A vibration damper design method

Abstract

A vibration damper design method first establishes a finite element model of the vibration damper system structure based on a computer; then, static calculations are performed on the finite element model of the vibration damper system structure; subsequently, an equivalent forced vibration model of the single-degree-of-freedom system of the vibration damper geometric model is performed, and harmonic response analysis of the vibration damper system structure is conducted; next, the target transfer function is identified, and the mass, stiffness, damping, deformation, and resonant frequency of the vibrator are optimized using the target transfer function as the optimization function. The optimized vibrator parameters are then verified to confirm the final parameters, and a vibrator is selected or customized based on the final parameters. This design not only simplifies the vibration damper selection method and improves product design efficiency, but also achieves a high degree of matching between the vibrator and the equipment.

Description

Technical Field

[0001] This invention relates to a vibration damper design, belonging to the field of mechanical equipment design, and particularly to a vibration damper design method. Background Technology

[0002] Mechanical equipment design often involves the design and selection of vibration dampers. This is especially true for high-precision mechanical equipment and products that require high levels of operational comfort. Vibration isolation and noise reduction are necessary to meet the equipment's performance specifications.

[0003] In related technologies, vibration dampers are mainly selected based on factors such as the weight of the supporting equipment and the rotational speed of the rotating machinery. Furthermore, the supports for engineering equipment are generally statically indeterminate, and often involve both fixed installations and partial installations with vibration dampers. While this method can match vibration dampers, it still has the following drawbacks:

[0004] In the existing technology, vibration damper selection is based on the vibration damper weight parameters selected from a known sample. To obtain a vibration damper with a high degree of matching, a large number of experiments are required for verification, resulting in low product design efficiency and low matching degree. The matched vibration damper and the equipment may produce unreasonable resonance, which poses certain safety hazards.

[0005] The information disclosed in this background section is intended only to enhance understanding of the overall background of this application and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings and problems of existing technologies, such as complicated vibration damper selection methods, low product design efficiency, and low matching degree, and to provide a vibration damper design method that is simple in selecting vibration dampers, improves product design efficiency, and has a high degree of matching.

[0007] To achieve the above objectives, the technical solution of the present invention is: a vibration damper design method, the vibration damper design method comprising the following steps:

[0008] Step 1: Establish a finite element model of the vibration damper system structure using a computer;

[0009] The method for establishing the finite element model of the vibration damper system structure is as follows: establishing a vibration damper geometric model, which includes a first vibration damping device; equating the first vibration damping device to a spring model, which includes a spring and a damper; and meshing the vibration damper geometric model, applying constraints and external loads.

[0010] Step 2: Perform static calculations for the vibration damper system structure;

[0011] The method for performing static calculations of the vibration damper system structure is as follows: Static calculation optimization is performed using the finite element model from step one to obtain spring parameters including mass, stiffness, damping, deformation, and resonance frequency requirements, thus obtaining initial spring parameters; the spring reaction force is extracted using the initial spring parameters, and the spring mass is calculated to obtain the spring mass parameters.

[0012] Step 3: Equivalent forced vibration model of a single-degree-of-freedom system using the geometric model of the vibration damper;

[0013] The method for equipping the geometric model of the vibration damper with the forced vibration model of a single-degree-of-freedom system is as follows: the geometric model of the vibration damper is equivalent to the forced vibration model of a single-degree-of-freedom system using the dynamic equations of the single-degree-of-freedom system; the resonant frequency of the first vibration damping device is calculated using the system theoretical transfer function.

[0014] Step 4: Structural harmonic response analysis of the vibration damper system;

[0015] The method for analyzing the structural harmonic response of the vibration damper system is as follows: based on the finite element model, harmonic response analysis is performed to obtain the upper displacement response curve of the vibration damper and the equipment installation point. Then, the upper displacement response curve is systematically identified to obtain the installation point displacement-external load transfer function, i.e., the system identification transfer function. The resonance frequency of the first vibration damping device is calculated using the system identification transfer function.

[0016] Step 5: Confirm the target transfer function;

[0017] The method for confirming the target transfer function is any one of the following:

[0018] The first method: If the difference between the resonant frequencies of the first vibration damping device in the system theoretical transfer function and the first vibration damping device in the system identification transfer function is less than a preset value, then the system theoretical transfer function is adopted as the target transfer function.

[0019] The second approach: If the difference between the resonant frequencies of the first vibration damping device in the theoretical transfer function of the system and the first vibration damping device in the system identification transfer function is greater than or equal to a preset value, then the system identification transfer function is adopted as the target transfer function.

[0020] Step 6: Optimize the target transfer function parameters;

[0021] The method for optimizing the target transfer function parameters is as follows: Based on the target transfer function in step five, the initial spring parameters are optimized. The optimization objective is that the vibration damper support position does not resonate within the frequency domain of the external load. The spring parameters obtained at this time are the target optimization parameters.

[0022] Step 7: Verify the optimization results of the finite element model

[0023] The method for verifying the optimization results of the finite element model is as follows: Using the target optimization parameters from step six as input conditions, perform harmonic response analysis using the finite element model from step one to obtain the upper displacement response curve. Compare and analyze this upper displacement response curve with the upper displacement response curve from step four to verify whether the optimized parameters meet the requirements for eliminating resonance. The verification objective is: the vibration damper system will not experience resonance within the frequency domain of the external load. The verification result is any one of the following:

[0024] The first approach is to select a suitable vibration damper based on the parameters if the comparative verification objective is met.

