A design method and structure for a dynamic vibration-absorbing superstructure for rotating machinery

Abstract

This invention discloses a design method and structure for a dynamic vibration-absorbing superstructure for rotating machinery, belonging to the field of vibration reduction in rotating machinery. One objective is to provide a design method for a dynamic vibration-absorbing superstructure for rotating machinery; another objective is to design a dynamic vibration-absorbing superstructure for rotating machinery based on the aforementioned design method. The implementation method of this invention involves designing the superstructure frame and oscillator using the design method, and optimizing parameters to achieve vibration reduction requirements in different frequency bands. The outermost ring of the frame is the part that generates the main elastic deformation, providing radial support stiffness. By changing the parameters of the outermost ring of the frame, the critical speed of the rotor can be adjusted. The oscillator, based on a dynamic vibration-absorbing mechanism, reduces rotor vibration and is mounted on the frame. This invention can be used not only for vibration suppression at the rotor's critical speed but also for vibration suppression at operating speeds, and also has the advantages of high load-bearing capacity, large inner-outer diameter ratio, simple structure, and flexible and easily adjustable vibration reduction frequency band.

Description

Technical Field

[0001] This invention relates to a design method and structure for a dynamic vibration-absorbing superstructure for rotating machinery, belonging to the field of vibration reduction in rotating machinery. Background Technology

[0002] The unbalanced response of rotating machinery not only causes vibration and noise but also affects the stability of the rotor system, leading to safety issues. Currently widely used traditional rotor vibration damping devices mainly include squeeze film dampers, elastic wave rings, rubber dampers, and dynamic vibration absorbers. Among these, squeeze film dampers suffer from drawbacks such as strong nonlinearity, high cost, high assembly precision requirements, the need for an additional oil supply system, and complex structure. Rubber dampers have low load-bearing stiffness, but their damping performance is difficult to predict accurately, making efficient active design for vibration attenuation frequencies impossible. While elastic wave rings have high load-bearing stiffness, they also suffer from low damping and poor damping predictability. Existing dynamic vibration absorbers for rotors generally have the disadvantages of large size, inability to adjust critical speeds, and the need for additional installation space due to their location outside the original bearing positions, which can also affect the rotor's dynamic characteristics. Furthermore, these devices primarily suppress rotor vibration at critical speeds but cannot effectively suppress rotor unbalanced responses at operating speeds.

[0003] When the rotor passes the critical speed, it will generate huge vibrations, which may damage the rotor. Therefore, the operating speed of the rotor should be as far away from the critical speed as possible. In current engineering, oil film dampers are often used to dampen and dissipate energy to help the rotor pass the critical speed, or elastic supports are used to reduce the rotor's critical speed, so that the rotor's operating speed is far away from the critical speed. Furthermore, using elastic supports can also reduce the vibration response of the rotor when it passes the critical speed. Therefore, the design of the rotor's radial support stiffness is also an important part of the rotor system design. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, one objective of this invention is to provide a design method for a dynamic vibration-absorbing superstructure for rotating machinery, and another objective is to obtain a dynamic vibration-absorbing superstructure for vibration reduction of rotating machinery using the aforementioned design method. This invention can adjust the critical speed of the rotor by designing the radial support stiffness, and it can be used not only for vibration suppression at the rotor's critical speed but also for vibration suppression at the rotor's operating speed. It also has advantages such as strong load-bearing capacity, large inner-outer diameter ratio, simple structure, and flexible and easy-to-adjust vibration reduction frequency band.

[0005] To achieve the above objectives, the present invention adopts the following technical solution.

[0006] This invention discloses a method for designing a dynamic vibration-absorbing superstructure for rotating machinery, comprising the following steps:

[0007] Step 1: Based on the bearing outer ring size and the assembly space requirements of the rotating machinery, determine the outer radius R1, inner radius R2, and axial width B of the superstructure frame.

[0008] Step 2: Based on the radial support stiffness requirements of the rotating machinery, the geometric parameters of the outermost ring of the frame are initially set, and the radial support stiffness of the frame is adjusted by optimizing the geometric parameters of the outermost ring of the frame; the geometric parameters include: the thickness t1 of the outermost ring of the frame and the width b1 of the outermost ring of the frame;

[0009] The radial support stiffness is calculated using the steady-state analysis method in CAE software: a fixed constraint is set on the outermost boss of the outermost ring of the frame, and a surface load excitation F1 in the same direction is applied to the mating surface of the frame and the outer ring of the bearing. After obtaining the frame displacement X1, the radial support stiffness of the frame is calculated using the formula F1 / X1.

[0010] The relationship between the radial support stiffness of the frame and the geometric parameters is as follows: the outermost ring thickness t1 of the frame is positively correlated with the radial support stiffness of the frame, and the outermost ring width b1 of the frame is positively correlated with the radial support stiffness of the frame.

[0011] Step 3: Based on the assembly space requirements and lightweight requirements, determine the number of oscillators and the mass size of each mass ring. The larger the mass ring, the better the vibration reduction effect and the wider the vibration reduction bandwidth.

