A method for parameter selection of a drive shaft power absorber

Abstract

The application discloses a kind of drive shaft power absorber parameter selection method, comprising the following steps: obtaining the free modal of drive shaft;Single degree of freedom power absorber dynamics model is established;The first order natural frequency of main vibration system is determined;Drive shaft power absorber mass is determined;The optimal damping ratio and optimal natural frequency of drive shaft power absorber are determined using fixed point theory.The application determines the simply supported support model of drive shaft as the model of main vibration system according to the connection mode of drive shaft and two universal joints, and determines the optimal natural frequency and optimal damping ratio of drive shaft power absorber according to fixed point theory, thereby providing reference basis for parameter selection of drive shaft power absorber.

Description

Technical Field

[0001] This invention relates to the field of NVH optimization design of automotive chassis, and in particular to a method for obtaining the first-order modal natural frequency of a simply supported model of a drive shaft based on a specific drive shaft and universal joint connection at both ends, and a method for selecting the mass, damping ratio, and natural frequency of the drive shaft dynamic vibration absorber. Background Technology

[0002] The structure of a car chassis is extremely complex, and it is difficult to ensure that the natural frequencies of each component avoid the excitation frequencies of the engine and the ground. Therefore, some NVH (Noise, Vibration, and Harshness) issues may still exist in vehicles in the later stages of development. Solving this by redesigning the structure would not only increase costs but also extend the vehicle's development cycle. To avoid resonance without altering the existing structure of components at risk of resonance, installing dynamic vibration absorbers is an ideal vibration reduction method. Dynamic vibration absorbers are simple to install, provide good vibration reduction, and are inexpensive, making them suitable for addressing NVH issues in the later stages of vehicle development. Therefore, the selection of various performance parameters for dynamic vibration absorbers is crucial to ensure their effective elimination of resonance and improvement of vehicle NVH performance in practical applications.

[0003] Installing dynamic vibration absorbers with different performance parameters one by one on the drive shaft and determining their optimal performance parameters through actual vehicle testing would be labor-intensive and costly. Therefore, determining the optimal performance parameters of dynamic vibration absorbers by selecting a suitable main vibration system model and performing theoretical calculations is of great significance.

[0004] To obtain the optimal performance parameters of a dynamic vibration absorber through theoretical calculations, it is first necessary to determine the parameters of the main vibration system in the dynamic model of a single-mass drive shaft dynamic vibration absorber. Currently, the most common drive shaft assembly structure consists of one end connected to a fixed universal joint and the other end connected to a sliding universal joint; its first-order natural frequency is affected by the connection method. In published literature, the selection of the main vibration system is often vague, and there are no clear standards for selecting the mass of the dynamic vibration absorber. Summary of the Invention

[0005] This invention considers the connection method between the drive shaft and the universal joints at both ends in a specific drive shaft assembly (one end of the drive shaft assembly uses a fixed universal joint, and the other end uses a sliding universal joint), and establishes a method for calculating the first-order natural frequency of the main vibration system using a simply supported drive shaft model as the main vibration system. The first-order natural frequency of the simply supported drive shaft model is obtained through the formula for calculating the natural frequency of the simply supported model, thus determining all parameters of the main vibration system. A reference value for the ratio of the drive shaft dynamic vibration absorber's mass to the main vibration system's mass is determined by considering vibration reduction effect, cost, layout space, and lightweighting. According to optimization theory, after determining the mass ratio, the optimal natural frequency and optimal damping ratio of the drive shaft dynamic vibration absorber can be determined. This method can provide a reference for the parameter selection of the drive shaft dynamic vibration absorber.

[0006] To achieve the objective of this invention, the present invention provides a method for selecting parameters of a drive shaft dynamic vibration absorber, comprising the following steps:

[0007] (1) Obtain the free modes of the drive shaft: This can be done using a hammer impact test and a finite element simulation method. After obtaining the first two free modes of the drive shaft, calculate the ratio between them.

