Design method of rotor system similarity test model considering gravity acceleration distortion
By determining the similarity parameters of the rotor system substructure, the problem of the difference in vibration response between the model and the prototype caused by gravitational acceleration distortion was solved, and the cost and cycle optimization of the similar test model were achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHEASTERN UNIV CHINA
- Filing Date
- 2026-01-23
- Publication Date
- 2026-06-09
AI Technical Summary
Existing technologies cannot effectively address the discrepancy between the vibration response of the rotor system model and the prototype caused by gravitational acceleration distortion, leading to increased experimental costs, risks, and timelines.
By determining the similarity parameters of the rotor system substructures, including the similarity relationships of the shaft mass, turntable mass, and support structure mass, and combining the similarity relationships of the shaft polar moment of inertia and the turntable polar moment of inertia, experimental parameters are calculated and a similarity test model is established.
This approach ensures that the natural frequencies and vibration responses of the model and prototype are consistent while maintaining a scaled-down appearance, thus reducing experimental costs, time, and risks.
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Figure CN122174376A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of simulation modeling technology, and in particular to a design method and related equipment for a rotor system similar test model that considers gravitational acceleration distortion. Background Technology
[0002] Existing techniques obtain the vibration characteristics of a model and a model with similar dimensions through simulation or experimentation, and then use the least squares method to fit the input-output relationship between the models to obtain a similarity relationship. The drawback is that this method cannot account for the distortion of gravitational acceleration, resulting in the inability to predict the vibration response in the direction of gravity (vertical direction). Furthermore, the obtained prototype and model have different dynamic characteristics; the natural frequency of the model is higher than that of the prototype. This means that when using the model to predict the vibration response of the prototype at a certain rotational speed, the model experiment needs to reach a higher rotational speed. This requires high-performance drive equipment, more advanced assembly processes, etc., leading to a significant increase in experimental costs, risks, and time.
[0003] Another existing technique uses sensitivity analysis to establish similarity relationships and optimization algorithms to establish the relationship between model output and prototype output. However, this requires prior knowledge of the prototype's vibration response, which is often unavailable in practical engineering. Furthermore, it cannot accurately represent gravitational acceleration distortion, and the model's natural frequency is higher than the prototype's, requiring high-performance drive equipment and more advanced assembly processes, leading to a significant increase in experimental costs, risks, and timelines. Alternatively, similarity relationships can be established by deriving the control equations of the rotor system, but neither approach solves the problem of the inability to scale the gravitational acceleration between the prototype and the model.
[0004] Furthermore, the inherent frequency of the models constructed in the existing technology is higher than that of the prototype, requiring high-performance drive equipment, more advanced assembly processes, etc., which leads to a significant increase in experimental costs, risks, and time. Summary of the Invention
[0005] In view of this, the present invention provides a method for designing a similar test model of a rotor system considering gravitational acceleration distortion, to solve the problem in the prior art that the gravitational acceleration of the prototype and model cannot be scaled down. To achieve one, some, or all of the above objectives, or other objectives, the present invention proposes a method for designing a similar test model of a rotor system considering gravitational acceleration distortion, comprising: The similarity parameters of the substructures on the target rotor system are determined according to the preset similarity relationship. The preset similarity relationship includes the relationship between the similarity values of the shaft mass, the similarity values of the turntable mass and the similarity values of the support structure mass, and the relationship between the similarity values of the shaft polar moment of inertia and the similarity values of the turntable polar moment of inertia. The substructure includes the shaft, the turntable and the support structure. Based on the similarity parameters, model material parameters, and actual parameters of the target rotor system, experimental parameters are calculated according to preset rules. A similar experimental model corresponding to the target rotor system is established based on the experimental parameters.
[0006] Optionally, the preset similarity relationship is as follows: the similarity value of the shaft mass is equal to the similarity value of the turntable mass, and is also equal to the similarity value of the supporting structure mass; the similarity value of the extreme moment of inertia of the shaft is equal to the similarity value of the extreme moment of inertia of the turntable.
[0007] Optionally, the similarity parameters include the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, and the similarity ratio of the vibration displacement. The functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio is as follows:
[0008] In the formula, the subscript oh, Oh, t, These represent the rotor's natural frequency, rotational speed, and time, respectively; subscripts. r、l , E、r These represent the cross-sectional radius, length, elastic modulus, and density of the shaft, respectively; the superscript 's' indicates the shaft.
