter similarity ratio κ D Single disc thickness similarity ratio kappa H Similar to bearing stiffness ratio κ K (ii) a Crack depth similarity ratio
Figure BDA0003647904350000064
Ratio of similarity to shaft diameter κ d The same is true.
Thirdly, obtaining a similar model according to the conversion of the prototype size and the similarity ratio of each part;
fourthly, carrying out rotor dynamics analysis on the prototype and the similar model, and analyzing the critical rotating speed, the natural frequency and the modal diagram of the prototype and the similar model;
the second step comprises the following specific steps:
1) according to the vibration equation of the rotor system, the following can be obtained:
Figure BDA0003647904350000061
m is the mass of the rotor per unit length; e is the elastic modulus of the rotating shaft; i is the section distance of the rotating shaft; a is the moment of inertia of the mass per unit length of the turntable relative to the axis of rotation; p is the rotor imbalance force; p ═ me 1 f 2 Where f is the natural frequency of the rotor, e 1 An unbalance curve is formed; x is the length of the rotating shaft; y is the synthetic deflection of the rotating shaft; t is time; i is an imaginary unit;
introducing the inclination angle alpha and normal stress sigma of the elastic curve of the rotating shaft to perfect the dynamic state of the rotor system, namely:
Figure BDA0003647904350000062
wherein M is * As a bending moment, M * Gx, G is gravity; w is bending-resistant section coefficient, W ═ pi d 3 D is the diameter of the rotating shaft;
according to the formulas (1) and (2), an integral simulation method is used for establishing a similarity relation to obtain a similar pi group, and according to the pi theorem, in order to meet the requirement that the dynamics of a prototype rotor system and a model rotor system are similar, the corresponding pi values are equal:
Figure BDA0003647904350000063
subscript c represents a similar model, subscript n represents a prototype;
the formula (3) is simplified by introducing the following factors, and corresponding variables in the pi group are replaced to be only represented by simple variables of omega, d, rho, g and x:
Figure BDA0003647904350000071
g is the gravity of the rotating shaft; j. the design is a square p Is the rotational inertia of the turntable; rho is the density of the rotating shaft material; d is the diameter of the rotating shaft; omega is the rotation speed of the system;
taking E, d, x and rho of the rotating shaft as design parameters, and obtaining the similarity ratio of the rotating shaft as follows:
Figure BDA0003647904350000072
when the material is unchanged before and after the similarity conversion, κ ρ ＝κ E ＝κ g 1, obtaining the formula:
Figure BDA0003647904350000073
2) according to the rotational inertia and the mass formula of the turntable, the similarity relation of the turntable can be obtained:
Figure BDA0003647904350000074
Figure BDA0003647904350000081
wherein b is the ratio of the inner diameter and the outer diameter of the turntable of the single-disc crack rotor prototype, and D is the outer diameter of the turntable; d is the inner diameter of the turntable, which is the same as the diameter of the rotating shaft; h is the thickness of the turntable; ρ' is the turntable density; j. the design is a square p Is the moment of inertia; kappa Jp Is the rotational inertia similarity ratio of the rotating disc; kappa m' The mass similarity ratio of the rotating disc is; c represents a similar model and n represents a prototype. m' is the mass of the turntable;
when the rotor-support system is similar, the ratio of the mass of the turntable to the moment of inertia to the ratio of the mass of the shaft to the moment of inertia is the same, and the thickness of the turntable kappa can be obtained without changing the material before and after the conversion H And the diameter of the rotating disc kappa D The similarity ratio of (A):
Figure BDA0003647904350000082
3) because the requirement of similar dynamics is met, the acting force proportion in the rotor system and the bearing system is the same; according to the formula of stiffness k ═ m 1 f 2 And the formula k of the bearing mass similarity ratio is introduced m1 ＝κ d 2 κ x Formula of similarity ratio with natural frequency
Figure BDA0003647904350000083
The bearing rigidity similarity ratio can be obtained:
Figure BDA0003647904350000084
4) based on a simple straight crack growing on the rotating shaft, using the crack depth a 1 And the width b of the front end of the crack 1 Describing that the crack unit adopts a blocking method, and the area where the crack is located is divided into a crack module I8, a crack module II9, a crack module III 10 and a crack module IV 11 from the cross section of the crack 7 to two sides; the interface of the crack module I8 and the interface of the crack module II9 are mutually attached without a gap, but can be displaced so as to simulate cracks; the crack module I8, the crack module II9, the crack module III 10 and the crack module IV 11, and the crack module III 10 and the crack module IV 11 are in a connected state and cannot be displaced; so as to simulate the mutual connection of the rest parts except the cracks and the rotating shaft; because the four modules are mutually connected with the rest shaft sections and no gap exists between the surfaces, when the similar transformation is carried out on the cracks, the similar transformation is carried out on the modules where the cracks are located; depth of crack a 1 The same similarity transformation, i.e. the ratio of similarity of crack depths, is performed as part of the shaft diameter
Figure BDA0003647904350000087
Ratio of similarity to shaft diameter κ d The same is that:
Figure BDA0003647904350000086
the test was performed using the single disc cracked rotor shown in fig. 1 as an example, and the parameters of the rotor are shown in table 1.
