Young modulus calculation method of circular section rod

Abstract

The invention relates to the technical field of material mechanical parameter testing, and discloses a Young modulus calculation method of a circular section rod, which comprises the following steps: acquiring information of section radius r, length h and mass m of a sample by using a high-precision measuring tool; acquiring time domain sound pressure signals under two supporting states by using a professional microphone; converting a time domain sound pressure signal into a frequency domain signal, and respectively identifying a second-order damping bending vibration frequency and a third-order damping bending vibration frequency on a spectrogram; the damping influence is ignored; calculating h / r to obtain a corresponding coefficient; substituting all parameters into a formula to obtain a Young modulus value; and calculating the average Young modulus. According to the Young modulus calculation method, the universality of the calculation method for the circular section rod in different practical application scenes is enhanced, and the Young modulus can be accurately calculated as long as corresponding parameters are obtained and substituted no matter how the size of the sample changes.

Description

Technical Field

[0001] The invention relates to the technical field of material mechanical parameter testing, in particular to a method for calculating the Young's modulus of a circular cross-section rod. Background Art

[0002] Young's modulus is a key parameter in material mechanics. It reflects the material's ability to resist deformation and is of great significance for material selection, structural design, and engineering applications. Different materials have different Young's moduli. Accurate determination of their values ​​can help engineers and scientists better understand the properties of materials and predict the behavior of materials under different load conditions, thereby ensuring the safety and reliability of structures.

[0003] With the continuous advancement of science and technology, people have higher and higher requirements for the measurement of mechanical properties of materials. The traditional Young's modulus calculation method can no longer meet the needs of modern engineering and scientific research in some aspects. In a greenhouse environment, factors such as temperature and humidity may affect the mechanical properties of materials. In addition, noise and interference in a greenhouse environment may also affect the accuracy of the measurement results.

[0004] Therefore, it is necessary to develop a more accurate, convenient and universal Young's modulus calculation method to solve the problem of how to overcome the influence of environmental factors and accurately measure the Young's modulus of circular cross-section rods. Summary of the invention

[0005] The embodiment of the present application provides a method for calculating the Young's modulus of a circular cross-section rod, thereby solving the problem in the related art of overcoming the influence of environmental factors and accurately measuring the Young's modulus of a circular cross-section rod.

[0006] According to one aspect of an embodiment of the present application, a method for calculating the Young's modulus of a circular cross-section rod is provided, comprising the following steps:

[0007] S100: Use high-precision measuring tools to obtain information on the cross-sectional radius r, length h, and mass m of the sample;

[0008] S200: A professional microphone is used to obtain the time domain sound pressure signals in two support states;

[0009] S300: Convert the time domain sound pressure signal into a frequency domain signal and identify the second-order damped bending vibration frequency on its spectrum diagram and the third-order damped bending vibration frequency

[0010] S400: Ignore the damping effect, that is

[0011] S500: Calculate h / r and substitute it into the formula to get the coefficient function

[0012] S600: Substitute the function coefficients and the radius r, length h, mass m, the second-order ideal natural flexural vibration frequency f α2 and the third-order ideal natural flexural vibration frequency f α3 into the formula to obtain the Young's modulus value E α2 、E α3 ;

[0013] S700: Calculate its average Young's modulus E Avg =(E α2 +E α3 ) / 2.

[0014] Furthermore, the S400 results in the experimentally measured low-order natural flexural vibration frequency being lower than the ideal value under the damping effect. Since the damping effect of most materials is very small, the approximate values of the second-order damped natural flexural vibration frequency and the third-order damped natural flexural vibration frequency of the specimen material measured under two support states can be directly substituted into the coefficient function formula for calculating the Young's modulus of the material.

[0015] Furthermore, the coefficient functions in the S500 have the following formulas respectively:

[0016]

[0017] Furthermore, in the S600, the relationship between the low-order ideal natural flexural vibration frequency and the first-order ideal natural longitudinal vibration frequency f β1 of a circular cross-section rod (10 < h / r < 100) is established, and the parameters are substituted into the following formula:

[0018]

[0019] where f α2 (Hz) is the second-order natural flexural vibration frequency of the circular cross-section rod; f α3 (Hz) is the third-order natural flexural vibration frequency of the circular cross-section rod; h (m) is the length of the circular cross-section rod; r (m) is the cross-sectional radius of the round bar; m (kg) is the mass of the circular cross-section rod; E α2 、E α3 are the Young's modulus values of the material measured at different flexural frequencies respectively, and for the same material, their values are approximately equal.

