Method and system for determining at least one mechanical property of sample

Abstract

The present invention relates to a method and a system for determining at least one mechanical property of a sample, the method comprising the steps of: providing said sample wherein said sample comprises dimensions in a main direction; mounting the sample at the mounting end of the sample, wherein the free end of the sample is freely movable in a direction perpendicular to the main direction; shaking the mounted end of the sample at an excitation frequency to excite oscillatory bending of the sample about a centerline perpendicular to the main direction; determining a bending radius of the sample at a predetermined deflection of the sample or at a determined deflection; calculating bending stress by using the bending radius; and calculating the at least one mechanical property of the sample using the bending stress and a number of oscillations of the sample until the sample fails, or the bending stress at a plurality of excitation frequencies, or the bending stress at a plurality of excitation frequencies, and a description of the geometry of the sample.

Description

Technical Field

[0001] The present disclosure relates to methods and systems for determining at least one mechanical property of a sample. Background Art

[0002] Measuring mechanical properties of a sample, such as bending fatigue strength, damping, or elastic constants, typically requires complex and expensive equipment for testing and measurement. Summary of the Invention

[0003] One aspect of the present disclosure is to provide a method and system for determining at least one mechanical property of a sample, which is simplified compared to the prior art, thereby reducing costs and effort.

[0004] The above aspect is solved by the method according to independent claim 1 of the present application. The method according to the present disclosure includes the following steps: providing a sample, wherein the sample includes dimensions in a main direction; mounting the sample at a mounting end of the sample, wherein a free end of the sample can move freely in a direction perpendicular to the main direction; shaking the mounted end of the sample at an excitation frequency to excite the sample to oscillate and bend about a center line perpendicular to the main direction; determining a bending radius of the sample at a predetermined deflection or a determined deflection of the sample; calculating a bending stress using the bending radius; and calculating the at least one mechanical property of the sample using the bending stress and the number of oscillations of the sample until failure, or the bending stress at multiple excitation frequencies, or the bending stress at multiple excitation frequencies and a description of the geometry of the sample.

[0005] The basic concept of the method according to the present disclosure is to force the sample to perform an oscillating motion of its free end relative to the mounting end, and determine the bending radius of the sample at a predetermined deflection or a determined deflection of the sample. The bending radius is a direct measure of the bending stress applied to the sample. Determining the bending radius of the sample based on the measured values of the sample is a fast and robust high-precision calculation. Then, the corresponding mechanical properties of the sample can be calculated based on some assumptions.

[0006] The predetermined deflection or the determined deflection is non-zero, that is, the sample is in a bent state during the oscillation at the time point of measuring the sample, so as to determine the bending radius. Importantly, once the minimum bending radius, that is, the maximum bending of the sample, is determined under multiple subsequent oscillations of the sample, the bending radius is determined each time for the same deflection of the sample.

[0007] According to an embodiment, the predetermined deflection or the determined deflection can be adjusted before or during the execution of the method.

[0008] The bending stress σ of the bent and thus curved sample bending can be derived from the thickness t of the sample, the bending radius R, and the Young's modulus E of the material according to the following equation: σ bending

[0009] According to an embodiment, the thickness of a sample is measured using a micrometer screw. The Young's modulus is provided, for example, by a sample material data sheet, and the radius is measured.

[0010] According to an embodiment, the surface of the sample is planar or cylindrical.

[0011] According to an embodiment of the present disclosure, the sample may have the shape of a strip, a rod, or a plate.

[0012] According to an embodiment, the sample is a strip, wherein the dimension of the sample in the main direction is greater than the dimension of the sample in each of the two transverse directions, wherein the transverse directions are perpendicular to each other and both are perpendicular to the main direction.

[0013] According to an embodiment, the material of the sample is selected from the group consisting of plastics, metals, paper, and wood or a combination thereof.

[0014] According to an embodiment, the step of determining the bending radius includes measuring the bending radius or measuring a parameter indicating the bending radius.

