Multiple dynamic vibration absorbers applied to an asymmetric rotor system and their design methods

Abstract

The present invention discloses a multiple dynamic vibration absorber applied in an asymmetric rotor system and a design method thereof. The rotating shaft of the asymmetric rotor system has non-axisymmetric characteristics or the supporting structure has non-isotropic characteristics, and there are problems of excessive vibration and instability when passing through the critical speed and the 1 / 2 critical speed. The multiple dynamic vibration absorber is composed of an annular base and a plurality of cantilever beam oscillators, and is installed on the rotating shaft through rolling bearings. The multiple dynamic vibration absorber does not rotate with the asymmetric rotor system. The cantilever beam oscillators are equidistantly installed along the circumferential direction on the annular base, and the average value of their natural frequencies is close to the center frequency of the instability zone frequency band of the asymmetric rotor system. During the operation of the asymmetric rotor system, the cantilever beam oscillators absorb part of the vibration energy of the system. By optimizing the structural parameters of the multiple dynamic vibration absorber, the damping level of the system is greatly improved, the resonance amplitude at the critical speed of the system is reduced, and the instability phenomenon of the system is suppressed.

Description

Technical Field

[0001] The present invention relates to the field of structural vibration control, and more particularly to a multiple dynamic vibration absorber applied in an asymmetric rotor system and a design method thereof. Background Art

[0002] Rotating machinery is one of the landmark devices that measure the development level of a country's equipment manufacturing industry, and plays an irreplaceable role in national life, industrial production and national defense construction. As the core component of rotating machinery, the rotor system usually needs to maintain a high operating speed under complex and harsh working conditions. Once a failure occurs, it will cause significant economic losses and even accidents of equipment destruction and casualties. Therefore, the rotor system determines the reliability and safety of the operation of rotating machinery. An asymmetric rotor system is a rotor system with an asymmetric axisymmetric rotor structure or an anisotropic support structure widely existing in rotating machinery, such as a two-pole generator rotor, a wind turbine rotor, a crankshaft, a cracked rotor, and a rotor system supported by anisotropic sliding bearings and rolling bearings. However, under the action of its own gravity and unbalanced force loads, an asymmetric rotor system will exhibit obvious resonance peaks when passing through the 1 / 2 critical speed, and when passing through the critical speed, there will be phenomena such as an increase in the number of resonance peaks, an increase in amplitude, a broadening of the vibration frequency band, and instability. These complex vibration characteristics and the emerging instability phenomena greatly increase the probability of failure of the asymmetric rotor system, and at the same time also restrict the further development of rotating machinery with an asymmetric rotor system. Therefore, the safe and stable operation of the asymmetric rotor system is of utmost importance, and it is urgent to develop a vibration damping device that can effectively reduce the vibration amplitude of the asymmetric rotor system, suppress the instability phenomenon of the asymmetric rotor system, and operate stably for a long time under complex and harsh working conditions. Summary of the Invention

[0003] The present invention is to avoid the deficiencies of the prior art, and provides a multiple dynamic vibration absorber applied in an asymmetric rotor system and a design method thereof. By setting the natural frequencies of multiple cantilever beam oscillators of the multiple dynamic vibration absorber to match the vibration characteristics of the asymmetric rotor system, the vibration amplitude of the asymmetric rotor system passing through the corresponding frequency band is reduced, the instability phenomenon occurring in the corresponding frequency band is eliminated, and the safety and stability of the long-term operation of the asymmetric rotor system are improved.

[0004] The present invention adopts the following technical solutions to solve the technical problems:

[0005] The multi - dynamic vibration absorber of the present invention is applied to an asymmetric rotor system. The asymmetric rotor system includes a rotating member and a supporting member. The rotating member includes a rotating shaft and a disk fixedly arranged on the rotating shaft. The supporting member is a supporting structure that supports the rotating shaft through rolling bearings or sliding bearings. The asymmetric rotor system means that the rotating shaft has non - axisymmetric characteristics, or the damping and stiffness parameters of the supporting structure have non - isotropic characteristics. The asymmetric rotor system has vibration and instability problems when passing through the critical speed and 1 / 2 critical speed. The characteristics of the present invention are: the structural form of the multi - dynamic vibration absorber is set as:

