Oil-film-free elastic ring and linear and nonlinear dynamic characteristic design method thereof

Abstract

The invention discloses an oil-film-free elastic ring and a linear and nonlinear dynamic characteristic design method thereof. The method comprises the following steps: firstly, determining stiffness demand values of fulcrums according to critical rotating speed requirements, designing an initial structure of the elastic ring according to the stiffness demand values of the fulcrums, and performing linear and nonlinear stiffness analysis on the initial structure; then critical rotating speed analysis and nonlinear rigidity sensitivity analysis during nonlinear rigidity of the elastic ring are carried out, and secondary structural design of the elastic ring is carried out according to sensitive factors; and finally, carrying out second-time structure nonlinear rigidity analysis and dynamic characteristic analysis, and if the requirements are not met, carrying out repeated iteration until the requirements are met, and determining a final structure scheme of the elastic ring. Linear and nonlinear stiffness effects are comprehensively considered, structural parameters of the elastic ring are optimized, it is ensured that dynamic characteristics of the elastic ring within the working rotating speed range meet design requirements, the problems of critical rotating speed drifting and vibration are avoided, and the design precision and operation stability of a rotor system are improved.

Description

Technical Field

[0001] The present invention belongs to the field of rotor dynamics of aero-engines and gas turbines, and relates to the optimization design of the dynamic characteristics of a rotor support system. In particular, it relates to an oil-free elastic ring and a design method for its linear and nonlinear dynamic characteristics. By comprehensively considering the linear stiffness and contact nonlinear stiffness of the oil-free elastic ring, it is ensured that the dynamic characteristics of the rotor system meet the design requirements under different stiffness conditions. Background Art

[0002] The rotor dynamics design of an aero-engine is one of the core technologies in aero-engine design. One of the key technologies in rotor dynamics design is the critical speed design. In order to avoid the critical speed falling into the main operating speed range as much as possible, elastic supports are usually arranged at the support positions. By adjusting the stiffness of the elastic supports, the natural frequency of the rotor system is changed, thereby adjusting the critical speed. The elastic ring is one of the commonly used elastic supports in current aero-engines. It is located between the outer ring of the bearing and the bearing housing. The elastic ring is provided with circumferentially uniformly staggered inner and outer protrusions. Its main function is to absorb and dissipate the rotor vibration energy through elastic deformation, thereby reducing the vibration transmitted to the casing. A typical elastic ring structure is as Figure 1 shown.

[0003] The applications of the elastic ring in aero-engines include those with oil film and without oil film. Generally, for medium and long-life engines, the bearings are lubricated with lubricating oil, and correspondingly, lubricating oil is introduced onto the elastic ring to form an elastic ring squeeze film damper. Compared with a pure squeeze film damper without an elastic ring, since the protrusions of the elastic ring divide the squeeze film into many cavities, it is generally considered that the nonlinear effect of the elastic ring squeeze film damper is not strong, and the elastic ring is designed according to its linear stiffness during critical speed design.

[0004] For short-life engines, the bearings are not lubricated with lubricating oil, and the corresponding elastic ring is also an oil-free elastic ring, which avoids the problem of oil film nonlinearity. However, since the geometric dimensions between the oil-free elastic ring and the outer ring of the bearing and the bearing housing are transition fits, the inner and outer protrusions of the elastic ring are in direct contact with the outer ring of the bearing and the bearing housing, and the contact nonlinear problem is inevitable and more prominent than that of the oil film elastic ring. Therefore, when designing the dynamic characteristics of the oil-free elastic ring, not only the linear stiffness but also the contact nonlinear stiffness must be considered to ensure that the critical speeds under both linear and nonlinear stiffness meet the requirements.

