A frequency-adjustable dynamic vibration absorber based on a gear train and a design method thereof

Abstract

The present invention proposes a frequency-adjustable dynamic vibration absorber based on a gear train and a design method, including an upper mass block and a lower gear base cell array. The gear base cell array includes tightly arranged gear base cells in n rows and m columns. Each gear base cell and each gear base cell and the top mass block are rigidly connected; the gear base cell includes an inner gear cylinder, a sun gear and multiple planetary gears, and each planetary gear is meshed with the inner gear cylinder and the sun gear. The present invention applies the gear train structure to the elastic element of the dynamic vibration absorber, which can realize rapid, stable and continuous adjustment of the natural frequency of the semi-active vibration absorber.

Description

Technical Field

[0001] The present application relates to the technical field of vibration reduction and noise reduction, and in particular to a frequency-adjustable dynamic vibration absorber based on a gear train and a design method thereof. Background Art

[0002] Dynamic vibration absorption technology involves attaching a subsystem consisting of springs, dampers, and masses to a main system to absorb the main system's energy, thereby suppressing the main system's vibrations. Dynamic vibration absorbers can be divided into three categories based on their external energy input requirements: passive, semi-active, and active. Passive dynamic vibration absorbers offer simple structures and low costs, but their effective vibration absorption frequency band is narrow and their versatility is limited. Despite extensive research on broadening the effective vibration absorption frequency band of passive dynamic vibration absorbers, they remain unable to effectively suppress multiple resonance peaks within a wide excitation frequency band. Active dynamic vibration absorbers, by directly applying forces between the main system and the subsystem, can achieve good vibration absorption with minimal additional mass. However, their complex structure, high energy consumption, and high cost significantly limit their practical engineering applications. Semi-active dynamic vibration absorbers modify the absorber's mass, damping, and stiffness so that its natural frequency changes in response to the excitation frequency, thereby maximizing the absorber's performance. Semi-active dynamic vibration absorbers, featuring low energy consumption, simple control, and excellent stability, have been extensively studied in recent years with the advancement of control theory and computer technology. Examples include frequency-adjustable cantilever beam dynamic vibration absorbers, dynamic vibration absorbers that achieve self-frequency adjustment by varying stiffness and dynamic mass, and negative stiffness dynamic vibration absorbers using frequency identification and control strategies.

[0003] Semi-active dynamic vibration absorbers can change their natural frequency in response to changes in the excitation frequency by changing the mass, damping, and stiffness of the absorber. However, they still have shortcomings in terms of stability, continuity, and speed of adjustment. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a frequency-adjustable dynamic vibration absorber and design method based on a gear system in response to the above-mentioned problems. The present invention is a semi-active dynamic vibration absorber. By applying the gear system structure to the elastic element of the dynamic vibration absorber, the natural frequency of the semi-active vibration absorber can be adjusted quickly, stably and continuously.

[0005] The embodiment of the present application is implemented as follows:

[0006] An embodiment of the present application provides a frequency-adjustable dynamic vibration absorber based on a gear system, which is characterized in that it includes an upper mass block and a lower gear base cell array, wherein the gear base cell array includes tightly arranged n rows and m columns of gear base cells, and each of the gear base cells and the gear base cells and the top mass block are rigidly connected.

[0007] In some optional embodiments, the gear base unit includes an inner gear cylinder, a sun gear, and a plurality of planetary gears, and each of the planetary gears is meshed with the inner gear cylinder and the sun gear.

[0008] In some optional embodiments, the gear base cell is made of carbon fiber reinforced polyetheretherketone composite material.

[0009] In some optional embodiments, the upper mass block is made of tungsten-based high-density alloy.

[0010] In some optional embodiments, the length of the upper mass block is the same as the length of the lower gear base cell array; the width of the upper mass block is the same as the tooth width of the gear base cell.