[0025] The second approach: If the comparison and verification objective is not met, proceed to step six to further optimize the spring parameters.

[0026] The vibration damper geometric model also includes a second vibration damper;

[0027] The vibration damper design method includes the following steps:

[0028] Step 1: Establish a finite element model of the vibration damper system structure using a computer;

[0029] The method for establishing the finite element model of the vibration damper system structure is as follows: establish a vibration damper geometric model, which includes a first vibration damping device and a second vibration damping device; equate the first vibration damping device and the second vibration damping device to a spring model, which includes a spring and a damper; mesh the vibration damper geometric model, apply constraints and external loads;

[0030] Step 2: Perform static calculations for the vibration damper system structure;

[0031] The method for performing static calculations of the vibration damper system structure is as follows: Static calculation optimization is performed using the finite element model from step one to obtain spring parameters including mass, stiffness, damping, deformation, and resonance frequency requirements, thus obtaining initial spring parameters; the spring reaction force is extracted using the initial spring parameters, and the spring mass is calculated to obtain the spring mass parameters.

[0032] Step 3: Equivalent forced vibration model of a single-degree-of-freedom system using the geometric model of the vibration damper;

[0033] The method for equipping the geometric model of the vibration damper with the forced vibration model of a single-degree-of-freedom system is as follows: the geometric model of the vibration damper is equivalent to the forced vibration model of a single-degree-of-freedom system using the dynamic equations of the single-degree-of-freedom system; the resonance frequencies of the first and second vibration damping devices are calculated using the system theoretical transfer function.

[0034] Step 4: Structural harmonic response analysis of the vibration damper system;

[0035] The method for analyzing the structural harmonic response of the vibration damper system is as follows: based on the finite element model, harmonic response analysis is performed to obtain the upper displacement response curve of the vibration damper and the equipment installation point. Then, the upper displacement response curve is systematically identified to obtain the installation point displacement-external load transfer function, i.e., the system identification transfer function. The resonance frequency of the first vibration damping device and the second vibration damping device is calculated using the system identification transfer function.

[0036] Step 5: Confirm the target transfer function;

[0037] The method for confirming the target transfer function is any one of the following:

[0038] The first method: If the difference between the resonant frequencies of the first vibration damping device in the system theoretical transfer function and the first vibration damping device in the system identification transfer function is less than a preset value, and at the same time, the difference between the resonant frequencies of the second vibration damping device in the system theoretical transfer function and the second vibration damping device in the system identification transfer function is less than a preset value, then the system theoretical transfer function is adopted as the target transfer function.

[0039] The second approach: If the difference between the resonant frequencies of the first vibration damping device in the theoretical transfer function of the system and the first vibration damping device in the system identification transfer function is greater than or equal to a preset value, and at the same time, the difference between the resonant frequencies of the second vibration damping device in the theoretical transfer function of the system and the second vibration damping device in the system identification transfer function is greater than or equal to a preset value, then the system identification transfer function is adopted as the target transfer function.

[0040] Step 6: Optimize the target transfer function parameters;

[0041] The method for optimizing the target transfer function parameters is as follows: Based on the target transfer function in step five, the initial spring parameters are optimized. The optimization objective is that the vibration damper support position does not resonate within the frequency domain of the external load. The spring parameters obtained at this time are the target optimization parameters.

[0042] Step 7: Verify the optimization results of the finite element model

[0043] The method for verifying the optimization results of the finite element model is as follows: Using the target optimization parameters from step six as input conditions, perform harmonic response analysis using the finite element model from step one to obtain the upper displacement response curve. Compare and analyze this upper displacement response curve with the upper displacement response curve from step four to verify whether the optimized parameters meet the requirements for eliminating resonance. The verification objective is: the vibration damper system will not experience resonance within the frequency domain of the external load. The verification result is any one of the following:

[0044] The first approach is to select a suitable vibration damper based on the parameters if the comparative verification objective is met.

[0045] The second approach: If the comparison and verification objective is not met, proceed to step six to further optimize the spring parameters.

[0046] In step two, the method for extracting the spring reaction force using the initial spring parameters and calculating the sprung mass to obtain the sprung mass parameter is as follows: extract the spring reaction force F using the initial spring parameters as the object, and regard the spring reaction force F as the spring preload of a single degree of freedom system, that is, the gravity of the sprung mass of a single degree of freedom system. The calculation formula is M = F / g, where g is the acceleration due to gravity, and the sprung mass parameter M is obtained.

[0047] The equation used in step three to transform the vibration damper geometric model (1) into a single-degree-of-freedom forced vibration model using the single-degree-of-freedom system dynamics equation is as follows:

[0048]

[0049] Where M is the sprung mass, C is the damping, K is the spring stiffness, x is the displacement above the damper, and F(t) is the external load.

[0050] The formula for the theoretical transfer function of the system in step three is as follows:

[0051]

[0052] Where X(s) is the displacement above the damper, F(s) is the external load, S is the Laplace operator, M is the sprung mass, C is the damping, and K is the spring stiffness.

[0053] The method for harmonic response analysis in step four is as follows: perform harmonic response analysis based on the finite element model and draw the displacement Bode plot, which is the displacement response curve above the vibration damper and the equipment installation point.

