A frequency and damping independently adjustable dynamic vibration absorber and a design method thereof

Abstract

The application discloses a frequency and damping independently adjustable dynamic vibration absorber and a design method thereof, and relates to the technical field of semi-active control of structural vibration. The structure is composed of an inertial actuator and a shunt circuit. The shunt circuit comprises a negative inductance and negative resistance compensation circuit and an inductance-resistance-capacitance parallel circuit. Two wiring ends of a voice coil of the inertial actuator are connected with the shunt circuit to form a complete loop. The independent adjustment of the inherent frequency and the damping of the inertial actuator can be realized by adjusting the parameters of the shunt circuit. Therefore, the dynamic vibration absorber has the characteristics of controlling vibration of any disturbance frequency. The application does not need any mechanical driving device, and the inherent frequency and the damping adjustment of the dynamic vibration absorber are independent of each other.

Description

Technical Field

[0001] This invention belongs to the field of structural vibration control technology, specifically relating to a dynamic vibration absorber with independently adjustable frequency and damping and its design method. Background Technology

[0002] Power machinery generates vibrations during operation, and mechanical vibration is a major cause of mechanical structural failure. Because of its advantages such as simple structure, stable performance, and ease of implementation, dynamic vibration absorbers are widely used to suppress vibrations in power machinery structures.

[0003] Dynamic vibration absorbers can generally be classified into three main categories: passive, active, and semi-active. Passive dynamic vibration absorbers, due to their non-adjustable structural parameters and natural frequencies, can only be used to control vibrations near their natural frequencies. Active dynamic vibration absorbers offer wide-frequency vibration reduction performance, but require complex control feedback systems, resulting in higher costs. Furthermore, improper design of the control system parameters can lead to system instability, significantly limiting their application in engineering. Semi-active dynamic vibration absorbers, on the other hand, allow their natural frequencies to vary within a certain range by adjusting their stiffness or mass. The vibration control effect of semi-active dynamic vibration absorbers is similar to that of active dynamic vibration absorbers, but they are simpler to implement and less expensive. Therefore, semi-active dynamic vibration absorbers have become a research hotspot in recent years. However, existing semi-active dynamic vibration absorbers have two main defects: (1) Existing semi-active dynamic vibration absorber designs usually require mechanical drive components to adjust the stiffness of the absorber, which makes it difficult to miniaturize the structure of the absorber; (2) Existing semi-active dynamic vibration absorbers usually cannot adjust their damping. That is to say, when the natural frequency of the absorber changes, its damping value cannot be adjusted to the optimal damping value, which affects the control effect of the semi-active dynamic vibration absorber.

[0004] To address the shortcomings of current semi-active vibration absorbers, such as the need for mechanical drive devices, complex structures, and inability to adjust damping, this invention proposes a dynamic vibration absorber with independently adjustable frequency and damping based on a shunt inertial actuator. The inertial actuator can be viewed as a single-degree-of-freedom mass-damped-spring resonant system with a voice coil, thus it can be used as a passive or active dynamic vibration absorber. Furthermore, by designing a shunt circuit to connect the voice coil of the inertial actuator, its natural frequency and damping can be independently adjusted. This vibration absorber features independent adjustment of its natural frequency and damping without altering the physical structure of the inertial actuator. Summary of the Invention

[0005] The purpose of this invention is to provide a dynamic vibration absorber with independently adjustable frequency and damping, and its design method. It has a simple structure, does not require additional mechanical drive components or feedback control systems, and can independently adjust the natural frequency and damping of the vibration absorber.

[0006] The present invention is achieved through the following technical solution.