[0006] The multi - dynamic vibration absorber is composed of an annular base and a plurality of cantilever beam vibrators. The annular base is installed on the rotating shaft through rolling bearings. Each cantilever beam vibrator is arranged circumferentially on the annular base, and each cantilever beam vibrator is a dynamic vibration absorber;

[0007] The inner ring of the rolling bearing rotates with the rotating shaft, and the annular base is fixedly installed on the outer ring of the rolling bearing, so that the annular base does not rotate with the asymmetric rotor system;

[0008] The cantilever beam vibrator is composed of an elastic beam and a mass block. The elastic beam is a beam with a constant cross - section or a beam with a non - constant cross - section. The beam with a constant cross - section is a rectangular beam with a constant cross - section. A plurality of cantilever beam vibrators are arranged circumferentially and equidistantly on the annular base. The root of the elastic beam is fixedly connected to the annular base, the front end of the elastic beam is fixedly connected to the mass block, and the body of the elastic beam extends along the axis direction of the rotating shaft;

[0009] The natural frequencies of the plurality of cantilever beam vibrators are different from each other and are equally spaced or non - equally spaced within a set vibrator frequency band. The average value of all vibrator frequencies is close to the center frequency of the instability region frequency band of the asymmetric rotor system. When the asymmetric rotor system passes through the critical speed and 1 / 2 critical speed, each cantilever beam vibrator absorbs part of the vibration energy of the system and dissipates it through the self - damping of the cantilever beam vibrator, so as to improve the damping level of the entire system, reduce the resonance amplitude of the asymmetric rotor system when passing through the critical speed and 1 / 2 critical speed, and eliminate the instability phenomenon caused by asymmetric factors;

[0010] The instability region of the asymmetric rotor system is the rotational speed range corresponding to when the real part of the complex eigenvalue of the system is positive. The center frequency of the instability region frequency band is the rotational frequency corresponding to the average value of the maximum rotational speed and the minimum rotational speed of the instability region;

[0011] The characteristics of the multi - dynamic vibration absorber of the present invention applied to an asymmetric rotor system also lie in that: the annular base is a whole - ring structure, or a split - ring structure composed of two half - rings connected by bolts, and the annular base and the outer ring of the rolling bearing are in an interference fit.

[0012] The characteristics of the multiple dynamic vibration absorber applied in the asymmetric rotor system of the present invention also lie in that: the fixed connection between the root of the elastic beam and the annular base is welding or screw connection or mortise and tenon connection; the welding means welding the root of the elastic beam and the annular base together; the screw connection means machining a smooth hole at the root of the elastic beam, machining a threaded hole on the annular base, and installing the root of the elastic beam and the annular base together through screws; the mortise and tenon connection means machining a mortise groove matching the root of the elastic beam on the annular base and installing it with the root of the elastic beam as the tenon.

[0013] The characteristics of the multiple dynamic vibration absorber applied in the asymmetric rotor system of the present invention also lie in that: the number of cantilever beam vibrators in the multiple dynamic vibration absorber is not less than 3 and not more than 30; the total mass of the multiple dynamic vibration absorber is 1%-15% of the mass of the asymmetric rotor system; the machining error of the natural frequency of each cantilever beam vibrator is not more than 5%, and the deviation between the average value of the frequencies of all vibrators and the center frequency of the instability zone frequency band is not more than 10%.

[0014] The design method of the multiple dynamic vibration absorber applied in the asymmetric rotor system of the present invention is characterized in that:

[0015] For the multiple dynamic vibration absorber applied in the asymmetric rotor system, design the vibrator frequency band of the multiple dynamic vibration absorber according to the following steps:

[0016] Step 1: Solve to obtain the instability zone frequency band W of the asymmetric rotor system r

[0017] Based on the finite element method, establish the dynamic model of the asymmetric rotor system, and solve the vibration response R of the asymmetric rotor system r and the complex eigenvalue F r , plot the curve K of the maximum value of the real part of the complex eigenvalue F r changing with frequency, take the minimum frequency f r and the maximum frequency f r corresponding to each positive number on the curve K rmin and the frequency band enclosed by them is the instability zone frequency band W rmax ; r ;