[0015] According to an embodiment, the step of determining the bending radius includes: measuring the profile of the surface of the sample along a line, wherein the line is parallel to the main direction or wherein the line and the main direction form an angle less than 90°, with the sample being at a predetermined deflection or a determined deflection; and calculating the bending radius based on the profile.

[0016] According to an embodiment, the profile of the surface of the sample is measured using a profilometer. In one embodiment, the profilometer is a non-contact profilometer, such as a laser profilometer. The non-contact profilometer measures the profile of the surface of the sample without the need for mechanical interaction with the surface. The profilometer measures the profile of the surface of the sample at a high repetition rate and is commercially available. Generally, in order to quantify the roughness of the sample, a profilometer, especially a laser profilometer, is used to measure the surface profile. However, according to the present disclosure, the profilometer can also be used to determine the microscopic shape of the surface, i.e., the bending radius.

[0017] The main direction can be described to connect the mounted end and the free end of the sample. Thus, the sample mounted at the mounted end of the sample will undergo bending about an axis not parallel to the main direction. Therefore, the line for profilometry must be different from the direction perpendicular to the main direction.

[0018] According to an embodiment, the length of the line will depend on the sample and the laser profilometer. For example, the length of the line can be in the range of 3 mm to 10 mm, such as in the range of 4 mm to 8 mm.

[0019] According to an embodiment, the surface of the sample is measured along the contour of a line as the distance of the surface of the sample from a reference line. The reference line is parallel to the planar surface of the sample and is in an undeflected zero position. This distance is the parameter to be measured by the sensor. This distance indicates the bending radius or is a direct measure of the bending radius.

[0020] According to an embodiment, after measuring the contour of the surface of the sample, the contour is described in Cartesian coordinates so that the bending radius of the surface can be analyzed by calculations prescribed by basic geometric considerations.

[0021] According to an embodiment of the present invention, the mechanical property of the sample is the bending fatigue strength of the sample, wherein the bending fatigue strength is calculated based on the bending stress and the number of oscillations of the sample until the sample fails.

[0022] According to an embodiment, the mechanical property of the sample is the damping factor of the sample, wherein the damping factor is calculated based on the bending stress at multiple excitation frequencies.

[0023] According to an embodiment, the mechanical property of the sample is the resonant frequency of the sample, wherein the resonant frequency is calculated based on the bending stress at multiple excitation frequencies and the geometry of the sample.

[0024] To calculate the bending stress σ bending , the Young's modulus E is required. In one embodiment, the Young's modulus E is derived from a table or a textbook. In another embodiment, a method similar to the method according to the present invention is used to determine the Young's modulus E of the sample, wherein the method for determining the Young's modulus E includes the following steps: providing a sample, wherein the sample includes dimensions in a main direction; mounting the sample at the mounting end of the sample, wherein the free end of the sample can move freely in a direction perpendicular to the main direction; shaking the mounted end of the sample at an excitation frequency to excite the sample to oscillate and bend about a center line perpendicular to the main direction; measuring the amplitude of the sample at a fixed point on the sample for multiple excitation frequencies; determining the resonant frequency of the sample based on the amplitude measured at the excitation frequency; and calculating the Young's modulus using the determined resonant frequency and the geometry of the sample. At the resonant frequency of the sample, the amplitude of the oscillating sample will exhibit a maximum value.

[0025] According to an embodiment, the step of measuring the amplitude of the oscillating sample includes the following steps: for each step of the excitation frequency, measuring the maximum deflection of a single point on the contour line of the surface of the sample.

[0026] The Young's modulus E can be expressed as where ω is the resonant frequency determined by measuring the resonance curve, k is a parameter corresponding to the characteristic vibration mode, and I is the second area moment of the sample with a rectangular cross-section ( ), where the width is the width of the sample perpendicular to the main direction, and is the mass density of the sample material, and Ω is the cross-sectional area.