[0054] The method for optimizing the spring mass, stiffness, damping, deformation, and resonance frequency parameters in step six is ​​as follows: draw a displacement Bode plot based on the target transfer function, analyze the frequency response based on the displacement Bode plot, and adjust the damping parameters until there are no peak values, that is, no resonance occurs at the damper support position.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] 1. A vibration damper design method according to the present invention includes the following steps: 1. Establishing a finite element model of the vibration damper system structure; 2. Performing static calculations of the vibration damper system structure; 3. Equivalent forced vibration model of the single-degree-of-freedom system of the vibration damper geometric model; 4. Harmonic response analysis of the vibration damper system structure; 5. Confirming the target transfer function; 6. Optimizing the parameters of the target transfer function; 7. Verifying the optimization results of the finite element model; In this invention, by establishing a finite element model of the vibration damper system structure, performing static calculations on the finite element model, and using single-degree-of-freedom dynamic equivalence and harmonic response analysis, the method calculates the vibration damper system structure under different transfer functions. The invention involves analyzing the resonant frequency of vibration dampers, comparing and analyzing peak parameters, and adjusting and optimizing the mass, stiffness, damping, deformation, and resonant frequency of the dampers to eliminate unreasonable resonances. The optimization results are then verified to obtain damper parameters that meet the requirements. During this process, geometric modeling analysis is performed using software, and statics principles are applied to establish a forced vibration model of a single-degree-of-freedom system. Harmonic response analysis of the damper system structure is conducted to confirm the required optimization function. The damper parameters are repeatedly adjusted and iterated until the structural strength requirements are met. Finally, the appropriate damper is precisely matched to the equipment based on these parameters. Therefore, this invention not only simplifies the damper selection method but also achieves a high degree of matching and reduces safety hazards.

[0057] 2. In the vibration damper design method of this invention, the resonant frequency of the vibration damper is calculated using both the theoretical transfer function and the identified transfer function of the system, and then compared. The optimal transfer function is selected to optimize the vibration damping system. The various parameters of the vibration damper are repeatedly adjusted and optimized until the resonance peak of the vibration damping system disappears, thereby reducing unreasonable resonance between devices and improving the matching degree between the vibration damper and the equipment. Therefore, this invention not only has a high degree of matching between the vibration damper and the equipment, but also a high level of safety.

[0058] 3. In the vibration damper design method of this invention, the establishment of the finite element model, static calculations, single-degree-of-freedom dynamic calculations, harmonic response analysis, and system identification are all based on software calculations. This reduces the extensive experimental verification process in vibration damper selection, saves workload, and results in a more suitable vibration damper model, thus improving product design efficiency. Therefore, this invention not only simplifies the vibration damper selection method but also improves product design efficiency. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the present invention.

[0060] Figure 2 This is a schematic diagram of the geometric model of the vibration damper in step one of Embodiment 1 of the present invention.

[0061] Figure 3This is a schematic diagram of the forced vibration model of a single-degree-of-freedom system in step three of Embodiment 1 of the present invention.

[0062] Figure 4 This is a schematic diagram of the resonance frequency curves under different damping parameters in step three of embodiment 1 of the present invention.

[0063] Figure 5 This is a schematic diagram of the displacement response curve of the single-degree-of-freedom system in step three of embodiment 1 of the present invention.

[0064] Figure 6 This is a schematic diagram of the upper displacement response curve of the harmonic response analysis in step four of Embodiment 1 of the present invention.

[0065] Figure 7 This is a schematic diagram of the system identification result in step four of Embodiment 1 of the present invention.

[0066] Figure 8 This is a schematic diagram comparing the transfer functions of different targets in step five of Embodiment 1 of the present invention.

[0067] Figure 9 This is a schematic diagram of the optimized upper displacement response curve in step six of Embodiment 1 of the present invention.

[0068] In the figure: vibration damper geometric model 1, geometric pipe 101, first vibration damping device 102, second vibration damping device 103, first free end 104, second free end 105, third free end 106. Detailed Implementation

[0069] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0070] See Figure 1 — Figure 9 A vibration damper design method, the vibration damper design method comprising the following steps:

[0071] Step 1: Establish a finite element model of the vibration damper system structure using a computer;

[0072] The method for establishing the finite element model of the vibration damper system structure is as follows: establish a vibration damper geometric model 1, which includes a first vibration damping device 102; convert the first vibration damping device 102 into a spring model, which includes a spring and a damper; perform mesh generation, apply constraints and external loads to the vibration damper geometric model 1.

[0073] Step 2: Perform static calculations for the vibration damper system structure;

[0074] The method for performing static calculations of the vibration damper system structure is as follows: Static calculation optimization is performed using the finite element model from step one to obtain spring parameters including mass, stiffness, damping, deformation, and resonance frequency requirements, thus obtaining initial spring parameters; the spring reaction force is extracted using the initial spring parameters, and the spring mass is calculated to obtain the spring mass parameters.

[0075] Step 3: Geometric Model of the Vibration Damper 1. Equivalent Forced Vibration Model of a Single-Degree-of-Freedom System;

[0076] The method for equivalence of the single-degree-of-freedom system forced vibration model of the vibration damper geometric model 1 is as follows: the vibration damper geometric model 1 is equivalent to the single-degree-of-freedom system forced vibration model using the dynamic equation of the single-degree-of-freedom system; the resonance frequency of the first vibration damping device 102 is calculated using the system theoretical transfer function;

[0077] Step 4: Structural harmonic response analysis of the vibration damper system;

[0078] The method for analyzing the structural harmonic response of the vibration damper system is as follows: based on the finite element model, harmonic response analysis is performed to obtain the upper displacement response curve of the vibration damper and the equipment installation point. Then, the upper displacement response curve is systematically identified to obtain the installation point displacement-external load transfer function, i.e., the system identification transfer function. The resonance frequency of the first vibration damping device 102 is calculated using the system identification transfer function.