TABLE 1 Single disc crack rotor parameters
Table 1: typical single disc crack rotor prototype parameter table
Figure BDA0003647904350000085
Figure BDA0003647904350000091
From the formula (6), the shaft diameter similarity ratio is first determinedκ d And the ratio of similarity of axial length kappa is obtained according to the fact that the natural frequency before and after the axial similarity transformation does not change x . In this embodiment, the shaft diameter similarity ratio κ is determined according to the similarity ratio between the similarity model and the prototype d The content of the organic acid is 0.5,
Figure BDA0003647904350000092
then, it can be known that: kappa x ＝0.707。
B is calculated to be 0.19 from the inner and outer diameters of the turntable 4 in table 1. B is 0.19, k d ＝0.5，κ x 0.707 its carry-in (8) gives a disc thickness similarity ratio κ H Similarity ratio with disc diameter kappa D ：
κ H ＝0.34
κ D ＝0.713
The stiffness similarity ratio can be obtained from equation (9): kappa K ＝0.177。
Based on the growth of the crack 7 on the rotating shaft, the crack depth similarity ratio
Figure BDA0003647904350000095
Ratio of similarity to shaft diameter κ d The same is that:
Figure BDA0003647904350000094
according to the steps, the calculated similar model parameters are as follows:
table 2: parameters of similar model
Figure BDA0003647904350000093
Figure BDA0003647904350000101
The natural frequency, the critical rotation speed and the mode diagram before and after the single-disc crack rotor similarity transformation can be obtained through rotor dynamics calculation. The critical rotation speed and the natural frequency are shown in tables 3 and 4. The first three-order mode diagrams of the single-disk crack rotor are shown in fig. 4 and 5.
Table 3: critical speed comparison result of single-disk crack rotor
Modality Single-disc crack rotor prototype Similar model Error of the measurement
1 2045.8 2053.4 0.37％
2 13926 14366 3.16％
3 22804 23091 1.26％
Table 4: single disc crack rotor natural frequency comparison results
Modality Single-disc crack rotor prototype Similar model Error of the measurement
1 34.091 34.22 0.38％
2 203.16 210.84 3.78％
3 379.04 384.33 1.40％
Compared with the results, the error calculation of the prototype and the similar model shows that the method has higher precision on the first three-order critical rotation speed and the natural frequency and can meet the general requirements. By comparing the first three-order mode diagrams of the prototype and the similar model in fig. 4 and 5, it can be seen that the variation trends are substantially consistent. This shows that the similar model can better describe the mode shape of the prototype.
The analysis proves that the method can carry out effective similarity conversion on the single-disc crack rotor.
The present invention is not limited to the above-described embodiments, and any obvious improvements, substitutions or modifications can be made by those skilled in the art without departing from the spirit of the present invention.

Claims (4)

1. A single-disc crack rotor dynamic characteristic evaluation method based on a similar theory is characterized by comprising the following steps:
the method comprises the steps of firstly, dividing a single-disc crack rotor prototype into a rotating shaft, a rotating disc and cracks, and determining the sizes of all parts of the single-disc crack rotor prototype;
secondly, according to the requirement of similarity conversion, the similarity ratio kappa of the shaft diameter is firstly determined d Then, the axial length similarity ratio kappa is obtained in turn according to a formula derived from a similarity theory x Diameter similarity ratio of rotating disks kappa D Thickness similarity ratio of turntable kappa H Similar to bearing stiffness ratio κ K (ii) a Crack depth similarity ratio
Figure FDA0003647904340000011
Ratio of similarity to shaft diameter κ d The same;
thirdly, obtaining a similar model according to the size of the single-disc crack rotor prototype and the conversion of the similarity ratio of each part;
and fourthly, carrying out rotor dynamics analysis on the prototype and the similar model, and analyzing the critical rotating speed and the natural frequency of the prototype and the similar model.
2. The single-disk crack rotor dynamic characteristic evaluation method based on the similarity theory according to claim 1, wherein the sizes of the parts of the single-disk crack rotor prototype determined in the first step include a length of the rotating shaft, a diameter of the rotating shaft, a thickness of the rotating disk, an outer diameter and an inner diameter of the rotating disk, and a depth of the crack.