[0005] The traditional elastic ring design method, taking the simplified design method of elastic ring support structure stiffness design disclosed in Chinese invention patent application CN114638059A as an example, realizes fast and efficient calculation by designing a simplified model of the elastic ring, but it mainly focuses on the calculation and optimization of linear stiffness, and does not fully consider the contact nonlinear stiffness problem of the oil-free elastic ring. This method is acceptable in the application of oil-film elastic ring, but it will bring large errors in the application of oil-free elastic ring. Due to the existence of contact nonlinearity, the actual stiffness of the oil-free elastic ring will change significantly with the change of load, resulting in the drift of the natural frequency and critical speed of the rotor system. If only linear stiffness is calculated during design, the actual critical speed may fall within the working speed range. In addition, during the working process of the oil-free elastic ring, its nonlinear stiffness characteristics are closely related to a variety of structural parameters (including the number of bosses, boss width, boss height, elastic ring thickness, inner and outer boss gaps, etc.). The interaction between these parameters is complex and difficult to predict and analyze by simple linear superposition principle, resulting in a large deviation between the design results and the actual working state.

[0006] In summary, the dynamic design of existing oil-free elastic rings still faces many challenges in nonlinear stiffness optimization. Therefore, how to comprehensively consider the linear and nonlinear stiffness effects in the design process of elastic rings and reasonably adjust the structural parameters to ensure that the critical speed is away from the main working speed area and reduce the vibration risk is a technical problem that needs to be solved urgently in the field of rotor dynamics design of aero engines and gas turbines. Summary of the invention

[0007] 1. Purpose of the invention In view of the above-mentioned defects and shortcomings in the dynamic characteristics design of the oil-free film elastic ring structure for aircraft engines or gas turbines, the present invention aims to provide an oil-free film elastic ring and a linear and nonlinear dynamic characteristics design method thereof. First, the linear stiffness design and nonlinear stiffness analysis of the elastic ring are performed according to the fulcrum stiffness requirements, and then the nonlinear stiffness sensitive factors of the elastic ring are analyzed. Based on this, the secondary structure design and dynamic characteristics analysis of the elastic ring are performed, so that the dynamic characteristics of both linear and nonlinear stiffness meet the requirements.

[0008] (II) Technical solution In order to achieve the purpose of the invention and solve the technical problems, the present invention adopts the following technical solutions: The first invention object of the present invention is to provide a linear and nonlinear dynamic characteristics design method for an oil-free elastic ring, which is used to optimize the dynamic characteristics of an oil-free elastic ring to improve system stability and reduce critical speed drift caused by nonlinear stiffness. The main implementation steps of the method are as follows: SS1. Determine the stiffness characteristics and stiffness requirements of each support point: Establish a finite element model for rotor dynamics analysis that includes a rotor, bearings, and a support structure according to the structure of the rotor system. Determine the required critical speed value based on the operating speed range, and determine the stiffness characteristics and required stiffness values of each support point through critical speed calculation and analysis. SS2. Initial structural design of the linear stiffness of the elastic ring: According to the determined elastic support points and their required stiffness values, calculate the linear stiffness of the elastic ring using the formula method, and accordingly determine the initial structure and geometric parameters of the elastic ring. SS3. Linear and nonlinear stiffness analysis of the initial structure of the elastic ring: Based on the determined initial structure and geometric parameters, establish a finite element model of the elastic ring assembly that includes the elastic ring, the outer ring of the bearing, and the bearing housing, and conduct linear and nonlinear stiffness analysis of the initial structure of the elastic ring. SS4. Critical speed analysis under the nonlinear stiffness of the elastic ring: Keep the stiffness of each rigid support point of the rotor system unchanged, import the nonlinear stiffness characteristics of the elastic ring into the finite element model for rotor dynamics analysis, analyze the critical speed of the rotor under the nonlinear stiffness of the elastic ring, and determine whether it meets the design requirements of maintaining a specified margin from the operating speed. If not, further optimize the design. SS5. Analysis of sensitive factors of the nonlinear stiffness of the elastic ring: Change the relevant structure and geometric parameters of the elastic ring, conduct analysis of sensitive factors and nonlinear stiffness of the elastic ring, and determine the degree and law of the influence of each parameter on the nonlinear stiffness of the elastic ring. SS6. Secondary structural optimization design of the oil-free elastic ring: According to the results of the nonlinear sensitivity factor analysis, conduct a second structural design of the elastic ring, adjust its structure and geometric parameters, reduce the nonlinear stiffness, and increase the threshold speed at which the nonlinear stiffness occurs. SS7. Stiffness analysis and dynamic characteristic analysis of the secondary structure: For the second structure of the elastic ring, repeat step SS3 to conduct linear and nonlinear stiffness analysis, and import its nonlinear stiffness characteristics into the finite element model for rotor dynamics analysis. Repeat step SS4 to conduct dynamic characteristic analysis, and verify whether the critical speeds under linear and nonlinear stiffness both meet the design requirements. SS8. Iterative optimization and determination of the final structural scheme: If the second structure still does not meet the design requirements, adjust the parameters and repeatedly iterate steps SS6~SS7 until the dynamic characteristics under linear and nonlinear stiffness both meet the requirements, and determine the final structural scheme of the elastic ring.