[0012] Step 4: Establish a simplified rotor-bearing-superstructure dynamic model, as shown in the following formula:

[0013]

[0014]

[0015]

[0016]

[0017] …

[0018]

[0019] Where M, C, K, and F are the rotor's mass matrix, damping matrix, stiffness matrix, and load matrix, respectively; K1 is the bearing stiffness; m, c, and k are the mass matrix, damping matrix, and stiffness matrix of the superstructure frame; m j k j Let X be the mass matrix and stiffness matrix of the oscillator; x, x, x j For the displacement matrices of the rotor, superstructure, and oscillator;

[0020] Step 5: Based on the rotor-bearing-superstructure dynamic model obtained in Step 4, with minimizing the rotor displacement within the vibration reduction frequency band as the optimization objective, and the spring stiffness coefficients of each oscillator as design variables, a set of spring stiffness coefficients that meet the requirements are calculated using the parameter optimization module of the numerical analysis software. Combined with the mass size of the mass loop obtained in Step 3, the formula is used to... A set of natural frequencies of the oscillator is obtained;

[0021] As a preferred option, the GA toolbox provided by MATLAB was used for optimization to obtain a set of spring stiffness coefficients that meet the requirements.

[0022] Step Six: Initially set the geometric parameters of the elastic element. Then, based on the outer radius R1, inner radius R2, and axial width B of the superstructure frame obtained in Step One, the outermost ring thickness t1 and outermost ring width b1 obtained in Step Two, the number of oscillators and the mass of each mass ring obtained in Step Three, establish a finite element model of the superstructure. Optimize the geometric parameters of the elastic element using the finite element model of the superstructure so that the natural frequency of the superstructure oscillator is equal to the natural frequency obtained in Step Five. The geometric parameters of the elastic element include the elastic element thickness t2, elastic element width b2, and elastic element arc length l2.

[0023] Natural frequency The characteristic frequencies are calculated using the characteristic frequency analysis module in CAE software: fixed constraint boundary conditions are set for the outermost ring of the superstructure frame, and then characteristic frequency analysis is performed to obtain the natural frequencies of the superstructure oscillator; the relationship between the geometric parameters of the elastic element and the natural frequencies of the superstructure oscillator is as follows: the thickness t2 of the elastic element is positively correlated with the natural frequency of the superstructure oscillator, the width b2 of the elastic element is positively correlated with the natural frequency of the superstructure oscillator, and the arc length l2 of the elastic element is negatively correlated with the natural frequency of the superstructure oscillator;

[0024] Step 7: Based on the superstructure finite element model obtained in Step 6, set boundary conditions, and use the modal reduction method to convert the superstructure finite element model into a state space model, and verify the accuracy of the equivalent state space model until the error of the equivalent state space model is less than the preset accuracy requirement.

[0025] The boundary conditions for the superstructure finite element model are:

[0026] Set a fixed constraint on the outermost boss of the outermost ring of the frame;

[0027] The modal reduction method for the equivalent state-space model of the superstructure is as follows:

[0028] The main modes of the superstructure finite element model with boundary conditions are extracted, including characteristic frequencies and mode shapes, and then the decoupled equivalent state-space model of the superstructure in modal coordinates is obtained, which is shown in the following form:

[0029]

[0030] Among them, M T Let C be the equivalent mass matrix of the superstructure in modal coordinates. T K is the equivalent damping matrix of the superstructure in modal coordinates. T F is the equivalent stiffness matrix of the superstructure in modal coordinates. T Let be the equivalent load matrix of the superstructure in modal coordinates, and q be the equivalent displacement matrix of the superstructure in modal coordinates.

[0031] The modal equivalence method, also known as the modal superposition method, uses the undamped mode shapes of the system as a spatial basis. Through coordinate transformation, it decouples the original dynamic equations, solves several independent equations to obtain modal displacements, and then obtains the system response by superimposing the contributions of each mode. Since the contribution of each mode varies under different excitations, under a certain form of excitation, only a few main mode shapes need to be extracted to describe the response of the original system relatively accurately. If all mode shapes of the system are used, the relationship becomes exact rather than approximate.

[0032] The method for verifying the accuracy of the superstructure equivalent state-space model is as follows:

[0033] The frequency response of a superstructure finite element model within a specified frequency range is calculated using the direct method in CAE software.

[0034] In CAE software, the modal method is used to calculate the frequency response of an equivalent state-space model within a specified frequency range.

[0035] The simulation boundary conditions are as follows: a fixed constraint is set on the outermost boss of the outermost ring of the frame; a surface load excitation of the same direction and a specified frequency range (harmonic excitation in the modal method) is applied to the mating surface of the frame and the outer ring of the bearing; and then the frequency response is calculated. The surface load excitation corresponding to the modal method is harmonic excitation.

[0036] By extracting the average displacement of the mating surfaces of the frame and the outer ring of the bearing within a specified frequency range, and comparing the displacement X2 of the direct method with the displacement X3 of the modal method, if the error meets the requirements, the equivalent state space model meets the requirements, and step eight is executed; if the error does not meet the preset accuracy requirements, the number of main modes of the modal equivalent method is increased to reduce the error of the equivalent state space model until the error meets the preset accuracy requirements.

