Method for measuring Young modulus of metal material based on modal test and simulation
By combining modal testing and finite element simulation, the Young's modulus measurement process was simplified, solving the need for efficient and low-cost measurement of complex structural components and industrial sites, and achieving high-precision Young's modulus identification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-27
- Publication Date
- 2026-05-15
AI Technical Summary
Existing methods for measuring Young's modulus are difficult to achieve efficient, low-cost, and accurate measurements in complex structural components and industrial settings. Traditional methods require the preparation of standard samples or rely on complex equipment and multi-point excitation, and are susceptible to noise interference.
The natural frequencies of the metal components are obtained through modal testing. A frequency error objective function is constructed by combining finite element simulation and parameter optimization. Young's modulus is obtained by polynomial fitting and linear interpolation. The optimal value is adjusted by boundary constraints to ensure accuracy.
It enables rapid, non-destructive Young's modulus determination without the need for standard samples and specialized equipment, simplifying the testing process, lowering the equipment and operational barriers, and making it suitable for high-precision testing of complex structures.
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Figure CN122046802A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of mechanical property testing technology for metallic materials, and more specifically, to a method for measuring the Young's modulus of metallic materials based on modal testing and simulation. Background Technology
[0002] Young's modulus is a core mechanical parameter characterizing the elastic properties of metallic materials, playing a crucial role in structural design, material selection, and service condition assessment. Traditional methods for measuring Young's modulus mainly include the tensile method, bending method, and vibration method. Among these, the tensile method, while highly accurate, requires the preparation of standard specimens, has a long testing cycle, high cost, and is not suitable for pre-formed or non-removable components. The resonance frequency method within the vibration method has the advantages of being non-contact and fast, but it often relies on ideal models such as simply supported beams or cantilever beams, making it difficult to extend to complex structures.
[0003] In recent years, inversion methods based on modal analysis have gradually emerged, identifying material parameters by comparing experimental modes with simulation results. However, existing technologies generally require simultaneous acquisition of natural frequencies and mode shapes, and the use of the MAC (Modal Confidence) criterion for mode shape matching. This leads to a complex testing process: multiple accelerometers need to be deployed for multi-point excitation and response acquisition, and high requirements are placed on the professional level of testing personnel and equipment configuration, making it difficult to promote and apply in production sites or maintenance environments. In addition, mode shapes are easily affected by the density of measurement points, small changes in boundary conditions, and noise interference, resulting in poor stability of the identification results, further limiting its engineering practicality.
[0004] Therefore, there is an urgent need for a method to determine Young's modulus that simplifies the testing process, lowers the equipment and operational threshold, and still ensures measurement accuracy. This method is especially suitable for industrial sites without laboratory facilities, complex structural parts, or batch testing scenarios. Summary of the Invention
[0005] To achieve the above objectives, this application provides a method for measuring the Young's modulus of metallic materials based on modal testing and simulation, comprising the following steps: Modal testing is performed on a metal component made of a specified metallic material to obtain the first n measured natural frequencies of the metal component, which are expressed as: ; Obtain the geometric model of the metal component and establish a finite element model; Acquire the measurement characteristics of the metal component, including initial material parameters and boundary constraints; Finite element simulation calculations were performed using Young's modulus. Let n be the first n simulated natural frequencies of the metal component, expressed as: Young's modulus The values and the corresponding first n simulated natural frequencies constitute the analysis data; Construct a frequency error objective function and obtain the optimal value of Young's modulus based on the analyzed data. The objective function for frequency error is the weighted sum of squares of the relative frequency errors, expressed as: , where E is Young's modulus.
[0006] The optimal value of Young's modulus is obtained based on the analyzed data. Then, the optimal value of Young's modulus was verified. The effectiveness, if the optimal value of Young's modulus If invalid, adjust the boundary constraints and re-perform the finite element simulation to obtain the optimal value of Young's modulus. .
[0007] The initial material parameters include the initial Young's modulus. E 0 Poisson's ratio ν and density ρ Boundary constraints are defined based on the actual installation method of the metal components.
[0008] Modal testing includes: One or more acceleration sensors are arranged on the surface of a metal component; A hammer is used to strike metal components, and the response signal is collected by an acceleration sensor. The response signal is processed using modal analysis software to extract the first n measured natural frequencies.
[0009] Furthermore, obtaining the initial material parameters of the metal component includes: Volume V is obtained through a finite element modal calculation model; The mass m is obtained by weighing the metal component; Initial value of Young's modulus E 0 and Poisson's ratio ν Obtained from data of similar materials; density ρ The calculation method is as follows: ρ=m / V .