[0018] Step 2: Solve to obtain the center frequency f r of the instability zone frequency band W r and the frequency band width A

[0019] From the minimum frequency f r and the maximum frequency f rmin of the instability zone frequency band W rmax obtained in the above Step 1, calculate the center frequency f r of the instability zone frequency band W r according to Equation (1);

[0020] f r = (f rmin + f rmax ) / 2 (1)

[0021] Calculate the bandwidth A of the instability region frequency band W according to Equation (2). r of the frequency band width A;

[0022] A = f rmax - f rmin (2)

[0023] Step 3: Solve to obtain the optimal center frequency f vopt and the optimal bandwidth B opt

[0024] The center frequency f v of the oscillator frequency band is the average value of the natural frequencies of all cantilever beam oscillators, as shown in Equation (3).

[0025]

[0026] In Equation (3):

[0027] f k is the natural frequency of the k-th oscillator, k = 1, 2,..., n, and f k < f k+1 ; n is the number of cantilever beam oscillators;

[0028] The bandwidth B of the oscillator frequency band is the difference between the maximum value f vmax and the minimum value f vmin of the natural frequencies of the cantilever beam oscillators, as shown in Equation (4).

[0029] B = f vmax - f vmin (4)

[0030] Set the traversal range of the optimal center frequency f vopt of the oscillator frequency band to be (1 ± 10%)f r , and set the traversal range of the optimal bandwidth B opt of the oscillator to be A - 3A. Combine the finite element method and the lumped parameter method to establish a dynamic model of the absorber - asymmetric rotor system, and solve the vibration response R r of the absorber - asymmetric rotor system with a center frequency traversal range of (1 ± 10%)f v and a bandwidth traversal range of A - 3A, and the complex eigenvalues F v , and plot the surface K v of the maximum value of the real part of the complex eigenvalue F varying with the center frequency and the bandwidth, v1 and take the region S v1 enclosed by all negative values on the surface Kv , plot the maximum value of the vibration response R v varying with the center frequency and the bandwidth within the said region S v to obtain the surface K v2 , and select the center frequency and the bandwidth at the point with the minimum amplitude on the surface K v2 as the optimal center frequency f vopt and the optimal bandwidth B opt ;

[0031] Step 4: Solve to obtain the oscillator frequency and the preferred oscillator frequency band W of the multiple dynamic vibration absorbers v

[0032] When the natural frequencies of multiple cantilever beam oscillators are equally spaced within the set frequency range, calculate the oscillator frequencies according to Equation (5);

[0033]

[0034] When the natural frequencies of multiple cantilever beam oscillators are not equally spaced within the set frequency range, calculate the minimum oscillator frequency f vmin and the maximum oscillator frequency f vmax ;

[0035] f vmin = (2f vopt - B opt ) / 2 (6)

[0036] f vmax = (2f vopt + B opt ) / 2 (7)

[0037] The frequency band enclosed by the minimum oscillator frequency f vmin and the maximum oscillator frequency f vmax is the preferred oscillator frequency band W v .

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] 1. The multiple dynamic vibration absorber in the present invention includes multiple dynamic vibration absorbers, and the control frequencies of each absorber can be designed separately, and the control frequency band of the entire multiple dynamic vibration absorber is relatively wide;

[0040] 2. The multiple dynamic vibration absorber in the present invention can effectively synchronously reduce the resonance response within the critical and 1 / 2 critical speed ranges, and can effectively suppress the unstable phenomenon of the asymmetric rotor, which is beneficial to the efficient and stable operation of the rotor;

[0041] 3. The multiple dynamic vibration absorber in the present invention does not rotate with the rotor and does not increase the moment of inertia of the asymmetric rotor system;

[0042] 4. In the present invention, multiple cantilever beam oscillators extend along the axis direction of the rotating shaft and are arranged in an equidistant circumferential distribution manner, with a compact structure, small mass, and the ability to absorb vibrations in all directions of the asymmetric rotor system.