[0020] Furthermore, circular cross-section rod specimens with different material properties are selected. For specimens of each material, under the same greenhouse environment, the Young's modulus is calculated according to S100 to S700 described above, and the results obtained from each calculation are recorded.

[0021] Furthermore, analyze the dispersion degree of the Young's modulus calculation results of specimens of different materials, set the dispersion degree threshold as X, and the dispersion degree of the calculation results as ΔX;

[0022] When ΔX < X, it indicates that this calculation method has high stability and reliability for this material;

[0023] When ΔX ≥ X, it is necessary to further check the possible error factors during the test process.

[0024] Furthermore, due to the differences in vibration characteristics and other aspects of rods of different sizes, rods with radii and lengths within a certain range are grouped and tested and analyzed separately.

[0025] Furthermore, a database is established to store the test data and calculation results of circular cross-section rods of different materials and different sizes; the database can include the basic information of the specimens, the time-domain sound pressure signals, frequency-domain signals and data of bending vibration frequencies during the test process, as well as the finally calculated Young's modulus and average Young's modulus.

[0026] Furthermore, analyze the interference degree of environmental noise on the acquisition of time-domain sound pressure signals by professional microphones, and adopt appropriate noise reduction and signal processing methods to reduce the impact on the calculation results of the Young's modulus.

[0027] Furthermore, conduct regular repeated tests on the same batch of circular cross-section rod specimens and observe the change of their Young's modulus over time.

[0028] Furthermore, establish a quality control system to ensure that every link in the whole test and calculation process complies with the standard specifications, regularly calibrate the measuring tools, and detect and maintain the performance of the microphones.

[0029] Furthermore, use numerical simulation means such as finite element analysis to simulate the vibration characteristics of circular cross-section rods and compare and verify with the experimental test results.

[0030] Compared with the prior art, the beneficial effects of the present invention are:

[0031] 1. Through measurements under multiple support states, richer vibration information can be obtained, which helps to more comprehensively analyze the mechanical properties of the specimens. The sound pressure signals under different support states can reflect the vibration behavior of the specimens under different constraint conditions, providing more basis for accurately identifying the bending vibration frequency;

[0032] 2. The frequency domain signal can clearly show the energy distribution of different frequency components, making the bending vibration frequency easier to identify and extract. The second-order and third-order damped bending vibration frequencies can be separated from the complex signal through the spectrum diagram, reducing the interference of other frequency components and improving the accuracy of vibration frequency identification.

[0033] 3. The establishment of the formula is based on a certain theoretical foundation and can more accurately describe the relationship between the mechanical behavior of circular cross-section rods and various parameters. Using these theoretical models for calculations, more reliable Young's modulus values ​​can be obtained, providing strong support for engineering design and material research.

[0034] The technical solution of the present application is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The accompanying drawings, which constitute a part of the specification, illustrate embodiments of the present application and, together with the description, serve to explain the principles of the present application.

[0036] The present application can be more clearly understood from the following detailed description with reference to the accompanying drawings, in which:

[0037] Figure 1 A schematic diagram of a flow chart of a method for calculating the Young's modulus of a circular cross-section rod proposed in this application;

[0038] Figure 2 This is a test schematic diagram of a method for calculating the Young's modulus of a circular cross-section rod proposed in this application. DETAILED DESCRIPTION

[0039] Various exemplary embodiments of the present application will now be described in detail with reference to the accompanying drawings. It should be noted that unless otherwise specifically stated, the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present application.

[0040] At the same time, it should be understood that for the convenience of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship.

[0041] The following description of at least one exemplary embodiment is merely illustrative in nature and is not intended to limit the present application, its application, or uses.

[0042] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0043] It should be noted that like reference numerals and letters refer to similar items in the following figures, and therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0044] In addition, the technical solutions between the various embodiments of the present application can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by this application.

[0045] It should be noted that all directional indications in the embodiments of the present application (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0046] Combine the following Figure 1-Figure 2 To describe a Young's modulus calculation method for a circular cross-section rod according to an exemplary embodiment of the present application. It should be noted that the following application scenarios are only shown to facilitate understanding of the spirit and principles of the present application, and the embodiments of the present application are not limited in this regard. On the contrary, the embodiments of the present application can be applied to any applicable scenario.

[0047] The present application also proposes a method for calculating the Young's modulus of a circular cross-section rod.

[0048] Figure 1 The following schematically shows a flow chart of a method for calculating the Young's modulus of a circular cross-section rod according to an embodiment of the present application. Figure 1 As shown, the method is applied in a greenhouse environment and comprises the following steps:

[0049] Step 1: Use high-precision measuring tools to obtain the cross-sectional radius r, length h, and mass m information of the sample.