[0037] Step 8: Couple the state-space model obtained in Step 7 to the rotor-bearing-superstructure dynamic model in Step 4 to verify the effectiveness of the superstructure in suppressing the vibration of rotating machinery. If the vibration reduction optimization requirements are met, proceed to Step 9. If not, further adjust the geometric parameters of the elastic element and return to Step 7 until the vibration reduction design requirements are met.

[0038] The geometric parameters of the elastic element include the thickness t2, the width b2, and the arc length l2 of the elastic element.

[0039] Step Nine: Based on the outer radius R1, inner radius R2, and axial width B of the superstructure frame obtained in Step One, the outermost ring thickness t1 and outermost ring width b1 of the frame obtained in Step Two, the number of oscillators and the mass size of each mass ring obtained in Step Three, and the elastic element thickness t2, elastic element width b2, and elastic element arc length l2 obtained in Step Eight, a superstructure that meets the requirements for suppressing radial vibration is obtained.

[0040] This invention discloses a dynamic vibration-absorbing superstructure for rotating machinery, designed based on the aforementioned design method. The dynamic vibration-absorbing superstructure for rotating machinery is installed between the outer ring of a bearing and the base.

[0041] The dynamic vibration-absorbing superstructure includes a frame for load-bearing and several oscillators mounted on the frame. The rings extending from the left and right sides of the frame are used to mount the oscillators. The outermost ring of the frame is the part of the frame that generates the main elastic deformation. The inner and outer sides of the outermost ring of the frame contain the same number of alternating bosses. The bosses form an additional support point at the bottom and allow the outermost ring of the frame to generate elastic deformation.

[0042] The oscillator mainly consists of a mass ring and four orthogonally arranged elastic elements. The mass ring and the elastic elements are detachably connected; the oscillator and the frame are detachably connected.

[0043] Preferably, the detachable connection is a screw connection.

[0044] Preferably, the elastic element has mounting plates at both ends, which are detachably connected to the frame and the mass ring, such as by screws. The detachable connection between the frame and the mass ring allows for the replacement of different mass rings and elastic elements according to the vibration damping conditions, thereby flexibly adjusting the vibration damping frequency band. The main geometric parameters of the elastic element are: elastic element thickness t2, elastic element width b2, and elastic element arc length l2.

[0045] Furthermore, the mass ring has four orthogonally arranged grooves, the size of which is similar to that of the mounting plate, and it cooperates with the elastic element mounting plate to install the elastic element. Under the same conditions, the larger the mass of the mass ring, the better the vibration reduction effect.

[0046] Furthermore, the circular rings extending from the left and right sides of the frame are provided with four orthogonally arranged grooves. The size of the grooves is similar to that of the mounting plate and they cooperate with the elastic element mounting plate to install the vibrator.

[0047] Preferably, the outermost ring of the frame is provided with a damping layer on both the inner and outer sides, which can further reduce the vibration of the rotor through the damping energy dissipation mechanism.

[0048] Preferably, to ensure good consistency of the radial support stiffness of the frame in all directions, the number of bosses on one side should be greater than or equal to 1.

[0049] Beneficial results:

[0050] 1. The present invention discloses a design method for a dynamic vibration-absorbing superstructure for rotating machinery. The steps are simple and the calculation is convenient. It also takes into account the influence of the coupling between the rotor, bearing and superstructure, so that the dynamic vibration-absorbing superstructure obtained based on the design method has a better vibration suppression effect than the direct design of rotor vibration damper.

[0051] 2. Existing dynamic vibration absorbers for rotors directly use springs as the elastic element, which occupies a large space and is installed elsewhere outside the rotor bearing by means of suspension. This not only has an adverse effect on the dynamic response of the rotor, but also cannot adjust the rotor's critical speed. The dynamic vibration absorption superstructure for rotating machinery disclosed in this invention uses structural components to replace springs, which has a small volume and is directly installed between the bearing and the base, requiring no additional installation space, and can adjust the rotor's critical speed.

[0052] 3. Existing extrusion oil film dampers, elastic waveform rings, and rubber rings can only provide good vibration suppression in the frequency range near the rotor's critical speed, and their vibration suppression capability at the rotor's operating speed is relatively weak. The dynamic vibration absorption superstructure design method for rotating machinery disclosed in this invention is applicable not only to the frequency range near the critical speed but also to the frequency range near the rotor's operating speed, enabling the dynamic vibration absorption superstructure obtained based on the design method to effectively suppress vibrations near the rotor's operating speed.