3. The single-disk crack rotor dynamic characteristic evaluation method based on the similarity theory as claimed in claim 1, wherein the similarity theory is adopted to carry out similarity theory transformation on the single-disk crack rotor, and the method comprises the following specific steps:
1) according to the vibration equation of the rotor system, the following can be obtained:
Figure FDA0003647904340000012
m is the mass of the rotor per unit length; e is the elastic modulus of the rotating shaft; i is the section distance of the rotating shaft; a is the moment of inertia of the mass per unit length of the turntable relative to the axis of rotation; p is the rotor imbalance force; p ═ me 1 f 2 Where f is the natural frequency of the rotor, e 1 An unbalance curve is formed; x is the length of the rotating shaft; y is the synthetic deflection of the rotating shaft; t is time; i is an imaginary unit;
introducing an inclination angle alpha and a normal stress sigma of a rotating shaft elastic curve to perfect the dynamic state of the rotor system, namely:
Figure FDA0003647904340000013
wherein M is * As bending moment, M * Gx, G is gravity; w is bending-resistant section coefficient, W ═ pi d 3 D is the diameter of the rotating shaft;
according to the formulas (1) and (2), a similar relation is established by using an integral simulation method to obtain a similar pi group, and according to the pi theorem, in order to meet the condition that the dynamics of a prototype rotor system and a model rotor system are similar, the corresponding pi values are ensured to be equal:
Figure FDA0003647904340000021
subscript c represents a similar model, subscript n represents a prototype;
the following factors are introduced to simplify the above equation (3), and corresponding variables in the pi group are replaced to be only represented by simple variables of ω, d, ρ, g, and x:
Figure FDA0003647904340000022
g is the gravity of the rotating shaft; j. the design is a square p Is the rotational inertia of the turntable; rho is the density of the rotating shaft material; d is the diameter of the rotating shaft;omega is the rotation speed of the system; taking E, d, x and rho of the rotating shaft as design parameters, and obtaining the similarity ratio of the rotating shaft as follows:
Figure FDA0003647904340000023
when the material is unchanged before and after the similarity conversion, κ ρ ＝κ E ＝κ g 1, get the formula:
Figure FDA0003647904340000031
2) according to the rotational inertia and the mass formula of the turntable, the similarity relation of the turntable can be obtained:
Figure FDA0003647904340000032
Figure FDA0003647904340000033
Figure FDA0003647904340000034
wherein b is the ratio of the inner diameter and the outer diameter of the turntable of the single-disc crack rotor prototype, and D is the outer diameter of the turntable; d is the inner diameter of the turntable, which is the same as the diameter of the rotating shaft; h is the thickness of the turntable; ρ' is the turntable density; j. the design is a square p Is the moment of inertia; kappa Jp The rotating inertia of the rotating disc is similar to that of the rotating disc; kappa type m' The mass similarity ratio of the rotating disc is; c represents a similar model and n represents a prototype. m' is the mass of the turntable;
when the rotor-support system is similar, the ratio of the mass and the moment of inertia of the turntable to the ratio of the mass and the moment of inertia of the shaft are similar, and the thickness kappa of the turntable can be obtained without changing the material before and after changing H And the diameter of the rotating disc kappa D The similarity ratio of (A):
Figure FDA0003647904340000035
3) because the requirement of similar dynamics is met, the acting force proportion in the rotor system and the bearing system is the same; according to the formula of stiffness k ═ m 1 f 2 And the formula k of the bearing mass similarity ratio is introduced m1 ＝κ d 2 κ x Formula of similarity ratio with natural frequency
Figure FDA0003647904340000036
The bearing rigidity similarity ratio can be obtained:
Figure FDA0003647904340000037
4) based on a simple straight crack growing on the rotating shaft, the crack depth a 1 And the width b of the front end of the crack 1 Describing that a blocking method is adopted for the crack unit, and the area where the crack is located is divided into a crack module I (8), a crack module II (9), a crack module III (10) and a crack module IV (11) from the cross section of the crack (7) to two sides; the interface of the crack module I (8) and the interface of the crack module II (9) are mutually attached without a gap, but can be displaced, so as to simulate cracks; the crack module I (8), the crack module II (9), the crack module III (10) and the crack module IV (11) and the crack module III (10) and the crack module IV (11) are in a connection state and cannot be displaced; simulating the mutual connection of the rest parts except the cracks and the rotating shaft; because the four modules are mutually connected with the rest shaft sections and no gap exists between the surfaces, when the similar transformation is carried out on the cracks, the similar transformation is carried out on the modules where the cracks are located; depth of crack a 1 The same similarity transformation, i.e. the ratio of similarity of crack depths, is performed as part of the shaft diameter
Figure FDA0003647904340000041
Ratio of similarity to shaft diameter κ d The same is that:
Figure FDA0003647904340000042
4. the single-disk crack rotor dynamic characteristic evaluation method based on the similarity theory according to claim 3, characterized in that: in the formula (6), the shaft diameter similarity ratio κ is first determined d And the axial length similarity ratio kappa is obtained according to the fact that the natural frequencies before and after the axial similarity transformation do not change x The formula used is:
Figure FDA0003647904340000043
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115828446A (en) * 2022-11-02 2023-03-21 中国航发沈阳发动机研究所 Method for improving rotor stacking optimization quality and calculation speed

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115828446A (en) * 2022-11-02 2023-03-21 中国航发沈阳发动机研究所 Method for improving rotor stacking optimization quality and calculation speed
CN115828446B (en) * 2022-11-02 2024-01-30 中国航发沈阳发动机研究所 Method for improving rotor stacking optimization quality and calculation speed

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