[0050] Specifically, when measuring mass m, a precision balance is used, which can accurately weigh very small mass changes and accurately obtain the actual mass of circular cross-section rod samples of different materials and sizes. Especially for some samples with small mass or mass differences that need to be accurately distinguished, a precision balance can meet the measurement requirements and ensure the accuracy of the measured mass data.

[0051] Step 2 uses a professional microphone to obtain the time domain sound pressure signals in two supporting states.

[0052] Specifically, two different support states are adopted, such as Figure 2The figure shows a circular cross-section rod in two support states. The vibration characteristics of the different support states are significantly different. By setting these two support states, the second-order and third-order damped bending vibration modes of the circular cross-section rod specimen can be excited respectively, which is helpful for the subsequent more comprehensive and accurate calculation of Young's modulus.

[0053] Step 3: Convert the time domain sound pressure signal into a frequency domain signal and identify the second-order damped bending vibration frequency on its spectrum diagram. and the third-order damped bending vibration frequency

[0054] Specifically, through the conversion of signals and accurate identification of key frequencies, key information on the vibration characteristics of circular cross-section rods was discovered during the analysis and conversion from time domain to frequency domain, which laid an important foundation for the subsequent smooth calculation of accurate Young's modulus.

[0055] Step 4 ignores the damping effect, that is

[0056] Specifically, for most materials, the damping effect is very small, and ignoring the damping effect can greatly simplify the calculation process of Young's modulus. It avoids complex damping calculations, reduces the difficulty and amount of calculations, and makes the calculation method simpler and easier.

[0057] Step 5 Calculate h / r and substitute it into the formula to get the coefficient function

[0058] Specifically, by calculating h / r and substituting it into the formula to obtain the coefficient function, the influence of the sample's geometry on the calculation of Young's modulus is fully considered. Different h / r ratios reflect the geometric characteristics of circular cross-section rods of different sizes. The coefficient function can be adjusted according to these characteristics, which improves the adaptability of the calculation method to samples of different sizes. This makes the method applicable to circular cross-section rods of various sizes, expanding the scope of application of the method. Whether it is a small-sized specimen or a large-sized rod, reasonable calculations can be performed through this step, which improves the versatility of the method.

[0059] Step 6: Set the function coefficients and radius r, length h, mass m, second-order ideal natural bending vibration frequency f α2 and the third-order ideal natural bending vibration frequency f α3 Substitute into the formula to obtain its Young's modulus value E α2 、E α3 .

[0060] Specifically, the establishment of the formula is based on a certain theoretical basis and can accurately describe the relationship between the mechanical behavior of a circular cross-section rod and various parameters. By using these theoretical models for calculation, a relatively reliable value of Young's modulus can be obtained, providing strong support for engineering design and material research.

[0061] Step 7 Calculate its average Young's modulus E Avg =(E α2 +E α3 ) / 2.

[0062] Specifically, the calculation of the average Young's modulus can be statistically analyzed, such as calculating the standard deviation, etc., to further evaluate the dispersion degree and uncertainty of the results. This helps to better understand the quality and reliability of the experimental data and provides a more accurate basis for subsequent analysis and application.

[0063] Figure 2 Schematically shown is a schematic diagram of the test of Young's modulus of a rod with a circular cross-section. The S400 causes the experimentally measured low-order natural bending vibration frequency to be lower than the ideal value under the damping effect. Since the damping effect of most materials is very small, the approximate value of this material damping can be directly substituted into the coefficient function formula for calculating the Young's modulus of the material.

[0064] It can be understood that although the damping effect does cause the experimentally measured low-order natural bending vibration frequency to be lower than the ideal value, considering the actual situation that the damping effect of most materials is small, directly substituting this approximate value into the coefficient function formula for calculating Young's modulus is a reasonable and advantageous treatment method, which plays an important supporting role in the feasibility and application value of the entire calculation method.

[0065] Specifically, in the S500, the coefficient function The formulas are respectively:

[0066]

[0067] Specifically, in the S600, the relationship between the low-order ideal natural bending vibration frequency and the first-order ideal natural longitudinal stretching vibration frequency f β1 of a circular cross-section rod (10 < h / r < 100) is established, and the parameters are substituted into the following formula:

[0068]

[0069] Among them, f α2 (Hz) is the second-order natural bending vibration frequency of the circular cross-section rod; f α3(Hz) is the third-order natural bending vibration frequency of a circular cross-section rod; h (m) is the length of the circular cross-section rod; r (m) is the cross-sectional radius of the round bar; m (kg) is the mass of the circular cross-section rod; E α2 and E α3 are ideal isotropic materials.