[0010] Obtaining the optimal value of Young's modulus Includes the following steps: Acquire the analysis data and check whether the content of the analysis data consists of Young's modulus value E and the corresponding first n simulated natural frequencies; Extract the contents of the data for analysis and calculate the frequency error objective function value corresponding to Young's modulus E. ; Determine the objective function value of the minimum frequency error, expressed as: ; At the minimum frequency error objective function value A quadratic polynomial fitting was performed in the vicinity to obtain the optimal value of Young's modulus E. opt ; The optimal value of Young's modulus E is obtained by linear interpolation. opt The first n natural frequencies.
[0011] Furthermore, the optimal value of the Young's modulus is verified. The validity refers to: Based on the optimal value of Young's modulus Calculate the relative frequency error; if the relative frequency error of all participating orders is less than a preset threshold, then determine the optimal value of the Young's modulus. Valid; otherwise, the optimal value of the Young's modulus is determined. If invalid, readjust the boundary constraints and recalculate the optimal value of Young's modulus. .
[0012] The relative frequency error is expressed as: .
[0013] This invention eliminates the need for preparing standard specimens or using specialized equipment such as universal testing machines. It enables rapid and non-destructive determination of Young's modulus of metallic materials simply by matching multiple natural frequencies, significantly simplifying the testing process, reducing the number of sensors required, and simplifying data processing. The method of this invention has no special requirements for the geometry and size of the specimen and can be widely applied to the non-destructive elastic modulus testing of various complex structural metallic components. It is particularly suitable for rapid on-site evaluation and material performance characterization in practical engineering scenarios. Attached Figure Description
[0014] Figure 1 This is a flowchart illustrating the steps of a method for measuring the Young's modulus of metallic materials according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a metal material component structure provided according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the first-order mode provided according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the second-order mode provided according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the third-order mode provided according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the optimized Young's modulus of metallic materials according to an embodiment of the present invention. Detailed Implementation
[0015] The method for measuring the Young's modulus of metallic materials provided by this invention abandons the measurement and comparison of mode shapes, makes full use of the sensitivity of the structure's natural frequency to the material stiffness, and combines finite element simulation and parameter optimization to achieve efficient, accurate and non-destructive identification of the Young's modulus.
[0016] The specific implementation of the present invention will now be described in detail with reference to the accompanying drawings.
[0017] The method for measuring the Young's modulus of metallic materials provided by this invention is as follows: Figure 1 As shown, it includes the following steps: Step S100: Perform modal testing on the metal component made of the specified metal material to obtain the first n measured natural frequencies of the metal component, denoted as: ; Specifically, when performing modal testing, one or more accelerometers are placed on the surface of the metal component; the metal component is struck with a hammer, and the accelerometers collect the response signals; the response signals are processed using modal analysis software to extract the first n measured natural frequencies.
[0018] This invention provides a specific embodiment: the metal component is a metal beam with a topology-optimized structure, which is complex and is processed using 3D printing technology. The beam structure is shown below. Figure 2 The material is GH4169.
[0019] In this step, the metal beam is placed on a foam pad, and the metal component is struck with a hammer. The acceleration values at the measuring points are picked up by an accelerometer. Through data analysis, the first three clear and stable natural frequencies of the metal component are obtained as follows: .
[0020] Step S110: Obtain the geometric model of the metal component and establish a finite element model; the network density of the finite element model meets the convergence requirements of modal calculation; In this step, the actual three-dimensional geometric model of the metal component can be obtained through CAD drawings, 3D scanning, or precision measurement, and the size of the model is consistent with that of the metal component.
[0021] A three-dimensional solid model of the metal component is established in the finite element analysis software. Appropriate element types (such as hexahedral or tetrahedral elements) are used for mesh generation, and the mesh density is ensured to meet the convergence requirements of modal calculation.
[0022] The embodiments provided by this invention import a three-dimensional CAD model into ANSYS software to establish a finite element modal calculation model, and the size of the calculation model is consistent with that of the test model; when the mesh size is adjusted from 3mm to 2mm, the natural frequency changes within 2%, so the mesh size is set to 2mm.