[0043] 5. The structure of the present invention is simple and reliable, with low cost and strong environmental adaptability, which is beneficial to practical applications. Description of the Drawings

[0044] Figure 1 It is a schematic structural diagram of an asymmetric rotor system equipped with a multiple dynamic vibration absorber in the present invention;

[0045] Figure 2 It is a schematic structural diagram of an integral multiple dynamic vibration absorber with eight oscillators welded in the present invention;

[0046] Figure 3 It is a schematic structural diagram of a split multiple dynamic vibration absorber with six oscillators connected by screws in the present invention;

[0047] Figure 4 It is a schematic structural diagram of an integral multiple dynamic vibration absorber with eight oscillators connected by tenon and mortise joints in the present invention;

[0048] Figure 5 It is a comparative diagram of the simulation effects of amplitude suppression of the multiple dynamic vibration absorber in the present invention;

[0049] Figure 6 It is a comparative diagram of the simulation effects of instability suppression of the multiple dynamic vibration absorber in the present invention.

[0050] Reference numerals in the drawings: 1 asymmetric rotor system, 1a rotating shaft, 1b wheel disc, 1c supporting structure, 2 rolling bearing, 3 multiple dynamic vibration absorber, 3a annular base, 3b cantilever beam oscillator. Detailed Embodiments

[0051] Referring to Figure 1 , in this embodiment, the asymmetric rotor system 1 is composed of rotating components such as the rotating shaft 1a and the wheel disc 1b, and supporting structures 1c such as rolling bearings or sliding bearings and bearing supports; the rotating shaft 1a of the asymmetric rotor system 1 has the characteristic of non-axisymmetry or the damping and stiffness parameters of the supporting structure 1c have the characteristic of non-isotropy; the asymmetric rotor system 1 has problems of excessive vibration and instability when passing through the critical speed and 1 / 2 critical speed.

[0052] Referring to Figure 1 and Figure 2, in this embodiment, the multiple dynamic vibration absorbers 3 for vibration reduction and instability suppression of the asymmetric rotor system are composed of an annular base 3a and multiple cantilever beam vibrators 3b, and are installed on the rotating shaft 1a through rolling bearings 2. Each cantilever beam vibrator is a dynamic vibration absorber, and its natural frequency can be designed separately; during operation, the inner ring of the rolling bearing 2 rotates with the rotating shaft 1a, and the outer ring is installed with the annular base 3a. The multiple dynamic vibration absorbers 3 do not rotate with the asymmetric rotor system; the cantilever beam vibrator 3b is composed of an elastic beam and a mass block. The elastic beam can be a beam with a constant cross-section or a beam with a non-constant cross-section. A beam with a constant cross-section is easy to manufacture, and a rectangular beam with a constant cross-section is a better choice. A beam with a non-constant cross-section can meet special requirements for design and installation; multiple cantilever beam vibrators 3b are circumferentially arranged at equal intervals on the annular base 3a, and the roots of the cantilever beam vibrators 3b are welded or screwed or tenon-mortised to the annular base 3a and extend along the axis direction of the rotating shaft 1a to absorb vibrations in all directions of the asymmetric rotor system and reduce the structural size of the multiple dynamic vibration absorbers.

[0053] The multiple cantilever beam vibrators have a variety of different natural frequencies, and the natural frequencies of the multiple cantilever beam vibrators 3b are equally spaced or non-equally spaced within a certain frequency range. By installing the asymmetric rotor system 1 on a test bench for testing or analyzing through the finite element method, it is determined that the rotational speed range where the real part of the complex eigenvalue of the system is greater than zero during the operation of the asymmetric rotor system 1 is the instability region of the asymmetric rotor system. The rotational frequency corresponding to the average value of the maximum rotational speed and the minimum rotational speed in the instability region is the center frequency of the instability region frequency band, and the average value of the natural frequencies of the multiple cantilever beam vibrators is set to be close to the center frequency of the instability region frequency band of the asymmetric rotor system 1; when the asymmetric rotor system 1 passes through the critical speed and the 1 / 2 critical speed, each cantilever beam vibrator 3b absorbs part of the vibration energy of the system and dissipates it through the self-damping of the cantilever beam vibrator to improve the damping level of the entire system, reduce the resonance amplitude when the asymmetric rotor system 1 passes through the critical speed and the 1 / 2 critical speed, and eliminate the instability phenomenon caused by asymmetric factors.