[0070] Specifically, select a variety of circular cross-section rod specimens with different material properties. For each material specimen, under the same greenhouse environment, calculate the Young's modulus according to S100 to S700 described above, and record the results obtained each time.

[0071] As can be seen from the above, by comparing the calculation processes and results of different material specimens, we can deeply understand how the material's own properties interact with each link in the calculation method. For example, for a rubber material with better elasticity, its damping characteristics during vibration may be very different from those of a rigid metal material, which may affect the identification of the vibration frequency in step S300 and the processing effect of the damping influence in step S400, etc. Analyzing these influences helps to further optimize the calculation method so that it can better adapt to the characteristics of various materials.

[0072] It can be understood that recording the results obtained each time can form a rich data set. Through the collation, statistics, and analysis of these data, we can intuitively see information such as the numerical distribution of the Young's modulus of different material specimens and the degree of dispersion of the calculation results. For example, we can calculate statistics such as the average value and standard deviation of the Young's modulus of different material specimens to measure the accuracy and stability of this calculation method for each material, and also find the difference degree of the Young's modulus between different materials, providing strong data support for material screening, application, and further theoretical research.

[0073] Specifically, analyze the degree of dispersion of the Young's modulus calculation results of different material specimens, set the degree of dispersion threshold as X, and the degree of dispersion of the calculation results is ΔX;

[0074] When ΔX < X, it indicates that this calculation method has high stability and reliability for this material;

[0075] When ΔX ≥ X, it is necessary to further check the possible error factors in the test process.

[0076] It can be understood that when the degree of dispersion of the calculation results is less than the set threshold, as described above, this indicates that this calculation method has high stability and reliability for this material. At this time, it can be considered that this method can be well applied to the determination of the Young's modulus of this material under the current conditions, and the calculation results can be safely applied to subsequent material selection, structural design, and other related work;

[0077] If the discreteness of the calculated results exceeds the threshold, it means that there are likely to be some error factors that affect the accuracy of the results during the test. These factors may come from multiple aspects. For example, the high-precision measurement tool used in step S100 may have a decrease in accuracy or inaccurate calibration, resulting in deviations in the basic data such as the radius, length, and mass of the sample; or in step S200, the professional microphone is subject to abnormal external interference, making the acquired time-domain sound pressure signal inaccurate, which in turn affects the subsequent frequency identification and the final Young's modulus calculation. Therefore, it is necessary to conduct a comprehensive and detailed inspection of the entire test process, troubleshoot possible problems in each link, recalibrate the measurement tools, optimize the test environment, review the data processing process, etc., until the root cause of the error that causes the excessive discreteness is found and resolved, so that the calculation method can be accurately and reliably used for the Young's modulus calculation of the material.

[0078] Specifically, due to the differences in vibration characteristics among rods of different sizes, rods within a certain range of radius and length are grouped together and tested and analyzed separately.

[0079] It can be understood that the length of the rod determines the possible range of values ​​of its vibration wavelength. When a longer rod vibrates, its vibration period is relatively long, the corresponding vibration frequency will be lower, and the distribution of vibration modes of different orders will be more dispersed; while a shorter rod has a relatively short vibration period and a higher vibration frequency, and the vibration mode is more compact.

[0080] Specifically, a database is established to store the test data and calculation results of circular cross-section rods of different materials and sizes; the database may include basic information of the specimen, time domain sound pressure signals, frequency domain signals and bending vibration frequency data during the test, as well as the Young's modulus and average Young's modulus finally calculated.

[0081] It is understandable that when calculating the Young's modulus of circular cross-section rods of different materials and sizes, a large amount of complex data will be generated, covering a wide range of information from the basic properties of the specimen to the intermediate data of each test link and the final calculation results. By establishing a database, these scattered data can be integrated according to certain rules and logic to achieve unified management, making it easier for researchers to find, call and view relevant data at any time, avoiding data loss or confusion.

[0082] Specifically, the degree of interference of environmental noise on the time-domain sound pressure signal obtained by professional microphones is analyzed, and appropriate noise reduction and signal processing methods are used to reduce the impact on the calculation results of Young's modulus.

[0083] Specifically, the same batch of circular cross-section rod specimens are tested repeatedly at regular intervals to observe how their Young's modulus changes over time.

[0084] Specifically, a quality control system is established to ensure that every link in the entire testing and calculation process meets standard specifications, measurement tools are calibrated regularly, and the performance of microphones is tested and maintained.