[0053] 4. Existing extrusion oil film dampers, elastic wave rings, and rubber rings have the disadvantages of high price, poor vibration reduction effect, and low stiffness. The dynamic vibration absorption superstructure for rotating machinery disclosed in this invention uses conventional metals as its material, and the manufacturing and integration of each component are simple. Compared with the above three commonly used rotor vibration reduction devices, it has the advantages of low cost, good vibration reduction effect, and high stiffness. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the vibration-damping superstructure of Embodiment 1 of the present invention;

[0055] Figure 2 This is a schematic diagram of the framework structure of Embodiment 1 of the present invention;

[0056] Figure 3 This is a steady-state displacement diagram of the frame in Embodiment 1 of the present invention;

[0057] Figure 4 This is a schematic diagram of the mass ring structure in Embodiment 1 of the present invention;

[0058] Figure 5 This is a simplified theoretical model of the rotor-bearing-superstructure in Embodiment 1 of the present invention; wherein, Figure a is a dynamic model of the rotor system based on MATLAB; Figure b is a schematic diagram of the rotor system;

[0059] Figure 6 The results of the rotor system optimization using a genetic algorithm in Embodiment 1 of the present invention are shown in Figure a, which is the convergence diagram of the genetic algorithm; and Figure b is the displacement amplitude-frequency response curve of the rotor system.

[0060] Figure 7 This is a schematic diagram of the elastic element structure in Embodiment 1 of the present invention;

[0061] Figure 8 The modal shape diagram of the oscillator structure in Embodiment 1 of the present invention is shown.

[0062] Figure 9 This is a schematic diagram of the oscillator structure in Embodiment 1 of the present invention;

[0063] Figure 10 This is a comparison chart of the results of the direct method and the modal method in Embodiment 1 of the present invention;

[0064] Figure 11 The rotor displacement amplitude-frequency response curve of Embodiment 1 of the present invention, which includes a superstructure;

[0065] Figure 12 The rotor displacement amplitude-frequency response curves under different radial support stiffnesses in Embodiment 2 of the present invention are shown.

[0066] Figure 13 The steps of superstructure design method;

[0067] Figure 14 This is a rendering of the superstructure.

[0068] Among them, 1-superstructure frame, 2-outermost ring of frame, 3-protrusion, 4-circular ring, 5-mass ring, 6-elastic element, 7-oscillator. Detailed Implementation

[0069] In the description of this invention, it should be noted that the terms "upper," "lower," "left," "right," "inner," "outer," "vertical," and "horizontal," 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 this 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 this 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.

[0070] The present invention discloses a dynamic vibration-absorbing superstructure design method and structure for vibration reduction of rotating machinery. The left side of the accompanying drawings is defined as the front side, the right side as the rear side, the upper side as the upper side, the lower side as the lower side, the outside of the paper of the accompanying drawings as the left side, and the inside of the paper of the accompanying drawings as the right side. The directions of "front", "rear", "left", "right", "up" and "down" are determined accordingly.

[0071] Example 1

[0072] like Figure 1 As shown in the figure, this embodiment discloses a dynamic vibration-absorbing superstructure for rotating machinery, which is installed between the outer ring of the bearing and the base. It includes a frame 2 for bearing and two oscillators 7 installed on the frame, and the two oscillators 7 have the same parameters.

[0073] The circular rings 4 extending from the left and right sides of the frame 1 are provided with four orthogonally arranged grooves. The size of the grooves is similar to that of the mounting plate and is used to install the vibrator 7. The outermost ring 2 of the frame is the part of the frame 1 that generates the main elastic deformation. Its inner and outer sides contain 5 alternating protrusions 3.

[0074] In this example, the main design parameters of the outermost ring 2 of the frame are the thickness t1 and the width b1. By adjusting these two parameters, the radial support stiffness of the frame 1 can be adjusted.

[0075] The oscillator consists of a mass ring 5 and four orthogonally arranged elastic elements 6.

[0076] The inner side of the mass ring 5 has four orthogonally arranged grooves, the size of which is similar to that of the mounting plate, for mounting the elastic element 6.

[0077] To further reduce rotor radial vibration, this embodiment lays a damping layer with a structural damping of 0.2 on both sides of the outermost ring 1 of the superstructure frame.

[0078] In this example, the main design parameters of the elastic element 6 are thickness t2, width b2, and arc length l2. The stiffness of the elastic element 6 can be adjusted by adjusting these three parameters.

[0079] In this embodiment, the bearing model is 7011c angular contact ball bearing, and two bearings on one side are installed back to back. The shaft parameters are 20*800mm (radius*length). The rotor support stiffness requirement is 5e6 N / m. According to the calculation, the critical speed frequency of the rotor is 110Hz. It is required to reduce the unbalanced response at a working speed of 4200rpm / min and a frequency of 90Hz, and to minimize the assembly space.

[0080] In this embodiment, the frame 1 and the elastic element 6 are made of aluminum, and the mass ring 5 is made of steel. The material parameters are shown in Table 1.

[0081] Table 1 Material Parameters

[0082] aluminum 0.3 70 2700 steel 0.27 210 7850

[0083] The superstructure in this embodiment is designed through steps one through nine below, and the specific implementation steps are as follows:

[0084] Step 1: In this embodiment, based on the bearing outer ring size and the assembly space requirements of the rotating machinery, the outer radius R1 of the superstructure frame is determined to be 75mm, the inner radius of the superstructure frame is selected to be 45mm, and the axial width of the superstructure frame is 60mm; other dimensional parameters of the superstructure frame 1 can be reasonably designed, which has little impact on the superstructure function.