[0009] The second object of the present invention is to provide an oil-free elastic ring obtained based on the above linear and nonlinear dynamic characteristic design method.

[0010] (III) Technical effects Compared with the prior art, the oil-free film elastic ring and its linear and nonlinear dynamic characteristic design method of the present invention have the following beneficial and remarkable technical effects: (1) When designing the dynamic characteristics of the oil-free film elastic ring of the present invention, not only the linear stiffness of the oil-free film elastic ring is considered, but also the nonlinear stiffness is considered. When the linear and nonlinear stiffnesses of the oil-free film elastic ring are considered, the dynamic characteristics all meet the requirements. This avoids the problem that in conventional design, only linear stiffness is considered in the working process, but nonlinear characteristics appear, and the nonlinearity causes the actual critical speed to drift into the main working speed region, resulting in large vibrations in the main working speed region.

[0011] (2) By adopting the method of the present invention, the design accuracy of the rotor critical speed is high, the coincidence degree with the actual critical speed is better, the probability of large vibrations in the main working speed region is small, and the operation stability and reliability of the rotor system are improved. This design method has strong implementability and strong engineering adaptability, and can directly guide the engineering design of similar structures of aero-engines and gas turbines, and has important engineering application value.

[0012] (3) In the process of dynamic design of the oil-free film elastic ring of the present invention, a nonlinear stiffness optimization mechanism is innovatively introduced, which not only improves the dynamic performance of the elastic ring, but also effectively reduces the safety hazards brought by the critical speed drift, enhances the reliability of the engine and gas turbine rotor systems, and provides technical support for the design and optimization of high-performance rotating machinery. Description of the drawings

[0013] Figure 1 is a schematic structural diagram of an elastic ring squeeze film damper; Figure 2 is a flow chart of the linear and nonlinear dynamic characteristic design of the oil-free film elastic ring; Figure 3 is a schematic structural diagram of a rotor; Figure 4 is a schematic diagram of a finite element model of an elastic ring; Figure 5 is a diagram showing the relationship between the stiffness of the elastic ring and the whirling displacement; Figure 6 is a non-linear comparison diagram of the stiffness of the elastic ring. Detailed implementation manners

[0014] In order to better understand the characteristics and engineering applicability of the present invention, the linear and nonlinear dynamic characteristic design method of the oil-free film elastic ring provided by the present invention will be described in more detail according to the Figure 2 shown process. The described embodiments are part of the embodiments of the present invention, rather than all embodiments, and are intended to explain the present invention and should not be construed as a limitation of the present invention.

[0015] As shown in Figure 2 Figure , the oil-free film elastic ring linear and nonlinear dynamic characteristic design method provided by the embodiment of the present invention mainly includes the following steps when implemented: SS1. Determine the stiffness characteristics and stiffness requirement values of each fulcrum: According to the structure of the rotor system, a finite element model for rotor dynamics analysis including the rotor, bearings, and support structure is established. The schematic diagram of the rotor structure is shown in Figure 3 . Determine the critical speed requirement value according to the operating speed range of the rotor system, and determine the stiffness characteristics and stiffness requirement values of each fulcrum through critical speed calculation and analysis. Preferably, when determining the critical speed requirement value, comprehensively consider the operating speed range, general long-term operating speed, rated operating speed, and the safety margin requirement between the critical speed and the operating speed. The safety margin between the critical speed and the operating speed is determined according to 15% of the operating speed value, that is, the critical speed needs to meet less than 85% of the operating speed.