[0008] (2) Establishment of the dynamic model of the single-degree-of-freedom dynamic vibration absorber: Analyze the natural frequencies of the first two free modes of the drive shaft. If the ratio of the two meets the requirements, the damping of the main vibration system can be ignored. Establish the dynamic model of the single-degree-of-freedom dynamic vibration absorber without damping of the main vibration system, and derive the expression for the amplitude ratio of the main vibration system under the action of harmonic force:

[0009]

[0010] In the formula, X1 is the displacement of the main vibration system, and X... st ω is the static deformation of the main vibration system, α is the ratio of the natural frequency of the dynamic vibration absorber to the natural frequency of the main vibration system, λ is the ratio of the excitation frequency to the natural frequency of the main vibration system, ξ is the damping ratio of the dynamic vibration absorber, and μ is the mass ratio of the dynamic vibration absorber to the main vibration system.

[0011] (3) Determination of the first natural frequency of the main vibration system: Analyze the connection between the drive shaft and the universal joints at both ends. If the axial displacement of only one end of the drive shaft is constrained, while the displacement of the other end is unconstrained, and the rotation of the drive shaft around its own axis is not restricted, then the simply supported model of the drive shaft can be used as the model of the main vibration system in this model. The first natural frequency of the simply supported model of the drive shaft can be obtained through theoretical calculation, or it can be converted from the first natural frequency of the free mode obtained in step (1).

[0012] (4) The quality of the drive shaft dynamic vibration absorber is determined by comprehensively considering factors such as layout space, cost, lightweighting and vibration reduction effect.

[0013] (5) The optimal damping ratio and optimal natural frequency of the drive shaft dynamic vibration absorber are determined using fixed-point theory. The relationship between the optimal damping ratio and optimal natural frequency ratio of the dynamic vibration absorber and the mass of the main vibration system is obtained through fixed-point theory:

[0014]

[0015]

[0016] In the formula, ξ OPT For the optimal damping ratio of the dynamic vibration absorber, α OPT This is the optimal natural frequency ratio for the dynamic vibration absorber.

[0017] In step (1), the free modes of the drive shaft can be obtained by using a hammer impact test or a finite element simulation method.

[0018] When using the finite element simulation method in step (1), the natural frequencies of the first 6 modes of the drive shaft obtained by finite element calculation are 0, because these 6 modes reflect the rigid body displacement of the drive shaft. The 7th mode is the natural frequency of the first bending mode of the drive shaft, that is, the natural frequency of the first free mode.

[0019] The ratio in step (2) must satisfy the following condition: For a bending vibration system of a continuous elastic body such as an automobile drive shaft, if the first and second order bending natural frequencies f1 and f2 of the main vibration system satisfy the condition In this case, the damping of the main vibration system can be ignored.

[0020] The derivation process of the amplitude ratio expression of the main vibration system under the action of harmonic force in step (2) is as follows:

[0021] The system dynamic equations are obtained based on the dynamic model of the single-degree-of-freedom dynamic vibration absorber:

[0022]

[0023] The harmonic force F in formula (4) (t) =F0sinωt is written as F (t) =f0e jωt And let the displacement of the main vibration system be... in Let j be the complex amplitude of the main vibration system, F0 be the amplitude of the excitation force, and t be the time. Substituting the expression for the displacement X1 of the main vibration system into formula (4), the complex amplitude of the main vibration system can be solved. The expression:

[0024] Substituting the expression for the displacement X1 of the main vibration system into formula (4), we obtain the complex amplitude of the main vibration system. The expression:

[0025]

[0026] Pick From the real part, we obtain the expression for the amplitude X1 of the principal oscillation system:

[0027]

[0028] By writing formula (6) in dimensionless form, we can obtain the aforementioned... The expression.

[0029] The expression for the damping ratio ξ of the dynamic vibration absorber in step (2) is:

[0030]

[0031] In the formula, c is the damping of the dynamic vibration absorber, m2 is the mass of the dynamic vibration absorber, and ω2 is the natural frequency of the dynamic vibration absorber.

[0032] The main vibration system selection method used in step (3) is only applicable to drive shaft assemblies that use a fixed universal joint on one side and a sliding universal joint on the other side, and where there is a certain gap between the internal parts of the universal joint.