[0079] Step 5: Confirm the target transfer function;

[0080] The method for confirming the target transfer function is any one of the following:

[0081] The first method: If the difference between the resonant frequencies of the first vibration damping device 102 in the system theoretical transfer function and the first vibration damping device 102 in the system identification transfer function is less than a preset value, then the system theoretical transfer function is adopted as the target transfer function.

[0082] The second method: If the difference between the resonant frequencies of the first vibration damping device 102 in the theoretical transfer function of the system and the first vibration damping device 102 in the system identification transfer function is greater than or equal to a preset value, then the system identification transfer function is adopted as the target transfer function.

[0083] Step 6: Optimize the target transfer function parameters;

[0084] The method for optimizing the target transfer function parameters is as follows: Based on the target transfer function in step five, the initial spring parameters are optimized. The optimization objective is that the vibration damper support position does not resonate within the frequency domain of the external load. The spring parameters obtained at this time are the target optimization parameters.

[0085] Step 7: Verify the optimization results of the finite element model

[0086] The method for verifying the optimization results of the finite element model is as follows: Using the target optimization parameters from step six as input conditions, perform harmonic response analysis using the finite element model from step one to obtain the upper displacement response curve. Compare and analyze this upper displacement response curve with the upper displacement response curve from step four to verify whether the optimized parameters meet the requirements for eliminating resonance. The verification objective is: the vibration damper system will not experience resonance within the frequency domain of the external load. The verification result is any one of the following:

[0087] The first approach is to select a suitable vibration damper based on the parameters if the comparative verification objective is met.

[0088] The second approach: If the comparison and verification objective is not met, proceed to step six to further optimize the spring parameters.

[0089] The vibration damper geometric model 1 also includes a second vibration damper 103;

[0090] The vibration damper design method includes the following steps:

[0091] Step 1: Establish a finite element model of the vibration damper system structure using a computer;

[0092] The method for establishing the finite element model of the vibration damper system structure is as follows: establish a vibration damper geometric model 1, which includes a first vibration damping device 102 and a second vibration damping device 103; convert the first vibration damping device 102 and the second vibration damping device 103 into equivalent spring models, which include springs and dampers; mesh the vibration damper geometric model 1, apply constraints and external loads;

[0093] Step 2: Perform static calculations for the vibration damper system structure;

[0094] The method for performing static calculations of the vibration damper system structure is as follows: Static calculation optimization is performed using the finite element model from step one to obtain spring parameters including mass, stiffness, damping, deformation, and resonance frequency requirements, thus obtaining initial spring parameters; the spring reaction force is extracted using the initial spring parameters, and the spring mass is calculated to obtain the spring mass parameters.

[0095] Step 3: Geometric Model of the Vibration Damper 1. Equivalent Forced Vibration Model of a Single-Degree-of-Freedom System;

[0096] The method for equivalence of the single-degree-of-freedom system forced vibration model of the vibration damper geometric model 1 is as follows: the vibration damper geometric model 1 is equivalent to the single-degree-of-freedom system forced vibration model by using the dynamic equation of the single-degree-of-freedom system; the resonance frequency of the first vibration damping device 102 and the second vibration damping device 103 is calculated by using the system theoretical transfer function;

[0097] Step 4: Structural harmonic response analysis of the vibration damper system;

[0098] The method for analyzing the structural harmonic response of the vibration damper system is as follows: based on the finite element model, harmonic response analysis is performed to obtain the upper displacement response curve of the vibration damper and the equipment installation point. Then, the upper displacement response curve is systematically identified to obtain the installation point displacement-external load transfer function, i.e., the system identification transfer function. The resonance frequency of the first vibration damping device 102 and the second vibration damping device 103 is calculated using the system identification transfer function.

[0099] Step 5: Confirm the target transfer function;

[0100] The method for confirming the target transfer function is any one of the following:

[0101] The first method: If the difference between the resonant frequencies of the first vibration damping device 102 in the system theoretical transfer function and the first vibration damping device 102 in the system identification transfer function is less than a preset value, and at the same time, the difference between the resonant frequencies of the second vibration damping device 103 in the system theoretical transfer function and the second vibration damping device 103 in the system identification transfer function is less than a preset value, then the system theoretical transfer function is adopted as the target transfer function.

[0102] The second method: If the difference between the resonant frequencies of the first vibration damping device 102 in the theoretical transfer function of the system and the first vibration damping device 102 in the system identification transfer function is greater than or equal to a preset value, and at the same time, the difference between the resonant frequencies of the second vibration damping device 103 in the theoretical transfer function of the system and the second vibration damping device 103 in the system identification transfer function is greater than or equal to a preset value, then the system identification transfer function is adopted as the target transfer function.

[0103] Step 6: Optimize the target transfer function parameters;

[0104] The method for optimizing the target transfer function parameters is as follows: Based on the target transfer function in step five, the initial spring parameters are optimized. The optimization objective is that the vibration damper support position does not resonate within the frequency domain of the external load. The spring parameters obtained at this time are the target optimization parameters.