[0016] More specifically, for a rotor system with a long-term operating speed above 30000 r / min, considering a 15% margin, the critical speed needs to be controlled below 25500 r / min. According to the critical speed and the stator bearing structure, extract the first three natural frequencies of the rotor system through finite element modal analysis, and combine with the Campbell diagram to determine the separation margin between the critical speed and the operating speed. Finally, it is determined that the No. 1 fulcrum is an elastic support with a stiffness of 2 10 7 N / m; the No. 2 main bearing fulcrum is a rigid support with a fulcrum stiffness of 6 10 7 N / m; the No. 3 fulcrum is an elastic support with a stiffness of 3.6 10 6 N / m.

[0017] SS2. Initial structure design of the linear stiffness of the elastic ring: According to the determined elastic fulcrum and its stiffness requirement value, calculate the linear stiffness of the elastic ring using the stiffness design formula, and determine the initial structure and geometric parameters of the elastic ring accordingly. The initial structure design of the linear stiffness of the oil-free film elastic ring includes determining the following structure and geometric parameters: the number of bosses n (affecting the contact area and local stiffness), the width of the boss a (determining the overall stiffness level), the thickness of the elastic ring h (affecting the overall elastic deformation ability), the height of the boss s (the demarcation point between linear and nonlinear stiffness, and its increase will raise the threshold speed of stiffness nonlinearity), the root fillet diameter d (reducing local stress concentration), the inner diameter of the elastic ring D 1 and the outer diameterD 2 (determining the assembly state and initial stress distribution) and the fit clearance between the boss and the outer ring of the bearing and the bearing housing (affecting the contact state and the nonlinear characteristics of stiffness).

[0018] Based on the above method, according to the determined fulcrum stiffness value, the basic parameters of the above-mentioned No. 1 elastic ring determined by using the conventional stiffness design formula are as follows: the number of bosses n = 8, the width of the boss a = 4 mm, the thickness of the elastic ring h = 1.1 mm, the height of the boss s = 0.2 mm, the root fillet diameter d = φ10 mm, the inner diameter D 1 = φ55 mm, the outer diameter D 2 = φ58 mm, and the fit clearances between the inner and outer bosses of the elastic ring and the inner and outer rings are zero.

[0019] SS3. Linear and nonlinear stiffness analysis of the initial structure of the elastic ring: Based on the determined initial structure and geometric parameters, a finite element model of the elastic ring assembly including the elastic ring, the outer ring of the bearing, and the bearing housing is established to conduct linear and nonlinear stiffness analysis of the initial structure of the elastic ring.

[0020] Preferably, the method for establishing the finite element model of the elastic ring assembly is as follows: three-dimensional solid elements are used to model the elastic ring, the outer ring of the bearing, and the bearing housing, and contact pairs are set to simulate the contact nonlinearity between the elastic ring and the outer ring of the bearing and the bearing housing; in the finite element analysis, by applying different magnitudes of whirling displacements to the elastic ring, the corresponding reaction forces are calculated to obtain the linear and nonlinear stiffnesses of the elastic ring under different whirling displacements, and the variation relationship of the elastic ring stiffness with the whirling displacement is obtained.

[0021] Further, the linear stiffness analysis is carried out based on the condition that the whirling displacement is less than the height of the boss. When the whirling displacement is less than the height of the boss, the elastic ring exhibits linear stiffness characteristics; the nonlinear stiffness analysis is carried out based on the condition that the whirling displacement is greater than or equal to the height of the boss. When the whirling displacement is greater than or equal to the height of the boss, the elastic ring stiffness exhibits nonlinear characteristics.