[0009] The mathematical expression for the similarity ratio of the vibration displacements is:
[0010] In the formula, the subscript x and y These represent the displacements of the shaft along the x and y directions, respectively. e This is the turntable eccentricity.
[0011] Optionally, before the step of calculating the experimental parameters according to a preset rule based on the similarity parameters, model material parameters, and the actual parameters of the target rotor system, the method further includes: Based on the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, and combined with the vibration displacement similarity ratio, the functional relationship between the critical rotational speed similarity ratio and the vibration displacement similarity ratio is determined. Based on the functional relationship between the critical speed similarity ratio and the vibration displacement similarity ratio, it is determined that when the preset condition is met, the value of the natural frequency similarity ratio is 1. The preset condition indicates that the critical speed and vibration displacement of the target rotor system and the similar test model corresponding to the target rotor system are consistent.
[0012] Optionally, the step of calculating experimental parameters according to preset rules based on the similarity parameters, model material parameters, and actual parameters of the target rotor system includes: Substituting the value of the natural frequency similarity ratio into the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, we obtain the first formula; Substituting the preset formula representing the relationship between the similarity ratio of the shaft length and the similarity ratio of the shaft radius in the preset rules into the first formula, we obtain the second formula; The similarity ratio of the material parameters is determined based on the model material parameters and the actual parameters of the target rotor system. The similarity ratio of the material parameters and the similarity ratio of the shaft length are then substituted into the second formula to calculate the relationship parameter between the similarity ratio of the shaft length and the similarity ratio of the shaft radius. This relationship parameter is then used as the experimental parameter.
[0013] Optionally, the step of determining the similarity parameters of the substructures on the target rotor system according to a preset similarity relationship further includes: Based on the equations of motion of the rotating shaft and Rayleigh beam theory, we can obtain the following simultaneous equations:
[0014] Using equation analysis, the simultaneous equations are transformed into the objective equation:
[0015] Based on the relationship between rotational speed and time, the similarity relationship between rotational speed and time in the similarity parameters is obtained as follows:
[0016] Based on the objective equation and the similarity relationship between rotational speed and time, the similarity relationship between displacement and eccentricity in the similarity parameters is obtained:
[0017] Based on the preset similarity relationship, the similarity ratio of the turntable's unit mass among the similarity parameters is determined as follows: .
[0018] Optionally, the step of determining the similarity parameters of the substructures on the target rotor system according to a preset similarity relationship further includes: The similarity ratio of the polar moments of inertia of the turntable can be expressed as:
[0019] For length of l s Based on the similarity ratio of the unit mass of the turntable, the similarity ratio of the mass of the turntable in the similarity parameters is obtained as follows:
[0020] By simultaneously solving the objective equations, the similarity relationship between rotational speed and time, the similarity ratio of vibrational displacement, and the similarity ratio of shaft mass, the length of the similarity parameters is obtained. l s The similarity ratio of the polar moments of inertia of the axis of rotation is:
[0021] Based on the preset similarity relationship, the similarity ratio of the turntable's outer diameter and thickness in the similarity parameters is obtained:
[0022] .
[0023] Optionally, the step of determining the similarity parameters of the substructures on the target rotor system according to a preset similarity relationship further includes: Using the equation analysis method, the motion equations of the support structure are transformed into motion functions of the support structure:
[0024] Substituting the preset similarity relationship and the similarity ratio of the shaft mass into the motion function of the support structure, we obtain the simultaneous equations of the support structure:
[0025] Based on the simultaneous equations of the support structure and the similarity ratio of the unit mass of the turntable, the similarity ratio of the support damping in the similarity parameters is obtained:
[0026] The similarity ratio of the support stiffness in the similarity parameters is obtained by solving the simultaneous equations of the support structure and the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio: .