[0105] Step 7: Verify the optimization results of the finite element model

[0106] The method for verifying the optimization results of the finite element model is as follows: Using the target optimization parameters from step six as input conditions, perform harmonic response analysis using the finite element model from step one to obtain the upper displacement response curve. Compare and analyze this upper displacement response curve with the upper displacement response curve from step four to verify whether the optimized parameters meet the requirements for eliminating resonance. The verification objective is: the vibration damper system will not experience resonance within the frequency domain of the external load. The verification result is any one of the following:

[0107] The first approach is to select a suitable vibration damper based on the parameters if the comparative verification objective is met.

[0108] The second approach: If the comparison and verification objective is not met, proceed to step six to further optimize the spring parameters.

[0109] In step two, the method for extracting the spring reaction force using the initial spring parameters and calculating the sprung mass to obtain the sprung mass parameter is as follows: extract the spring reaction force F using the initial spring parameters as the object, and regard the spring reaction force F as the spring preload of a single degree of freedom system, that is, the gravity of the sprung mass of a single degree of freedom system. The calculation formula is M = F / g, where g is the acceleration due to gravity, and the sprung mass parameter M is obtained.

[0110] The equation used in step three to transform the vibration damper geometric model (1) into a single-degree-of-freedom forced vibration model using the single-degree-of-freedom system dynamics equation is as follows:

[0111]

[0112] Where M is the sprung mass, C is the damping, K is the spring stiffness, x is the displacement above the damper, and F(t) is the external load.

[0113] The formula for the theoretical transfer function of the system in step three is as follows:

[0114]

[0115] Where X(s) is the displacement above the damper, F(s) is the external load, S is the Laplace operator, M is the sprung mass, C is the damping, and K is the spring stiffness.

[0116] The method for harmonic response analysis in step four is as follows: perform harmonic response analysis based on the finite element model and draw the displacement Bode plot, which is the displacement response curve above the vibration damper and the equipment installation point.

[0117] The method for optimizing the spring mass, stiffness, damping, deformation, and resonance frequency parameters in step six is ​​as follows: draw a displacement Bode plot based on the target transfer function, analyze the frequency response based on the displacement Bode plot, and adjust the damping parameters until there are no peak values, that is, no resonance occurs at the damper support position.

[0118] The principle of this invention is explained as follows:

[0119] In this invention, a geometric model of the vibration damper is established based on software, and single-degree-of-freedom dynamic calculations, theoretical transfer function calculations, and system identification transfer function calculations are performed. Displacement Bode plots are plotted for peak value analysis and comparison. During this process, geometric modeling analysis is conducted using software, statics principles are applied to calculate and establish a forced vibration model of the single-degree-of-freedom system, and harmonic response analysis is performed on the vibration damper system structure to confirm the required optimization functions. The vibration damper parameters are repeatedly adjusted and iterated until the structural strength requirements are met. This significantly reduces the numerous experimental verification steps in vibration damper selection, improves product design efficiency, and the matched vibration damper eliminates unreasonable resonance, reducing safety hazards.

[0120] The theoretical transfer function formula used in this invention is as follows:

[0121]

[0122] Where X(s) is the displacement above the damper, F(s) is the external load, S is the Laplace operator, M is the sprung mass, C is the damping, and K is the spring stiffness;

[0123] The theoretical transfer function of this system includes parameters such as the mass, stiffness, damping, deformation, and resonant frequency of the spring. The formulas for calculating the resonant frequency of the damper system, whether damped or undamped, are as follows:

[0124] (1) The formula for the undamped resonance frequency is:

[0125] Where: ω n Where is the undamped resonant frequency, K is the damper stiffness, and M is the sprung mass;

[0126] (2) The formula for the damped resonance frequency is:

[0127]

[0128] Where: ω d For the damped resonant frequency, ω n ζ is the undamped resonant frequency, and ζ is the damping coefficient.

[0129] The formula for calculating the damping coefficient is:

[0130] Where: ζ is the damping coefficient, C is the damping, K is the damper stiffness, and M is the sprung mass.

[0131] In step one of this invention, the method for applying constraints and external loads to the geometric model (1) of the vibration damper is as follows: the geometric pipe (101) includes a first free end (104), a second free end (105) and a third free end (106); the first vibration damping device (102) is disposed on the geometric pipe (101) between the first free end (104) and the second free end (105); the second vibration damping device (103) is disposed on the geometric pipe (101) between the second free end (105) and the third free end (106); the first free end (104), the second free end (105) and the third free end (106) are all fixedly constrained; an external load is applied downward to the spring model;

[0132] In step two of this invention, the optimization objectives for static optimization include: spring stiffness of 4800-5300 N / mm and deformation of 0.1 mm-1 mm; damping of the first damping device 102 of 5-35 N (mm / s) and the second damping device 103 of 5-35 N (mm / s); mass of the first damping device 102 of 6-12 kg and mass of the second damping device 103 of 9-14 kg.

[0133] Example 1:

[0134] See Figures 1-9 A vibration damper design method, the vibration damper design method comprising the following steps:

[0135] Step 1: Establish a finite element model of the vibration damper system structure using a computer;

[0136] The method for establishing the finite element model of the vibration damper system structure is as follows: A vibration damper geometric model 1 is established, comprising a geometric pipe 101, a first vibration damping device 102, and a second vibration damping device 103. The geometric pipe 101 includes a first free end 104, a second free end 105, and a third free end 106. The first vibration damping device 102 is disposed on the geometric pipe 101 between the first free end 104 and the second free end 105. The second vibration damping device 103 is disposed on the geometric pipe 101 between the second free end 105 and the third free end 106. Fixed constraints are applied to the first free end 104, the second free end 105, and the third free end 106. The first vibration damping device 102 and the second vibration damping device 103 are equivalent to spring models, which include springs and dampers. The vibration damper geometric model 1 is meshed, and preprocessed with constraints and external loads.