[0022] Based on the above method, a finite element analysis model of the No. 1 elastic ring is established, as shown in Figure 4 . When the whirling displacement is less than the height of the boss of 0.2 mm, the stiffness of the elastic ring is linear stiffness. Therefore, any value within the range of 0 - 0.18 mm is selected as the whirling displacement value, and the calculated linear stiffness of the elastic ring is 2 10 7 N / m. When the whirling displacement is greater than the height of the boss of 0.2 mm, the contact between the boss and the inner and outer rings shows nonlinearity, so the nonlinear stiffness of the elastic ring also shows up. The variation relationship of the elastic ring stiffness with the whirling displacement is shown inFigure 5 , from Figure 5 It can be seen that when the whirling displacement approaches 0.2 mm, the nonlinear stiffness of the elastic ring gradually emerges. This is because when the whirling displacement approaches the boss height, the boss begins to contact the inner and outer rings, resulting in an increase in the contact area and a rapid increase in stiffness. When the whirling displacement is greater than 0.2 mm, the contact between the boss and the inner and outer rings becomes closer, and the stiffness of the elastic ring increases rapidly.

[0023] SS4. Analysis of critical speed under the nonlinear stiffness of the elastic ring: Keeping the stiffness of each rigid support point of the rotor system unchanged, introducing the nonlinear stiffness characteristics of the elastic ring into the finite element model of rotor dynamics analysis, analyzing the critical speed of the rotor under the nonlinear stiffness of the elastic ring, and judging whether it meets the design requirements of maintaining a specified margin from the operating speed. If not, further optimize the design. Preferably, the method for analyzing the critical speed under the nonlinear stiffness of the elastic ring is as follows: In the finite element model of rotor dynamics, keep the stiffness of the rigid support points unchanged, gradually increase the stiffness value of the elastic ring, calculate the corresponding critical speed, and judge whether it meets the design requirements of maintaining a 15% margin from the operating speed. If the margin of the critical speed is insufficient, it is necessary to further optimize the structure of the elastic ring.

[0024] Based on the above method, using the finite element analysis model of rotor dynamics, keep the stiffness of the 2nd and 3rd support points unchanged and increase the stiffness of the 1st support point. When the stiffness of the 1st support point increases to 3 10 7 N / m, when the corresponding whirling displacement is 0.195 mm, the critical speed is 27312 r / min, and the margin from the long-term operating speed of 30000 r / min is 9%; when the stiffness of the 1st support point increases to 4 10 7 N / m, when the corresponding whirling displacement is 0.2 mm, the critical speed is 29462 r / min, and the margin from the long-term operating speed of 30000 r / min is 2%. The margin is less than 15% and does not meet the critical speed design requirements.

[0025] SS5. Analysis of sensitive factors for the nonlinear stiffness of the elastic ring: Change the relevant structure and geometric parameters of the elastic ring, conduct analysis of sensitive factors for the nonlinear stiffness of the elastic ring and nonlinear stiffness analysis, and determine the influence degree and law of each parameter on the nonlinear stiffness of the elastic ring. Preferably, the parameters for the analysis of sensitive factors for the nonlinear stiffness of the elastic ring include the boss clearance, boss width, boss height, elastic ring thickness, and / or the number of bosses. By changing a single parameter while keeping other parameters unchanged, then conduct nonlinear stiffness analysis of the elastic ring, compare the variation relationship of the elastic ring stiffness with the whirling displacement under different parameter conditions, and determine the influence law and sensitivity degree of each parameter on the nonlinear stiffness characteristics of the elastic ring.

[0026] Since the stiffness nonlinearity of the oil-free film elastic ring is caused by contact, changing the contact state between the inner and outer bosses and the inner and outer rings of the elastic ring can change the stiffness nonlinearity. The factors affecting the contact state include: boss clearance, boss width, number of bosses, etc. Keeping the number of bosses unchanged: ① Analyzed the stiffness nonlinearity of the elastic ring with a width a = 4 mm and with and without clearance between the inner and outer bosses; ② Analyzed the stiffness nonlinearity of the elastic ring with a width a = 2 mm and with and without clearance between the inner and outer bosses. Among them, for the case with clearance, the outer boss clearance is 0.02 mm and the inner boss clearance is 0.015 mm. The comparison of the stiffness nonlinearity in the four cases is shown in Figure 6 .