[0033] In step (3), the i-th natural frequency f of the main vibration system in the simply supported drive shaft model is... i The calculation formula is:

[0034]

[0035] Where E is the elastic modulus of the material; I is the moment of inertia of the axial section; ρ is the density of the material; A is the area of ​​the axial section; and l is the length of the shaft.

[0036] In step (3), the first-order natural frequency of the simply supported drive shaft model is obtained as follows:

[0037] By setting i to 1 in formula (8), the first natural frequency of the simply supported drive shaft model can be obtained through formula (8).

[0038] Alternatively, the first-order natural frequency of the simply supported drive shaft model can be obtained by dividing the first-order free modal natural frequency obtained in step (1) by 2.267.

[0039] In step (5), for a single-degree-of-freedom drive shaft dynamic vibration absorber, after determining the mass ratio μ of the dynamic vibration absorber and the main vibration system and the ratio α of the natural frequency of the dynamic vibration absorber and the natural frequency of the main vibration system, the frequency response curve of the main vibration system under different damping ratios of the dynamic vibration absorber can be obtained. In the frequency response curve, there are two fixed points S and T. No matter how the damping ratio of the dynamic vibration absorber changes, the amplitude ratio curve passes through these two points. These two points are fixed points. This theory is the fixed point theory. During the process of the damping ratio of the drive shaft dynamic vibration absorber increasing from 0 to +∞, the two peaks of the amplitude ratio curve gradually converge and become a single peak. Therefore, there must exist a damping ratio that makes the peak of the amplitude ratio curve at points S and T. At this time, the amplitude ratio of the main vibration system is the lowest. This damping ratio is the optimal damping ratio of the dynamic vibration absorber. Making points S and T at the same height can obtain the optimal natural frequency ratio of the system. At this time, the maximum amplitude ratio of the system will reach the minimum value.

[0040] Compared with the prior art, the present invention has at least the following positive effects:

[0041] 1) Based on the specific connection method between the drive shaft and the universal joints at both ends, the simply supported model of the drive shaft is determined as the main vibration system model, which makes it easier to obtain the first-order free modal natural frequency of the drive shaft through theoretical calculation or by hammering, finite element method, etc., and finally obtain the first-order natural frequency of the simply supported model of the drive shaft.

[0042] 2) This invention takes into account factors such as vibration reduction effect, cost, and lightweighting to determine the range of mass selection for the drive shaft dynamic vibration absorber.

[0043] 3) This invention determines the optimal natural frequency and optimal damping ratio of the drive shaft dynamic vibration absorber based on the fixed-point theory, thereby providing a reference for the parameter selection of the drive shaft dynamic vibration absorber. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the steps of a method for selecting parameters of a drive shaft dynamic vibration absorber according to an embodiment of the present invention;

[0045] Figure 2 This is a schematic diagram of the dynamic model of a single-degree-of-freedom dynamic vibration absorber;

[0046] Figure 3 This is a schematic diagram of the drive shaft connection method to which this invention applies;

[0047] Figure 4 A comparison diagram of the first-order natural frequencies of a simply supported drive shaft model obtained by different methods;

[0048] Figure 5Taking a single-mass driven shaft dynamic vibration absorber model with a system mass ratio μ = 0.1 and a natural frequency ratio α = 1 as an example, the frequency response curves under different damping ratios when subjected to harmonic force excitation are shown.

[0049] Figure 6(a) shows the frequency response curve of the main vibration system when it is subjected to harmonic force excitation without the installation of a dynamic vibration absorber. The main vibration system has a mass m1 = 3.270 kg and a first-order natural frequency ω1 = 145.856 Hz.

[0050] Figure 6(b) shows the frequency response curve of the main vibration system subjected to the same harmonic force after the parameters of the drive shaft power vibration absorber are determined according to steps (4) and (5) and installed.

