Methods and systems for determining at least one mechanical property of a sample

Abstract

The present invention relates to a method and system for determining at least one mechanical property of a sample, the method comprising the steps of: providing the sample, wherein the sample includes dimensions in a principal direction; mounting the sample at a mounting end of the sample, wherein a free end of the sample is freely movable in a direction perpendicular to the principal direction; agitating the mounted end of the sample at an excitation frequency to excite oscillatory bending of the sample about a centerline perpendicular to the principal direction; determining a bending radius of the sample at a predetermined deflection or a determined deflection; 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 up to sample 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.

Description

Technical Field

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

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

[0003] One aspect of this 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 cost and effort.

[0004] The above aspects are addressed by the method according to this application. The method according to this disclosure includes the following steps: providing a sample, wherein the sample includes dimensions in a principal direction; mounting the sample at a mounting end of the sample, wherein the free end of the sample is freely movable in a direction perpendicular to the principal 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 principal direction; determining the bending radius of the sample at a predetermined deflection or under a determined deflection; calculating the bending stress using the bending radius; and calculating said at least one mechanical property of the sample using the bending stress and the number of oscillations of the sample until sample 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 this disclosure is to force the sample to oscillate relative to its mounting end relative to its free end, and to determine the bending radius of the sample under a predetermined deflection or a determined deflection. The bending radius is a direct measure of the bending stress applied to the sample. Determining the bending radius of the sample based on measurements is a fast, robust, and highly accurate calculation. The corresponding mechanical properties of the sample can then be calculated based on certain assumptions.

[0006] The predetermined or determined deflection is non-zero, meaning the sample is in a bent state during the oscillation at the time point at which the sample is measured, in order to determine the bending radius. Importantly, once the minimum bending radius, i.e., the maximum bending of the sample, is determined over multiple subsequent oscillations of the sample, the bending radius is determined for the same deflection of the sample each time.

[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 a bent and therefore bent sample bending The following equations can be derived from the sample thickness t, bending radius R, and Young's modulus E of the material:

[0009]

[0010] According to an embodiment, the thickness of the sample is measured using a micron screw. Young's modulus is provided, for example, from the sample material data sheet, and the radius is measured.

[0011] According to the embodiments, the surface of the sample is planar or cylindrical.

[0012] According to embodiments of this disclosure, the sample may have the shape of a strip, rod, or plate.

[0013] According to an embodiment, the sample is a strip, wherein the size of the sample in the principal direction is greater than the size of the sample in each of the two transverse directions, wherein the transverse directions are perpendicular to each other and are both perpendicular to the principal direction.

[0014] According to the embodiments, the material of the sample is selected from the group consisting of plastic, metal, paper and wood, or a combination thereof.

[0015] According to an embodiment, the step of determining the bending radius includes measuring the bending radius or measuring a parameter indicating the bending radius.

[0016] According to an embodiment, the step of determining the bending radius includes: measuring the profile of the sample surface along a line while the sample is under a predetermined or determined deflection, wherein the line is parallel to the principal direction, or wherein the line forms an angle of less than 90° with the principal direction; and calculating the bending radius based on the profile.

[0017] According to an embodiment, a profilometer is used to measure the profile of a sample's surface. In one embodiment, the profilometer is a non-contact profilometer, such as a laser profilometer. Non-contact profilometers measure the profile of a sample's surface without requiring mechanical interaction with the surface. The profilometer measures the profile of a sample's surface with high repeatability and is commercially available. Typically, profilometers, particularly laser profilometers, are used to measure the profile of a surface in order to quantify the roughness of a sample. However, according to this disclosure, a profilometer can also be used to determine the microstructure of a surface, i.e., the radius of curvature.

[0018] The principal direction can be described to connect the mounted end and the free end of the sample. Therefore, the sample mounted at the mounted end will experience bending around an axis that is not parallel to the principal direction. Consequently, the profile measurement line must differ from the direction perpendicular to the principal direction.

[0019] According to an embodiment, the length of the line will depend on the sample and the laser profilometer. For example, the line length can be in the range of 3 mm to 10 mm, such as in the range of 4 mm to 8 mm.

[0020] According to an embodiment, the surface of the sample is measured along the contour of a line as the distance from the sample surface to a reference line. The reference line is parallel to the planar surface of the sample and is in a non-deflected zero position. This distance is a parameter to be measured by a sensor. This distance indicates the bending radius or a direct measure of the bending radius.

[0021] According to an embodiment, after measuring the profile of the sample's surface, the profile is described in Cartesian coordinates, thereby enabling the analysis of the surface's radius of curvature through calculations defined by fundamental geometric considerations.

[0022] 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.

[0023] According to the 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.

