A method for measuring ultrasonic resonance spectra with automatic calculation of elastic constants

Abstract

The existing ultrasonic resonance spectrum measurement method for measuring elastic constants not only requires complicated manual operation and processing, but also the measurement results are heavily dependent on the experience and technical level of the measurement personnel. The present invention proposes an ultrasonic resonance spectrum measurement method for automatically calculating elastic constants. The method includes: extracting the peak value of the resonance spectrum of a standard cylindrical measurement sample; estimating the shear modulus and Young's modulus, and filtering the data according to the elastic modulus limit; estimating the Poisson's ratio, and filtering the data according to the Poisson's ratio limit; calculating the material parameter C 11 、C 44 Calculate frequency deviation; and determine elastic constants. This method allows a computer to automatically perform frequency matching operations through an algorithm, eliminating excessive reliance on measurement personnel and automating the measurement of elastic constants using ultrasonic resonance spectroscopy. Furthermore, the entire measurement process is simple, and the results are accurate and reliable.

Description

Technical Field

[0001] The invention belongs to the field of material elastic constant measurement, and in particular relates to an ultrasonic resonance spectrum measurement method for automatically calculating elastic constants. Background Art

[0002] Resonant ultrasound spectroscopy (RUS) is a new method developed in the 1990s for measuring the elastic constants of materials. This method is not only the most accurate method for measuring the elastic constants of high-Q solid materials, but also offers the advantages of being sample-safe and highly reproducible. The process of measuring the elastic constants of materials using RUS can be divided into three stages: 1) preparing a sample of a specific shape (cylindrical, rectangular, or spherical) and accurately measuring its dimensional parameters and density; 2) exciting the sample with continuously varying frequency ultrasound to obtain the sample's resonance spectrum; and 3) employing an inverse algorithm to invert the elastic constants of the sample.

[0003] The key to measuring material elastic constants using ultrasonic resonance spectroscopy lies in accurately performing inversion calculations and analysis. The inputs to the inversion calculations are: several measured resonant frequencies, the sample's dimensions and density, and initial estimates of the material's elastic constants (such as C11 and C44). Based on the sample dimensions, density, and initial estimates of the material's elastic constants, the sample's natural frequency can be calculated using numerical methods such as the Rayleigh-Ritz method. By subtracting the calculated sample's natural frequency from the measured resonant frequency in a specific order, the frequency estimation error corresponding to the elastic constant estimate can be obtained. Using the frequency estimation error as the target evaluation function, the Levenberg-Marquardt (LM) algorithm is used to iteratively update the material's elastic constant value multiple times, ultimately yielding the true value of the material's elastic constant.

[0004] When measuring elastic constants using ultrasonic resonance spectroscopy, the traditional inversion calculation process requires complex manual operations and processing. First, the measurement personnel need to make a reasonable estimate of the elastic constant value of the material. The estimated value cannot deviate significantly from the true value, otherwise the subsequent inversion iteration will not converge. Second, after estimating the elastic constant and obtaining the resonant frequency, the measurement personnel need to effectively match the measured resonant frequency with the calculated resonant frequency and assign appropriate weight values. It is easy to understand that if the measured frequency does not correctly match the calculated frequency, the target evaluation function will deviate, and the correct elastic constant cannot be solved.

[0005] In addition, due to the influence of factors such as the ultrasonic transducer and the workpiece position, some natural frequencies of the workpiece cannot be effectively measured. In this case, the corresponding natural frequency weight value needs to be set to 0 to eliminate the adverse effects on the objective evaluation function.Figure 1 This is a case where the measured frequency and the calculated frequency are matched; the calculated frequency values ​​(Modeled / kHz) are arranged in order, while the measured frequency values ​​(Experimental / kHz) and their positions and weights (Weight Factor) in the table require careful and repeated adjustments by the measurement personnel. The specific adjustment strategy depends on the measurement personnel's technical level and ability. Figure 2 As shown, the measured spectrum (white curve) has two distinct resonant frequency peaks at 284.0kHz and 289.9kHz. Correspondingly, the calculated frequency values ​​(blue vertical lines) are 285.6kHz and 287.4kHz, which differ somewhat from the measured frequency values. Ideally, if the elastic constants are sufficiently accurate, these two measured and calculated frequency values ​​would converge after matching, and many other frequency values ​​would also converge after matching. However, in actual measurements, the elastic constants of the material are unknown and yet to be determined, and obtaining the true value requires multiple attempts and error comparisons.

[0006] As previously mentioned, accurate and reliable matching of the measured and calculated frequencies is a prerequisite and guarantee for obtaining accurate results when measuring elastic constants using ultrasonic resonance spectroscopy. However, achieving this exact matching requires repeated attempts and consumes considerable time, which is a major obstacle to the efficiency and effectiveness of ultrasonic resonance spectroscopy.