[0027] Implementing the embodiments of the present invention will have the following beneficial effects: Similarity parameters for substructures on the target rotor system are determined according to preset similarity relationships, including similarity relationships between the shaft mass, turntable mass, and support structure mass, and similarity relationships between the shaft polar moment of inertia and turntable polar moment of inertia. The substructures include the shaft, turntable, and support structure. Experimental parameters are calculated based on the similarity parameters and the actual parameters of the target rotor system. A similarity test model corresponding to the target rotor system is established based on the experimental parameters. The rotor system is divided into three substructures: shaft, turntable, and support. It is proposed that satisfying the similarity of the substructures ensures the similarity of the entire rotor system. The resulting similarity test model, while being scaled down, ensures that the natural frequency and vibration response are completely consistent with the target rotor system, which can further reduce the cost, cycle, and risk of similarity model experiments. Attached Figure Description
[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0029] in: Figure 1 This is a flowchart illustrating a method for designing a similar test model of a rotor system considering gravitational acceleration distortion, as provided in an embodiment of this application. Figure 2 This is a schematic diagram illustrating the derivation of similarity relationships in a rotor system similarity test model design method considering gravitational acceleration distortion provided in an embodiment of this application; Figure 3 This is a schematic diagram of a finite element model of a rotor system, which is a rotor system similar test model design method considering gravitational acceleration distortion provided in an embodiment of this application. Detailed Implementation
[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0031] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. In the description of this invention, it should be noted that unless otherwise explicitly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0032] like Figure 1 As shown in the embodiments of this application, a method for designing a similar test model of a rotor system considering gravitational acceleration distortion is provided, including: S110. Determine the similarity parameters of the substructures on the target rotor system according to the preset similarity relationship. The preset similarity relationship includes the relationship between the similarity values of the shaft mass, the similarity values of the turntable mass and the similarity values of the support structure mass, and the relationship between the similarity values of the shaft polar moment of inertia and the similarity values of the turntable polar moment of inertia. The substructure includes the shaft, the turntable and the support structure. S120. Based on the similarity parameters, model material parameters, and actual parameters of the target rotor system, calculate the experimental parameters according to preset rules. S130. Based on the experimental parameters, establish a similar test model corresponding to the target rotor system.
[0033] For example, such as Figure 2 As shown, different similarity ratios are assigned to the shaft length and radius of the rotor system. Then, a method for deriving the similarity relationship of the rotor system based on substructures is proposed. The basic idea is to achieve the similarity of the rotor system by satisfying the similarity of mass and moment of inertia between substructures (shaft, disk, and support). The dashed lines indicate that the parameters at both ends are equal. The substructures satisfy the following similarity relationship: (1) (2) In the formula, the superscripts s, d, and b represent the shaft, turntable, and support, respectively; the subscripts m and J p These represent mass and polar moment of inertia, respectively.
[0034] In one possible implementation, the preset similarity relationship is as follows: the similarity value of the shaft mass is equal to the similarity value of the turntable mass, and equal to the similarity value of the supporting structure mass; the similarity value of the extreme moment of inertia of the shaft is equal to the similarity value of the extreme moment of inertia of the turntable.
[0035] Optionally, the similarity parameters include the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, and the similarity ratio of the vibration displacement. The functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio is as follows:
[0036] In the formula, the subscript oh, Oh, t, These represent the rotor's natural frequency, rotational speed, and time, respectively; subscripts. r、l , E、r These represent the cross-sectional radius, length, elastic modulus, and density of the shaft, respectively; the superscript 's' indicates the shaft.
[0037] The mathematical expression for the similarity ratio of the vibration displacements is:
[0038] In the formula, the subscript x and y They are the axis of rotation x and y Directional displacement; e This is the turntable eccentricity.
[0039] Optionally, the step of determining the similarity parameters of the substructures on the target rotor system according to a preset similarity relationship further includes: Based on the equations of motion of the rotating shaft and Rayleigh beam theory, we can obtain the following simultaneous equations:
[0040] In the formula, , and These are the mass, diameter, moment of inertia, and polar moment of inertia of the infinitesimal segment of the rotating shaft, respectively. The mass of the turntable per unit length; e The eccentricity of the turntable; x , y , z They are respectively along the micro-element segment x , y and z Displacement in direction; E s , I These represent the elastic modulus and moment of inertia of the shaft, respectively.
[0041] Using equation analysis, the simultaneous equations are transformed into the objective equation:
[0042] subscript in formula and g These represent the mass of the shaft and the acceleration due to gravity, respectively.
[0043] Based on the relationship between rotational speed and time The similarity relationship between rotational speed and time in the similarity parameters is obtained:
[0044] In the formula i This represents the angular displacement of the rotor.