[0051] Figure 6(c) is a comparison of the vibration reduction effect before and after installing the drive shaft dynamic vibration absorber. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the present invention clearer and more explicit, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0053] Please see Figure 1 The present invention provides a method for selecting parameters of a drive shaft dynamic vibration absorber, comprising the following steps:

[0054] (1) Obtain the free modes of the drive shaft. After obtaining the first two free modes of the drive shaft, calculate the ratio between the first two free modes. If the natural frequency of the second free mode of the drive shaft is more than twice the natural frequency of the first free mode, the damping of the main vibration system, i.e., the drive shaft, can be ignored.

[0055] The free modes of the drive shaft can be obtained by using hammer impact testing and finite element simulation.

[0056] In some embodiments of the present invention, a hammer striking method is used: the splines at both ends of the drive shaft are suspended in the air by nylon ropes to ensure that no part of the drive shaft comes into contact with other objects, a triaxial acceleration sensor is attached to the drive shaft, the drive shaft is struck with a hammer, and the transmitted acceleration signal is collected by a HEAD data acquisition device. The HEAD data acquisition device automatically outputs the nth order free mode natural frequency of the drive shaft.

[0057] In some embodiments of this invention, a finite element simulation method is employed: the digital model of the drive shaft is imported into finite element software (such as ABAQUS), and steps such as mesh generation, material property setting, and modal analysis are performed to obtain the free modes of the drive shaft. It is worth noting that the natural frequencies of the first six modes of the drive shaft obtained through finite element calculation are 0, because these six modes reflect the rigid body displacement of the drive shaft. The seventh mode is the first-order bending mode natural frequency of the drive shaft, i.e., the first-order free mode natural frequency.

[0058] (2) Analyze the natural frequencies of the first two free modes of the drive shaft. If the ratio of the two meets the requirements, the damping of the main vibration system can be ignored. Establish the dynamic model of the single-degree-of-freedom dynamic vibration absorber without damping of the main vibration system, and obtain the expression of the amplitude ratio of the main vibration system under the action of simple harmonic force.

[0059] In some embodiments of the present invention, the dynamic model of the single-degree-of-freedom dynamic vibration absorber is as follows: Figure 2 As shown, m1 and m2 are the masses of the main vibration system and the dynamic vibration absorber, respectively; K1 and K2 are the stiffnesses of the main vibration system and the dynamic vibration absorber, respectively; c is the damping of the dynamic vibration absorber; F (t) X1 represents the harmonic force applied to the main vibration system from the outside; X2 represents the displacements of the main vibration system and the dynamic vibration absorber, respectively. Based on the dynamic model of the single-degree-of-freedom dynamic vibration absorber, the system dynamic equations can be derived as follows:

[0060]

[0061] The harmonic force F in formula (4) (t) =F0sinωt is written as F (t) =f0e jωt And let the displacement of the main vibration system be... in Let j be the complex amplitude of the main vibration system, F0 be the amplitude of the excitation force, and t be the time. Substituting the expression for the displacement X1 of the main vibration system into formula (4), the complex amplitude of the main vibration system can be solved. The expression:

[0062]

[0063] Pick From the real part, we obtain the expression for the amplitude X1 of the principal oscillation system:

[0064]

[0065] By writing formula (6) in dimensionless form, we can obtain... The expression is formula (1).

[0066] In the formula, The first natural frequency of the main oscillation system; The static deformation of the main vibration system; The mass ratio of the dynamic vibration absorber to the main vibration system; It is the ratio of the excitation frequency to the natural frequency of the main oscillation system; The ratio of the natural frequency of the dynamic vibration absorber to the natural frequency of the main vibration system; The damping ratio of the dynamic vibration absorber is given by formula (1). Formula (1) is an important basis for judging the vibration reduction effect of the dynamic vibration absorber of the drive shaft.

[0067] In some embodiments of the present invention, in determining whether the ratio of the two meets a preset requirement, if the natural frequency of the second-order free mode of the drive shaft is more than twice the natural frequency of the first-order free mode, that is... At this point, the damping of the main vibration system, i.e., the drive shaft, can be ignored.