[0024] According to an embodiment, the mechanical property of the sample is the resonant frequency of the sample, which is calculated based on the bending stress at multiple excitation frequencies and the geometry of the sample.

[0025] 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 textbook. In another embodiment, the Young's modulus E of the sample is determined using a method similar to that according to the invention, wherein the method for determining the Young's modulus E includes the following steps: providing a sample, wherein the sample includes dimensions in the principal direction; mounting the sample at a mounted end of the sample, wherein the free end of the sample is freely movable in a direction perpendicular to the principal direction; shaking the mounted end of the sample at an excitation frequency to excite the sample to oscillate and bend about a centerline perpendicular to the principal direction; measuring the amplitude of the sample at fixed points 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.

[0026] According to an embodiment, the step of measuring the amplitude of an oscillating sample includes the following steps: for each step of the excitation frequency, measuring the maximum deflection of a single point on a line of the surface profile of the sample.

[0027] Young's modulus E can be expressed as

[0028]

[0029] Where ω is the resonant frequency determined by measuring the resonance curve, k is the parameter corresponding to the characteristic vibration mode, and I is the second area moment of the sample with a rectangular cross-section. The width is the width of the sample perpendicular to the main direction, and Ω represents the mass density of the sample material, and Ω represents the cross-sectional area.

[0030] According to an embodiment, the deflection is measured relative to the excitation frequency, starting from 10 Hz or 20 Hz below the expected resonant frequency, and the excitation frequency is stepped in increments of 0.1 Hz until the excitation frequency is above the resonant frequency by 10 Hz or 20 Hz. However, the step size can be larger or smaller than the step size mentioned herein.

[0031] According to the embodiments, the mechanical properties are the G-modulus or Poisson's ratio of the sample.

[0032] In the embodiments, the mechanical properties of the sample being measured are damping factor, resonant frequency of the sample, or Young's modulus, and multiple excitation frequencies include the mechanical resonant motion of the sample.

[0033] Due to the clamping of the sample at one end and the oscillating motion of the free end, the resonant frequency involved is the resonant frequency of the oscillating motion of the sample, which causes the sample to bend around one or more axes perpendicular to the principal direction.

[0034] In this embodiment, the excitation frequency remains constant while determining the mechanical properties, and is equal to the mechanical resonant frequency of the sample. Driving the sample to oscillate and bend at this resonant frequency results in the maximum possible bending of the sample and therefore the maximum bending stress.

[0035] In this embodiment, the sample is excited with a resonant frequency, and the bending radius is determined at the maximum deflection of the sample. Thus, the maximum deflection is either a predetermined deflection or a determined deflection. The maximum deflection corresponds to the maximum amplitude of the oscillation.

[0036] It is important to ensure that the predetermined or determined deflection of the sample's bending radius is always on the same side relative to the sample's unbent zero position.

[0037] In an embodiment, the mechanical properties of the sample are the bending fatigue strength of the sample, the steps of determining the bending radius of the sample under a predetermined deflection or under a determined deflection and calculating the bending stress using the bending radius are performed multiple times, and at least the amplitude or excitation frequency of the rocking is controlled to minimize the difference between the bending stress and the predetermined desired bending stress.

[0038] In one embodiment, statistical evaluation of multiple substantially identical samples is used to determine the at least one mechanical property.

[0039] In this embodiment, the flexural fatigue strength of the samples and optionally relevant statistical parameters (e.g., standard deviation, 95% or 99% fatigue strength) are determined and calculated through a stepwise evaluation or Weller curve evaluation performed on multiple samples. The typical number of samples required is 10 to 30.

[0040] According to an embodiment, the plurality of samples are a plurality of substantially identical or identical samples. Substantially identical samples require that the plurality of samples have substantially the same geometry. In one embodiment, the plurality of samples are made of substantially the same material. Regarding geometry, substantially identical means identical within typical tolerances for manufacturing mechanical samples. Regarding material, substantially identical material is material containing the same chemical composition but potentially varying in microstructure of the plurality of samples, for example, including different precipitates, inclusions, or surface defects.

[0041] In the foregoing and the following description of the embodiments, 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 described features apply to both the method and the system.

[0042] At least one of the foregoing aspects is also addressed by a system according to the present disclosure. A system according to the present disclosure for measuring at least one mechanical property of a sample comprises: 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 indicating the bending radius of the sample under a predetermined deflection or a defined 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 also configured to control the excitation frequency of the shaker. Furthermore, the control unit is configured to determine the bending radius based on the parameter, to calculate the bending stress using the bending radius, and to calculate said at least one mechanical property of the sample using the bending stress and the number of oscillations of the sample up to sample 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.