[0011] In some optional embodiments, there are four planetary gears in the gear base unit, which are arranged in pairs. The two planetary gears in a pair are symmetrically arranged on both sides of the sun gear and are collinear with the center of the sun gear.

[0012] In some optional embodiments, the lines connecting the centers of the two pairs of planetary gears intersect vertically.

[0013] A design method for a frequency-adjustable dynamic vibration absorber based on a gear train, characterized by comprising the following steps:

[0014] Step a: During operation, the vertical stiffness of the dynamic vibration absorber is mainly provided by the internal gear cylinder between the two pairs of planetary gear support points. The mechanical model for calculating the stiffness of the internal gear cylinder can be simplified to a plane curved rod with a rectangular cross section and a central angle of θ. First, considering the case where the planetary gears are symmetrically supported about the y-axis, the curvature radius r of the neutral layer of the internal gear cylinder is:

[0015]

[0016] The static moment of the cross section of the plane curved rod about the neutral axis is:

[0017] S=Ae=A(Rr)

[0018] Where: R1 is the curvature radius of the outer edge of the inner gear cylinder, mm;

[0019] R2 is the curvature radius of the inner edge of the inner gear cylinder, mm;

[0020] h is the cross-sectional height, i.e. the difference in radius between the inner and outer edges of the internal gear cylinder, h = R1-R2, mm;

[0021] b is the cross-sectional width, i.e. the tooth width, in mm;

[0022] A is the cross-sectional area, A = b × h, mm 2 ;

[0023] e is the distance between the neutral axis and the centroid axis, mm;

[0024] R is the radius of curvature of the cross-section centroid, R = (R1 + R2) / 2, mm;

[0025] Due to the symmetry of the structure, we take half of it for study. The internal force equation of any cross section of the curved rod is:

[0026]

[0027] Where: M α is the bending moment at any section, N·mm;

[0028] F N is the axial force at any section, N;

[0029] F Q is the shear force at any section, N;

[0030] α is the angle between any section and the y-axis, rad;

[0031] F is the vertical external force, N;

[0032] M is the bending moment at the center section of the curved rod, N·mm;

[0033] P is the axial force at the center section of the curved rod, N;

[0034] Deformation energy of the curved rod:

[0035]

[0036] Where: E is the elastic modulus, MPa;

[0037] G is the shear modulus, MPa;

[0038] c is a factor related to the cross-sectional shape, and is taken as 1.2 for a rectangular cross section;

[0039] According to the deformation coordination condition, that is, the rotation angle and horizontal displacement of the center section of the curved rod are 0, according to the Karl-Martin theorem, we can get:

[0040]

[0041] Solving the above equations together yields the bending moment M and axial force P at the center section of the curved rod:

[0042] M=FR[GR 1 (3sin2θ-6sinθ+3θ-θcos2θ-2θcosθ)+Ge 1 (3sin2θ-6sinθ+2θ-2θcosθ)+Ee 1c(sin2θ-2θ-2sinθ+2θcosθ)+GeR(12sinθ-θsin2θ-5θ+θcos2θ+4θcosθ)+EeRc(θ-sin2θ+2sinθ-2θcosθ+θcos26)] / 2[GR 1 (2-2cos2θ-2θ2-θsin2θ)+2Ge 1 (1-cos2θ)+GeR(2θ 1 +4cos2θ+θsin2θ-4)+EeRc(θsin2θ-2θ 1 )]

[0043] P=Fsinθ[GR 2 (2-2cosθ-θsinθ)+2Ge 2 (1-cosθ)+GeR(4cosθ-4+θsin)+EeRcθsinθ] / [GR 2 (4sin 2 θ-2θ 2 -θsin2θ)+4Ge 2 sin 2 θ+GeR(2θ 2 -8sin 2 θ+θsin2θ)+EeRc(θsin2θ-2θ 2 )]

[0044] From Karlsruhe's theorem and Hooke's law we know that:

[0045]

[0046] Where: δ Ay is the vertical displacement at the center section of the curved rod, mm;

[0047] The vertical equivalent stiffness of the plane curved rod with a central angle of θ is obtained by simultaneous solution:

[0048]

[0049] In the formula: N=M / F, mm; Q=P / F;

[0050] In summary, since the two pairs of planetary gears are perpendicular to each other, the theoretical analytical formula for the stiffness k of the plane curved rod is expressed as:

[0051] k=k θ +k π / 2-θ .