[0085] Step 2: In this embodiment, based on the requirement that the radial support stiffness of the rotating machinery is 5e6 N / m, the geometric parameters of the outermost ring of the frame are initially set as follows: outermost ring thickness t1 = 1mm, outermost ring width b1 = 60mm, and the outermost ring thickness t1 and outermost ring width b1 parameters are optimized to adjust the radial support stiffness of the frame.

[0086] The calculation method is as follows: steady-state simulation analysis is performed using the solid mechanics module in COMSOL Multiphysics 5.6 software. The simulation boundary is: a fixed constraint is set on the outer boss 3 of the outermost ring 2 of the frame, and a surface load excitation of 100N in the same direction is applied to the mating surface of the frame 1 and the outer ring of the bearing.

[0087] When parameters t1 = 1 mm and b1 = 60 mm, the static displacement of the frame is approximately 0.001 mm. The radial stiffness of the frame, calculated using the formula F / X, is approximately 1e8 N / m, which does not meet the requirements. Therefore, t1 and b1 need to be further reduced to meet the requirements for radial support stiffness.

[0088] When parameters t1 = 0.6 mm and b1 = 15 mm, the static displacement of the frame is approximately 0.02 mm. The radial stiffness of the frame, calculated using the formula F / X, is approximately 5e6 N / m, which meets the requirements. A schematic diagram of the frame structure is shown below. Figure 2 As shown, the steady-state analysis results are as follows: Figure 3 As shown.

[0089] Step 3: Based on the aforementioned requirement for minimal assembly space and the limitation of only one vibration damping frequency band, two identical oscillators 7 are selected and placed on either side of frame 1. Considering the superstructure's inner diameter of 90mm, axial width of 60mm, and lightweight requirements, the inner diameter of mass ring 5 is selected as 112mm, the outer diameter as 124mm, and the mass as approximately 0.26kg. Thus, the geometric and material parameters of the superstructure frame 1 and mass ring 5 are preliminarily determined. The mass of frame 1 is approximately 0.6kg, and the mass of a single mass ring 5 is approximately 0.26kg. Mass ring 5 is as follows... Figure 4 As shown;

[0090] Step 4: Establish a simplified rotor-bearing-superstructure dynamic model, such as... Figure 5 As shown, where Figure 5 'a' represents the rotor system dynamics model based on MATLAB. Figure 5 b is a schematic diagram of the rotor system.

[0091] The formula is shown below:

[0092]

[0093]

[0094]

[0095]

[0096] Where M, C, K, and F are the rotor's mass matrix, damping matrix, stiffness matrix, and load matrix; K1 is the bearing stiffness; m, c, and k are the mass matrix, damping matrix, and stiffness matrix of the superstructure frame 1; m1 and k1 are the mass matrix and stiffness matrix of the first oscillator, and m2 and k2 are the mass matrix and stiffness matrix of the second oscillator; X, x, x1, and x2 are the displacement matrices of the rotor, the superstructure, the first oscillator, and the second oscillator.

[0097] Step 5: Based on the dynamic model obtained in Step 4, minimizing the rotor displacement in the frequency range around 90Hz is the optimization objective. Using the spring stiffness coefficients of the two oscillators as design variables, optimization is performed using the GA toolbox provided in MATLAB. Two spring stiffness coefficients that meet the requirements are obtained, both approximately 8.2e4 N / m. Combined with the mass of a single mass ring 7 obtained in Step 3 (0.26 kg), the formula is used... The natural frequency of oscillator 7 should be approximately 89.5 Hz;

[0098] Among them, the optimization results using MATLAB's built-in GA toolbox are as follows: Figure 6 As shown, where Figure 6 a is the convergence graph of the genetic algorithm. Figure 6 b is the rotor system response diagram. It can be seen that when the superstructure has no oscillator, the first critical speed of the rotor is about 110Hz. When the superstructure contains an oscillator, the first critical speed of the rotor changes slightly, and the rotor imbalance response at 90Hz is effectively reduced, which meets the design requirements.

[0099] Step Six: Initially set the geometric parameters of elastic element 6 as follows: elastic element thickness t2 = 0.6 mm, elastic element width b2 = 2 mm, elastic element arc length l2 = 23 mm. A schematic diagram of elastic element 6 is shown below. Figure 7 As shown, based on the outer radius R1, inner radius R2, and axial width B of the superstructure frame obtained in step one, the outermost ring thickness t1 and outermost ring width b1 obtained in step two, and the number of oscillators and the mass of each mass ring obtained in step three, a finite element model of the superstructure is established, as follows. Figure 8 As shown. Based on this, the geometric parameters of the elastic element 6 are optimized so that the natural frequency of the superstructure oscillator 7 is equal to the natural frequency obtained in step five; the geometric parameters of the elastic element 6 are: elastic element thickness t2, elastic element width b2, and elastic element arc length l2;

[0100] The calculation method is as follows: the solid mechanics module in COMSOL Multiphysics 5.6 software is used to perform characteristic frequency simulation analysis. The simulation boundary is: set fixed constraint boundary conditions for the outermost boss 3 of the outermost ring 2 of the superstructure frame, and then perform characteristic frequency analysis to obtain the natural frequency of the superstructure oscillator 7.