[0007] To achieve test automation, researchers have optimized and integrated the ultrasonic resonance spectrum measurement program, but the task of matching the measurement frequencies cannot be completed automatically. Therefore, there is an urgent need to optimize the existing measurement method so that it can automatically complete the relevant parameter measurement using a computer. Summary of the Invention

[0008] In view of this, the present invention proposes an ultrasonic resonance spectrum measurement method for automatically calculating elastic constants.

[0009] An ultrasonic resonance spectrum measurement method for automatically calculating elastic constants, the ultrasonic resonance spectrum measurement method comprising the following steps:

[0010] S10 extracts the peak value of the resonance spectrum of the measured sample and quantitatively obtains the specific positions of N resonance frequency peaks. Let the i-th resonance frequency peak be Here, the value range of i is 1...N;

[0011] S20 estimates the shear modulus and Young's modulus, and performs data screening according to the elastic modulus limit;

[0012] S30 estimates Poisson's ratio and performs data screening according to Poisson's ratio limit;

[0013] S40 calculates material parameters C 11 、C 44

[0014] S50 calculates frequency deviation

[0015] S60 Determination of elastic constants

[0016] Optionally, the specific steps of S20 are:

[0017] The measured resonant frequency value The shear modulus G of the measured sample is estimated using formula (1) and obtained as

[0018]

[0019] In formula (1), H is the height of the measured sample, ρ is the density of the measured sample, and i ranges from 1 to N;

[0020] The Young's modulus E of the measured sample is estimated using formula (2) and obtained as

[0021] Estimate the Young's modulus of the measured sample.

[0022]

[0023] In formula (2), k j is a constant in the range of [1-2], j ranges from 1 to M, and M is a positive integer greater than or equal to 1;

[0024] Filter the estimated shear modulus and Young's modulus by elastic modulus limits.

[0025]

[0026]

[0027] In formula (3), G max is the maximum value of the shear modulus of the material; in formula (4), E max is the maximum value of Young's modulus of the material.

[0028] Optionally, the specific steps of S30 are:

[0029]

[0030]

[0031] In formula (6), μ min 、μ max are the minimum and maximum values ​​of Poisson’s ratio respectively;

[0032] Optionally, the specific steps of S40 are:

[0033]

[0034]

[0035] Optionally, the specific steps of S50 are:

[0036] Perform forward numerical calculation on the resonance frequency of the measured sample to obtain the calculated resonance frequency value of the sample

[0037] Find and measure frequency based on the principle of closest distance The calculated resonance frequency value of the match is recorded as will with The calculated resonant frequency value that satisfies the closest distance principle is recorded as Sum of squares by relative deviation

[0038]

[0039]

[0040] In formula (10), The closest measurement frequency The calculated resonant frequency value.

[0041] Optionally, the specific steps of S60 are:

[0042] Determine The minimum value of The minimum value corresponds to and Analyze and measure the elastic constant value of the sample: C 11 、C 44 ,E,G,μ.

[0043] Optionally, in S40, according to the restrictions and To filter:

[0044]

[0045]

[0046] In formulas (11) and (12), C 11min 、C 11max 、C 44min 、C 44max C 11 The minimum and maximum values ​​of C 44 The minimum and maximum values ​​of .

[0047] The beneficial effects of the present invention are as follows: after extracting the peak frequency of the resonance spectrum of the standard cylindrical measurement sample, the present invention estimates the shear modulus corresponding to each spectrum frequency peak and constructs multiple Young's moduli for each shear modulus, and then uses the elastic modulus limit to screen the corresponding data; uses the elastic modulus that meets the limit to calculate the Poisson's ratio, and similarly screens the Poisson's ratio value using the Poisson's ratio limit, and uses the Poisson's ratio that meets the limit to calculate the elastic constant. The calculated elastic constant is used to complete the forward numerical calculation to obtain the calculated resonance frequency value, and the calculated resonance frequency value that matches the measured frequency value is searched according to the principle of the closest distance, the relative deviation is calculated to find the sum of squares, and the elastic modulus corresponding to the measured frequency value with the minimum square sum is found, and then the relevant elastic parameters are calculated. The entire process fully improves the pertinence of frequency matching and avoids invalid frequency matching operations through reasonable and rough setting of relevant parameters (such as the calculation of shear modulus, Young's modulus, and Poisson's ratio in S20 and S30), setting limit screening, and nearest distance matching, thereby effectively improving the frequency matching effect. The entire process can be realized by computer, which has the function of automatically calculating matching measurements, avoiding the setting of initial elastic constant values, and eliminating the need to rely on the technical level and operating experience of the measurement personnel to repeatedly match the frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Summary of measured and calculated frequencies for manual matching;

[0049] Figure 2 This is a comparison chart of manual estimation and measurement frequency;

[0050] Figure 3 A process for automatically calculating elastic constants;

[0051] Figure 4 Extraction of frequency peaks in the resonance spectrum;

[0052] Figure 5 It is the frequency comparison after automatic calculation;

[0053] Figure 6 A summary of automatic matching results. DETAILED DESCRIPTION

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative labor.