[0054] In specific implementation, the corresponding technical measures also include:

[0055] The annular base 3a is a whole ring structure. The whole ring structure has a small size and a small mass. As shown in Figure 2 , or it is a split ring structure composed of bolt-connecting two half rings. The split ring structure is easy to disassemble and assemble. As shown in Figure 3 ; The annular base 3a and the outer ring of the rolling bearing 2 are in an interference fit. For the whole ring structure, the annular base 3a can be heated and installed by the hot-fitting method or the rolling bearing 2 can be cooled and installed by the cold-fitting method; the split ring structure realizes the interference fit installation with the rolling bearing 2 through bolts and nuts.

[0056] The fixed connection between the root of the elastic beam and the annular base 3a is welding or screw connection or mortise and tenon connection; welding means welding the root of the elastic beam and the annular base 3a together, which can simplify the processing and assembly procedures and has a stable and firm connection, as shown in Figure 2 ; screw connection means machining a smooth hole at the root of the elastic beam, machining a threaded hole on the annular base 3a, and installing the root of the elastic beam and the annular base 3a together with screws. The screw connection is convenient for disassembly and assembly and is convenient for the adjustment and replacement of the cantilever beam oscillator 3b, as shown in Figure 3 ; mortise and tenon connection means machining a mortise groove matching the root of the elastic beam on the annular base 3a and installing it with the root of the elastic beam as the tenon. The mortise and tenon connection is stable and reliable and is convenient for disassembly and assembly, as shown in Figure 4 .

[0057] The number of cantilever beam oscillators 3b in the multiple dynamic vibration absorber 3 will significantly affect the vibration reduction and instability suppression effects. To obtain good effects, a larger number of cantilever beam oscillators need to be used. However, when the number is too large, it will also increase the processing and manufacturing difficulty. Therefore, the number of oscillators is not less than 3 and not more than 30. The total mass of the multiple dynamic vibration absorber also has a great impact on its vibration reduction performance. When the total mass is too small, the vibration energy that can be absorbed is limited. When the total mass is too large, it will have a greater impact on the asymmetric rotor system. Therefore, the total mass of the multiple dynamic vibration absorber 3 is 1% - 15% of the mass of the asymmetric rotor system 1. The natural frequency of the cantilever beam oscillator determines its effective working range. Therefore, the processing error cannot be too large. The processing error of the natural frequency of each cantilever beam oscillator is not greater than 5%. At the same time, to effectively reduce the vibration amplitude of the asymmetric rotor system and suppress the unstable phenomenon that appears, the distribution range of the natural frequency of the cantilever beam oscillator needs to match the instability region of the asymmetric rotor system. Therefore, the deviation of the average value of the natural frequency of the cantilever beam oscillator from the center frequency of the instability region is not greater than 10%.

[0058] In this embodiment, the preferred oscillator frequency band of the multiple dynamic vibration absorber is obtained according to the following steps:

[0059] Step 1: Solve to obtain the instability region frequency band W of the asymmetric rotor system r

[0060] Based on the finite element method, establish the dynamic model of the asymmetric rotor system, solve the vibration response R r and the complex eigenvalue F r , draw the curve K of the change of the maximum value of the real part of the complex eigenvalue F r with frequency, take the minimum frequency f r and the maximum frequency f r corresponding to each positive number on the curve K rmin and enclose the frequency band as the instability region frequency band W rmax ; r ;

[0061] Step 2: Solve to obtain the frequency band W of the instability region r for the center frequency f r and the frequency band width A

[0062] From the minimum frequency f r and the maximum frequency f rmin of the frequency band W of the instability region in the said Step 1, calculate to obtain the center frequency f rmax of the frequency band W of the instability region according to Equation (1); r r ;

[0063] f r =(f rmin +f rmax ) / 2 (1)

[0064] Calculate to obtain the frequency band width A of the frequency band W of the instability region according to Equation (2); r

[0065] A=f rmax -f rmin (2)

[0066] Step 3: Solve to obtain the optimal center frequency f vopt and the optimal frequency band width B opt

[0067] The center frequency of the oscillator frequency band is the average value of the natural frequencies of the cantilever beam oscillators, as shown in Equation (3)

[0068]

[0069] In Equation (3):