[0045] Based on the objective equation and the similarity relationship between rotational speed and time, the similarity relationship between displacement and eccentricity in the similarity parameters is obtained:
[0046] Based on the preset similarity relationship, the similarity ratio of the turntable's unit mass among the similarity parameters is determined as follows:
[0047] For example, for a rotating shaft, its length is l s The cross-sectional radius is r s Force analysis is performed on a unit length infinitesimal segment on the rotating shaft, and the equation of motion for the infinitesimal segment is as follows: (3) (4) (5) (6) In the formula, the superscript ' indicates the parameter of the infinitesimal segment of unit length; , and These are the mass, diameter moment of inertia, and polar moment of inertia of the infinitesimal segment, respectively. The mass of the turntable per unit length; e The eccentricity of the turntable; Oh Let be the rotational speed of the rotor system; x and y are the displacements along the x and y directions, respectively. and These are the accelerations of the axis of rotation along the x and y directions, respectively. and These are the rotation angles along the x and y directions, respectively; and ω represents the angular velocity along the x and y directions; and ω represents the angular acceleration along the x and y directions; and These are the shear forces in the x and y directions, respectively. M x and M y These are the bending moments in the x and y directions, respectively; and These are the external loads in the x and y directions, respectively.
[0048] In equation (5) Substituting into equation (3), we get: (7) According to Rayleigh beam theory, the bending moment and rotation angle of the infinitesimal element of the rotating shaft are: (8) Substituting equation (8) into equation (7), we get: (9) Using the equation analysis method, equation (9) can be transformed into the following similarity relationship: (10) Based on the relationship between rotational speed and time Where angle θ is a dimensionless physical quantity, the derived similarity relationship between rotational speed and time is as follows: (11) Combining the first and fifth terms of equation (10), and substituting equation (11) into it, we can obtain the similarity relationship between displacement x and eccentricity e: (12) According to equation (1), the mass similarity ratios of the turntable and the shaft are equal, therefore the similarity ratios of their unit masses are also equal. Thus, the similarity ratio of the turntable's unit mass is: (13) By combining the second and fifth terms of equation (10), and then combining equations (11) and (13), the similarity ratio of the natural frequency ω and the rotational speed Ω can be obtained: (14) Combining the fifth and sixth terms of equation (10) with equation (13), we can obtain the similarity ratio of the vibration displacement x: (15) Similarity ratio of gravitational acceleration l g It is always equal to 1. Furthermore, the diameter's moment of inertia... J d Polar moment of inertia J p Since they have the same dimensions, their related similarity ratios are all equal. Therefore, by combining the third and fourth terms of equation (10) with equation (11), the similarity relationship in equation (15) can be further written as: (16) It is worth noting that, according to the dimensional analysis method, the dimension of vibration displacement should be consistent with the dimension of size. However, in equation (16), the dimension of vibration displacement is the square of the dimension, which does not meet the dimensional requirements of the dimensional analysis method. The reason is that the similarity ratio λg of gravitational acceleration is equal to 1.
[0049] Optionally, the step of determining the similarity parameters of the substructures on the target rotor system according to a preset similarity relationship further includes: The similarity ratio of the polar moments of inertia of the turntable can be expressed as:
[0050] For length of l s Based on the similarity ratio of the unit mass of the turntable, the similarity ratio of the mass of the turntable in the similarity parameters is obtained as follows:
[0051] By simultaneously solving the objective equations, the similarity relationship between rotational speed and time, the similarity ratio of vibrational displacement, and the similarity ratio of shaft mass, the length of the similarity parameters is obtained. l s The similarity ratio of the polar moments of inertia of the axis of rotation is:
[0052] Based on the preset similarity relationship, the similarity ratio of the turntable's outer diameter and thickness in the similarity parameters is obtained:
[0053]
[0054] For example, for a turntable, the similarity relationship of the turntable is derived according to equations (1) and (2). For a thickness of l d The rigid disk has the following mass: (17) In the formula, m d For the quality of the turntable; r d The density of the turntable; R d and r d These are the outer and inner radii of the turntable, respectively.
[0055] The similarity ratio of the turntable mass is equal to the ratio of the mass of the prototype turntable to the mass of the model turntable, as follows: (18) In the formula, the subscripts (p) and (m) represent the parameters of the prototype and the model, respectively; It is the ratio of the inner radius to the outer radius of the prototype disk.