[0068] (3) Determination of the first natural frequency of the main oscillation system:

[0069] Analyzing the connection methods between the drive shaft and the universal joints at both ends, if one end of the drive shaft is connected to a sliding universal joint and the other end is connected to a fixed universal joint, such as... Figure 3 As shown, the axial displacement of one end of the drive shaft is constrained, while the displacement of the other end is unconstrained. Furthermore, due to the gaps between the internal components of both types of universal joints, there is no restriction on the rotation of the drive shaft around the axis. Based on these constraints of the drive shaft in the drive shaft assembly, a simply supported model of the drive shaft (where the axial displacement of one end of the shaft is constrained, the other end is unconstrained, and the entire shaft can move around its own axis) can be used as the model for the main vibration system. The i-th natural frequency f of the main vibration system in the simply supported drive shaft model is... i The calculation formula is:

[0070]

[0071] Where E is the elastic modulus of the material; I is the moment of inertia of the axial section; ρ is the density of the material; A is the area of ​​the axial section; and l is the length of the shaft.

[0072] Setting i = 1 in formula (7) yields the first natural frequency of the simply supported drive shaft model. Simultaneously, the first natural frequency of the simply supported drive shaft model can also be obtained by dividing the first free modal natural frequency obtained in step (1) by 2.267. The calculated data comparison is shown in the figure below. Figure 4 As shown.

[0073] (4) Determining the mass of the drive shaft dynamic vibration absorber:

[0074] In some embodiments of the present invention, actual vehicle tests have shown that a main vibration system amplitude ratio of around 3.5 can achieve a good vibration reduction effect. Therefore, considering factors such as installation space, cost, and lightweighting, the mass of the drive shaft power vibration absorber is usually set at 20% of the drive shaft mass.

[0075] (5) Determine the optimal damping ratio and optimal natural frequency ratio of the dynamic vibration absorber based on the fixed-point theory:

[0076] For a single-degree-of-freedom drive shaft dynamic vibration absorber, once the mass ratio μ of the dynamic vibration absorber to the main vibration system and the ratio α of the dynamic vibration absorber's natural frequency to the main vibration system's natural frequency are determined, the frequency response curves of the main vibration system under different damping ratios of the dynamic vibration absorber can be obtained. In the frequency response curve, there are two fixed points, S and T. Regardless of the change in the damping ratio of the dynamic vibration absorber, the amplitude ratio curve always passes through these two points; these two points are called fixed points, and this is known as the fixed-point theory. As the damping ratio of the drive shaft dynamic vibration absorber increases from 0 to +∞, the two peaks of the amplitude ratio curve gradually converge into a single peak. Therefore, there must exist a damping ratio that causes the peak of the amplitude ratio curve to be at points S and T. At this point, the amplitude ratio of the main vibration system is at its lowest. This damping ratio is the optimal damping ratio of the dynamic vibration absorber. Making points S and T equal in height yields the optimal natural frequency ratio of the system, at which point the maximum amplitude ratio of the system reaches its minimum value. Therefore, through this law, the relationship between the optimal damping ratio and optimal natural frequency ratio of the dynamic vibration absorber and the mass ratio of the main vibration system can be obtained:

[0077]

[0078]

[0079] In some embodiments of the present invention, taking a single-mass driven shaft dynamic vibration absorber model with a mass ratio μ = 0.1 between the dynamic vibration absorber and the main vibration system, a ratio α = 1 between the natural frequency of the dynamic vibration absorber and the natural frequency of the main vibration system, and a value λ between the harmonic force excitation frequency and the natural frequency of the system of 0.6 ≤ λ ≤ 1.3 as an example, regardless of how the damping ratio ξ of the dynamic vibration absorber changes, Figure 5 The mid-frequency response curve always passes through two fixed points, S and T, which is the fixed-point theory. As the damping ratio of the dynamic vibration absorber increases from 0 to +∞, the two peaks of the amplitude ratio curve gradually converge into a single peak. Therefore, there must exist a damping ratio that causes the peak of the amplitude ratio curve to be at points S and T. At this point, the amplitude ratio of the main vibration system is at its lowest; this damping ratio is the optimal damping ratio of the dynamic vibration absorber. Making points S and T equal in height yields the optimal natural frequency ratio of the system, at which point the maximum amplitude ratio of the system reaches its minimum. Therefore, the optimal damping ratio and optimal natural frequency ratio of the dynamic vibration absorber can be obtained through this law, where the optimal damping ratio ξ... OPT The optimal natural frequency ratio α can be obtained from formula (2). OPT It can be obtained from formula (3). It should be noted that the specific value given above is a specific example, and other values ​​may be used in other embodiments.