[0137] Step 2: Perform static calculations for the vibration damper system structure;

[0138] The method for performing static calculations of the vibration damper system structure is as follows: Static calculation optimization is performed using the finite element model from step one to obtain spring parameters including mass, stiffness, damping, deformation, and resonance frequency requirements, thus obtaining initial spring parameters; the spring reaction force is extracted using the initial spring parameters, and the spring mass is calculated to obtain the spring mass parameters.

[0139] Further static optimization objectives include: spring stiffness of 4800-5300 N / mm and deformation of 0.1 mm-1 mm; damping of the first damping device 102 of 5-35 N (mm / s) and the second damping device 103 of 5-35 N (mm / s); mass of the first damping device 102 of 6-12 kg and mass of the second damping device 103 of 9-14 kg.

[0140] Step 3: Geometric Model of the Vibration Damper 1. Equivalent Forced Vibration Model of a Single-Degree-of-Freedom System;

[0141] The method for equivalencing the single-degree-of-freedom forced vibration model of the vibration damper geometric model 1 is as follows: the vibration damper geometric model 1 is equivalent to a single-degree-of-freedom forced vibration model using the dynamic equations of the single-degree-of-freedom system; this model includes parameters such as mass, spring, damper, and external load;

[0142] The equation used for the single-degree-of-freedom dynamics is:

[0143]

[0144] Where M is the sprung mass, C is the damping, K is the spring stiffness, x is the displacement above the damper, and F(t) is the external load;

[0145] The resonant frequencies of the first vibration damping device 102 and the second vibration damping device 103 are calculated using the transfer function of system theory.

[0146] The theoretical transfer function of the system is defined as follows:

[0147]

[0148] Where X(s) is the displacement above the damper, F(s) is the external load, S is the Laplace operator, M is the sprung mass, C is the damping, and K is the spring stiffness;

[0149] The resonant frequency in the theoretical transfer function of the first vibration damper 102 is given by the formula:

[0150]

[0151] Among them: G 01 Let be the system theoretical transfer function of the first vibration damper 102, and (s) be the Laplace operator;

[0152] Furthermore, the resonant frequency in the theoretical transfer function of the first vibration damper 102 is found to be 127Hz;

[0153] The resonant frequency in the theoretical transfer function of the second vibration damper 103 is given by the formula:

[0154]

[0155] Among them: G 02 Let be the system theoretical transfer function of the second vibration damper 103, and (s) be the Laplace operator;

[0156] Furthermore, the resonant frequency in the theoretical transfer function of the second vibration damper 103 is found to be 109 Hz;

[0157] Step 4: Structural harmonic response analysis of the vibration damper system;

[0158] The method for analyzing the harmonic response of the vibration damper system structure is as follows: perform harmonic response analysis on the finite element model, obtain the upper displacement response curve of the vibration damper and the equipment installation point, and draw the displacement Bode diagram; then perform system identification on the upper displacement response curve to obtain the installation point displacement-external load transfer function, i.e., the system identification transfer function, and use the system identification transfer function to calculate the resonance frequency of the first vibration damping device 102 and the second vibration damping device 103.

[0159] The resonant frequency in the system identification transfer function of the first damper 102 is given by the formula:

[0160]

[0161] Among them: G 11 Let be the system identification transfer function of the first damper 102, and let (s) be the Laplace operator;

[0162] Furthermore, the resonant frequency in the system identification transfer function of the first damper 102 is found to be 137Hz;

[0163]

[0164] Among them: G 12 Let be the system identification transfer function of the second damper 103, and let (s) be the Laplace operator;

[0165] Furthermore, the resonant frequency in the system identification transfer function of the second damper 103 is found to be 108 Hz;

[0166] Step 5: Confirm the target transfer function;

[0167] The method for confirming the target transfer function is any one of the following:

[0168] The first method: If the resonant frequency difference between the first vibration damping device 102 in the system theoretical transfer function and the first vibration damping device 102 in the system identification transfer function is <10%, and at the same time, the resonant frequency difference between the second vibration damping device 103 in the system theoretical transfer function and the second vibration damping device 103 in the system identification transfer function is <10%, then the system theoretical transfer function is adopted as the target transfer function.

[0169] The second method: If the resonant frequency difference between the first vibration damping device 102 in the system theoretical transfer function and the first vibration damping device 102 in the system identification transfer function is ≥10%, and at the same time, the resonant frequency difference between the second vibration damping device 103 in the system theoretical transfer function and the second vibration damping device 103 in the system identification transfer function is ≥10%, then the system identification transfer function is adopted as the target transfer function.

[0170] Furthermore, in the theoretical transfer function of the system, the resonant frequency of the first damper 102 is 127Hz and the resonant frequency of the second damper 103 is 109Hz; in the system identification transfer function, the resonant frequency of the first damper 102 is 137Hz and the resonant frequency of the second damper 103 is 108Hz.