[0052] Step b: a single gear base unit is simplified into a single mass spring model. According to the spring series-parallel theory, the dynamic vibration absorber composed of n rows and m columns of gear base units and the upper mass block is simplified into an overall mass spring model, where m is the number of units that are connected to the gear base unit. cell is the mass of a single gear base unit cell. Each row of gear base units is considered as a unit with a mass of m r × mcell , the stiffness of both sides is m r ×k, the dynamic equation of the vibration absorber is as follows:

[0053]

[0054] Where Mü and Ku are the mass matrix and stiffness matrix respectively, both of which are (n+1)×(n+1) order matrices. The expressions of the two can be obtained by the influence coefficient method:

[0055]

[0056] Let the displacement matrix be:

[0057]

[0058] Where: A1~A n is the amplitude of each mass block from top to bottom in the overall mass-spring model;

[0059] Substituting the displacement matrix into the dynamic equation, so that the eigenvalue equation has a non-zero solution, the coefficient determinant is zero, and the frequency equation is obtained:

[0060]

[0061] By solving the above natural frequency equation, the vertical natural frequencies of the dynamic vibration absorber can be obtained.

[0062] The beneficial effects of the present application are: 1. The present application provides a frequency-adjustable dynamic vibration absorber based on a gear system and a design method, which is composed of a group of planetary gear system cell arrays and their top mass blocks. By rotating the sun gear in each cell by a certain angle, the planetary gear is driven to rotate to different positions to adjust the vertical stiffness of a single cell, thereby changing the vertical stiffness of the entire vibration absorber and realizing the adjustment of the natural frequency of the dynamic vibration absorber; 2. Targeted control can be performed on vibration problems under different working conditions, effectively solving the problem of multiple resonance peaks caused by complex broadband excitation; 3. Breaking through the macro and micro limitations of the structural size of the vibration absorber, greatly expanding the application range of this type of vibration absorber. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0064] Figure 1 This is an axonometric view of a dynamic vibration absorber according to an embodiment of the present application;

[0065] Figure 2 A front view of a dynamic vibration absorber according to an embodiment of the present application;

[0066] Figure 3 This is an axonometric view of a gear-based cell according to an embodiment of the present application;

[0067] Figure 4 A front view of a gear base unit cell according to an embodiment of the present application;

[0068] Figure 5 A simplified schematic diagram of a planar curved rod according to an embodiment of the present application;

[0069] Figure 6a This is a simplified schematic diagram of a planar curved rod symmetrical support according to an embodiment of the present application;

[0070] Figure 6b A simplified schematic diagram of a planar curved rod cut in half along the axis of symmetry according to an embodiment of the present application;

[0071] Figure 7a A schematic diagram of a single mass-spring model according to an embodiment of the present application;

[0072] Figure 7b Schematic diagram of a single mass-spring model according to an embodiment of the present application. DETAILED DESCRIPTION

[0073] To make the objectives, technical solutions, and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Generally, the components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0074] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for protection, but merely represents selected embodiments of the present application. All other embodiments obtained by persons of ordinary skill in the art based on the embodiments in the present application without creative work are within the scope of protection of the present application.

[0075] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0076] In the description of this application, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, or are the orientations or positional relationships in which the product of this application is typically placed when in use. These terms are intended only to facilitate the description of this application and simplify the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0077] Furthermore, terms such as "horizontal," "vertical," and "overhanging" do not necessarily imply that a component must be absolutely horizontal or overhanging, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but rather that it can be slightly tilted.

