A dynamic glass elastic modulus measurement device and method

Abstract

The present invention provides a device and method for measuring the elastic modulus of glass based on power, and belongs to the technical field of material elastic modulus detection. The device includes a base, a support, a cover plate, a base bolt, a cover plate bolt, a glass beam, a calibration beam and a torque wrench. The support is fixed to one end of the base by a bottom angle bolt, the cover plate is fixed to the support by a cover plate bolt, and one end of the glass beam is placed between the cover plate and the support. The device first performs a free vibration experiment on the calibration beam, calculates the vertical stiffness and rotational stiffness of the cover plate according to the first-order frequency of the calibration beam measured, and then brings the stiffness in two directions into the vibration equation of the elastic support beam to obtain the elastic modulus calculation formula. Then, a free vibration test is performed on the glass beam to be tested, and the elastic modulus of the glass to be tested is calculated according to the first-order frequency of the free vibration of the glass beam to be tested and related parameters. This method has the advantages of accurate testing, safety, non-destructiveness, convenience and economy for detecting the elastic modulus of glass, and is suitable for engineering practice.

Description

Technical Field

[0001] The invention relates to the technical field of material elastic modulus detection, and in particular to a dynamic-based glass elastic modulus measurement device and method. Background Art

[0002] As an important basic material in modern architecture, industry, science and technology, the elastic modulus of glass is one of the important mechanical parameters. The elastic modulus is the ratio of stress to strain under uniaxial stress. From a macroscopic point of view, it is a measure of the ability of an object to resist elastic deformation. From a microscopic point of view, it is a reflection of the bond strength between atoms, ions, and molecules. Its measurement methods can be summarized as two types based on dynamic and static forces. The static method is to put the material under static force, measure the relationship curve between stress and strain, and then calculate the elastic modulus according to the linear relationship of the elastic deformation zone based on Hooke's law. However, since glass is a brittle material, the traditional application of tensile testing to measure the elastic modulus of the material has high requirements on the sample shape. At the same time, the deviation of the placement of the glass sample in the tensile machine can easily cause the glass to break. Unlike the static method, the dynamic method uses the elastic modulus of the material and the corresponding structural frequency for measurement and calculation.

[0003] The standard "Test Method for Elastic Modulus of Ultra-Thin Glass" (GB / T_37788-2019) discloses a method for measuring the elastic modulus of glass based on cantilever beam theory, but only gluing the cantilever end with glue cannot meet the theoretical requirements of the cantilever beam's full constraint, and the use of cantilever beam theory calculation will result in large errors. The standard "Test Method for Elastic Modulus, Shear Modulus and Poisson's Ratio of Glass Materials" (GB / T_37780-2019) discloses a dynamic detection method based on a floating system, but it is well known that the dynamic experiment of the floating system has high requirements for boundary conditions and is difficult to simulate in actual engineering. The prior art relates to a device for measuring the elastic modulus of glass using the Newton ring principle, and discloses a device for measuring the elastic modulus of glass based on the Newton ring principle. However, it is more troublesome for the current Newton ring instrument to apply pressure while observing the central dark spot through a microscope, and the pressure value is difficult to accurately measure. The methods provided by the above standards or prior art have large errors or are difficult to achieve in measuring the elastic modulus of glass. Therefore, in this field, there is an urgent need for an accurate and repeatable elastic modulus test method. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a glass elastic modulus measuring device and method based on power.

[0005] The device includes a base, a support, a cover plate, a base bolt, a cover plate bolt, a glass beam, a calibration beam and a torque wrench. The support is fixed to one end of the base through the base bolt, and the torque wrench is used to fix one end of the calibration beam between the cover plate and the support with the cover plate bolt.

[0006] The vertical height reserved between the belly of the cover plate and the support is used to place the calibration beam, and the vertical height is not greater than the thickness of the calibration beam.

[0007] The glass beam has the same thickness as the calibration beam, and the glass beam can replace the calibration beam and be placed between the cover plate and the support.