[0070] n is the number of cantilever beam oscillators; f k is the natural frequency of the k-th oscillator, and f k <f k+1 ;

[0071] The frequency band width of the oscillator is the difference between the maximum and minimum natural frequencies of the cantilever beam oscillators, as shown in Equation (4):

[0072] B=f n -f1 (4)

[0073] Set the traversal range of the optimal center frequency f vopt of the oscillator frequency band to be (1±10%)f r , set the traversal range of the optimal frequency band width B opt of the oscillator to be A - 3A, combine the finite element method and the lumped parameter method to establish the dynamic model of the vibration absorber - asymmetric rotor system, and solve for the center frequency traversal range of (1±10%)f r ​Vibration response R of the absorber - asymmetric rotor system with the sum frequency band width traversing range of A - 3A v And complex eigenvalue F v , plot the complex eigenvalue F v The surface K of the maximum value of the real part varying with the center frequency and the sum frequency band width v1 , take the region S enclosed by all negative values on the surface K v1 ; v , plot the maximum value of the vibration response R v varying with the center frequency and the sum frequency band width in the region S v as the surface K v2 , take the center frequency and the sum frequency band width at the minimum amplitude on the surface K v2 as the optimal center frequency f vopt and the optimal frequency band width B opt ;

[0074] Step 4: Solve to obtain the oscillator frequency and the preferred oscillator frequency band W of the multiple dynamic absorbers v

[0075] When the natural frequencies of multiple cantilever beam oscillators are equally spaced within the set frequency range, calculate each oscillator frequency according to Equation (5);

[0076]

[0077] When the natural frequencies of multiple cantilever beam oscillators are not equally spaced within the set frequency range, calculate the minimum oscillator frequency f vmin and the maximum oscillator frequency f vmax using Equations (6) and (7);

[0078] f vmin =(2f vopt - B opt ) / 2 (6)

[0079] f vmax =(2f vopt + B opt ) / 2 (7)

[0080] The frequency band enclosed by the minimum oscillator frequency f vmin and the maximum oscillator frequency f vmax is the preferred oscillator frequency band W v .

[0081] Figure 1The total mass of the asymmetric rotor system shown is 9.75 kg. The starting angular frequency corresponding to the instability region is 165.8 rad / s, the ending angular frequency is 183.8 rad / s, the bandwidth of the instability region is 18 rad / s, the central angular frequency of the instability region bandwidth is 174.8 rad / s. Eight cantilever beam oscillators with different frequencies are equidistantly installed circumferentially on the annular base of the multiple dynamic vibration absorber. The total mass of the cantilever beam oscillators is set to 3% of the total mass of the asymmetric rotor system. The central angular frequency of the oscillator bandwidth is 164.3 rad / s, and the bandwidth is 41.1 rad / s. The natural angular frequencies of the eight cantilever beam oscillators are 143.8 rad / s, 149.6 rad / s, 155.5 rad / s, 161.4 rad / s, 167.2 rad / s, 173.1 rad / s, 179.0 rad / s, and 184.9 rad / s respectively. The vibration response solution and complex eigenvalue analysis are respectively carried out for the asymmetric rotor system and the asymmetric rotor system installed with a multiple dynamic vibration absorber. The analysis angular frequency range is 50 - 220 rad / s. The curves of the maximum values of the response and the real part of the complex eigenvalue of the asymmetric rotor system under the two cases varying with the angular frequency are as Figure 5 and Figure 6 shown. Figure 5 In Figure 5 , curve R1 is the curve of the maximum response amplitude of the asymmetric rotor system varying with the angular frequency, and curve R2 is the curve of the maximum response amplitude of the asymmetric rotor system installed with a multiple dynamic vibration absorber varying with the angular frequency. Figure 5 It can be seen that the maximum amplitude of the asymmetric rotor system without installing a multiple dynamic vibration absorber in the frequency range is 25.16 mm. After installing the multiple dynamic vibration absorber, the maximum amplitude of the asymmetric rotor system drops to 1.28 mm, and the vibration reduction effect is significant. Figure 6 In Figure 6 , curve F1 is the curve of the maximum value of the real part of the complex eigenvalue of the asymmetric rotor system varying with the angular frequency, and curve F2 is the curve of the maximum value of the real part of the complex eigenvalue of the asymmetric rotor system installed with a multiple dynamic vibration absorber varying with the angular frequency. Figure 6 It can be seen that there is a section in the frequency range where the maximum value of the real part of the complex eigenvalue of the asymmetric rotor system without installing a multiple dynamic vibration absorber is positive, that is, the instability phenomenon occurs. After installing the multiple dynamic vibration absorber, the maximum value of the real part of the complex eigenvalue of the asymmetric rotor system is non-positive, and the system is stable. The multiple dynamic vibration absorber can completely eliminate the instability phenomenon of the asymmetric rotor system.