[0056] The polar moment of inertia of the turntable can be expressed as: (19) The similarity ratio of the polar moments of inertia of the turntable can be expressed as: (20) For length of l s According to equation (13), the similarity ratio of the shaft mass is: (twenty one) By combining the first and fourth terms of equation (10), and in conjunction with equations (11), (16), and (21), the similarity ratio of the polar moment of inertia per unit length of the rotating shaft can be obtained: (twenty two) Therefore, the length is l s The similarity ratio of the polar moments of inertia of the axis of rotation is: (twenty three) According to equations (1) and (2), the similarity ratios of the mass and moment of inertia of the shaft and the turntable are equal. Therefore, by combining the similarity relationships of the mass (equations (18) and (21)) and moment of inertia (equations (20) and (23)) of the shaft and the turntable respectively, the following similarity relationship can be obtained: (twenty four) (25) Since the turntable is fixed to the shaft, the inner diameter of the turntable is approximately equal to the outer diameter of the shaft. Therefore, the ratio of the inner diameter of the turntable to the outer diameter of the shaft is equal, i.e. Furthermore, considering that the turntable and the shaft are made of the same material, we can obtain... , Therefore, the superscript in the similarity ratio of density and elastic modulus can be removed. Based on equations (24) and (25), the similarity ratio of the turntable's outer diameter and thickness can be derived: (26) (27) Optionally, the step of determining the similarity parameters of the substructures on the target rotor system according to a preset similarity relationship further includes: Using equation analysis, the motion equations of the support structure are transformed into motion functions of the support structure (similarity relationship):
[0057] Substituting the pre-defined similarity relationship and the similarity ratio of the shaft mass into the motion function (similarity relationship) of the support structure, we obtain the simultaneous equations of the support structure:
[0058] Based on the simultaneous equations of the support structure and the similarity ratio of the unit mass of the turntable, the similarity ratio of the support damping in the similarity parameters is obtained:
[0059] The similarity ratio of the support stiffness in the similarity parameters is obtained by solving the simultaneous equations of the support structure and the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio: .
[0060] For example, considering the support structure as a spring-damped unit, the equation of motion can be expressed as: (28) In the formula, m b , k b and c b These are the mass, stiffness, and damping of the support, respectively.Q The magnitude of the external force.
[0061] Using the equation analysis method, equation (28) can be transformed into the following similarity relation: (29) Substituting equations (1) and (21) into equation (29), we get: (30) Combining the first and second terms of equation (30) with equation (14), we can obtain the similarity ratio of the support damping: (31) The similarity ratio of the support stiffness can be obtained by combining the first and third terms of equation (30) and equation (14): (32)
[0062] Optionally, before the step of calculating the experimental parameters according to a preset rule based on the similarity parameters, model material parameters, and the actual parameters of the target rotor system, the method further includes: Based on the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, and combined with the vibration displacement similarity ratio, the functional relationship between the critical rotational speed similarity ratio and the vibration displacement similarity ratio is determined. Based on the functional relationship between the critical speed similarity ratio and the vibration displacement similarity ratio, it is determined that when the preset condition is met, the value of the natural frequency similarity ratio is 1. The preset condition indicates that the critical speed and vibration displacement of the target rotor system and the similar test model corresponding to the target rotor system are consistent.
[0063] Optionally, the step of calculating experimental parameters according to preset rules based on the similarity parameters, model material parameters, and actual parameters of the target rotor system includes: Substituting the value of the natural frequency similarity ratio into the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, we obtain the first formula; Substituting the preset formula representing the relationship between the similarity ratio of the shaft length and the similarity ratio of the shaft radius in the preset rules into the first formula, we obtain the second formula; The similarity ratio of the material parameters is determined based on the model material parameters and the actual parameters of the target rotor system. The similarity ratio of the material parameters and the similarity ratio of the shaft length are then substituted into the second formula to calculate the relationship parameter between the similarity ratio of the shaft length and the similarity ratio of the shaft radius. This relationship parameter is then used as the experimental parameter.