[0101] When the parameters t2 = 0.6 mm, b2 = 2 mm, and l2 is approximately 23 mm, the radial modal frequency is approximately 48.7 Hz, which does not meet the requirements. Therefore, it is necessary to further increase t1 and b1, or decrease l2, to meet the characteristic frequency requirements of the oscillator 7.

[0102] When parameters t2 = 0.8 mm, b2 = 10 mm, and l2 is approximately 27 mm, the radial modal frequency is approximately 89.8 Hz, which meets the requirements. The characteristic frequency analysis results are as follows: Figure 8 As shown.

[0103] At this point, the geometric parameters of mass ring 5 and elastic element 6 have been preliminarily designed, meaning the oscillator has been preliminarily designed. A schematic diagram of oscillator 7 is shown below. Figure 9 As shown.

[0104] Step 7: Based on the superstructure finite element model obtained in Step 6, set boundary conditions, and use the modal reduction method to convert the superstructure finite element model into a state space model, and verify the accuracy of the equivalent state space model until the error is small enough.

[0105] Direct calculation method: Frequency domain analysis was performed using the solid mechanics module in COMSOL Multiphysics 5.6 software. The simulation boundary was: fixed constraint boundary conditions were set for the outer boss 3 of the outermost ring 2 of the superstructure frame. In order to further reduce vibration, a structural damping property of 0.2 was assigned to the outermost ring 2 of the superstructure frame. A surface load excitation of 100N in the X direction was applied to the mating surface between the frame 1 and the outer ring of the bearing.

[0106] The modal equivalence method is as follows: using the solid mechanics module in COMSOL Multiphysics 5.6 software, the first 14 modes of the superstructure finite element are extracted and "frequency domain, modal" analysis is performed. The simulation boundary is: fixed constraint boundary conditions are set for the outer boss 3 of the outermost ring 2 of the superstructure frame. In order to further reduce vibration, a structural damping property of 0.2 is assigned to the outermost ring 2 of the superstructure frame. A surface load harmonic excitation of 100N in the X direction is applied to the mating surface between the frame 1 and the outer ring of the bearing.

[0107] The results of direct method and modal method analysis are as follows Figure 10 As shown, the orange curve is the amplitude-frequency response curve of the modal method in the 0-150Hz range under the above boundary conditions, and the blue curve is the amplitude-frequency response curve of the direct method in the 0-150Hz range under the above boundary conditions. It can be seen that the errors of the modal method and the direct method are very small, and it can be considered that the extraction of 14 modes meets the requirements.

[0108] Step 8: Following Step 7, a 14th-order equivalent state-space model of the superstructure after modal order reduction was obtained. This model was coupled into the rotor-bearing-superstructure dynamic model from Step 4, and the effectiveness of the superstructure in suppressing vibrations in rotating machinery was verified. Figure 11 As shown, it can be seen that the superstructure obtained by this design method can effectively reduce the unbalanced response of the rotor at 90Hz near the critical speed of 110Hz, meeting the design requirements, and proceeding to step nine.

[0109] If the vibration reduction frequency band does not meet the requirements, if the vibration reduction frequency band is biased to the left, the natural frequency of the oscillator 7 should be slightly increased. At this time, t1 and b1 need to be further increased, or l2 needs to be decreased, and return to step seven until the optimization requirements are met; if the vibration reduction frequency band is biased to the right, the natural frequency of the oscillator 7 should be slightly decreased. At this time, t1 and b1 need to be further decreased, or l2 needs to be increased, and return to step seven until the optimization requirements are met.

[0110] Step Nine: Based on the outer radius R1 = 75mm, inner radius R2 = 45mm, and axial width B = 60mm of the superstructure frame obtained in Step One; the outermost ring thickness t1 = 0.6mm and outermost ring width b1 = 15mm obtained in Step Two; the number of oscillators 7 equals 2 and the mass of the two mass rings 5 ​​is 0.26kg obtained in Step Three; and the elastic element thickness t2 = 0.8mm, elastic element width b2 = 10mm, and elastic element arc length l2 = 27mm obtained in Step Eight, a superstructure capable of suppressing radial vibration is obtained.

[0111] It is understandable that those skilled in the art can set all the dimensional and material parameters of the arc-shaped unit cell according to actual needs to suit various vibration reduction requirements in different scenarios.

[0112] Example 2

[0113] This embodiment illustrates that a dynamic vibration-absorbing superstructure for rotating machinery of the present invention has the function of adjusting the critical speed of the rotor and has a positive significance in suppressing the unbalanced response of the rotor itself.