[0023] Step S120: Obtain the measurement features of the metal component, including initial material parameters and boundary constraints; The initial material parameters of the metal component include the initial Young's modulus. E 0 Poisson's ratio ν and density ρ Methods for obtaining initial material parameters include: obtaining the volume V through a finite element modal calculation model; obtaining the mass m by weighing the metal component; and obtaining the initial value of Young's modulus. E 0 and Poisson's ratio ν Data can be obtained from similar material data; density ρ The calculation method is as follows: ρ=m / V .
[0024] Boundary constraints are defined based on the actual installation method of the metal components. For example, if the actual installation method of the components is fixed support, elastic support, or free state, boundary constraints are applied appropriately in the simulation.
[0025] In the embodiment provided by this invention, the mass of the component is obtained as m=1088g using an electronic scale, and the volume of the model is read as V=132.06cm² using modeling software. 3 The calculated density of the material is ρ = 8.24 g / cm³. 3 Based on the data in the reference material handbook, the Poisson's ratio is given as 0.3, and the initial value of Young's modulus is... E 0 = 204 GPa.
[0026] Step S130: Perform finite element simulation calculation: using Young's modulus As a variable, Poisson's ratio ν and density ρ The natural frequencies are calculated using fixed constants to generate analysis data. In practice, within ±20% E Parameter scanning is performed within the 0 range, and Young's modulus is extracted using equal interval step sizes (e.g., 0.5 GPa) during parameter scanning. Calculate the first n simulated natural frequencies, and express the first n simulated natural frequencies as: ; Extracted Young's modulus The values and the corresponding first n simulated natural frequencies constitute the analysis data.
[0027] In embodiments of the present invention, within ±20% E The parameters were scanned within the range of E ∈ [179.5, 220.5] GPa, using an equal interval step size of 0.5 GPa. The first three simulated natural frequencies were calculated based on the values of each E. The Young's modulus variable values and the corresponding calculated natural frequencies of the first three orders were stored in the file "Calculation Results.xlsx" as analysis data. The specific analysis data is shown in Table 1. Table 1. Frequency calculation results under different Young's moduli
[0028] Step S140: Define the objective function for frequency error and obtain the optimal value of Young's modulus based on the analysis data. ; Wherein, the objective function for frequency error is the weighted sum of squares of the relative frequency errors, expressed as: , where E is Young's modulus.
[0029] Obtaining the optimal value of Young's modulus The process can be implemented using Python or other programming languages, and includes the following steps: Step S1: Obtain the analysis data and check whether the content of the analysis data consists of Young's modulus value E and the corresponding first n simulated natural frequencies; Step S2: Extract the contents of the analysis data and calculate the frequency error objective function value corresponding to Young's modulus E. ; Step S3: Determine the objective function value for the minimum frequency error, expressed as: ; Step S4: Minimize the objective function value of the minimum frequency error A quadratic polynomial fitting was performed in the vicinity to obtain the optimal value of Young's modulus E. opt ; Step S5: Use linear interpolation to obtain the optimal value E of Young's modulus. opt The first n natural frequencies; In this embodiment of the invention, the optimal value of Young's modulus E is obtained. opt The corresponding first three natural frequencies The measured frequency, optimal Young's modulus, corresponding simulation frequency, frequency error at each order, and minimum objective function value are output respectively; the F(E) curve is plotted and E is labeled. opt Location, specifically as follows Figure 6 As shown.
[0030] Step S6: Verify the optimal value of Young's modulus Validity: If Young's modulus is optimal Invalid. Re-execute from step S120: adjust boundary constraints and perform finite element simulation. If the Young's modulus is optimal... If valid, the optimal value of Young's modulus can be output. .
[0031] Verification of the optimal value of Young's modulus The method for determining effectiveness is as follows: Based on the optimal value of Young's modulus Calculate the relative frequency error; the method for calculating the relative frequency error is expressed as follows: ; If the relative errors of the frequencies of all participating orders are less than a preset threshold (e.g., 2%), then the optimal value of Young's modulus is determined. efficient.
[0032] In this embodiment of the invention, the optimal value of Young's modulus E is calculated. opt The corresponding first three natural frequencies frequency relative error The final output optimization result E opt =186.831GPa The first three modes are as follows: Figures 3 to 5 As shown. The calculated relative errors between the natural frequencies and the measured natural frequencies are 0.851%, 0.080%, and 0.917%, respectively, all less than 2%. The measured Young's modulus of the material is 186.831 GPa.