[0064] For example, will l ω Substituting 1 into equation (14), we get: (33) Typically, the material of the prototype is known; once the material of the model is determined, the similarity ratio of density and elastic modulus (…) l ρ , l E The similarity ratio of the material parameters can naturally be determined. l ρ , l E No design is required; only the similarity ratio of the shaft length and radius is needed. , Design it. (The rest of the text appears to be a fragment and doesn't form a coherent sentence or paragraph.) and To further derive the undetermined coefficient α, the following relationship must be satisfied: (34) Furthermore, substituting equation (34) into equation (33) yields: (35) Taking the logarithm of both sides of equation (35) yields: (36) Therefore, α can be further derived: (37) Equations (34) and (37) give the model design conditions that satisfy the consistency of the critical rotational speeds of the prototype and the model. Therefore, the design conditions for consistent vibration displacements are further derived. According to equations (14) and (16), the similarity ratio between the critical rotational speed and the vibration displacement has the following relationship: (38) Therefore, when the condition of consistent critical speed is met ( l ω When the similarity ratio of the vibration displacement is 1, the similarity ratio of the vibration displacement is also equal to 1. That is, equations (34) and (37) are design conditions that simultaneously ensure that the critical speed and vibration displacement of the prototype and the model are consistent. It should be noted that for the results output by the model that is inconsistent with the critical speed and vibration displacement of the prototype, similarity transformation is required according to equations (14) and (16).
[0065] For example, two sets of prototypes (P1, P2) and models (M1, M2, D1, D2) were designed, with the established rotor system considered as a prototype. Figure 3As shown, in the first group, models M1 and M2 (made of 45# steel) are used to predict the prototype P1 (made of 45# steel); in the second group, models D1 and D2 (made of 45# steel) are used to predict the prototype P2 (made of titanium alloy). The length of the models in both groups is half that of the prototype. It is worth noting that in the first group, the prototype and models are made of the same material, 45# steel (ρ=7850kg / m3, E=210GPa, υ=0.26). The second group further considers the difference in materials between the prototype and models, using a model made of relatively inexpensive 45# steel to predict the prototype made of titanium alloy (…). r = 4350kg / m 3 , E = 105GPa u The prototype, made with a similarity coefficient of 0.26, further reduced the cost and manufacturing difficulty of similar model experiments. Furthermore, M1 and D1 are geometrically completely similar models, while M2 and D2 are models with the same critical rotational speed and vibration displacement as the prototype. The similarity ratios of the two sets of prototypes and models are shown in Tables 1 and 2, respectively.
[0066] Table 1. Similarity ratio of shaft parameters, support parameters, critical speed, and vibration displacement of models M1 and M2 relative to prototype P1.
[0067] Table 2. Similarity ratio of shaft parameters, support parameters, critical speed, and vibration displacement of models D1 and D2 relative to prototype P2.
[0068] For M2 and D2, the similarity ratio of the shaft lengths Once determined, the similarity ratio of the rotation axis radii The similarity ratio of the turntable size is determined according to equations (34) and (37) and does not require manual setting. The similarity ratio of the turntable size is determined according to equations (26) and (27), as shown in Table 3.
[0069] Table 3. Similarity ratio of turntable dimensions for models M1, M2, D1, and D2
[0070] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.
[0071] The above description discloses only preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. Therefore, equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.
Claims
1. A method for designing a similar test model for a rotor system considering gravitational acceleration distortion, characterized in that, include: The similarity parameters of the substructures on the target rotor system are determined according to the preset similarity relationship. The preset similarity relationship includes the relationship between the similarity values of the shaft mass, the similarity values of the turntable mass and the similarity values of the support structure mass, and the relationship between the similarity values of the shaft polar moment of inertia and the similarity values of the turntable polar moment of inertia. The substructure includes the shaft, the turntable and the support structure. Based on the similarity parameters, model material parameters, and actual parameters of the target rotor system, experimental parameters are calculated according to preset rules. A similar experimental model corresponding to the target rotor system is established based on the experimental parameters.
2. The method for designing a similar test model of a rotor system considering gravitational acceleration distortion as described in claim 1, characterized in that, The preset similarity relationship is as follows: the similarity value of the shaft mass is equal to the similarity value of the turntable mass, and is also equal to the similarity value of the supporting structure mass; the similarity value of the extreme moment of inertia of the shaft is equal to the similarity value of the extreme moment of inertia of the turntable.