[0114] In this embodiment, the rotor-bearing-superstructure dynamic model established in Example 1 is used, where the high-stiffness rotor has a support stiffness of 5e6 N / m and the low-stiffness rotor has a support stiffness of 5e4 N / m, with other parameters remaining the same. Frequency response analysis is performed on the two rotor systems, and the results are as follows. Figure 12 As shown in the figure, the red curve represents a rotor with high radial support stiffness, and the blue curve represents a rotor with low radial support stiffness. It can be observed that in the frequency range of 70Hz-150Hz, under the same unbalanced excitation, the rotor with low radial support stiffness has a smaller unbalanced response than the rotor with high radial support stiffness. However, in the frequency range of 0-70Hz, under the same unbalanced excitation, the rotor with high radial support stiffness has a smaller unbalanced response than the rotor with low radial support stiffness. Therefore, optimizing the rotor support stiffness can reduce the rotor unbalanced response.

[0115] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for designing a dynamic vibration-absorbing superstructure for rotating machinery, characterized in that: Includes the following steps, Step 1: Based on the outer ring size of the bearing and the assembly space requirements of the rotating machinery, determine the outer radius R1, inner radius R2, and axial width B of the superstructure frame (1). Step 2: Based on the radial support stiffness requirements of the rotating machinery, the geometric parameters of the outermost ring (2) of the frame are initially set, and the geometric parameters of the outermost ring (2) of the frame are optimized to adjust the radial support stiffness of the frame (1); the geometric parameters include: the thickness t1 of the outermost ring of the frame and the width b1 of the outermost ring of the frame. The radial support stiffness is calculated by steady-state analysis in CAE software: a fixed constraint is set on the outer boss (3) of the outermost ring (2) of the frame, and a surface load excitation F1 in the same direction is applied to the mating surface of the frame (1) and the outer ring of the bearing. After obtaining the displacement X1 of the frame (1), the radial support stiffness of the frame (1) is calculated by formula F1 / X1. The relationship between the radial support stiffness of the frame (1) and the geometric parameters is as follows: the outermost thickness t1 of the frame is positively correlated with the radial support stiffness of the frame (1), and the outermost width b1 of the frame is positively correlated with the radial support stiffness of the frame (1). Step 3: Based on the assembly space requirements and lightweight requirements, determine the number of oscillators (7) and the mass size of each mass ring (5). The larger the mass of the mass ring (5), the better the vibration reduction effect and the wider the vibration reduction frequency band. Step 4: Establish a simplified rotor-bearing-superstructure dynamic model, as shown in the following formula: … Where M, C, K, and F are the rotor's mass matrix, damping matrix, stiffness matrix, and load matrix, respectively; K1 is the bearing stiffness; m, c, and k are the mass matrix, damping matrix, and stiffness matrix of the superstructure frame; m j k j Let X be the oscillator mass matrix and stiffness matrix; x, x, x j For the displacement matrices of the rotor, superstructure, and oscillator; Step 5: Based on the rotor-bearing-superstructure dynamic model obtained in Step 4, with minimizing the rotor displacement within the vibration reduction frequency band as the optimization objective, and the spring stiffness coefficients of each oscillator as design variables, a set of spring stiffness coefficients that meet the requirements are calculated using the parameter optimization module of the numerical analysis software. Combined with the mass size of the mass loop (5) obtained in Step 3, the formula is used to... A set of natural frequencies of the oscillator is obtained; Step 6: Initially set the geometric parameters of the elastic element (6), and then establish a finite element model of the superstructure based on the outer radius R1, inner radius R2, and axial width B of the superstructure obtained in Step 1, the outermost thickness t1 and outermost width b1 of the frame obtained in Step 2, the number of oscillators (7) obtained in Step 3, and the mass of each mass ring (5). Optimize the geometric parameters of the elastic element (6) through the finite element model of the superstructure so that the natural frequency of the superstructure oscillator (7) is equal to the natural frequency obtained in Step 5. The geometric parameters of the elastic element (6) include the elastic element thickness t2, the elastic element width b2, and the elastic element arc length l2. Natural frequency The characteristic frequency is calculated by the characteristic frequency analysis in CAE software: fixed constraint boundary conditions are set for the outermost ring (2) of the superstructure frame, and then the characteristic frequency analysis is performed to obtain the natural frequency of the superstructure oscillator (7); the relationship between the geometric parameters of the elastic element (6) and the natural frequency of the superstructure oscillator (7) is as follows: the thickness t2 of the elastic element is positively correlated with the natural frequency of the superstructure oscillator (7), the width b2 of the elastic element is positively correlated with the natural frequency of the superstructure oscillator (7), and the arc length l2 of the elastic element is negatively correlated with the natural frequency of the superstructure oscillator (7); Step 7: Based on the superstructure finite element model obtained in Step 6, set boundary conditions, and use the modal reduction method to convert the superstructure finite element model into a state space model, and verify the accuracy of the equivalent state space model until the error of the equivalent state space model is less than the preset accuracy requirement. The boundary conditions for the superstructure finite element model are: Set a fixed constraint on the outermost boss (3) of the outermost ring (2) of the frame; The modal reduction method for the equivalent state-space model of the superstructure is as follows: The main modes of the superstructure finite element model with boundary conditions are extracted, including characteristic frequencies and mode shapes, and then the decoupled equivalent state-space model of the superstructure in modal coordinates is obtained, which is shown in the following form: Among them, M T Let C be the equivalent mass matrix of the superstructure in modal coordinates. T K is the equivalent damping matrix of the superstructure in modal coordinates. T F is the equivalent stiffness matrix of the superstructure in modal coordinates. T Let be the equivalent load matrix of the superstructure in modal coordinates, and q be the equivalent displacement matrix of the superstructure in modal coordinates. The method for verifying the accuracy of the superstructure equivalent state-space model is as follows: The frequency response of a superstructure finite element model within a specified frequency range is calculated using the direct method in CAE software. In CAE software, the modal method is used to calculate the frequency response of an equivalent state-space model within a specified frequency range. The simulation boundary is: a fixed constraint is set on the outer boss (3) of the outermost ring (2) of the frame, and a surface load excitation of the same direction and specified frequency range is applied to the mating surface of the frame and the outer ring of the bearing, and then the frequency response is calculated; the surface load excitation corresponding to the modal method is harmonic excitation; By extracting the average displacement of the mating surfaces of the frame and the outer ring of the bearing within a specified frequency range, and comparing the displacement X2 of the direct method with the displacement X3 of the modal method, if the error meets the requirements, the equivalent state space model meets the requirements, and step eight is executed; if the error does not meet the preset accuracy requirements, the number of main modes of the modal equivalent method is increased to reduce the error of the equivalent state space model until the error meets the preset accuracy requirements. Step 8: Couple the state space model obtained in Step 7 to the rotor-bearing-superstructure dynamic model in Step 4 to verify the effectiveness of the superstructure in suppressing the vibration of rotating machinery. If the vibration reduction optimization requirements are met, proceed to Step 9. If not, further adjust the geometric parameters of the elastic element (6) and return to Step 7 until the vibration reduction optimization requirements are met. The geometric parameters of the elastic element (6) include the elastic element thickness t2, the elastic element width b2, and the elastic element arc length l2; Step 9: Based on the outer radius R1, inner radius R2, and axial width B of the superstructure obtained in Step 1, the outermost ring thickness t1 and outermost ring width b1 of the frame obtained in Step 2, the number of oscillators (7) and the mass size of each mass ring (5) obtained in Step 3, and the elastic element thickness t2, elastic element width b2, and elastic element arc length l2 obtained in Step 8, a superstructure that meets the requirements for suppressing radial vibration is obtained.