[0027] It can be seen from Figure 6 that: (a) For the same boss width, the whirling displacement threshold value for the occurrence of stiffness nonlinearity with clearance is larger than that without clearance. Since the whirling displacement is positively correlated with the rotational speed, that is, the corresponding stiffness nonlinearity threshold rotational speed is higher; (b) With or without clearance, the linear stiffness and nonlinear stiffness of the boss width of 2 mm are lower than those of 4 mm, and the stiffness nonlinearity threshold rotational speed corresponding to the boss width of 2 mm is higher than that of 4 mm; (c) The stiffness nonlinearity threshold rotational speed is the highest for the boss width of 2 mm with clearance, and the lowest for the boss width of 4 mm without clearance.

[0028] SS6. Secondary structural optimization design of the oil-free film elastic ring: According to the results of the nonlinear sensitivity factor analysis, the second structural design of the elastic ring is carried out, and its structure and geometric parameters are adjusted to reduce the nonlinear stiffness and increase the threshold rotational speed at which the nonlinear stiffness occurs.

[0029] Preferably, the optimization direction of the second structural design of the elastic ring is: by reducing the boss width and increasing the clearance between the inner and outer bosses of the elastic ring and the bearing outer ring and the bearing housing, the stiffness value when the nonlinear stiffness of the elastic ring occurs is made as small as possible, and the threshold rotational speed at which the nonlinear stiffness occurs is made as high as possible, so that the critical rotational speed of the elastic ring under the condition of nonlinear stiffness can still meet the design requirements of maintaining a sufficient margin from the operating rotational speed.

[0030] Based on the above method, the stiffness nonlinearity of the oil-free film elastic ring is inevitable. In order to ensure that when the stiffness nonlinearity occurs, the critical rotational speed is below 30,000 r / min and there is a certain margin, it is necessary that when the nonlinear stiffness occurs, the stiffness is as small as possible and the nonlinear stiffness threshold rotational speed is as high as possible. Therefore, the boss width is changed from 4 mm to 2 mm, and the clearance-free state between the boss and the inner and outer rings is changed to a clearance of 0.02 mm between the outer boss and the outer ring and a clearance of 0.015 mm between the inner boss and the inner ring, and the others remain unchanged. The selection of these parameter values is to reduce the stiffness of the elastic ring and increase the threshold rotational speed at which the nonlinear stiffness occurs.

[0031] SS7. Secondary structure stiffness analysis and dynamic characteristic analysis: Repeat steps SS3 for the second structure of the elastic ring to perform linear and nonlinear stiffness analyses, and import its nonlinear stiffness characteristics into the finite element model for rotor dynamics analysis. Repeat step SS4 to perform dynamic characteristic analysis to verify whether the critical speeds under linear and nonlinear stiffnesses both meet the design requirements.

[0032] Preferably, the dynamic characteristic analysis of the second structure of the elastic ring includes: analyzing the critical speed corresponding to the linear stiffness of the elastic ring and its margin from the operating speed; analyzing the nonlinear stiffness and the corresponding critical speed range within the whirling displacement range close to and exceeding the boss height of the elastic ring, and calculating the margins of these critical speeds from the operating speed; and determining whether these margins all meet the design requirements.

[0033] Based on the above method, after the structure of the elastic ring is changed, the linear stiffness of the elastic ring is 1.1 10 7 N / m, the corresponding critical speed is 19600 r / min, and the margin from 30000 r / min is 35%, meeting the requirements. The nonlinear stiffness is as Figure 6 shown. When the whirling displacement of the elastic ring is 0.195 - 0.22 mm, the nonlinear stiffness is (1.2 - 2.3) 10 7 N / m, the corresponding critical speeds are 21007 - 25370 r / min, and the margin from 30000 r / min is 15%, meeting the requirements. For the elastic ring with no clearance relative to the boss width of 4 mm, the critical speeds at the whirling displacement of 0.195 - 0.2 mm are 27312 - 29462 r / min, and the critical speeds are reduced by approximately 4000 - 6000 r / min.