[0078] It should also be noted that, in the description of this application, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in this application based on the specific circumstances.

[0079] In this application, unless otherwise expressly specified or limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features being in contact not directly but through another feature between them. Moreover, a first feature being "above," "above," and "above" a second feature may include the first feature being directly above and obliquely above the second feature, or may simply mean that the first feature is higher in level than the second feature. A first feature being "below," "below," and "below" a second feature may include the first feature being directly below and obliquely below the second feature, or may simply mean that the first feature is lower in level than the second feature.

[0080] The features and performance of the present application are further described in detail below with reference to the embodiments.

[0081] like Figure 1As shown, in an embodiment of the present invention, a frequency-adjustable dynamic vibration absorber based on a gear train comprises an upper mass block 1 and a lower gear base cell array 2. The gear base cell array comprises gear base cells 3 arranged closely in n rows and m columns. Each gear base cell and the gear base cell and the top mass block are rigidly connected (see FIG. Figure 2 ).

[0082] like Figure 3 、 Figure 4 As shown, the gear base unit comprises an inner gear cylinder 4, a sun gear 5 and a plurality of planetary gears 6, and each planetary gear is meshed with the inner gear cylinder and the sun gear.

[0083] The frequency-adjustable dynamic vibration absorber based on a gear train is composed of a gear-based cell array and its upper mass. The gear-based cell array serves as the absorber's elastic element. By rotating the sun gear in each gear-based cell by a certain angle, the planetary gears are rotated to different positions to adjust the vertical stiffness of each gear-based cell. This, in turn, changes the vertical stiffness of the entire absorber, thereby adjusting the natural frequency of the dynamic vibration absorber and effectively suppressing multiple resonance peaks within a wide excitation frequency band.

[0084] The adjustable stiffness of the gear-based cellular structure is the key to the frequency adjustment of this new vibration absorber. Using the gear-based cellular array as the elastic element of the vibration absorber is a new approach to the structural design of frequency-adjustable dynamic vibration absorbers.

[0085] In this example, the gear base cell is made of carbon fiber reinforced polyetheretherketone composite material (PEEK-CF); the upper mass block is made of tungsten-based high-density alloy.

[0086] Polyetheretherketone (PEEK) offers excellent meshing load-bearing properties and is an excellent self-lubricating material. It maintains high tensile strength and flexural modulus even at high temperatures, and exhibits reliable creep and fatigue resistance, making it one of the top engineering materials for molded gears. Carbon fiber-reinforced PEEK composites further enhance mechanical properties such as strength and elastic modulus, offering excellent fatigue, impact, and wear resistance, and exhibit minimal strength loss in humid or high-temperature conditions. Using this material in parts effectively avoids surface defects such as cracks in metal or ceramic materials.

[0087] The high density, high strength, high hardness, low thermal expansion coefficient and other properties of tungsten-based high-density alloys have enabled them to be widely used as counterweights and balancing elements in transportation, weapons and equipment and other fields.

[0088] The frequency-adjustable dynamic vibration absorber based on a gear train is composed of n rows and m columns of gear-based cells and their upper mass blocks. Each gear-based cell and each cell-to-mass block are rigidly connected. The structure of the planetary gear train within the gear-based cells is adjusted according to actual needs and is identical for each cell. The number of rows in the cell array is determined by the low-frequency boundary required for the vibration absorber to operate, and the number of cell columns is selected to ensure dimensional coordination in the three dimensions of the vibration absorber: length, width, and height. The length and width of the upper mass block are consistent with the length of the gear-based cell array (cell outer diameter multiplied by the number of cell columns) and the cell tooth width, respectively. The height of the upper mass block is determined by the preset mass of the vibration absorber.