[0055] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific implementation methods and accompanying drawings.

[0056] Example 1

[0057] This embodiment demonstrates an automatic and simple ultrasonic resonance spectroscopy method for measuring elastic constants, which solves several problems that affect the measurement efficiency and effect when measuring elastic constants using ultrasonic resonance spectroscopy.

[0058] The entire measurement process is now described in detail as follows:

[0059] (1) Prepare the measurement sample and complete the relevant parameter measurement

[0060] Ultrasonic resonance spectroscopy (USR) measurements of elastic constants require a simple sample shape, such as a sphere, cuboid, or cylinder. Currently, in most applications, samples are processed into a cuboid shape before USR measurements. However, processing cuboid samples requires specialized clamping devices.

[0061] This embodiment directly restricts the measured sample to a cylindrical shape, facilitating both machining and subsequent processing and analysis of spectral data. Unlike suspended wire resonance and pulse excitation methods, the cylindrical sample in ultrasonic resonance spectroscopy does not require a slender rod, which facilitates sample preparation and reduces the likelihood of measurement deviations due to internal mass discontinuities.

[0062] After the cylindrical sample is machined, accurately measure its diameter D and height H using a vernier caliper or micrometer. Use a precision balance to accurately measure its mass m. The sample's volume V can be calculated from its diameter D and height H, and its density ρ can be obtained from its mass m.

[0063] (2) Measure the resonance spectrum of the sample

[0064] Two ultrasonic transducers are used to clamp the sample between them, keeping the sample securely and reliably fixed, and the sample and transducer in point-to-surface contact. During measurement, the signal generator excites one transducer with ultrasonic energy at a specific frequency, while the other transducer picks up the sample's vibration signal. The signal is amplified and collected before being input into a computer for subsequent analysis. When the excitation frequency is the same as the sample's natural vibration frequency, the sample will resonate, causing the signal amplitude of the receiving transducer to increase significantly, thereby forming a resonant frequency peak. By continuously changing the excitation frequency at fixed intervals and synchronously digitally converting the signal of the receiving transducer, the resonance spectrum of the sample can be obtained.

[0065] Figure 3 Demonstrates the subsequent elastic constant calculation process

[0066] (3) Elastic constant calculation process

[0067] S10 extracts resonance frequency peaks

[0068] Use a specific algorithm to extract the peak value of the resonance spectrum and quantitatively obtain the specific positions of multiple resonance frequency peaks at one time, such as Figure 4 As shown, a total of 42.96, 53.78, 87.31, etc. N peaks were extracted to form a measurement frequency peak set, and the elements in it are recorded as The value range of i is 1...N. Resonance frequency peak The detection and extraction are completed automatically by the computer without human intervention.

[0069] S20 estimates shear modulus and Young's modulus, and filters data based on elastic modulus limits

[0070] The measured resonant frequency value The shear modulus G of the measured sample is estimated using formula (1) and obtained as

[0071]

[0072] In formula (1), H is the height of the measured sample, ρ is the density of the measured sample, and i ranges from 1 to N. The Young's modulus E of the measured sample is estimated using formula (2), and the result is:

[0073] Estimate the Young's modulus of the measured sample.

[0074]

[0075] In formula (2), k j is a constant in the range of [1-2], j ranges from 1 to M, M is a positive integer greater than or equal to 1, and the size of M is determined by k j The step size of the calculation is determined. For example, k j The calculation step size is 0.1, then k 1 =1.0, k 2 =1.1……k 10 =1.9, k 11 =2.0, the value of M is 11.

[0076] According to the elastic modulus limit, the estimated shear modulus and Young's modulus are screened and the values ​​exceeding the elastic modulus limit are excluded.

[0077]

[0078]

[0079] In formula (3), G max is the maximum value of the shear modulus of the material; in formula (4), E maxThe maximum value of the Young's modulus of the material. There is no need to set a minimum value here; the default minimum value is 0, meaning all calculated EG values ​​are positive.

[0080] S30 estimates the Poisson's ratio and screens the data according to the Poisson's ratio limit, excluding the data that exceeds the Poisson's ratio limit.