[0007] A dynamic vibration absorber with independently adjustable frequency and damping is characterized in that: the structure consists of an inertial actuator (1) and a shunt circuit (2), such as Figure 1 As shown. The shunt circuit (2) includes a negative inductor-resistance compensation circuit (3) and a parallel circuit of inductor, resistor, and capacitor (4). The two terminals of the inertial actuator (1) are connected to the shunt circuit (2) to form a complete loop. The negative inductor-resistance compensation circuit (3) and the parallel circuit of inductor, resistor, and capacitor (4) are connected in series to form the shunt circuit (2). The negative inductor-resistance compensation circuit (3) is composed of a negative inductor (5) and a negative resistor (6) connected in series. The parallel circuit of inductor, resistor, and capacitor (4) is composed of an inductor branch, a capacitor branch, and a resistor branch connected in parallel; the inductor branch is composed of an inductor element (7) and a first switch (8) connected in series; the capacitor branch is composed of a capacitor element (9) and a second switch (10) connected in series; the resistor branch contains at least one resistor (11).

[0008] A design method for a dynamic vibration absorber with independently adjustable frequency and damping is implemented according to the following steps:

[0009] Step 1: Obtain the natural frequency f of the inertial actuator (1) by consulting the product manual or conducting experimental measurements. a Equivalent mass M a Equivalent stiffness K a Equivalent damping coefficient C a Electromechanical coupling coefficient T, DC resistance R of the voice coil of the inertial actuator (1) a Voice coil inductor L a ;

[0010] Step 2: Implement the negative inductance and negative resistance compensation circuit (3) by using a negative impedance converter, and set the inductance value of the negative inductor (5) to -L. a The resistance value of the negative resistor (6) is -R a ;

[0011] Step 3: Obtain the target natural frequency f of the controlled vibration structure (12) s and effective quality M s To obtain the optimal natural frequency f required for the adjustment of the inertial actuator (1) opt and the optimal damping coefficient C opt as follows

[0012]

[0013]

[0014] In the formula: μ=M a / M s, which represents the mass ratio of the inertial actuator (1) to the controlled vibration structure (12).

[0015] Step 4: Based on the damping coefficient required for the inertial actuator (1) obtained in Step 3, set the resistance (11) of the resistive branch to the following value:

[0016]

[0017] Step 5: Compare the natural frequency f of the inertial actuator (1). a The adjustment frequency f obtained in step three opt ,

[0018] If f a =f opt If the first switch (8) of the inductor branch and the second switch (10) of the capacitor branch in the parallel circuit of inductor, resistor and capacitor (4) are both disconnected.

[0019] If f a <f opt Then, in the parallel circuit of inductor, resistor, and capacitor (4), the second switch (10) of the capacitor branch is open, the first switch (8) of the inductor branch is closed, and the inductance (7) of the inductor branch is set as follows:

[0020]

[0021] If f a >f opt In the parallel circuit (4) of inductor, resistor, and capacitor, the first switch (8) of the inductor branch is open, the second switch (10) of the capacitor branch is closed, and the capacitance (9) of the capacitor branch is set as follows:

[0022]

[0023] Compared with existing technologies, the advantages of this invention are: This invention has a simple structure, requires no additional mechanical drive components or feedback control systems, and can independently adjust the natural frequency and damping of the vibration absorber. Therefore, this invention has lower costs, is easier to implement, and enables the vibration absorber to maintain optimal vibration reduction performance at different frequencies. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of a dynamic vibration absorber with independently adjustable frequency and damping as described in this invention.

[0025] Among them, 1-inertial actuator, 2-shunt circuit, 3-negative inductor and negative resistance compensation circuit, 4-parallel circuit of inductor, resistor and capacitor, 5-negative inductor, 6-negative resistor, 7-inductor element, 8-first switch, 9-capacitor element, 10-second switch, 11-resistor, 12-controlled vibration structure.

[0026] Figure 2 This is a comparison diagram of the vibration control effects of a dynamic vibration absorber with independently adjustable frequency and damping and an inertial actuator without a shunt circuit in the embodiment (condition 1).

[0027] Figure 3 This is a comparison diagram of the vibration control effects of a dynamic vibration absorber with independently adjustable frequency and damping and an inertial actuator without a shunt circuit in the embodiment (condition 2).