[0089] Example 1

[0090] There are four planetary gears in the gear base unit, arranged in pairs. The two pairs of planetary gears are symmetrically arranged on both sides of the sun gear and collinear with the center of the sun gear. The line connecting the centers of the two pairs of planetary gears intersects perpendicularly. Both the sun gear and the planetary gears are spur gears. The basic parameters are shown in Table 1, and the parameter relationships are shown in Equations (1-1) to (1-6). The origin of the coordinates x and y is the center point of the sun gear. The y direction is defined as the vertical direction, and the x direction is defined as the horizontal direction. i and B i Represents the center point of the planetary gear, and A1A2⊥B1B2.

[0091] Table 1 Basic parameters of gear base cell spur gear

[0092]

[0093] The relationship between the parameters of standard spur gears is as follows:

[0094] d=m×Z (1-1)

[0095] d a =d+2h a =m×Z+2m (1-2)

[0096] d f =d-2h f =m×Z-2.5m (1-3)

[0097] d=m×Z (1-4)

[0098] d a =d-2h a =m×Z-2m (1-5)

[0099] d f =d+2h f =m×Z+2.5m (1-6)

[0100] Where: ha is the tooth top height, mm;

[0101] hf is the tooth root height, mm.

[0102] In this embodiment, the vertical stiffness of the dynamic vibration absorber is mainly provided by the inner gear cylinder between the two pairs of planetary gear support points. The mechanical model for calculating the stiffness of the inner gear cylinder can be simplified to a plane curved rod with a rectangular cross section (see Figure 5 ), the central angle of the plane curved rod is 90°, first consider the case where the planetary gears A1 and B1 are supported symmetrically about the y axis (see Figure 6a ), that is, assuming that the central angle of the plane curved rod is 2θ, the curvature radius r of the neutral layer of the inner gear cylinder is:

[0103]

[0104] The static moment of the cross section of the plane curved rod about the neutral axis is:

[0105] S=Ae=A(Rr) (1-8)

[0106] Where: R1 is the curvature radius of the outer edge of the inner gear cylinder, R1 = D1 / 2, mm;

[0107] R2 is the radius of curvature of the inner edge of the inner gear cylinder (considering the influence of the teeth, the inner diameter of the inner gear ring is equal to the root circle diameter of the inner gear ring multiplied by the coefficient i = 0.9987), mm;

[0108] h is the cross-sectional height, i.e. the difference in radius between the inner and outer edges of the internal gear cylinder, h = R1-R2, mm;

[0109] b is the cross-sectional width, i.e. the tooth width, in mm;

[0110] A is the cross-sectional area, A = b × h, mm 2 ;

[0111] e is the distance between the neutral axis and the centroid axis, mm;

[0112] R is the radius of curvature of the cross-section centroid, R = (R1 + R2) / 2, mm;

[0113] Due to the symmetry of the structure, we take half of it for study (see Figure 6b ), the internal force equation of any cross section of the curved rod is:

[0114]

[0115] Where: M α is the bending moment at any section, N·mm;

[0116] F N is the axial force at any section, N;

[0117] F Q is the shear force at any section, N;

[0118] α is the angle between any section and the y-axis, rad;

[0119] F is the vertical external force, N;

[0120] M is the bending moment at the center section of the curved rod, N·mm;

[0121] P is the axial force at the center section of the curved rod, N;

[0122] Deformation energy of the curved rod:

[0123]

[0124] Where: E is the elastic modulus, MPa;

[0125] G is the shear modulus, MPa;

[0126] c is a factor related to the cross-sectional shape, and is 1.2 for a rectangular cross-section.