Claims

1. A multiple dynamic vibration absorber applied to an asymmetric rotor system, the asymmetric rotor system (1) comprising a rotating member and a supporting member, the rotating member including a rotating shaft (1a) and a disk (1b) fixedly arranged on the rotating shaft (1a), and the supporting member being a support structure (1c) that supports the rotating shaft (1a) through a rolling bearing or a sliding bearing; the asymmetric rotor system (1) means that the rotating shaft (1a) has an axisymmetric characteristic, or the damping and stiffness parameters of the support structure (1c) have an anisotropic characteristic; the asymmetric rotor system (1) has vibration and instability problems when passing through the critical speed and the 1 / 2 critical speed; characterized in that: Set the structural form of the multiple dynamic vibration absorber (3): The multiple dynamic vibration absorber (3) is composed of an annular base (3a) and a plurality of cantilever beam oscillators (3b). The annular base (3a) is installed on the rotating shaft (1a) through a rolling bearing (2). Each cantilever beam oscillator (3b) is arranged circumferentially on the annular base (3a), and each cantilever beam oscillator (3b) is a dynamic vibration absorber; The inner ring of the rolling bearing (2) rotates with the rotating shaft (1a), and the annular base (3a) is fixedly installed on the outer ring of the rolling bearing (2), so that the annular base (3a) does not rotate with the asymmetric rotor system; The cantilever beam oscillator (3b) is composed of an elastic beam and a mass block. The elastic beam is a beam with a constant cross-section or a non-constant cross-section. The beam with a constant cross-section is a rectangular beam with a constant cross-section; a plurality of cantilever beam oscillators (3b) are arranged equidistantly circumferentially on the annular base (3a), and the root of the elastic beam is fixedly connected to the annular base (3a), the front end of the elastic beam is fixedly connected to the mass block, and the body of the elastic beam extends along the axis direction of the rotating shaft (1a); The natural frequencies of the plurality of cantilever beam oscillators are different from each other, and are equally spaced or non-equally spaced within a set oscillator frequency band. The average value of all oscillator frequencies is close to the center frequency of the instability zone frequency band of the asymmetric rotor system (1), so that when the asymmetric rotor system (1) passes through the critical speed and the 1 / 2 critical speed, each cantilever beam oscillator (3b) absorbs part of the vibration energy of the system and dissipates it through the self-damping of the cantilever beam oscillator, so as to improve the damping level of the whole system, reduce the resonance amplitude at the critical speed and the 1 / 2 critical speed of the asymmetric rotor system (1), and eliminate the instability phenomenon caused by asymmetric factors; The instability zone of the asymmetric rotor system is the speed range corresponding to the positive real part of the complex eigenvalue of the system. The center frequency of the instability zone frequency band is the rotational frequency corresponding to the average value of the maximum speed and the minimum speed of the instability zone.

2. The multiple dynamic vibration absorber applied to the asymmetric rotor system according to claim 1, characterized in that: The annular base (3a) is a whole ring structure, or a split ring structure composed of two half rings connected by bolts, and the annular base (3a) and the outer ring of the rolling bearing (2) are in interference fit.

3. The multiple dynamic vibration absorber applied to the asymmetric rotor system according to claim 1, characterized in that: The fixed connection between the root of the elastic beam and the annular base (3a) is welding or screw connection or mortise and tenon connection; the welding means welding the root of the elastic beam to the annular base (3a) together; the screw connection means machining a smooth hole at the root of the elastic beam, machining a threaded hole on the annular base (3a), and installing the root of the elastic beam and the annular base (3a) together through screws; the mortise and tenon connection means machining a mortise groove matching the root of the elastic beam on the annular base (3a) and installing it with the root of the elastic beam as the tenon.