[0028] Figure 4 This is a comparison diagram of the vibration control effects of a dynamic vibration absorber with independently adjustable frequency and damping and an inertial actuator without a shunt circuit in the embodiment (condition 3).

[0029] Figure 5 This is a virtual damping analog diagram of a dynamic vibration absorber with independently adjustable frequency and damping as described in this invention.

[0030] Figure 6 This is an analogy diagram of virtual damping and virtual spring for a dynamic vibration absorber with independently adjustable frequency and damping as described in this invention.

[0031] Figure 7 This is an analogy diagram of virtual damping and virtual mass for a dynamic vibration absorber with independently adjustable frequency and damping as described in this invention. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0033] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the effective mass M is described below. s =1kg and effective stiffness K s The invention will be described in detail using an undamped single-degree-of-freedom vibration system as a controlled vibration structure.

[0034] 1. According to step one of the technical solution, select the VISATON EX45S inertial actuator. By consulting the product manual and conducting experimental measurements, obtain the natural frequency f of the inertial actuator. a =133.8Hz, equivalent quality M a =0.05kg, equivalent stiffness K a =35250N / m, equivalent damping coefficient C a =5.1 Ns / m, electromechanical coupling coefficient T = 4.6 N / A, DC resistance R of the voice coil of the inertial actuator a =7.0Ω and voice coil inductance L a =0.05mH.

[0035] 2. According to Step 2 of the technical solution, a negative inductor and negative resistor compensation circuit is implemented by using a negative impedance converter, and the value of the negative resistor is adjusted to -R a = -7.0 Ω, and the value of the negative inductor is -L a = -0.05 mH to cancel the DC resistance and inductance of the voice coil of the inertial actuator. The implementation of the negative resistor and negative inductor can be found in the literature (Horowitz P, Hill W. The Art of Electronics. New York: Cambridge University Press. 1996).

[0036] 3. According to Step 3 of the technical solution, the mass ratio μ of the dynamic vibration absorber to the controlled vibration structure is μ = M a / M s = 0.05. Thus, the damping coefficient C required for the inertial actuator is opt as

[0037]

[0038] Assume that there are three working conditions for the effective stiffness of the controlled vibration structure. For Working Condition 1, its effective stiffness is K s = 3095100 N / m; for Working Condition 2, its effective stiffness is K s = 778806 N / m; for Working Condition 3, its effective stiffness is K s = 394780 N / m, and the target natural frequency of the controlled vibration structure is

[0039]

[0040] Therefore, the adjustment frequency f of the inertial actuator is opt as

[0041]

[0042] Step 4: According to the damping coefficient that the vibration absorber needs to be set obtained in Step 3, set the resistance value of the resistance branch to:

[0043]

[0044] Step 5: Compare the natural frequency f a of the inertial actuator and the required adjustment frequency f opt ,

[0045] For Working Condition 1, it can be found that the natural frequency f a of the inertial actuator < fopt, and the natural frequency of the inertial actuator needs to be adjusted to a higher frequency. Therefore, the second switch of the capacitor branch in the inductor-resistor-capacitor parallel circuit is disconnected, and the first switch of the inductor branch is closed. The inductance value of the inductor branch is set to:

[0046]

[0047] For operating condition two, the natural frequency f of the inertial actuator can be observed. a =fopt, the natural frequency of the inertial actuator does not need to be adjusted, so the first switch of the inductor branch and the second switch of the capacitor branch in the parallel circuit of inductor, resistor and capacitor are both open.