[0127] According to the deformation coordination condition, that is, the rotation angle and horizontal displacement of the curved rod section AA are 0, according to the Cartesian theorem, we can get:

[0128]

[0129] Combining the above equations (1-12) to (1-14), we can obtain the bending moment M and axial force P at the curved rod section AA:

[0130]

[0131]

[0132] From Karlsruhe's theorem and Hooke's law we know that:

[0133]

[0134] Where: δAy is the vertical displacement at the center section of the curved rod, mm;

[0135] Solving the above two equations together yields the vertical equivalent stiffness of the planar curved rod with a central angle of θ as shown in Figure 6B:

[0136]

[0137] In the formula: N=M / F, mm; Q=P / F;

[0138] In summary, since the two pairs of planetary gears are perpendicular to each other, A1A2⊥B1B2, the theoretical analytical formula for the stiffness k of the plane curved rod is expressed as:

[0139] k=k θ +π / 2-θ (1-20)

[0140] In the calculation of the natural frequency of the gear-based dynamic vibration absorber, a single gear-based cell is simplified to a single mass-spring model (see Figure 7a ), according to the spring series-parallel theory, the dynamic vibration absorber consisting of n rows and m columns of gear base cells and the upper mass block is simplified to an overall mass spring model (see Figure 7b ), where m cell is the mass of a single gear base unit cell. Each row of gear base units is considered as a unit with a mass of m r × mcell , the stiffness of both sides is m r ×k, the dynamic equation of the vibration absorber is as follows:

[0141]

[0142] in and Ku are the mass matrix and stiffness matrix respectively, both are (n+1)×(n+1) order matrices. The expressions of the two can be obtained by the influence coefficient method:

[0143]

[0144] Let the displacement matrix be:

[0145]

[0146] Where: A1~A n is the amplitude of each mass block from top to bottom in the overall mass-spring model;

[0147] Substituting the displacement matrix into the dynamic equation (1-21) so that the eigenvalue equation has a non-zero solution, the coefficient determinant is zero, and the frequency equation is obtained:

[0148]

[0149] By solving the above natural frequency equation, the vertical natural frequencies of the dynamic vibration absorber can be obtained.

[0150] In the design process of the gear-based dynamic vibration absorber, the overall mass of the absorber is one of the key parameters of the dynamic vibration absorption process. Too small a mass will not bring about a good vibration absorption effect, while too large a mass will have an adverse effect on the overall design of the ship. According to the overall design requirements of the ship and the working principle of the vibration absorber, it is first necessary to determine the appropriate vibration absorber mass; at the same time, it is necessary to consider whether the vibration absorption working frequency band of the dynamic vibration absorber meets the requirements. The low-frequency working boundary of this vibration absorber is difficult to obtain. Therefore, according to the required minimum vibration absorption frequency, the number of rows of the gear-based dynamic vibration absorber gear-based cell array is determined; secondly, the stability of the gear-based dynamic vibration absorber should be comprehensively considered, and the coordination of its length, width and height dimensions should be ensured as much as possible to determine the reasonable number of cell columns; the length, width and height of the mass block at the top of the vibration absorber are determined according to the number of cell columns, the gear tooth width and the overall mass of the vibration absorber; finally, the design of the entire vibration absorber is a cyclical and spiral process, and it is often necessary to obtain a better vibration absorber type after multiple parameter improvements.

[0151] Example 2

[0152] Starting from the vibration issues existing in the aft compartment of a certain ship, a specific structural type of dynamic vibration absorber was constructed. The vibration control target was the 1 / 5L aft compartment of a certain ship, which consists of three decks and uses a single engine and single propeller. According to the vibration response calculation results, under propeller surface force excitation, the ship's aft vibration level response curve exhibits two distinct vibration peaks at 17.75Hz and 27.91Hz, corresponding to normal operating conditions and maximum speed conditions, respectively. Considering the vibration absorption frequency band required for vibration control in the aft compartment of the ship, a simulation calculation method was used to select the gear-based cellular structure. An overly large cellular would occupy too much space within the ship, adversely affecting the overall ship design; an undersized cellular would require an excessive number of rows within the gear-based cellular array to achieve a lower natural frequency of the vibration absorber and meet the vibration absorption frequency band requirements. Based on these considerations, a single cellular structure of the gear-based cellular that can be applied to this ship is proposed. The cellular parameters are shown in Table 2.