[0008] The method for measuring using the measuring device comprises the following steps:

[0009] S1: Select two calibration beams, denoted as calibration beam a and calibration beam b;

[0010] S2: Use a torque wrench to fix one end of the calibration beam a between the cover plate and the support;

[0011] S3: Apply an initial displacement to the free end of the calibration beam a to make the calibration beam vibrate freely and measure the first-order natural frequency f of the calibration beam a. a ;

[0012] S4: Measure and calibrate the first-order natural frequency f of beam b according to S2 and S3 b ;

[0013] S5: Calculate the vertical stiffness k of the cover plate according to the first-order natural frequency of the calibration beam a and the calibration beam b 1 and the rotational stiffness k 2 ;

[0014] S6: Use a torque wrench to fix the glass beam to be tested between the cover plate and the support, and measure the first-order natural frequency f of the glass beam to be tested according to S3;

[0015] S7: Calculate the elastic modulus E of the glass beam based on the first-order frequency of the glass beam g .

[0016] Among them, the vertical stiffness k of the cover plate in S5 is 1 and the rotational stiffness k 2 The calculation process is as follows:

[0017]

[0018]

[0019] Where:

[0020] a 1 =E a I a k a (cosh(l a k a )sin(l a k a )-cos(la k a )sinh(l a k a )),

[0021] a 2 =E a I a k a 3 (cos(l a k a )sinh(l a k a )+cosh(l a k a )sin(l a k a )),

[0022] a 3 =-cos(l a k a )cosh(l a k a )-1,

[0023] a 4 =E a 2 I a 2 k a 4 (cos(l a k a )cosh(l a k a )-1),

[0024] b 1 =E b I b k b (cosh(l b k b )sin(l b k b )-cos(l b k b )sinh(l b k b )),

[0025] b 2 =E b I b k b 3 (cos(l b k b )sinh(l b k b )+cosh(lb k b )sin(l b k b )),

[0026] b 3 = -cos(l b k b )cosh(l b k b )-1,

[0027] b 4 =E b 2 I b 2 k b 4 (cos(l b k b )cosh(l b k b )-1),

[0028] in,

[0029] k a , k b are the coefficients of calibration beam a and calibration beam b respectively, E a 、E b are the elastic modulus of calibration beam a and calibration beam b respectively;

[0030] l a , l b is the length of calibration beam a and calibration beam b;

[0031] I a ,I b are the section inertia moments of calibration beam a and calibration beam b respectively, A a , A b are the cross-sectional areas of the calibration beams a and b, respectively, A a =w a ×h a , A b =w b ×h b ;

[0032] w a 、w b is the width of calibration beam a and calibration beam b,

[0033] h a 、h b is the thickness of calibration beam a and calibration beam b,

[0034] ρ a ,b is the density of calibration beam a and calibration beam b;

[0035] f a 、f b To measure the first-order natural frequency of calibration beam a and calibration beam b,

[0036] ω a ,ω b is the calibration beam circular frequency, ω a =2πf a ,ω b =2πf b .

[0037] The calculation process of glass elastic modulus in S7 is as follows:

[0038] E g I g k g (cosh(lk g )sin(lk g )-cos(lk g )sinh(lk g ))k 1 +E g I g k g 3 (cos(lk g )sinh(lk g )+cosh(lk g )

[0039] sin(lk g ))k 2 -(cos(lk g )cosh(lk g )+1)k 1 k 2 +E g 2 I g 2 k g 4 (cos(lk g )cosh(lk g )-1)=0

[0040] Where:

[0041] k g is the coefficient of the glass beam, E g is the elastic modulus of the glass beam, which is the quantity to be solved;

[0042] k 1 is the vertical stiffness of the cover plate,

[0043] k 2 is the cover plate rotation stiffness,

[0044] l is the length of the glass beam,

[0045] I g is the moment of inertia of the glass beam section,

[0046] A g is the cross-sectional area of ​​the glass beam, A g =w g ×h g ;

[0047] w g is the width of the glass beam,

[0048] h g is the thickness of the glass beam,

[0049] ρ g is the density of the glass beam;

[0050] f is the measured first-order natural frequency of the glass beam,

[0051] ω is the circular frequency of the glass beam, ω=2πf.

[0052] The above E g The solution range is [E c ,1.5E c ],in

[0053] In S2, S4 and S6, the torques of the cover plate bolts for installing the fixed cover plates of the calibration beam a, calibration beam b and glass beam are the same.