[0048] For operating condition three, the natural frequency f of the inertial actuator can be observed. a >fopt, the natural frequency of the inertial actuator needs to be adjusted to a lower frequency, so the first switch of the inductor branch in the parallel circuit of inductor, resistor, and capacitor is open, and the second switch of the capacitor branch is closed. The capacitance value of the capacitor branch is set as follows:

[0049]

[0050] Figure 2 , Figure 3 , Figure 4 This graph shows a comparison of vibration control effects before and after adjusting the parameters of a dynamically adjustable vibration absorber with independently adjustable frequency and damping. The graph reveals that if the parameters of the dynamically adjustable vibration absorber are not adjusted (without the shunt circuit connected), its control effect is very limited. For conditions one and three, after adjusting the natural frequency and damping of the dynamically adjustable vibration absorber to their optimal values ​​using the shunt circuit, the peak amplitude response of the controlled single-degree-of-freedom system decreases by 28dB and 26dB respectively compared to before adjustment. For condition two, since the natural frequency of the dynamically adjustable vibration absorber does not need adjustment, even after adjusting the damping of the dynamically adjustable vibration absorber to its optimal value using the shunt circuit, the peak amplitude response of the controlled single-degree-of-freedom system still decreases by 3dB compared to before adjustment.

[0051] The working principle of this invention is as follows:

[0052] The dynamic vibration absorber is fixed to the vibration-absorbing object. As can be seen from the references (Mao Q, Huang S. Design of tuneable vibration absorber by using inertial actuator with proof-mass acceleration feedback. International Journal of Structural Stability and Dynamics, 2019, 19(8): 1950087; Mao Q, Li S, Huang S. Inertial actuator with virtualmass for active vibration control. International Journal of Acoustics and Vibration, 2020, 25(3): 445-452), the vibration control equation of the dynamic vibration absorber, composed of an inertial actuator and a shunt circuit, can be expressed as:

[0053] M a a a +C a (v a -v s )+K a (x a -x s )=T·I (7)

[0054] jωL a I+R a I = V sh -T·(v a -v s (8)

[0055] Where: M a C a and K a These represent the effective mass, damping coefficient, and spring stiffness of the inertial actuator, respectively; T is the electromagnetic coefficient of the inertial actuator's voice coil; a a v a and x a These are the acceleration, velocity, and displacement of the effective mass of the inertial actuator. s and x s These represent the velocity and displacement of the controlled vibration structure, respectively. sh I is the voltage across the shunt circuit. I is the voice coil current of the inertial actuator.

[0056] According to the theory of mechanical vibration, v a =jω·x a aa (ω)=-ω 2 ·x a v s =jω·x s , where j is an imaginary number and ω is the angular frequency.

[0057] The two terminals of the inertial actuator voice coil are connected to the shunt circuit to form a complete loop. Therefore, the voltage across the voice coil is equal to the voltage V across the shunt circuit. sh V sh The impedance Z of the shunt current can be used sh Its current I represents, i.e.

[0058] V in =-Z sh I (9)

[0059] from Figure 1 It can be seen that the impedance Z of the shunt current sh It can be represented as

[0060] Z sh =Z neg +Z LCR (10)

[0061] In the formula: Z neg Z represents the impedance of a negative inductance and negative resistance compensation circuit. neg =-jωL a -R a This is used to offset the DC resistance and inductance of the voice coil in the inertial actuator. LCR This represents the impedance of a parallel circuit of an inductor, resistor, and capacitor, i.e.

[0062]

[0063] In the formula: R sh L is the resistance value of the resistive branch in a parallel circuit of an inductor, resistor, and capacitor. sh C is the inductance value of the inductor branch in a parallel circuit of an inductor, resistor, and capacitor. sh This represents the capacitance value of the capacitor branch in a parallel circuit of an inductor, resistor, and capacitor.

[0064] Substituting equations (10) and (11) into equation (8), we can obtain the voice coil current I as follows:

[0065]

[0066] Substituting equation (12) into equation (7), we get:

[0067] (a) When the first and second switches in the parallel circuit of inductor, resistor, and capacitor are simultaneously open, the motion control equation of the inertial actuator is:

[0068]

[0069] From equation (13), it can be seen that when the first switch and the second switch are simultaneously disconnected, the shunt current is equivalent to arranging a virtual damper in the inertial actuator, and the damping coefficient of this virtual damper is T. 2 / R sh ,like Figure 5 As shown. At this point, its natural frequency and damping coefficient are respectively...