2. The method for designing a dynamic vibration-absorbing superstructure for rotating machinery as described in claim 1, characterized in that: The GA toolbox provided in MATLAB was used for optimization to obtain a set of spring stiffness coefficients that meet the requirements.

3. A dynamic vibration-absorbing superstructure for rotating machinery, obtained based on the design method of a dynamic vibration-absorbing superstructure for rotating machinery as described in claim 1 or 2, characterized in that: The dynamic vibration-absorbing superstructure for rotating machinery is installed between the outer ring of the bearing and the base; The dynamic vibration-absorbing superstructure includes a frame (1) for bearing and several oscillators (7) mounted on the frame (1). The rings (4) extending from the left and right sides of the frame (1) are used to mount the oscillators. The outermost ring (2) of the frame is the part of the frame (1) that generates the main elastic deformation. The inner and outer sides of the outermost ring (2) of the frame contain the same number of alternating bosses (3). The bosses (3) form an additional support point at the bottom and allow the outermost ring (2) of the frame to generate elastic deformation. The oscillator (7) consists of a mass ring (5) and four orthogonally arranged elastic elements (6). The mass ring (5) and the elastic elements (6) are detachably connected. The oscillator (7) and the frame (1) are detachably connected.

4. The dynamic vibration-absorbing superstructure for rotating machinery as described in claim 3, characterized in that: The elastic element (6) is provided with mounting plates at both ends. The mounting plates are detachably connected to the frame (1) and the mass ring (5). Different mass rings (5) and elastic elements (6) can be replaced according to the vibration reduction conditions, thereby flexibly adjusting the vibration reduction frequency band. The geometric parameters of the elastic element are: elastic element thickness t2, elastic element width b2, and elastic element arc length l2.

5. The dynamic vibration-absorbing superstructure for rotating machinery as described in claim 4, characterized in that: The mass ring (5) has four orthogonally arranged grooves. The size of the grooves is similar to that of the mounting plate and it cooperates with the elastic element mounting plate to install the elastic element (6). Under the same conditions, the larger the mass of the mass ring (5), the better the vibration reduction effect.

6. The dynamic vibration-absorbing superstructure for rotating machinery as described in claim 5, characterized in that: The rings (4) extending from the left and right sides of the frame (1) are provided with four orthogonally arranged grooves. The size of the grooves is similar to that of the mounting plate and they cooperate with the elastic element mounting plate to install the vibrator (7).

7. The dynamic vibration-absorbing superstructure for rotating machinery as described in claim 6, characterized in that: The outermost ring (2) of the frame is covered with damping layers on both the inner and outer sides.

8. The dynamic vibration-absorbing superstructure for rotating machinery as described in claim 7, characterized in that: The number of single-sided bosses (3) should be greater than or equal to 5.

Images