[0081]

[0082]

[0083] In formula (6), μ min 、μ max are the minimum and maximum values ​​of Poisson’s ratio respectively;

[0084] S40 calculates material parameters C11, C44

[0085]

[0086]

[0087] S50 calculates frequency deviation

[0088] Perform forward numerical calculation on the resonance frequency of the measured sample to obtain the calculated resonance frequency value of the sample

[0089] Find each measurement frequency according to the principle of closest distance Match the calculated resonance frequency value and compare the calculated resonance frequency value with the measured frequency The corresponding closest distance is recorded as will with The calculated resonant frequency value that satisfies the closest distance principle is recorded as Sum of squares by relative deviation

[0090]

[0091]

[0092] In formula (10), The closest measurement frequency The calculated resonant frequency value. Figure 5 and Figure 6 The matching results are displayed.

[0093] S60 Determination of elastic constants

[0094] By comparing the sum of squares of relative deviations, we can determine The minimum value of and Analyze and measure the elastic constant value of the sample: C 11 、C 44 , E, G, μ, which are the measured values ​​of the elastic constants of the material to be tested. The elastic modulus and Poisson's ratio of the material can be determined by the following formula: E = C 44 (3C 11 -4C 44 ) / (C 11 -C 44 ), μ=(C 11 -2C 44 ) / (2C 11 -2C 44 ).

[0095] Steps S10 to S60 can all be implemented using a computer program or algorithm. The entire measurement process is greatly simplified, with the frequency matching operation automatically performed by the computer through the algorithm. This invention automates the measurement of elastic constants using ultrasonic resonance spectroscopy, avoiding excessive reliance on human operators, effectively improving the degree of automation in the measurement process, and ensuring accurate and reliable measurement results.

[0096] Example 2

[0097] Compared with Example 1, this embodiment also adds reasonable and rough settings of C11 and C44 in step S40, further reducing the calculation frequency and improving the efficiency of automatic calculation.

[0098]

[0099]

[0100] In formulas (11) and (12), C 11min 、C 11max 、C 44min 、C 44max C 11 The minimum and maximum values ​​of C 44 The minimum and maximum values ​​of .

Claims

1. A method for measuring ultrasonic resonance spectrum for automatically calculating elastic constants, characterized in that: The ultrasonic resonance spectrum measurement method comprises the following steps: S10 extracts the peak value of the resonance spectrum of the measured sample and quantitatively obtains the specific positions of N resonance frequency peaks. Let the i-th resonance frequency peak be Here, the value range of i is 1...N; S20 estimates the shear modulus and Young's modulus, and performs data screening according to the elastic modulus limit; S30 estimates Poisson's ratio and performs data screening according to Poisson's ratio limit; S40 calculates material parameters C 11 、C 44 ; S50 calculates the frequency deviation; The specific steps of S50 are: performing forward numerical calculation on the resonance frequency of the measured sample to obtain the calculated resonance frequency value of the sample Find and measure frequency based on the principle of closest distance The calculated resonance frequency value of the match is recorded as will with The calculated resonant frequency value that satisfies the closest distance principle is recorded as Sum of squares by relative deviation In formula (10), The closest measurement frequency The calculated resonant frequency value of S60 determines the elastic constant; The specific steps of S60 are: The minimum value of The minimum value corresponds to and Analyze and measure the elastic constant value of the sample: C 11 、C 44 , E, G, μ, which are the measured values ​​of the elastic constants of the material to be tested. The elastic modulus and Poisson's ratio of the material can be determined by the following formula: E=C 44 (3C 11 -4C 44 ) / (C 11 -C 44 ), μ=(C 11 -2C 44 ) / (2C 11 -2C 44 ).

2. The ultrasonic resonance spectrum measuring method according to claim 1, wherein: The specific steps of S20 are: The shear modulus G of the measured sample is estimated using formula (1) and obtained as In formula (1), H is the height of the measurement sample, the shape of the measurement sample is cylindrical, ρ is the density of the measurement sample, and i ranges from 1 to N; The Young's modulus E of the measured sample is estimated using formula (2) and obtained as Estimate the Young's modulus of the measured sample; In formula (2), k j is a constant in the range of [1-2], j ranges from 1 to M, and M is a positive integer greater than or equal to 1; the estimated shear modulus and Young's modulus are screened according to the elastic modulus limit; In formula (3), G max is the maximum value of the shear modulus of the material; in formula (4), E max is the maximum value of Young's modulus of the material.

3. The ultrasonic resonance spectrum measurement method according to claim 1, wherein: The specific steps of S30 are: In formula (6), μ min 、μ max are the minimum and maximum values ​​of Poisson's ratio, respectively.

4. The ultrasonic resonance spectrum measurement method according to claim 1, wherein: The specific steps of S40 are:

5. The ultrasonic resonance spectrum measurement method according to any one of claims 1 to 4, characterized in that: In S40, according to the restriction and To filter: In formulas (11) and (12), C 11min 、C 11max 、C 44min 、C 44max C 11 The minimum and maximum values ​​of C 44 The minimum and maximum values ​​of .

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