[0070]

[0071]

[0072] Since the electromechanical coupling coefficient T is a real constant, it can be seen from equations (14) and (15) that by adjusting the resistance value R of the resistor branch in the parallel circuit of inductor, resistor, and capacitor, sh This allows the damping coefficient of the vibration absorber to be adjusted without changing its natural frequency.

[0073] (b) When the first switch in the parallel circuit of inductor, resistor, and capacitor is closed and the second switch is open, the motion control equation of the inertial actuator is:

[0074]

[0075] From equation (16), it can be seen that when the first switch is closed and the second switch is open, the shunt current is equivalent to arranging a virtual damper and a virtual spring in the inertial actuator, and the damping coefficient of the virtual damper is T. 2 / R sh The stiffness of the virtual spring is T. 2 / L sh ,like Figure 6 As shown. At this point, its natural frequency and damping coefficient are respectively...

[0076]

[0077]

[0078] From equations (17) and (18), it can be seen that by adjusting the resistance value R of the resistor branch in the parallel circuit of inductor, resistor, and capacitor, sh This allows adjustment of the damping coefficient of the vibration absorber without changing its natural frequency. Furthermore, by adjusting the inductance value L of the inductor branch in the parallel circuit of inductor, resistor, and capacitor... sh This allows the natural frequency of the vibration absorber to be increased without affecting its damping coefficient.

[0079] (c) When the first switch in the parallel circuit of inductor, resistor, and capacitor is open and the second switch is closed, the motion control equation of the inertial actuator is:

[0080]

[0081] From equation (19), it can be seen that when the first switch is open and the second switch is closed, the shunt current is equivalent to arranging a virtual damper and a virtual mass in the inertial actuator, and the damping coefficient of the virtual damper is T. 2 / R sh The virtual mass is equal to C. sh T 2 ,like Figure 7 As shown. At this point, its natural frequency and damping coefficient are respectively...

[0082]

[0083]

[0084] From equations (20) and (21), it can be seen that by adjusting the resistance value R of the resistor branch in the parallel circuit of inductor, resistor, and capacitor, sh This allows adjustment of the damping coefficient of the vibration absorber without changing its natural frequency. Furthermore, by adjusting the capacitance value L of the capacitor branch in the parallel circuit of inductor, resistor, and capacitor... sh This allows the natural frequency of the vibration absorber to be reduced without affecting its damping coefficient.

[0085] The above analysis shows that the dynamic vibration absorber described in this invention can independently adjust its natural frequency and damping coefficient through a shunt circuit.

[0086] According to the fixed-point optimization theory of dynamic vibration absorbers, the optimal damping coefficient C required when a dynamic vibration absorber is used to suppress structural vibration is... opt and natural frequency f opt They are respectively:

[0087]

[0088]

[0089] In the formula: μ=M a / M s M represents the mass ratio of the dynamic vibration absorber to the controlled vibration structure. s f represents the mass of the controlled vibration structure. s This represents the target natural frequency of the controlled vibration structure.

[0090] Observing equations (13)-(21), it can be found that regardless of the state of the first and second switches, the damping coefficient of the vibration absorber is always the same. In other words, the natural frequency and damping of the dynamic vibration absorber are independently adjustable, so the optimal damping coefficient value of the dynamic vibration absorber can be set first, i.e.

[0091]

[0092] From equation (24), the optimal resistance value of the resistor branch in the parallel circuit of inductor, resistor, and capacitor can be obtained.

[0093]

[0094] Further comparison of the inertial actuator's natural frequency f a and the required adjustment frequency f opt ,

[0095] (a) If f a =f opt In the parallel circuit of inductor, resistor, and capacitor, both the first and second switches of the capacitor branch and the inductor branch are open, and there is no need to set the inductance and capacitance values ​​in the parallel circuit of inductor, resistor, and capacitor.