[0027] According to an embodiment, the deflection is measured relative to the excitation frequency, starting from 10 Hz or 20 Hz below the expected resonance frequency, and the excitation frequency is stepped in steps that can be 0.1 Hz until the excitation frequency is 10 Hz or 20 Hz above the resonance frequency. However, the step size can be greater or less than the step size mentioned herein.

[0028] According to an embodiment, the mechanical property is the G-modulus or Poisson's ratio of the sample.

[0029] In an embodiment, where the mechanical property of the measured sample is the damping factor, the resonance frequency of the sample, or Young's modulus, the plurality of excitation frequencies includes the mechanical resonance motion of the sample.

[0030] Due to the clamping of the sample at one end and the oscillatory motion at the free end, the resonance frequency involved is the resonance frequency of the oscillatory motion of the sample that causes the sample to bend about one or more axes perpendicular to the main direction.

[0031] In an embodiment, where the excitation frequency does not change when determining the mechanical property, the excitation frequency is equal to the mechanical resonance frequency of the sample. Driving the oscillatory bending of the sample at this resonance frequency results in the maximum possible bending of the sample and thus the maximum bending stress.

[0032] In an embodiment, where the sample is excited with the resonance frequency, the bending radius is determined at the maximum deflection of the sample. Thus, the maximum deflection is a predetermined deflection or a determined deflection. The maximum deflection corresponds to the maximum amplitude of the oscillation.

[0033] It must be noted to ensure that the predetermined deflection or the determined deflection at which the bending radius of the sample is located is always determined on the same side relative to the unbent zero position of the sample.

[0034] In an embodiment, where the mechanical property of the sample is the bending fatigue strength of the sample, the steps of determining the bending radius of the sample at the predetermined deflection or the determined deflection of the sample and calculating the bending stress using the bending radius are performed multiple times, and at least the amplitude of the shaking or the excitation frequency is controlled to minimize the difference between the bending stress and the predetermined desired bending stress.

[0035] In an embodiment, a statistical evaluation of a plurality of substantially identical samples is used to determine the at least one mechanical property.

[0036] In an embodiment, the bending fatigue strength of the sample and optionally the relevant statistical parameters (e.g., standard deviation, 95% or 99% fatigue strength) are determined and calculated by step evaluation or Wöhler curve evaluation of multiple measurements performed on multiple samples. The typical number of samples required is 10 to 30.

[0037] According to an embodiment, the plurality of samples are a plurality of substantially identical or identical samples. Substantially identical samples require that the geometries of the plurality of samples are substantially the same. In one embodiment, the materials of the plurality of samples are substantially the same. With respect to the geometry, substantially the same means the same within the typical tolerances for manufacturing mechanical samples. With respect to the material, substantially the same material is a material that contains the same chemical composition but may vary in the microstructure of the plurality of samples, for example, including different precipitates or inclusions or surface defects.

[0038] In the foregoing and following descriptions of the embodiments and claims, with reference to a method for measuring at least one mechanical property of a sample or a system for measuring at least one mechanical property of a sample, the features described apply to both the method and the system.

[0039] At least one of the above aspects is also solved by a system according to independent claim 11 of the present disclosure. A system for measuring at least one mechanical property of a sample according to the present disclosure includes: a sample mount configured to hold the sample at a single mounting end of the sample; a shaker configured to oscillate the sample mount at an excitation frequency; a sensor configured to measure a parameter indicative of a bending radius of the sample at a predetermined deflection or a determined deflection of the sample; and a control unit. The control unit is connected to the shaker and the sensor to receive the parameter from the sensor. The control unit is further configured to control the excitation frequency of the shaker. In addition, the control unit is configured to determine the bending radius based on the parameter, to calculate a bending stress using the bending radius, and to calculate the at least one mechanical property of the sample using the bending stress and the number of oscillations of the sample until failure, or the bending stresses at a plurality of excitation frequencies, or the bending stresses at a plurality of excitation frequencies and a description of the geometry of the sample.