[0043] The foregoing and following detailed description 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 precise arrangements and means shown. In the drawings, like elements are indicated by like reference numerals. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of a system used to measure the mechanical properties of a sample;

[0045] Figure 2 It is a coordinate system, which shows the use of... Figure 1The system measures the surface profile of the sample and the values ​​derived from the profile. Detailed Implementation

[0046] Figure 1 A system 1 for measuring the mechanical properties of sample 2 is schematically shown. In the described example, sample 2 is a metal strip, whose bending fatigue strength, as a mechanical property, will be determined in the context of this application.

[0047] Sample 2 has a free end 3 and a mounting end 4. The mounting end 4 is clamped in a clamping device 5, which serves as a sample mounting base for an electromechanical shaker 6. Once the clamping device 5 is periodically moved up and down by the shaker 6, sample 2 begins to oscillate. During this oscillating motion, the free end 3 deflects upward and downward relative to the mounting end 4 of sample 2. Once the geometry of sample 2 is not deflected, it has a main extension in the main direction 20. The oscillating motion of the free end 3 occurs in a direction perpendicular to the main direction 20. Due to the oscillation, sample 2 bends around a centerline 21 perpendicular to the main direction 20.

[0048] During the periodic oscillation of the free end 3, a laser profilometer 9 is used as a sensor of system 1 to measure the profile 7 of the surface 8 of sample 2. The laser profilometer 9 measures the profile 7 as the distance of multiple light spots on line 10 on surface 8 from the reference plane 11. Once sample 2 is not excited by shaker 6, reference plane 11 is parallel to the planar surface 8 of sample 2.

[0049] The control unit 12 is connected to the driver 13 of the profilometer 9 and the rocker 6. The control unit 12 records the curve 7 measured by the profilometer 9. In addition, the control unit 12 controls the driver 13, thereby controlling the oscillating motion of the rocker 6.

[0050] In the described example, the control unit 12 controls the driver so that the sample 2 is excited at the resonant frequency. The resonant frequency is characterized by the maximum amplitude of the oscillating 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.

[0051] To determine the bending fatigue strength, sample 2 was oscillated until it failed. The number of oscillations of the sample until failure was counted and recorded along with the bending stress of sample 2 during the oscillation.

[0052] Fifteen essentially identical samples were measured in three groups. For the first group, five samples were measured under a first bending stress (e.g., 1200 MPa) to induce oscillations; for the second group, five samples were measured under a second bending stress (e.g., 1300 MPa); and for the third group, five samples were measured under a third bending stress (e.g., 1400 MPa). The first, second, and third bending stresses were different from each other, with the amplitude of the excitation varying from the first group to the second group, corresponding to the variation in bending stress. After measuring all three groups of samples, the Weller curves were plotted as the bending stress relative to the number of oscillations to failure (logarithm).

[0053] The key to the method executed by System 1 is how to derive the bending stress from profile 7. bending. Now refer to Figure 2 This part describes the method.

[0054] The following assumes that the curved profile 7 of the curved sample 2 belongs to a circle 14 with radius R. This radius R is the radius of curvature or bending radius of sample 2. Since profile 7 is an arc on this circle 14 with radius R, R can be determined based on the chord 15 and the arc height 16 of profile 7.

[0055] - The first and last x and y coordinates of contour 7 are taken as the start point 17 and end point 18 of chord 15.

[0056] -Based on these two points, determine the slope m and y-intercept b of the chord 15 connecting these two points 17 and 18, as well as the coordinates of the midpoint 19 along this line.

[0057] y = mx + b

[0058]

[0059] - Determine the length L of chord 15 between the starting point 17 and the ending point 18:

[0060]

[0061] The length s of the arc height 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, then iterates through all the (x, y) coordinates of the profile 7, and takes the one that gives the shortest length. This line may differ slightly from the line perpendicular to the chord; however, the deviation is on the order of a few micrometers, less than 1% of the length of the arc height 16.

[0062]

[0063] -Based on the formula below, the radius R is calculated based on the length s of the bow height 16 and half the length of the chord 15.

[0064]

[0065] - To provide some indication of how well the profile fits the circle (whose radius R is determined prior), the following steps are performed to fit the circle onto the profile. The coordinates x of the chord 15 are determined based on the slope m, the y-intercept b, and the midpoint 19. mid ,y mid Fit a vertical line on the chord that intersects the midpoint 19.

[0066] Y′=m′·x+b′

[0067]

[0068] b′=y mid -(m′·x mid )

[0069] -Based on the origin of the circle, the entire circle 14 belonging to the arc can be drawn. Using the origin as (X... o ,Y o The parametric formula for the circle 14 plots the circle as pairs of (x, y) points.

[0070] X circle =X O +R·cos(t)

[0071] Y circle =Y O +R·cos(t)

[0072] Since contour 7 is known to be located in the lower half of circle 14, and the exact X coordinate of contour 7 is also known, the corresponding Y coordinate of circle 14 can be calculated based on these X coordinates (e.g., between -4mm and 4mm). arc .