3. The method for designing a similar test model of a rotor system considering gravitational acceleration distortion as described in claim 1, characterized in that, The similarity parameters include the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, and the similarity ratio of the vibration displacement. The functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio is as follows: In the formula, the subscript ω, Ω, t These represent the rotor's natural frequency, rotational speed, and time, respectively; subscripts. r、l , E, ρ These represent the cross-sectional radius, length, elastic modulus, and density of the shaft, respectively; the superscript 's' indicates the shaft. The mathematical expression for the similarity ratio of the vibration displacements is: In the formula, and The displacement of the axis of rotation along the x and y directions; e This is the turntable eccentricity.
4. The method for designing a similar test model of a rotor system considering gravitational acceleration distortion as described in claim 3, characterized in that, Before the step of calculating the experimental parameters according to a preset rule based on the similarity parameters, model material parameters, and the actual parameters of the target rotor system, the method further includes: Based on the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, and combined with the vibration displacement similarity ratio, the functional relationship between the critical rotational speed similarity ratio and the vibration displacement similarity ratio is determined. Based on the functional relationship between the critical speed similarity ratio and the vibration displacement similarity ratio, it is determined that when the preset condition is met, the value of the natural frequency similarity ratio is 1. The preset condition indicates that the critical speed and vibration displacement of the target rotor system and the similar test model corresponding to the target rotor system are consistent.
5. The method for designing a similar test model of a rotor system considering gravitational acceleration distortion as described in claim 1, characterized in that, The step of calculating experimental parameters according to preset rules based on the similarity parameters, model material parameters, and actual parameters of the target rotor system includes: Substituting the value of the natural frequency similarity ratio into the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio, we obtain the first formula; Substituting the preset formula representing the relationship between the similarity ratio of the shaft length and the similarity ratio of the shaft radius in the preset rules into the first formula, we obtain the second formula; The similarity ratio of the material parameters is determined based on the model material parameters and the actual parameters of the target rotor system. The similarity ratio of the material parameters and the similarity ratio of the designed shaft length are then substituted into the second formula to calculate the similarity ratio of the shaft radius. The relationship parameter is then used as the experimental parameter.
6. The method for designing a similar test model of a rotor system considering gravitational acceleration distortion as described in claim 1, characterized in that, The step of determining the similarity parameters of the substructures on the target rotor system according to the preset similarity relationship further includes: Based on the equations of motion of the rotating shaft and Rayleigh beam theory, we can obtain the following simultaneous equations: Using equation analysis, the simultaneous equations are transformed into the objective equation: Based on the relationship between rotational speed and time, the similarity relationship between rotational speed and time in the similarity parameters is obtained as follows: Based on the objective equation and the similarity relationship between rotational speed and time, the similarity relationship between displacement and eccentricity in the similarity parameters is obtained: Based on the preset similarity relationship, the similarity ratio of the turntable's unit mass among the similarity parameters is determined as follows: 。 7. The method for designing a similar test model of a rotor system considering gravitational acceleration distortion as described in claim 6, characterized in that, The step of determining the similarity parameters of the substructures on the target rotor system according to the preset similarity relationship also includes: The similarity ratio of the polar moments of inertia of the turntable can be expressed as: For length of l s Based on the similarity ratio of the unit mass of the turntable, the similarity ratio of the mass of the turntable in the similarity parameters is obtained as follows: By simultaneously solving the objective equations, the similarity relationship between rotational speed and time, the similarity ratio of vibrational displacement, and the similarity ratio of shaft mass, the length of the similarity parameters is obtained. l s The similarity ratio of the polar moments of inertia of the axis of rotation is: Based on the preset similarity relationship, the similarity ratio of the turntable's outer diameter and thickness in the similarity parameters is obtained: 。 8. The method for designing a similar test model of a rotor system considering gravitational acceleration distortion as described in claim 7, characterized in that, The step of determining the similarity parameters of the substructures on the target rotor system according to the preset similarity relationship also includes: Using equation analysis, the motion equations of the support structure are transformed into similarity relationships of the support structure: Substituting the pre-defined similarity relationship and the similarity ratio of the shaft mass into the similarity relationship of the support structure, we obtain the simultaneous equations of the support structure: Based on the simultaneous equations of the support structure and the similarity ratio of the unit mass of the turntable, the similarity ratio of the support damping in the similarity parameters is obtained: The similarity ratio of the support stiffness in the similarity parameters is obtained by solving the simultaneous equations of the support structure and the functional relationship between the natural frequency similarity ratio and the rotational speed similarity ratio: 。