A method for improving the test accuracy of the loss factor of damping materials

Abstract

The present invention discloses a method for improving the test accuracy of the loss factor of damping materials with a correction formula at a required natural frequency of a certain order. The method includes preparing a substrate beam specimen and testing the Young's modulus of the substrate beam; at a required natural frequency of a certain order of the substrate beam, preparing two substrate beam specimens of the same size and the same material, and laying a layer of the material to be tested on one of them to form a composite damping beam; testing the frequency response curves of the substrate beam and the composite damping beam, and obtaining the loss factor η1 of the composite damping beam by using the correction formula of the half-power bandwidth method; finally, calculating to obtain the loss factor η2 of the damping material. The beneficial effects of the present invention are as follows: according to the required natural frequency of a certain order, preparing two substrate beam specimens of the same size and the same material; compared with the traditional formula, using the correction formula can improve the test accuracy of the damping loss factor; the proposed method has certain engineering significance and a wide application prospect.

Description

Technical Field

[0001] The present invention relates to the field of testing the damping characteristics of materials, and particularly to a method for improving the test accuracy of the loss factor of damping materials with a correction formula at a required natural frequency. Background Art

[0002] Damping is one of the dynamic mechanical properties of materials, which converts the energy of mechanical vibration into heat energy or other energy that can be dissipated, so as to achieve the purpose of vibration reduction. At present, damping vibration reduction technology is widely applied in engineering fields such as aviation, aerospace, ships, environmental engineering, mechanical equipment, and transportation vehicles.

[0003] The main methods for testing the material loss factor include the bending resonance method, the modal circle method, the phase method, the attenuation method, the input power method, etc. Among them, the bending resonance method is widely used in damping testing due to its simple operation.

[0004] In the test of the damping loss factor, the traditional formula of the bending resonance method omits the high-order small terms. However, when the loss factor of the damping material is relatively large, a relatively large error will be generated, affecting the accuracy of the test results. Summary of the Invention

[0005] The object of the present invention is to provide a scheme for preparing a substrate beam with specific dimensions at a required natural frequency; in order to improve the test accuracy of the loss factor, a method for improving the test accuracy of the loss factor of damping materials with a correction formula is proposed.

[0006] The technical solution of the present invention is: a method for improving the test accuracy of the loss factor of damping materials, the process is as Figure 1 shown, including the following steps:

[0007] Step 1: Prepare a substrate beam specimen, and solve the Young's modulus of the substrate beam according to the following formula;

[0008]

[0009] In the formula, ρ1 is the density of the substrate beam, L1 is the length of the substrate beam, H1 is the thickness of the substrate beam, f i is the i-th natural frequency of the substrate beam;

[0010] Step 2: Select the second natural frequency of the required substrate beam, and prepare a substrate beam with specific dimensions according to the following formula;

[0011]

[0012] In the formula, ω n is the required n-th natural frequency. In the present invention, the second natural frequency is selected as an example;

[0013] Step 3: Fabricate two substrate beam specimens of the same size and material. Apply a layer of the damping material to be measured on one of the substrate beam specimens to form a composite damping beam.

[0014] Step 4: Test the frequency response curves of the substrate beam and the composite damping beam respectively; calculate the Young's modulus ratio of the damping layer to the substrate beam according to the following formula;

[0015]

[0016] u = (1 + Dh)·f 2

[0017] v = 4 + 6h + 4h 2

[0018]

[0019] In the formula, h = H2 / H1, which is the ratio of the thickness H2 of the damping layer to the thickness H1 of the substrate beam; e = E2 / E1, which is the ratio of the Young's modulus E2 of the damping layer to the Young's modulus E1 of the substrate beam; D = ρ2 / ρ1 is the ratio of the density ρ2 of the damping layer to the density ρ1 of the substrate beam; f = f 2n / f 1n is the resonance frequency f 2n of the composite damping beam and the resonance frequency f 1n of the substrate beam.

[0020] Step 5: Obtain the loss factor of the composite damping beam according to the semi - power bandwidth method correction formula;

[0021] Third - order correction formula:

[0022] Omit the third - order small terms to obtain the traditional formula:

[0023] In the formula, Δf is the frequency bandwidth, and f r is the resonance frequency;

[0024] Obtain the loss factor η1 of the composite damping beam according to the third - order correction formula

[0025] Step 6: Obtain the loss factor η2 of the damping material according to the following formula

[0026]

[0027] The beneficial effects of the present invention are as follows: Prepare two substrate beam specimens of the same size and material according to a required certain - order natural frequency; compared with the traditional formula, using the correction formula can improve the test accuracy of the damping loss factor; the proposed method has certain engineering significance and broad application prospects. Description of the Drawings

[0028] Figure 1 Flow chart of the method for testing the loss factor of the damping material proposed by the present invention

[0029] Figure 2 Schematic diagram of the test system

[0030] Figure 3 Reference diagram of the size of the base beam at the required natural frequency (taking the second-order natural frequency as an example)

[0031] Figure 4 Comparison result of the error between the traditional formula and the third-order correction formula of the bending resonance method

[0032] Figure 5 Frequency response curve of the base beam specimen at 0 - 1000 Hz