[0171] The resonant frequency of the first damper 102 in the system theoretical transfer function differs from the resonant frequency of the first damper 102 in the system identification transfer function by 10 Hz; the resonant frequency of the second damper 103 in the system theoretical transfer function differs from the resonant frequency of the second damper 103 in the system identification transfer function by 1 Hz; both differences are less than 10%; therefore, the system theoretical transfer function is confirmed to be the function used for subsequent optimization parameters.

[0172] Step 6: Optimize the target transfer function parameters;

[0173] The method for optimizing the target transfer function parameters is as follows: Based on the target transfer function in step five, optimize the initial spring parameters; plot the displacement Bode plot based on the target transfer function, analyze the frequency response based on the displacement Bode plot curve, and adjust the damping parameters until there are no peak values, i.e., no resonance occurs at the damper support position; the optimization objective is to prevent resonance at the damper support position within the frequency domain of the external load, and the spring parameters obtained at this point are the target optimization parameters; the final optimization result is a spring stiffness of 5000 N / mm, a deformation of 0.82 mm, a damping of 9.6 N (mm / s) for the first damping device 102, a damping of 9.8 N (mm / s) for the second damping device 103, a mass of 8 kg for the first damping device 102, and a mass of 10.6 kg for the second damping device 103; the initial parameters are acceptable and do not require adjustment.

[0174] Step 7: Verify the optimization results of the finite element model

[0175] The method for verifying the optimization results of the finite element model is as follows: Using the target optimization parameters from step six as input conditions, perform harmonic response analysis using the finite element model from step one to obtain the upper displacement response curve, i.e., the displacement Bode plot; compare and analyze this upper displacement response curve with the upper displacement response curve from step four to verify whether the optimized parameters meet the requirements for eliminating resonance. The verification objective is: the vibration damper system will not experience resonance within the frequency domain of the external load; the verification result is any one of the following:

[0176] The first approach is to select a suitable vibration damper based on the parameters if the comparative verification objective is met.

[0177] The second approach: If the comparison and verification objective is not met, proceed to step six to further optimize the spring parameters.

[0178] Furthermore, the frequency domain of the external load is 0-200Hz;

[0179] The above description is only a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. Any equivalent modifications or changes made by those skilled in the art based on the content disclosed in the present invention should be included within the scope of protection set forth in the claims.

Claims

1. A vibration damper design method, characterized in that, The vibration damper design method includes the following steps: Step 1: Establish a finite element model of the vibration damper system structure using a computer; The method for establishing the finite element model of the vibration damper system structure is as follows: establish a vibration damper geometric model (1), which includes a first vibration damping device (102); the first vibration damping device (102) is equivalent to a spring model, which includes a spring and a damper; mesh the vibration damper geometric model (1), apply constraints and external loads; Step 2: Perform static calculations for the vibration damper system structure; The method for performing static calculations of the vibration damper system structure is as follows: Static calculation optimization is performed using the finite element model from step one to obtain spring parameters including mass, stiffness, damping, deformation, and resonance frequency requirements, thus obtaining initial spring parameters; the spring reaction force is extracted using the initial spring parameters, and the spring mass is calculated to obtain the spring mass parameters. Step 3, Geometric Model of Vibration Damper (1) Equivalent Forced Vibration Model of Single-Degree-of-Freedom System; The method for equivalence between the geometric model (1) of the vibration damper and the forced vibration model of the single-degree-of-freedom system is as follows: the geometric model (1) of the vibration damper is equivalent to the forced vibration model of the single-degree-of-freedom system using the dynamic equation of the single-degree-of-freedom system; the resonant frequency of the first vibration damping device (102) is calculated using the system theoretical transfer function; Step 4: Structural harmonic response analysis of the vibration damper system; The method for analyzing the structural harmonic response of the vibration damper system is as follows: based on the finite element model, the harmonic response analysis is performed to obtain the upper displacement response curve of the vibration damper and the equipment installation point. Then, the upper displacement response curve is systematically identified to obtain the installation point displacement-external load transfer function, i.e., the system identification transfer function. The resonance frequency of the first vibration damping device (102) is calculated using the system identification transfer function. Step 5: Confirm the target transfer function; The method for confirming the target transfer function is any one of the following: The first method: If the difference between the resonant frequencies of the first vibration damping device (102) in the system theoretical transfer function and the first vibration damping device (102) in the system identification transfer function is less than a preset value, then the system theoretical transfer function is adopted as the target transfer function. The second method: If the difference between the resonant frequencies of the first vibration damping device (102) in the theoretical transfer function of the system and the first vibration damping device (102) in the system identification transfer function is greater than or equal to the preset value, then the system identification transfer function is adopted as the target transfer function. Step 6: Optimize the target transfer function parameters; The method for optimizing the target transfer function parameters is as follows: Based on the target transfer function in step five, the initial spring parameters are optimized. The optimization objective is that the vibration damper support position does not resonate within the frequency domain of the external load. The spring parameters obtained at this time are the target optimization parameters. Step 7: Verify the optimization results of the finite element model The method for verifying the optimization results of the finite element model is as follows: Using the target optimization parameters from step six as input conditions, perform harmonic response analysis using the finite element model from step one to obtain the upper displacement response curve. Compare and analyze this upper displacement response curve with the upper displacement response curve from step four to verify whether the optimized parameters meet the requirements for eliminating resonance. The verification objective is: the vibration damper system will not experience resonance within the frequency domain of the external load. The verification result is any one of the following: The first approach is to select a suitable vibration damper based on the parameters if the comparative verification objective is met. The second approach: If the comparison and verification objective is not met, proceed to step six to further optimize the spring parameters.