[0153] Table 2 Parameters of standard spur gears

[0154]

[0155] The gear base cell array is made of carbon fiber reinforced polyetheretherketone composite material (PEEK-CF), and its basic mechanical parameters are shown in Table 3:

[0156] Table 3 Basic mechanical parameters of PEEK-CF (550CA30)

[0157]

[0158] The top mass block of the dynamic vibration absorber is made of tungsten-based high-density alloy with a density of 19g / cm3.

[0159] In this example, a gear-based dynamic vibration absorber consisting of a 6×4 cell array and a top mass block was proposed to address the vibration issues in the aft compartment, taking into account the stability of the dynamic vibration absorber during operation and ensuring its frequency modulation range, while also minimizing the space occupied by the ship. The top mass block is 680 mm long, 250 mm high, and 200 mm wide, matching the cell tooth width. The total mass of the absorber is 726 kg. By rotating the sun gear in each cell by the same angle, the vertical stiffness of each cell can be adjusted, thereby varying the stiffness of the entire absorber and adjusting the natural frequency of the dynamic vibration absorber to meet the vibration absorption requirements of various operating conditions. The natural frequencies of the absorber at different angles are summarized in Table 4.

[0160] Table 4 Theoretical calculation values ​​of the natural frequency of the gear-based dynamic vibration absorber

[0161]

[0162] Calculations show that the absorber's operating frequency band covers the excitation frequencies of the ship's propeller surface forces under all operating conditions. Its wide frequency modulation range enables ultra-broadband vibration absorption. By installing this gear-based dynamic absorber on the double-layer bottom plate frame at the stern of the hull, stern vibrations are effectively controlled.

[0163] The above is only a preferred embodiment of this intellectual achievement, but this intellectual achievement should not be limited to the contents disclosed in this embodiment and the accompanying drawings. All equivalents or modifications completed without departing from the spirit disclosed in this invention fall within the scope of protection of this invention.