[0033] Figure 6 Frequency response curve of the composite damping beam specimen at 0 - 1000 Hz Embodiment

[0034] In this embodiment, taking the selection of the second-order natural frequency as an example, two base beam specimens of the same size and material are made. A layer of the damping material to be tested is laid on one of the base beam specimens to form a composite damping beam. The third-order correction formula is used to calculate the loss factor of the damping material. The method specifically includes the following steps:

[0035] Step 1: Select the second-order natural frequency as 300 Hz. Referring to Figure 3 , it can be known that the effective size of the base beam is 0.18 m in length and 0.002 m in thickness. Referring to GB / T 18258—2000 "Test Method for Damping Performance", the width of the base beam is designed to be 0.01 m. Two base beam specimens of the same material with the size of 0.2 m in length, 0.01 m in width and 0.002 m in thickness are made. A layer of the damping material to be tested with a thickness of 0.002 m is laid on one of them to form a composite damping beam;

[0036] Step 2: Referring to Figure 2 , install the base beam specimen on the fixture, and control the effective length of the specimen to be 0.18 m. Apply white noise excitation to its free end in a non-contact manner, and obtain the corresponding vibration response. The sensor is used in a non-contact manner to pick up the amplitude response signal near the clamping end. The amplitude signal is amplified by an amplitude tester and collected into a multi-channel data analyzer, and the corresponding FFT windowing analysis is performed. The composite damping beam is tested in the same way;

[0037] In this embodiment, the frequency response curve of [0 Hz, 1000 Hz] is tested. The frequency response curve of the base beam is as shown in Figure 5 and the frequency response curve of the composite damping beam is as shown in Figure 6as shown;

[0038] Table 1. Resonance Frequencies of the First - Third Orders of the Base Beam and the Composite Damping Beam Specimens

[0039] Natural frequency The first order The second order The third order Base beam (Hz) 43.5 301.5 844.5 Composite damping beam (Hz) 43.0 298.0 840.0

[0040] Step 3: The density of the base beam ρ1 = 7800 kg / m 3 , the density of the damping material is 1200 kg / m 3 , calculate the Young's modulus of the damping material according to the following formula;

[0041]

[0042]

[0043] u = (1 + Dh)·f 2

[0044] v = 4 + 6h + 4h 2

[0045]

[0046] Substitute the data into the above formula to obtain the Young's moduli of the base beam and the composite damping beam; as shown in Table 2;

[0047] Table 2. The First - Third Order Young's Moduli of the Base Beam and the Composite Damping Beam

[0048]

[0049] Step 4: According to the third - order correction formula of the half - power bandwidth method, refer to Figure 6 , calculate the loss factor η1 of the composite damping beam, and the results are shown in Table 3;

[0050] Third - order correction formula:

[0051] Table 3. The First - Third Order Loss Factors of the Composite Damping Beam

[0052] Natural frequency The first order The second order The third order <![CDATA[Composite damping beam η1]]> 0.03964 0.03019 0.03198

[0053] Step 5: Calculate the loss factor η2 of the damping material according to the following formula, and the calculation results are shown in Table 4;

[0054]

[0055] Table 4. The First - Third Order Loss Factors of the Damping Material

[0056] Natural frequency The first order The second order The third order <![CDATA[Damping material η2]]> 0.3472 0.2649 0.2561

Claims

1. A method for improving the test accuracy of the loss factor of a damping material, comprising the following steps: Step 1: Prepare a base beam sample and solve the Young's modulus of the base beam according to the following formula; Where ρ1 is the density of the base beam, L1 is the length of the base beam, H1 is the thickness of the base beam, and f i is the i-th natural frequency of the base beam; C1 = 0.5596, Step 2: Select a certain order natural frequency of the required base beam, and prepare a base beam of a specific size according to the following formula; where ω n is the required nth natural frequency. In this invention, the second natural frequency is taken as an example; λ1L1≈1.875, λ2L1≈4.694, Step 3: prepare two base beam samples of the same size and material, and lay a layer of the damping material to be tested on one of the base beam samples to form a composite damping beam; Step 4: Test the frequency response curves of the base beam and the composite damping beam respectively; calculate the Young's modulus ratio of the damping layer to the base beam according to the following formula; where u = (1 + Dh)·f 2 , v = 4 + 6h + 4h 2 h = H2 / H1, which is the ratio of the thickness H2 of the damping layer to the thickness H1 of the base beam; e = E2 / E1, which is the ratio of the Young's modulus E2 of the damping layer to the Young's modulus E1 of the base beam; D = ρ2 / ρ1 is the ratio of the density ρ2 of the damping layer to the density ρ1 of the base beam; f = f 2n / f 1n is the ratio of the resonance frequency f 2n of the composite damping beam to the resonance frequency f 1n of the base beam; Step 5: Modify the formula according to the half-power bandwidth method to obtain the loss factor of the composite damping beam; Third-order correction formula: The third-order small terms are omitted to obtain the traditional formula: where Δf is the frequency bandwidth and f r is the resonance frequency; According to the third-order correction formula, the loss factor η1 of the composite damping beam is obtained Step 6: According to the following formula, calculate the loss factor η2 of the damping material 。

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