[0080] At this point, all parameters of the drive shaft dynamic vibration absorber have been determined.

[0081] In some embodiments of the present invention, the vibration reduction effect of a drive shaft dynamic vibration absorber designed with parameters obtained by the method is verified by the following examples:

[0082] Main vibration system parameters: Main vibration system mass m1 = 3.270 kg; first-order natural frequency ω1 = 145.856 Hz. The frequency response curve of the system under harmonic excitation without a dynamic vibration absorber is shown in Figure 6(a). The amplitude ratio reaches its peak when the excitation frequency equals the first-order natural frequency of the main vibration system. A drive shaft dynamic vibration absorber is now used to avoid resonance.

[0083] Parameters of the drive shaft dynamic vibration absorber: According to step (4), the mass of the drive shaft dynamic vibration absorber is m2 = m1 × 20% = 0.654 kg. According to formula (2), the damping ratio of the drive shaft dynamic vibration absorber is ξ = 0.25; according to formula (3), the first natural frequency of the drive shaft dynamic vibration absorber is ω2 = 121.546 Hz. The frequency response curve of the main vibration system subjected to the same harmonic force after installing the drive shaft dynamic vibration absorber is shown in Figure 6(b). The comparison diagram of the vibration reduction effect before and after installing the drive shaft dynamic vibration absorber is shown in Figure 6(c). Obviously, the vibration reduction effect of installing the drive shaft dynamic vibration absorber is obvious.

[0084] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for selecting parameters of a drive shaft dynamic vibration absorber, characterized in that, Includes the following steps: (1) Obtain the free modes of the drive shaft. After obtaining the first two free modes of the drive shaft, calculate the ratio of the natural frequency of the second free mode of the drive shaft to the natural frequency of the first free mode of the drive shaft. (2) Analyze the natural frequencies of the first two free modes of the drive shaft. If the ratio of the two meets the preset requirements, the damping of the main vibration system can be ignored. Establish the dynamic model of the single-degree-of-freedom dynamic vibration absorber without damping of the main vibration system, and obtain the expression for the amplitude ratio of the main vibration system under the action of harmonic force: In the formula, The displacement of the main vibration system The static deformation of the main vibration system The excitation frequency, The ratio of the natural frequency of the dynamic vibration absorber to the natural frequency of the main vibration system. It is the ratio of the excitation frequency to the natural frequency of the main oscillation system. The damping ratio of the dynamic vibration absorber. The mass ratio of the dynamic vibration absorber to the main vibration system; (3) Determination of the first natural frequency of the main vibration system: For a drive shaft assembly with a fixed universal joint at one end and a sliding universal joint at the other end, the drive shaft is constrained in axial displacement at one end only, and the displacement at the other end is not constrained. The rotation of the drive shaft around its own axis is not restricted. Therefore, the simply supported model of the drive shaft is used as the model of the main vibration system in this model. The first natural frequency of the simply supported model of the drive shaft is obtained by theoretical calculation or by conversion based on the first free mode natural frequency obtained in step (1). (4) The quality of the drive shaft dynamic vibration absorber is determined by comprehensively considering factors such as layout space, cost, lightweighting and vibration reduction effect; (5) The optimal damping ratio and optimal natural frequency of the drive shaft dynamic vibration absorber are determined using fixed-point theory. The relationship between the optimal damping ratio and optimal natural frequency ratio of the dynamic vibration absorber and the mass ratio of the main vibration system is obtained through fixed-point theory: In the formula, This is the optimal damping ratio for the dynamic vibration absorber. This is the optimal natural frequency ratio for the dynamic vibration absorber.

2. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 1, characterized in that: In step (1), the free modes of the drive shaft can be obtained by using a hammer impact test or a finite element simulation method.

3. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 1, characterized in that: When using the finite element simulation method in step (1), the natural frequencies of the first 6 modes of the drive shaft obtained by finite element calculation are 0, because these 6 modes reflect the rigid body displacement of the drive shaft. The 7th mode is the natural frequency of the first bending mode of the drive shaft, that is, the natural frequency of the first free mode.

4. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 1, characterized in that: The ratio in step (2) must satisfy the following condition: For a bending vibration system of a continuous elastic body such as an automobile drive shaft, if the first and second order bending natural frequencies of the main vibration system are... and Meet the conditions In this case, the damping of the main vibration system can be ignored.

5. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 1, characterized in that: The derivation process of the amplitude ratio expression of the main vibration system under the action of harmonic force in step (2) is as follows: The system dynamic equations are obtained based on the dynamic model of the single-degree-of-freedom dynamic vibration absorber: The harmonic force in formula (4) writing And let the displacement of the main vibration system be... ,in The complex amplitude of the main vibration system The imaginary unit; This represents the amplitude of the excitation force. For time, the displacement of the main vibration system is... Substituting the expression into formula (4), the complex amplitude of the main vibration system can be solved. The expression: Displace the main vibration system Substituting the expression into formula (4), we obtain the complex amplitude of the main vibration system. The expression: Pick The real part is used to obtain the amplitude of the main vibration system. The expression: By writing formula (6) in dimensionless form, we can obtain the aforementioned... The expression.

6. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 1, characterized in that: In step (2), the damping ratio of the dynamic vibration absorber The expression is: In the formula, For the damping of the dynamic vibration absorber, For the quality of the dynamic vibration absorber, This is the natural frequency of the dynamic vibration absorber.

7. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 1, characterized in that: The main vibration system selection method used in step (3) is only applicable to drive shaft assemblies that use a fixed universal joint on one side and a sliding universal joint on the other side, and where there is a certain gap between the internal parts of the universal joint.

8. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 1, characterized in that: In step (3), the first main vibration system in the simply supported drive shaft model... First natural frequency The calculation formula is: Where E is the elastic modulus of the material; The moment of inertia of the axial section; Where A is the density of the material; A is the cross-sectional area of ​​the axis. is the length of the axis.

9. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 8, characterized in that: In step (3), the first-order natural frequency of the simply supported drive shaft model is obtained as follows: In formula (8) If the value is 1, the first natural frequency of the simply supported model of the drive shaft can be obtained by formula (8); Alternatively, the first-order natural frequency of the simply supported drive shaft model can be obtained by dividing the first-order free modal natural frequency obtained in step (1) by 2.

267.

10. The method for selecting parameters of a drive shaft dynamic vibration absorber according to claim 1, characterized in that: In step (5), for a single-degree-of-freedom drive shaft dynamic vibration absorber, when the mass ratio of the dynamic vibration absorber to the main vibration system is determined... The ratio of the natural frequency of the dynamic vibration absorber to the natural frequency of the main vibration system Then, the frequency response curves of the main vibration system under different damping ratios of the dynamic vibration absorber can be obtained. In the frequency response curve, there are two fixed points S and T. No matter how the damping ratio of the dynamic vibration absorber changes, the amplitude ratio curve passes through these two points. These two points are the fixed points, and this theory is called the fixed point theory. As the damping ratio of the dynamic vibration absorber on the drive shaft increases from 0 to +∞, the two peaks of the amplitude ratio curve gradually converge and become a single peak. Therefore, there must exist a damping ratio that makes the peak of the amplitude ratio curve at points S and T. At this time, the amplitude ratio of the main vibration system is the lowest. This damping ratio is the optimal damping ratio of the dynamic vibration absorber. Making points S and T at the same height will yield the optimal natural frequency ratio of the system. At this time, the maximum amplitude ratio of the system will reach the minimum value.

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