[0034] SS8. Iterative optimization and determination of the final structure scheme: If the second structure still does not meet the design requirements, adjust the parameters and repeatedly iterate steps SS6 - SS7 until the dynamic characteristics under both linear and nonlinear stiffnesses meet the requirements, and determine the final structure scheme of the elastic ring.

[0035] In summary, the present invention clarifies the design method for the linear and nonlinear dynamic characteristics of the oil-free elastic ring. In order to reduce the stiffness nonlinearity of the oil-free elastic ring, starting from two aspects of increasing the clearance between the inner and outer bosses of the elastic ring and reducing the boss width to decrease the stiffness of the elastic ring, the threshold value of the nonlinear stiffness occurrence speed is increased, the nonlinear stiffness and the corresponding critical speed when the whirling displacement is near 0.2 mm of the boss height are reduced, so that a certain margin is maintained between the critical speed and the operating speed.

[0036] Through the above embodiments, the object of the present invention is fully and effectively achieved. Those skilled in the art can understand that the present invention includes but is not limited to the content described in the drawings and the above specific embodiments. Although the present invention has been described with respect to the currently considered most practical and preferred embodiments, it should be understood that the present invention is not limited to the disclosed embodiments, and any modifications that do not deviate from the functional and structural principles of the present invention will be included within the scope of the claims.

Claims

1. A method for designing linear and nonlinear dynamic characteristics of an oil-free elastic ring, characterized in that: The implementation steps of this method include: SS1. Establish a rotor dynamics analysis finite element model including the rotor, bearings and support structure according to the structure of the rotor system, determine the critical speed requirement value according to the operating speed range, and determine the stiffness characteristics and stiffness requirement value of each support point through critical speed calculation and analysis; SS2. According to the determined elastic support points and their stiffness requirements, the linear stiffness of the elastic ring is calculated by formula method, and the initial structure and geometric parameters of the elastic ring are determined accordingly; SS3. Based on the initial structure and geometric parameters, a finite element model of the elastic ring assembly including the elastic ring, bearing outer ring and bearing seat is established to perform linear and nonlinear stiffness analysis of the initial structure of the elastic ring; SS4. Keep the stiffness of each rigid support unchanged, import the nonlinear stiffness characteristics of the elastic ring into the rotor dynamics analysis finite element model, analyze the rotor critical speed under the nonlinear stiffness of the elastic ring, and determine whether it meets the design requirement of maintaining a specified margin with the operating speed. If not, further optimize the design; SS5. Change the relevant structure and geometric parameters of the elastic ring, analyze the sensitive factors and nonlinear stiffness of the elastic ring, and determine the influence degree and law of each parameter on the nonlinear stiffness of the elastic ring; SS6. According to the analysis results of nonlinear sensitive factors, the elastic ring is redesigned to adjust its structure and geometric parameters, reduce the nonlinear stiffness and increase the threshold speed at which the nonlinear stiffness occurs; SS7. Repeat step SS3 for the second structure to perform linear and nonlinear stiffness analysis, and import its nonlinear stiffness characteristics into the rotor dynamics analysis finite element model. Repeat step SS4 to perform dynamic characteristics analysis to verify whether the critical speed under linear and nonlinear stiffness meets the design requirements; SS8. If the second structure still does not meet the design requirements, adjust the parameters and iterate steps SS6~SS7 repeatedly until the dynamic characteristics under linear and nonlinear stiffness meet the requirements and the final structural solution of the elastic ring is determined.

2. The linear and nonlinear dynamic characteristics design method of an oil-free elastic ring according to claim 1, characterized in that: In the above step SS1, when determining the critical speed demand value, the operating speed range, the general long-term operating speed, the rated operating speed and / or the safety margin requirements between the critical speed and the operating speed are comprehensively considered, wherein the safety margin between the critical speed and the operating speed is determined according to 15% of the operating speed value, and the critical speed must be less than 85% of the operating speed.