2. The vibration damper design method according to claim 1, characterized in that: In step two, the method for extracting the spring reaction force using the initial spring parameters and calculating the sprung mass to obtain the sprung mass parameter is as follows: extract the spring reaction force F using the initial spring parameters as the object, and regard the spring reaction force F as the spring preload of a single degree of freedom system, that is, the gravity of the sprung mass of a single degree of freedom system. The calculation formula is M=F / g, where g is the acceleration due to gravity, and the sprung mass parameter M is obtained.

3. The vibration damper design method according to claim 1, characterized in that: The dynamic equations of the single-degree-of-freedom system used in step three are as follows: ； Where M is the sprung mass, C is the damping, K is the spring stiffness, x is the displacement above the damper, and F(t) is the external load.

4. The vibration damper design method according to claim 1, characterized in that: The formula for the theoretical transfer function of the system in step three is as follows: ； Where X(s) is the displacement above the damper, F(s) is the external load, S is the Laplace operator, M is the sprung mass, C is the damping, and K is the spring stiffness.

5. The vibration damper design method according to claim 1, characterized in that: The method for harmonic response analysis in step four is as follows: perform harmonic response analysis based on the finite element model and draw the displacement Bode plot, which is the displacement response curve above the vibration damper and the equipment installation point.

6. The vibration damper design method according to claim 1, characterized in that: The method for optimizing the initial spring parameters in step six is ​​as follows: draw a displacement Bode plot based on the target transfer function, analyze the frequency response based on the displacement Bode plot, and adjust the damping parameters until there are no peak values, that is, no resonance occurs at the vibration damper support position.

7. A vibration damper design method, characterized in that: The vibration damper design method includes the following steps: Step 1: Establish a finite element model of the vibration damper system structure using a computer; The method for establishing the finite element model of the vibration damper system structure is as follows: establish a vibration damper geometric model (1), which includes a first vibration damping device (102) and a second vibration damping device (103); convert the first vibration damping device (102) and the second vibration damping device (103) into equivalent spring models, which include springs and dampers; mesh the vibration damper geometric model (1), apply constraints and external loads; Step 2: Perform static calculations for the vibration damper system structure; The method for performing static calculations of the vibration damper system structure is as follows: Static calculation optimization is performed using the finite element model from step one to obtain spring parameters including mass, stiffness, damping, deformation, and resonance frequency requirements, thus obtaining initial spring parameters; the spring reaction force is extracted using the initial spring parameters, and the spring mass is calculated to obtain the spring mass parameters. Step 3, Geometric Model of Vibration Damper (1) Equivalent Forced Vibration Model of Single-Degree-of-Freedom System; The method for equivalence between the geometric model (1) of the vibration damper and the forced vibration model of the single-degree-of-freedom system is as follows: the geometric model (1) of the vibration damper is equivalent to the forced vibration model of the single-degree-of-freedom system using the dynamic equation of the single-degree-of-freedom system; the resonant frequency of the first vibration damping device (102) and the second vibration damping device (103) is calculated using the system theoretical transfer function; Step 4: Structural harmonic response analysis of the vibration damper system; The method for analyzing the structural harmonic response of the vibration damper system is as follows: based on the finite element model, the harmonic response analysis is performed to obtain the upper displacement response curve of the vibration damper and the equipment installation point. Then, the upper displacement response curve is systematically identified to obtain the installation point displacement-external load transfer function, i.e., the system identification transfer function. The resonance frequency of the first vibration damping device (102) and the second vibration damping device (103) is calculated using the system identification transfer function. Step 5: Confirm the target transfer function; The method for confirming the target transfer function is any one of the following: The first method: If the difference between the resonant frequencies of the first vibration damping device (102) in the system theoretical transfer function and the first vibration damping device (102) in the system identification transfer function is less than a preset value, and at the same time, the difference between the resonant frequencies of the second vibration damping device (103) in the system theoretical transfer function and the second vibration damping device (103) in the system identification transfer function is less than a preset value, then the system theoretical transfer function is adopted as the target transfer function; The second method: If the difference between the resonant frequencies of the first vibration damping device (102) in the theoretical transfer function of the system and the first vibration damping device (102) in the system identification transfer function is greater than or equal to a preset value, and at the same time, the difference between the resonant frequencies of the second vibration damping device (103) in the theoretical transfer function of the system and the second vibration damping device (103) in the system identification transfer function is greater than or equal to a preset value, then the system identification transfer function is adopted as the target transfer function. Step 6: Optimize the target transfer function parameters; The method for optimizing the target transfer function parameters is as follows: Based on the target transfer function in step five, the initial spring parameters are optimized. The optimization objective is that the vibration damper support position does not resonate within the frequency domain of the external load. The spring parameters obtained at this time are the target optimization parameters. Step 7: Verify the optimization results of the finite element model The method for verifying the optimization results of the finite element model is as follows: Using the target optimization parameters from step six as input conditions, perform harmonic response analysis using the finite element model from step one to obtain the upper displacement response curve. Compare and analyze this upper displacement response curve with the upper displacement response curve from step four to verify whether the optimized parameters meet the requirements for eliminating resonance. The verification objective is: the vibration damper system will not experience resonance within the frequency domain of the external load. The verification result is any one of the following: The first approach is to select a suitable vibration damper based on the parameters if the comparative verification objective is met. The second approach: If the comparison and verification objective is not met, proceed to step six to further optimize the spring parameters.

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