[0085] It is understandable that the test and calculation of the Young's modulus of a circular cross-section rod involves multiple links, multiple measuring tools, and operating steps. Deviations in any link may lead to large errors in the final calculation results and fail to truly reflect the mechanical properties of the material. Establishing a quality control system is like building a solid "protection net" for the entire process, which minimizes the source of error by ensuring that each link meets standard specifications.

[0086] Specifically, the vibration characteristics of circular cross-section rods are simulated using numerical simulation methods such as finite element analysis, and compared with experimental test results. Numerical simulation can provide a deeper understanding of the mechanical behavior of the rod and provide theoretical support for the improvement of the Young's modulus calculation method.

[0087] It is understandable that although experimental tests can obtain some vibration data of rods in actual situations, the results may be uncertain due to the influence of various factors such as experimental environment, measurement accuracy, and operating errors. By comparing and verifying the results obtained by numerical simulation, the accuracy and reliability of the experimental results can be judged. For example, if the bending vibration frequency of a certain order obtained by numerical simulation is highly consistent with the experimental test results, then the validity of the experimental data can be confirmed to a large extent; conversely, if there is a large difference between the two, it is necessary to further investigate whether it is a problem in the experimental link or a problem with the model and parameter settings during the simulation process.

[0088] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the invention disclosed herein. The present application is intended to cover any variations, uses or adaptations of the present application, which follow the general principles of the present application and include common knowledge or customary techniques in the art that are not disclosed in the present application. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the following claims.

[0089] It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A method for calculating the Young's modulus of a circular cross-section rod, characterized in that: It includes the following steps: S100: Obtain the cross-sectional radius r, length h, and mass m information of the specimen using a high-precision measuring tool; S200: Use a professional microphone to obtain the time-domain sound pressure signals under two support states; S300: Convert the time domain sound pressure signal into a frequency domain signal and identify the second-order damped bending vibration frequency on its spectrum diagram and the third-order damped bending vibration frequency S400: Ignore the damping effect, that is S500: Calculate h / r and substitute it into the formula to get the coefficient function S600: The coefficient and radius r, length h, mass m, second-order ideal natural bending vibration frequency f α2 and the third-order ideal natural bending vibration frequency f α3 Substitute into the formula to obtain its Young's modulus value E α2 、E α3 ; S700: Calculate the average Young's modulus E Avg =(E α2 +E α3 ) / 2.

2. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: The second-order damped natural bending vibration frequency of the sample material measured under two support states is and the third-order damped natural bending vibration frequency The approximate value of is directly substituted into the coefficient function formula to calculate the Young's modulus of the material.

3. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: The coefficient function in S500 The formulas are:

4. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: Establish the relationship between the low-order ideal natural bending vibration frequency of a circular-section rod (10 < h / r < 100) and the first-order ideal natural longitudinal telescopic vibration frequency f in the S600, and substitute the parameters into the following formula: β1 and Among them, f α2 (Hz) is the second-order natural bending vibration frequency of the circular cross-section rod; f α3 (Hz) is the third-order natural bending vibration frequency of the circular cross-section rod; h (m) is the length of the circular cross-section rod; r (m) is the cross-sectional radius of the round rod; m (kg) is the mass of the circular cross-section rod; E α2 、E α3 They are the Young's modulus values ​​of the materials measured at different bending frequencies, and their values ​​are approximately the same for the same material.

5. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: Select a variety of circular cross-section rod specimens with different material properties. For specimens of each material, calculate the Young's modulus according to S100 to S700 described above under the same greenhouse environment, and record the results obtained from each calculation.

6. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: Analyze the dispersion degree of the Young's modulus calculation results of specimens of different materials, set the dispersion degree threshold as X, and the dispersion degree of the calculation results as ΔX; When ΔX < X, it indicates that the calculation method has high stability and reliability for this material; When ΔX ≥ X, it is necessary to further check the possible error factors during the testing process.

7. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: Since there are differences in vibration characteristics and other aspects among rods of different sizes, the rods with radii and lengths within a certain range are grouped and tested and analyzed separately.

8. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: Establish a database to store the test data and calculation results of circular cross-section rods of different materials and different sizes; the database can include the basic information of the specimens, the time-domain sound pressure signals, frequency-domain signals, and data of bending vibration frequencies during the testing process, as well as the finally calculated Young's modulus and average Young's modulus.

9. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: Analyze the interference degree of environmental noise on the time-domain sound pressure signals obtained by the professional microphone, and adopt appropriate noise reduction and signal processing methods to reduce the impact on the Young's modulus calculation results.

10. The Young's modulus calculation method of a circular cross-section rod according to claim 1, characterized in that: Conduct regular repeated tests on the same batch of circular cross-section rod specimens and observe the change of their Young's modulus over time.

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