[0040] The foregoing and following detailed descriptions of the embodiments will be understood when read in conjunction with the accompanying drawings. It should be understood that the depicted embodiments are not limited to the exact arrangements and means shown. In the drawings, like elements are represented by like reference numerals. Description of the Drawings

[0041] Figure 1 is a schematic diagram of a system for measuring the mechanical properties of a sample;

[0042] Figure 2 is a coordinate system in which a representation of the profile of the surface of a sample measured with the Figure 1 system and values derived from the profile are shown. Detailed Description

[0043] Figure 1Schematically shown is a system 1 configured to measure the mechanical properties of a sample 2. In the described example, the sample 2 is a metal strip, and its flexural fatigue strength as a mechanical property will be determined in the sense of this application.

[0044] The sample 2 has a free end 3 and a mounting end 4. The mounting end 4 is clamped at a clamping device 5 of a sample mount which is an electromechanical shaker 6. Once the clamping device 5 is periodically moved up and down by the shaker 6, the sample 2 starts an oscillatory motion. During this oscillatory motion, the free end 3 deflects up and down relative to the mounting end 4 of the sample 2. The geometry of the sample 2 has a main extension in the main direction 20 when not deflected. The oscillatory motion of the free end 3 occurs in a direction perpendicular to the main direction 20. Due to the oscillation, the sample 2 bends about a center line 21 perpendicular to the main direction 20.

[0045] During the periodic oscillation of the free end 3, a laser profiler 9 is used as a sensor of the system 1 to measure the profile 7 of the surface 8 of the sample 2. The laser profiler 9 measures the profile 7 as the distances of a plurality of light spots on a line 10 on the surface 8 from a reference plane 11. Once the sample 2 is not excited by the shaker 6, the reference plane 11 is parallel to the planar surface 8 of the sample 2.

[0046] A control unit 12 is connected to the profiler 9 and a driver 13 of the shaker 6. The control unit 12 records the curve 7 measured by the profiler 9. In addition, the control unit 12 controls the driver 13, thereby controlling the oscillatory motion of the shaker 6.

[0047] In the described example, the control unit 12 controls the driver such that the sample 2 is excited at its resonant frequency. The resonant frequency is characterized by the maximum amplitude of the oscillatory motion of the free end 3 of the sample 2 and thus the maximum deflection of the free end 3. The deflection can be directly observed in the profile 7 recorded by the control unit 12. The control of the oscillation causes the excitation of the sample 2 to occur at the resonant frequency, resulting in the maximum bending stress of the sample 2.

[0048] To determine the flexural fatigue strength, the sample 2 is oscillated until it fails. The number of oscillations of the sample until the sample 2 fails is counted and recorded together with the bending stress of the sample 2 during the oscillation.

[0049] Basically the same 15 samples 2 are measured in three groups. For the first group, five samples that excite the oscillation of these samples under a first bending stress (e.g., 1200 MPa) are measured. For the second group, five samples that excite the oscillation of these samples under a second bending stress (e.g., 1300 MPa) are measured. And for the third group, five samples that excite the oscillation of these samples under a third bending stress (e.g., 1400 MPa) are measured. The first, second, and third bending stresses are different from each other, where the amplitude of excitation varies from the first group to the second group and corresponds to the change in bending stress. After all three groups of samples 2 are measured, the Wöhler curve is plotted as the bending stress with respect to the number of oscillations to failure (logarithmic).

[0050] The key to the method performed by the system 1 is how to derive the bending stress σ from the profile 7 bending . Now refer to Figure 2 to describe this part of the method.