3. The linear and nonlinear dynamic characteristics design method of an oil-free elastic ring according to claim 1, characterized in that: In the above step SS2, the initial structural design of the linear stiffness of the oil-free elastic ring includes determining the following structural and geometric parameters: the number of bosses n , Boss width a , elastic ring thickness h , Boss height s , Root fillet diameter d , Inner diameter of elastic ring D 1. Elastic ring outer diameter D 2 And the fitting clearance between the boss, the bearing outer ring and the bearing seat.

4. The method for designing linear and nonlinear dynamic characteristics of an oil-free elastic ring according to claim 1, characterized in that: In the above step SS3, the method for establishing the finite element model of the elastic ring assembly is: using three-dimensional solid units to model the elastic ring, the bearing outer ring and the bearing seat, setting contact pairs to simulate the contact nonlinearity between the elastic ring and the bearing outer ring and the bearing seat; in the finite element analysis, by applying eddy displacements of different sizes to the elastic ring, calculating the corresponding support reaction force, obtaining the linear and nonlinear stiffness of the elastic ring under different eddy displacements, and obtaining the relationship between the elastic ring stiffness and the eddy displacement.

5. The method for designing linear and nonlinear dynamic characteristics of an oil-free elastic ring according to claim 4, characterized in that: In the above step SS3, the linear stiffness analysis is performed based on the condition that the vortex displacement is less than the boss height. When the vortex displacement is less than the boss height, the elastic ring exhibits linear stiffness characteristics; the nonlinear stiffness analysis is performed based on the condition that the vortex displacement is greater than or equal to the boss height. When the vortex displacement is greater than or equal to the boss height, the elastic ring stiffness exhibits nonlinear characteristics.

6. The linear and nonlinear dynamic characteristics design method of an oil-free elastic ring according to claim 1, characterized in that: In the above step SS4, the critical speed analysis method under the nonlinear stiffness of the elastic ring is: in the rotor dynamics finite element model, keep the rigid support stiffness unchanged, gradually increase the stiffness value of the elastic ring, calculate the corresponding critical speed, and judge whether it meets the design requirement of maintaining a 15% margin with the operating speed. If the critical speed margin is insufficient, the elastic ring structure needs to be further optimized.

7. The method for designing linear and nonlinear dynamic characteristics of an oil-free elastic ring according to claim 1, characterized in that: In the above step SS5, the parameters for analyzing the sensitive factors of the nonlinear stiffness of the elastic ring include boss gap, boss width, boss height, elastic ring thickness and / or boss number. By changing a single parameter while keeping other parameters unchanged, the nonlinear stiffness analysis of the elastic ring is performed, and the relationship between the change of the elastic ring stiffness and the eddy displacement under different parameter conditions is compared to determine the influence law and sensitivity of each parameter on the nonlinear stiffness characteristics of the elastic ring.

8. The method for designing linear and nonlinear dynamic characteristics of an oil-free elastic ring according to claim 1, characterized in that: In the above step SS6, the optimization direction of the second structural design of the elastic ring is: by reducing the boss width and increasing the fitting clearance between the inner and outer bosses of the elastic ring and the outer ring of the bearing and the bearing seat, the stiffness value of the elastic ring when the nonlinear stiffness occurs is as small as possible, and the threshold speed for the occurrence of nonlinear stiffness is as high as possible.

9. The method for designing linear and nonlinear dynamic characteristics of an oil-free elastic ring according to claim 1, characterized in that: In the above step SS7, the dynamic characteristics analysis of the second structure of the elastic ring includes: analyzing the critical speed corresponding to the linear stiffness of the elastic ring and its margin with the working speed; analyzing the nonlinear stiffness of the elastic ring within the eddy displacement range close to and exceeding the boss height and the corresponding critical speed range, and calculating the margins between these critical speeds and the working speed; judging whether these margins meet the design requirements.

10. An oil-free elastic ring, characterized in that: The structural design of the elastic ring is based on the linear and nonlinear dynamic characteristics design method of the oil-free elastic ring according to any one of claims 1 to 9.

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