[0096] (b) If f a <f opt Then the natural frequency of the dynamic vibration absorber needs to be increased to f. opt Therefore, in the parallel circuit of inductor, resistor, and capacitor, the second switch of the capacitor branch is open, and the first switch of the inductor branch is closed. From equation (17), we know that the natural frequency of the dynamic vibration absorber is...

[0097]

[0098] Adjust the natural frequency of the vibration absorber to f opt That is, f a sh =f opt Therefore, from equation (26), the inductance value of the inductor branch is set as follows:

[0099]

[0100] (c) If f a >f opt Then it is necessary to reduce the natural frequency of the dynamic vibration absorber to f. opt Therefore, in the parallel circuit of inductor, resistor, and capacitor, the first switch of the inductor branch is open, and the second switch of the capacitor branch is closed. From equation (20), we know that the natural frequency of the dynamic vibration absorber is:

[0101]

[0102] Adjust the natural frequency of the vibration absorber to f opt That is, f a sh =fopt Therefore, from equation (28), the capacitance value of the capacitor branch is set as follows:

[0103]

[0104] The above description is merely a preferred embodiment of the present invention and does not limit the implementation and protection scope of the present invention. Those skilled in the art should realize that any equivalent substitutions and obvious changes made based on the description and illustrations of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a dynamic vibration absorber with independently adjustable frequency and damping, characterized in that, The dynamic vibration absorber consists of an inertial actuator (1) and a shunt circuit (2). The shunt circuit includes a negative inductor-resistance compensation circuit (3) and a parallel circuit of inductor-resistance-capacitor (4). The two terminals of the inertial actuator are connected to the shunt circuit to form a complete loop. The negative inductor-resistance compensation circuit (3) and the parallel circuit of inductor-resistance-capacitor (4) are connected in series to form the shunt circuit (2). The negative inductor-resistance compensation circuit (3) is composed of a negative inductor (5) and a negative resistor (6) connected in series. The parallel circuit of inductor-resistance-capacitor (4) is composed of an inductor branch, a capacitor branch and a resistor branch connected in parallel. The inductor branch is composed of an inductor element (7) and a first switch (8) connected in series. The capacitor branch is composed of a capacitor element (9) and a second switch (10) connected in series. The resistor branch contains at least one resistor (11). This design method is implemented according to the following steps: Step 1: Obtain the natural frequency f of the inertial actuator (1) by consulting the product manual or conducting experimental measurements. a Equivalent mass M a Equivalent stiffness K a Equivalent damping coefficient C a Electromechanical coupling coefficient T, DC resistance R of the voice coil of the inertial actuator (1) a Voice coil inductor L a ; Step 2: Implement the negative inductance and negative resistance compensation circuit (3) by using a negative impedance converter, and set the inductance value of the negative inductor (5) to -L. a The resistance value of the negative resistor (6) is -R. a ; Step 3: Obtain the target natural frequency f of the controlled vibration structure (12) s and effective quality M s To obtain the optimal natural frequency f required for the inertial actuator (1) opt and the optimal damping coefficient C opt as follows (1) (2) In the formula: , representing the mass ratio of the inertial actuator (1) to the controlled vibration structure (12); Step 4: Based on the damping coefficient required for the inertial actuator (1) obtained in Step 3, set the resistance (11) of the resistive branch to the following value: (3) Step 5: Compare the natural frequency f of the inertial actuator (1). a The optimal natural frequency f obtained in step three opt , If f a =f opt If the first switch (8) of the inductor branch and the second switch (10) of the capacitor branch in the parallel circuit of inductor, resistor and capacitor (4) are both disconnected; If f a <f opt Then, in the parallel circuit of inductor, resistor, and capacitor (4), the second switch (10) of the capacitor branch is open, the first switch (8) of the inductor branch is closed, and the value of the inductor element (7) of the inductor branch is set as follows: (4) If f a >f opt In the parallel circuit of inductor, resistor, and capacitor (4), the first switch (8) of the inductor branch is open, the second switch (10) of the capacitor branch is closed, and the value of the capacitor element (9) of the capacitor branch is set as follows: (5)。

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