[0073]

[0074] Now, the Y-coordinate of the fitted circle 7 is known for each given X-coordinate. Compare the Y-coordinates of the fitted circle and the contour. These values ​​should be within tens of micrometers.

[0075] The difference between the fitted circle and the captured contour can be used to determine the quality of the fit.

[0076] The bending stress of a curved cantilever can be derived from the material thickness t, radius of curvature R, and Young's modulus E of the material according to the following equation:

[0077]

[0078] The thickness of the material can be measured using a micron screw, the Young's modulus is provided by the material data sheet, and the radius is measured using a testing system.

[0079] For the purposes of the original disclosure, it should be noted that all features will be apparent to those skilled in the art from this specification, the drawings, and the claims, even if they are specifically described only in combination with certain other features. Therefore, all features can be combined individually and in any desired combination with other features or groups of features disclosed herein, unless this has been expressly excluded or the technical circumstances render such a combination impossible or unambiguous. A full and explicit description of all conceivable combinations of features has been omitted here solely for the sake of brevity and readability.

[0080] Although the invention has been shown and described in detail in the accompanying drawings and the foregoing description, these illustrations and descriptions are merely exemplary and are not intended to limit the scope of protection defined by the claims. The invention is not limited to the disclosed embodiments.

[0081] Variations of the disclosed embodiments will be apparent to those skilled in the art from the accompanying drawings, description, and appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite articles "a" or "an" do not exclude a plurality. The mere fact that certain features are claimed in different claims does not exclude combinations thereof. The reference numerals in the claims are not intended to limit the scope of protection.

[0082] Figure Labels

[0083] 1 system

[0084] 2 samples

[0085] 3. Free ends of the sample

[0086] 4 Installation end

[0087] 5 clamping devices

[0088] 6 shakers

[0089] 7 outlines

[0090] Surface of sample 2

[0091] 9 Profilometer

[0092] 10 lines

[0093] 11 Reference Plane

[0094] 12 control units

[0095] 13 drives

[0096] 14 circles

[0097] 15-string

[0098] 16 arch height

[0099] 17 starting point

[0100] 18 End

[0101] 19 Midpoint

[0102] 20 main directions

[0103] 21 center line

Claims

1. A method for determining at least one mechanical property of a sample (2), the method comprising the steps of: 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 an oscillatory bending of the sample (2) about a centerline (21) perpendicular to the main direction (20); determining a bending radius (R) of the sample (2) at a predetermined deflection of the sample (2) or at a determined deflection of the sample (2); calculating a bending stress using the bending radius (R); and calculating the at least one mechanical property of the sample (2) using the bending stress and a number of oscillations of the sample (2) until failure of the sample (2), 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 (2).

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

3. The method of claim 1, wherein the mechanical property of the sample (2) is a bending fatigue strength of the sample (2), wherein the bending fatigue strength is calculated from the bending stress and a number of oscillations of the sample (2) until failure of the sample (2).

4. The method of claim 1, 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 of claim 1, wherein the mechanical property of the sample (2) is a resonance frequency of the sample (2), wherein the resonance frequency is calculated from the bending stress at a plurality of excitation frequencies and a geometry of the sample (2).

6. The method of claim 5, wherein in addition to the mechanical property of the sample, a Young's modulus of the sample is determined by the steps of: measuring an amplitude of the sample at a fixed point on the sample for a plurality of excitation frequencies; determining the resonance frequency of the sample from the measured amplitudes at the excitation frequencies; and calculating a Young's modulus using the determined resonance frequency and a geometry of the sample.

7. The method of claim 4, wherein the plurality of excitation frequencies comprises a mechanical resonance frequency of the sample (2).

8. The method of claim 1, wherein the excitation frequency is equal to a mechanical resonance frequency of the sample (2). ​ 9. The method according to claim 1, wherein the steps of determining a bending radius (R) of the sample (2) at a predetermined deflection or a determined deflection of the sample (2) and calculating a bending stress using the bending radius (R) are performed multiple times and at least the amplitude or the excitation frequency of the shaking is controlled to minimize the difference of the bending stress to a predetermined desired bending stress.

10. The method according to claim 1, wherein a statistical evaluation using a plurality of substantially identical samples is used to determine the at least one mechanical property.

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 deflection or a determined deflection of the sample; and a control unit (12), the control unit (12) being 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) from the parameter, to calculate a bending stress using the bending radius (R), and to calculate the at least one mechanical property of the sample (2) using the bending stress and a number of oscillations of the sample (2) until failure of the sample (2), 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 (2). ​ ​ ​ ​ ​ ​ ​

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