4. The multiple dynamic vibration absorber applied to an asymmetric rotor system according to claim 1, characterized in that: The number of cantilever beam oscillators (3b) in the multiple dynamic vibration absorber is not less than 3 and not more than 30; The total mass of the multiple dynamic vibration absorber (3) is 1% - 15% of the mass of the asymmetric rotor system (1); The machining error of the natural frequency of each cantilever beam oscillator is not greater than 5%, and the deviation between the average value of the frequencies of all oscillators and the center frequency of the instability region frequency band is not greater than 10%.

5. A design method for a multiple dynamic vibration absorber applied in an asymmetric rotor system, characterized in that: For the multiple dynamic vibration absorber applied in the asymmetric rotor system according to claim 1, design the oscillator frequency band of the multiple dynamic vibration absorber according to the following steps: Step 1: Solve to obtain the instability zone frequency band W of the asymmetric rotor system r Establish a dynamic model of the asymmetric rotor system (1) based on the finite element method, and solve the vibration response R of the asymmetric rotor system (1) r and the complex eigenvalues F r , plot the curve K of the maximum real part of the complex eigenvalue F r changing with frequency r , take the minimum frequency f r and the maximum frequency f rmin corresponding to each positive number on the curve K rmax and the frequency band enclosed by them is the instability region frequency band W r ; Step 2: Solve to obtain the frequency band W of the instability region r The center frequency f r And the bandwidth A From the minimum frequency f r and the maximum frequency f rmin of the instability zone frequency band W in the said step 1, calculate the center frequency f rmax of the instability zone frequency band W according to formula (1) to obtain r ; r ​ f r = (f rmin + f rmax ) / 2 (1) Calculate the frequency band W of the instability region according to formula (2). r The bandwidth A of A = f rmax -f rmin (2) Step 3: Solve to obtain the optimal center frequency f of the oscillator band vopt and the optimal bandwidth B opt The center frequency f of the oscillator band v is the average value of the natural frequencies of all the cantilever beam oscillators as shown in Equation (3) In formula (3): f k is the natural frequency of the k-th oscillator, where k = 1, 2, …, n, and f k < f k+1 ; n is the number of cantilever beam oscillators; The bandwidth B of the oscillator is the difference between the maximum value f vmax and the minimum value f vmin of the natural frequency of the cantilever beam oscillator, as shown in Equation (4). B = f vmax -f vmin (4) Set the optimal center frequency f of the oscillator vopt The traversal range of which is (1±10%)f r Set the optimal bandwidth B of the oscillator opt The traversal range of which is A - 3A. Combine the finite element method and the lumped parameter method to establish the dynamic model of the absorber - asymmetric rotor system, and solve the vibration response R of the absorber - asymmetric rotor system with the center frequency traversal range of (1±10%)f r and the bandwidth traversal range of A - 3A, and the complex eigenvalue F v Plot the surface K of the maximum real part of the complex eigenvalue F v changing with the center frequency and the bandwidth v Take the region S enclosed by all negative values on the surface K v1 Plot the surface K of the maximum value of the vibration response R v1 changing with the center frequency and the bandwidth in the region S v Take the center frequency and the bandwidth at the minimum amplitude on the surface K v as the optimal center frequency f v and the optimal bandwidth B v2 ; v2 vopt opt ;​​ Step 4: Solve to obtain the oscillator frequency and the preferred oscillator frequency band W of the multiple dynamic vibration absorber v When the natural frequencies of multiple cantilever beam oscillators are equally spaced within a set frequency range, calculate the frequency of each oscillator according to formula (5); When the natural frequencies of multiple cantilever beam oscillators are non-uniformly distributed within the set frequency range, the minimum oscillator frequency f is calculated according to Equations (6) and (7). vmin and the maximum oscillator frequency f vmax ; f vmin = (2f vopt - B opt ) / 2 (6) f vmax = (2f vopt + B opt ) / 2 (7) The preferred oscillator frequency band W v is the frequency band enclosed by the minimum oscillator frequency f vmin and the maximum oscillator frequency f vmax .

Images