[0051] It is hereinafter assumed that the bending profile 7 of the bent sample 2 belongs to a circle 14 with a radius R. This radius R is the radius of curvature or bending radius of the sample 2. Since the profile 7 is an arc on this circle 14 with a radius R, R can be determined based on the chord 15 and the height of the segment 16 of the profile 7: - The first and last x, y coordinates of the profile 7 are taken as the starting point 17 and the ending point 18 of the chord 15. - Based on these two points, the slope m and the y-axis intercept b of the chord 15 connecting these two points 17, 18 are determined, as well as the coordinates of the midpoint 19 along this line. - The length L of the chord 15 is determined between the starting point 17 and the ending point 18: - The length s of the height of the segment 16 is determined by finding the shortest distance between the midpoint 19 and the profile 7. The algorithm takes the (x, y) coordinates of the midpoint 19 and then iterates through all the (x, y) coordinates of the profile 7 and takes the coordinate that gives the shortest length. This line may be somewhat different from the line perpendicular to the chord. However, the deviation is on the order of a few micrometers, which is less than 1% of the length of the height of the segment 16. - Based on the following formula, the radius R is calculated according to the length s of the height of the segment 16 and the half-length of the chord 15. - To have some indication of how well a contour fits on a circle (whose radius R was previously determined), the following steps are performed to fit a circle on the contour. Based on the slope m, the y-axis intercept b, and the midpoint 19, the coordinates x mid , y mid of the chord line 15 are determined, and a vertical line is fitted on the chord that intersects the midpoint 19. - Based on the origin of the circle, the entire circle 14 belonging to the arc can be drawn. Using the parametric plot formula of a circle with the origin at (X o , Y o ), the circle 14 is drawn as individual (x, y) point pairs. - Since it is known that the contour 7 lies in the lower half of the circle 14 and the exact X coordinates of the contour 7 are also known, the corresponding Y coordinates y of the circle 14 can be calculated based on these X coordinates x (e.g., between -4 mm and 4 mm). arc . - Now, the Y coordinates of the fitted circle 7 are known for each given X coordinate. The Y coordinates of the fitted circle and the contour are compared. These values should be within a few tens of micrometers.

[0052] The difference between the fitted circle and the captured contour can be used to determine the quality of the fit.

[0053] The bending stress of the bent cantilever can be derived from the thickness t of the material, the radius of curvature R, and the Young's modulus E of the material according to the following equation:

[0054] The thickness of the material can be measured with a micrometer screw, the Young's modulus is provided by the material data sheet, and the radius is measured using a test system.

[0055] For the purposes of the original disclosure, it should be noted that all features become obvious to a person skilled in the art from the present specification, the drawings, and the claims, even if they are only specifically described in combination with certain additional features. Therefore, all features can also be combined individually and in any desired combination with other features or groups of features disclosed herein, unless this has been explicitly excluded or the technical situation makes such a combination impossible or meaningless. A comprehensive and explicit description of all conceivable combinations of features has been omitted here only for the sake of brevity and readability of the specification.

[0056] Although the present invention has been shown and described in detail in the drawings and the foregoing description, such illustration and description are merely exemplary and are not intended to limit the scope of protection defined by the claims. The present invention is not limited to the disclosed embodiments.

[0057] Variations of the disclosed embodiments will be apparent to those skilled in the art from the drawings, the description, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. The mere fact that certain features are claimed in different claims does not exclude their combination. The reference signs in the claims are not intended to limit the scope of protection. Reference Sign