Claims

1. A design method for a frequency-adjustable dynamic vibration absorber based on a gear train, the frequency-adjustable dynamic vibration absorber comprising an upper mass block and a lower gear base cell array, the gear base cell array comprising closely arranged gear base cells in n rows and m columns, each of the gear base cells being rigidly connected to each other and to the upper mass block; the gear base cell comprising an inner gear cylinder, a sun gear, and a plurality of planetary gears, each of the planetary gears meshing with the inner gear cylinder and the sun gear; the length of the upper mass block being the same as the length of the lower gear base cell array; the width of the upper mass block being the same as the tooth width of the gear base cell; the number of planetary gears in the gear base cell being four, arranged in pairs, the two planetary gears being symmetrically arranged on either side of the sun gear, collinear with the center of the sun gear, and the line connecting the centers of the two pairs of planetary gears being perpendicular to each other; It is characterized by: The steps include: Step a: During operation, the vertical stiffness of the dynamic vibration absorber is mainly provided by the internal gear cylinder between the two pairs of planetary gear support points. The mechanical model for calculating the stiffness of the internal gear cylinder can be simplified to a plane curved rod with a rectangular cross section and a central angle of θ. First, considering the case where the planetary gears are symmetrically supported about the y-axis, the curvature radius r of the neutral layer of the internal gear cylinder is: The static moment of the cross section of the plane curved rod about the neutral axis is: S=Ae=A(Rr) Where: R1 is the curvature radius of the outer edge of the inner gear cylinder, mm; R2 is the curvature radius of the inner edge of the inner gear cylinder, mm; h is the cross-sectional height, i.e. the difference in radius between the inner and outer edges of the internal gear cylinder, h = R1-R2, mm; b is the cross-sectional width, i.e. the tooth width, in mm; A is the cross-sectional area, A = b × h, mm 2 ; e is the distance between the neutral axis and the centroid axis, mm; R is the radius of curvature of the cross-section centroid, R = (R1 + R2) / 2, mm; Due to the symmetry of the structure, we take half of it for study. The internal force equation of any cross section of the curved rod is: Where: M α is the bending moment at any section, N·mm; F N is the axial force at any section, N; F Q is the shear force at any section, N; α is the angle between any section and the y-axis, rad; F is the vertical external force, N; M is the bending moment at the center section of the curved rod, N·mm; P is the axial force at the center section of the curved rod, N; Deformation energy of the curved rod: Where: E is the elastic modulus, MPa; G is the shear modulus, MPa; c is a factor related to the cross-sectional shape, and is taken as 1.2 for a rectangular cross section; According to the deformation coordination condition, that is, the rotation angle and horizontal displacement of the center section of the curved rod are 0, according to the Karl-Martin theorem, we can get: Solving the above equations together yields the bending moment M and axial force P at the center section of the curved rod: M=FR[GR 2 (3sin 2θ-6sinθ+3θ-θcos 2θ-2θcosθ)+Ge 2 (3sin 2θ-6sinθ+2θ-2θcosθ)+Ee 2 c(sin 2θ-2θ-2sinθ+2θcosθ)+GeR(12sinθ-6sin 2θ-5θ+θcos 2θ+4θcosθ)+EeRc(θ-sin2θ+2sinθ-2θcosθ+θcos 2θ)] / 2[GR 2 (2- 2cos 2θ-2θ 2 -θsin 2θ)+2Ge 2 (1-cos 2θ)+GeR(2θ 2 +4cos 2θ+θsin 2θ-4)+EeRc(θsin 2θ-2θ 2 )] P=Fsinθ[GR 2 (2-2cosθ-θsinθ)+2Ge 2 (1-cosθ)+GeR(4cosθ-4+θsinθ)+EeRcθsinθ] / [GR 2 (4sin 2 θ-2θ 2 -θsin 2θ)+4Ge 2 sin 2 θ+GeR(2θ 2 -8sin 2 θ+θsin 2θ)+EeRc(θsin 2θ-2θ 2 )] From Karlsruhe's theorem and Hooke's law we know that: Where: δ Ay is the vertical displacement at the center section of the curved rod, mm; The vertical equivalent stiffness of the plane curved rod with a central angle of θ is obtained by simultaneous solution: In the formula: N=M / F, mm; Q=P / F; In summary, since the two pairs of planetary gears are perpendicular to each other, the theoretical analytical formula for the stiffness k of the plane curved rod is expressed as: Step b: a single gear base unit is simplified into a single mass spring model. According to the spring series-parallel theory, the dynamic vibration absorber composed of n rows and m columns of gear base units and the upper mass block is simplified into an overall mass spring model, where m is the number of units that are connected to the gear base unit. cell is the mass of a single gear base unit cell. Each row of gear base units is considered as a unit with a mass of m r × mcell , the stiffness of both sides is m r ×k, the dynamic equation of the vibration absorber is as follows: in and Ku are the mass matrix and stiffness matrix respectively, both are (n+1)×(n+1) order matrices. The expressions of the two can be obtained by the influence coefficient method: Let the displacement matrix be: Where: A1~A n is the amplitude of each mass block from top to bottom in the overall mass-spring model; Substituting the displacement matrix into the dynamic equation, so that the eigenvalue equation has a non-zero solution, the coefficient determinant is zero, and the natural frequency equation is obtained: By solving the above natural frequency equation, the vertical natural frequencies of the dynamic vibration absorber can be obtained.

2. The design method of a frequency-adjustable dynamic vibration absorber based on a gear train according to claim 1, characterized in that: The gear base cell is made of carbon fiber reinforced polyetheretherketone composite material.

3. The design method of a frequency-adjustable dynamic vibration absorber based on a gear train according to claim 1 or 2, characterized in that: The upper mass block is made of tungsten-based high-density alloy.

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