[0033] The method for measuring Young's modulus of metallic materials based on modal testing and simulation provided by this invention has significant advantages such as low cost, high efficiency, wide applicability, and high accuracy. This method eliminates the need for preparing standard specimens or using specialized equipment such as universal testing machines. It only requires obtaining the multi-order natural frequencies of the specimen through a standard modal testing system (such as a force hammer, accelerometer, and dynamic signal analyzer), without measuring mode shapes, significantly simplifying the testing process, reducing the number of sensors, and simplifying data processing. By establishing a finite element model corresponding to the experiment, using Young's modulus as the parameter to be identified, a target function for the deviation between the experimental and simulated natural frequencies is constructed, and an optimization algorithm is used for automatic inversion, ultimately obtaining a high-precision Young's modulus value. This method has no special requirements for the geometry and size of the specimen and can be widely applied to the non-destructive elastic modulus testing of various complex structural metallic components. It is particularly suitable for rapid on-site evaluation and material performance characterization in practical engineering scenarios.
[0034] The above-disclosed embodiments are merely a few specific examples of the present invention. However, the present invention is not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.
Claims
1. A method for measuring the Young's modulus of metallic materials based on modal testing and simulation, characterized in that, Includes the following steps: Modal testing is performed on a metal component made of a specified metallic material to obtain the first n measured natural frequencies of the metal component, which are expressed as: ; Obtain the geometric model of the metal component and establish a finite element model; The measurement characteristics of the metal component are obtained, including initial material parameters and boundary constraints. Finite element simulation calculations were performed using Young's modulus. Let n be the variables, and obtain the first n simulated natural frequencies of the metal component, expressed as: The Young's modulus The values and the corresponding first n simulated natural frequencies constitute the analysis data; Construct a frequency error objective function, and obtain the optimal value of Young's modulus based on the analyzed data. Wherein, the objective function for frequency error is the weighted sum of squares of the relative frequency errors, expressed as: , where E is Young's modulus.
2. The method for measuring the Young's modulus of metallic materials based on modal testing and simulation according to claim 1, characterized in that, The optimal value of Young's modulus is obtained based on the analyzed data. Then, the optimal value of the Young's modulus was verified. The effectiveness, if the optimal value of the Young's modulus. If invalid, adjust the boundary constraints and re-perform the finite element simulation to obtain the optimal value of Young's modulus. .
3. The method for measuring the Young's modulus of metallic materials based on modal testing and simulation according to claim 1, characterized in that, The initial material parameters include the initial Young's modulus. E 0 Poisson's ratio ν and density ρ The boundary constraints are defined according to the actual installation method of the metal components.
4. The method for measuring the Young's modulus of metallic materials according to claim 1, characterized in that, The modal testing includes: One or more acceleration sensors are arranged on the surface of the metal component; A hammer is used to strike metal components, and the response signal is collected by an acceleration sensor. The response signal is processed using modal analysis software to extract the first n measured natural frequencies.
5. The method for measuring the Young's modulus of metallic materials according to claim 3, characterized in that, Obtaining the initial material parameters of the metal component includes: The volume V was obtained through a finite element modal calculation model; The mass m is obtained by weighing the metal component; The initial value of Young's modulus E 0 and Poisson's ratio ν Obtained from data of similar materials; The density ρ The calculation method is as follows: ρ=m / V .
6. The method for measuring the Young's modulus of metallic materials according to claim 1, characterized in that, The optimal value of Young's modulus is obtained. Includes the following steps: Acquire the analysis data and check whether the content of the analysis data consists of Young's modulus value E and the corresponding first n simulated natural frequencies; Extract the contents of the data for analysis and calculate the frequency error objective function value corresponding to Young's modulus E. ; Determine the objective function value of the minimum frequency error, expressed as: ; At the minimum frequency error objective function value A quadratic polynomial fitting was performed in the vicinity to obtain the optimal value of Young's modulus E. opt ; The optimal value of Young's modulus E is obtained by linear interpolation. opt The first n natural frequencies.
7. The method for measuring the Young's modulus of metallic materials according to claim 2, characterized in that, The verification of the optimal value of Young's modulus The validity refers to: According to the optimal value of Young's modulus Calculate the relative frequency error; if the relative frequency error of all participating orders is less than a preset threshold, then determine the optimal value of the Young's modulus. Valid; otherwise, the optimal value of the Young's modulus is determined. If invalid, readjust the boundary constraints and recalculate the optimal value of Young's modulus. .
8. The method for measuring the Young's modulus of metallic materials according to claim 7, characterized in that, The relative frequency error is expressed as: .