[0058] 1 System

[0059] 2 Sample

[0060] 3 Free End of the Sample

[0061] 4 Mounting End

[0062] 5 Clamping Device

[0063] 6 Shaker

[0064] 7 Profile

[0065] 8 Surface of Sample 2

[0066] 9 Profiler

[0067] 10 Line

[0068] 11 Reference Plane

[0069] 12 Control Unit

[0070] 13 Driver

[0071] 14 Circle

[0072] 15 Chord

[0073] 16 Sagitta

[0074] 17 Starting Point

[0075] 18 End Point

[0076] 19 Midpoint

[0077] 20 Main Direction

[0078] 21 Center Line

Claims

1. A method for determining at least one mechanical property of a sample (2), the method comprising the following steps: Providing the sample (2), wherein the sample (2) comprises a dimension in a main direction (20); Mounting the sample (2) at a mounting end (4) of the sample (2), wherein a free end (3) of the sample (2) is free to move in a direction perpendicular to the main direction (20); shaking the mounted end of the sample (2) at an excitation frequency to excite oscillatory bending of the sample (2) about a center line (21) perpendicular to the main direction (20); determining a bending radius (R) of the sample (2) at a predetermined deflection or a determined deflection of the sample (2); Calculating the bending stress using the bending radius (R); and calculating the at least one mechanical property of the sample (2) using the bending stress and the number of oscillations of the sample (2) until the sample (2) fails, or the bending stress at multiple excitation frequencies, or the bending stress at multiple excitation frequencies and a description of the geometry of the sample (2).

2. The method according to claim 1, wherein the step of determining the bending radius (R) comprises: measuring a profile of the surface of the sample (2) along a line with the sample at the predetermined deflection or the determined deflection, wherein the line is parallel to the principal direction, or wherein said line and said main direction form an angle of less than 90 degrees; and The bending radius (R) is calculated based on the profile.

3. The method according to any one of the preceding claims, wherein the mechanical property of the sample (2) is the bending fatigue strength of the sample (2), wherein the bending fatigue strength is calculated from the bending stress and the number of oscillations of the sample (2) until the sample (2) fails.

4. The method according to any one of the preceding claims, wherein the mechanical property of the sample (2) is a damping factor of the sample (2), wherein the damping factor is calculated from the bending stress at a plurality of excitation frequencies.

5. The method according to any of the preceding claims, wherein the mechanical property of the sample (2) is a resonant frequency of the sample (2), wherein the resonant frequency is calculated from the bending stress at a plurality of excitation frequencies and the geometry of the sample (2).

6. The method according to any one of the preceding claims, wherein in addition to the mechanical properties of the sample, the Young's modulus of the sample is determined by: measuring the amplitude of vibration of the sample at a fixed point on the sample for a plurality of excitation frequencies; determining the resonant frequency of the sample based on the measured amplitude at the excitation frequency; as well as Young's modulus is calculated using the determined resonant frequency and the sample geometry.

7. The method according to any one of claims 4 to 6, wherein the plurality of excitation frequencies comprises a mechanical resonance frequency of the sample (2).

8. The method according to any one of claims 1 to 3, wherein the excitation frequency is equal to the mechanical resonance frequency of the sample (2).

9. The method according to any one of claims 1 to 3, wherein the bending radius (R) of the sample (2) under a predetermined deflection or a determined deflection of the sample is determined; and the step of calculating the bending stress using the bending radius (R) is performed multiple times, and at least the amplitude or excitation frequency of the shaking is controlled to minimize the difference between the bending stress and the predetermined expected bending stress.

10. The method according to any one of the preceding claims, wherein the at least one mechanical property is determined using a statistical evaluation of a plurality of substantially identical samples.

11. A system (1) for measuring at least one mechanical property of a sample, the system comprising a sample mount (5) configured to hold the sample (2) at a single mounting end (4) of the sample (2); a shaker (6) configured to oscillate the sample mount (5) at an excitation frequency; a sensor configured to measure a parameter indicative of a bending radius (R) of the sample (2) at a predetermined or determined deflection of the sample; and a control unit (12), The control unit (12) is connected to the shaker (6), wherein the control unit (12) is configured to control the excitation frequency of the shaker (6), wherein the control unit (12) is connected to the sensor (9) to receive the parameter from the sensor, and wherein the control unit is configured to determine a bending radius (R) according to the parameter, to calculate the bending stress using the bending radius (R), and For calculating at least one mechanical property of the sample (2) using the bending stress and the number of oscillations of the sample (2) until failure of the sample (2), or the bending stress at multiple excitation frequencies, or the bending stress at multiple excitation frequencies and a description of the geometry of the sample (2).

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