[0054] The beneficial effects of the above technical solution of the present invention are as follows:

[0055] In the above scheme, the elastic modulus of glass is measured by the vibration theory of the elastic support beam. By calculating the stiffness of both sides of the elastic beam and then inverting the elastic modulus of glass according to the measured frequency, the elastic modulus of glass can be quickly tested, the test result is highly accurate, and the experimental installation is simple, easy to operate, the detection speed is fast, and it belongs to non-destructive testing. This method has the advantages of accurate testing, safety, non-destructiveness, convenience and economy for testing the elastic modulus of glass, and is suitable for engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic structural diagram of a dynamic glass elastic modulus measuring device of the present invention;

[0057] Figure 2 It is a diagram of the accessories of the dynamic glass elastic modulus measuring device of the present invention;

[0058] Figure 3 It is a schematic diagram of the detection process of the dynamic glass elastic modulus measurement method of the present invention;

[0059] Figure 4 The free vibration signal of the calibrated beam a with a length of 0.4 m in the embodiment of the present invention;

[0060] Figure 5 The free vibration signal of the calibrated beam b with a length of 0.5 m in the embodiment of the present invention;

[0061] Figure 6 It is the free vibration signal of the glass beam to be detected with a length of 0.6 m in the embodiment of the present invention.

[0062] Among them: 1-base; 2-support; 3-cover plate; 4-base bolts; 5-cover plate bolts; 6-glass beam; 7-calibration beam a; 8-calibration beam b; 9-torque wrench. DETAILED DESCRIPTION

[0063] In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0064] The invention provides a glass elastic modulus measuring device and method based on power.

[0065] like Figure 1 and Figure 2 As shown, the device includes a base 1, a support 2, a cover plate 3, a base bolt 4, a cover plate bolt 5, a glass beam 6, a calibration beam and a torque wrench 9.

[0066] The support 2 is fixed to one end of the base 1 by means of a foot bolt 4 , and one end of the calibration beam 6 is fixed between the cover plate 3 and the support 2 by means of a cover plate bolt 5 using a torque wrench 9 .

[0067] The vertical height reserved between the belly of the cover plate 3 and the support 2 is used to place the calibration beam, and the vertical height is not greater than the thickness of the calibration beam.

[0068] The glass beam 6 has the same thickness as the calibration beam, and the glass beam 6 can replace the calibration beam and be placed between the cover plate 3 and the support 2 .

[0069] like Figure 3 As shown, the measuring method of the measuring device comprises the following steps:

[0070] S1: Select two calibration beams, which are denoted as calibration beam a7 and calibration beam b8;

[0071] S2: Use a torque wrench 9 to fix one end of the calibration beam a7 between the cover plate 3 and the support 2;

[0072] S3: Apply initial displacement to the free end of calibration beam a7 to make the calibration beam vibrate freely and measure the first-order natural frequency f of calibration beam a. a ;

[0073] S4: Measure and calibrate the first-order natural frequency f of beam b8 according to S2 and S3 b ;

[0074] S5: Calculate the vertical stiffness k of the cover plate according to the first-order natural frequency of the calibration beam a and the calibration beam b 1 and the rotational stiffness k 2 ;

[0075] S6: Use a torque wrench 9 to fix the glass beam 6 to be tested between the cover plate 3 and the support 2, and measure the first-order natural frequency f of the glass beam 6 to be tested according to S3;

[0076] S7: Calculate the elastic modulus E of the glass beam based on the first-order frequency of the glass beam g .

[0077] This will be described below with reference to specific embodiments.

[0078] During the measurement, first place one end of the calibration beam a7 in the support 2, fix the calibration beam a7 to the support through the cover plate bolts 5, and use a torque wrench to determine that the torque of each bolt is 6.5N·m. The calibration beam a7 is 0.4m long, 0.0398m wide, 0.0059m high, and has a density of 2515.1kg / m 3 , elastic modulus is 74.13GPa, calibration beam b8 is 0.5m long, 0.0398m wide, 0.0059m high, and has a density of 2515.1kg / m 3 , the elastic modulus is 74.13GPa.

[0079] Take the calibration beam a7 and measure the free vibration time history signal using the laser displacement sensor as follows: Figure 4 As shown, the first-order frequency of free vibration is calculated according to the following formula.

[0080]

[0081] Where, t i is the time corresponding to the i-th vibration peak, t i+j is the time corresponding to the vibration peak value j cycles apart. The calculation is shown in Table 1. The average of the two calculation results gives the first-order natural frequency of 31.355 Hz.

[0082] Table 1 Frequency calculation

[0083] frequency <![CDATA[t i (s)]]> <![CDATA[t i+j (s)]]> j f(Hz) <![CDATA[1 st ]]> 3.013 3.970 30 31.356 <![CDATA[2 nd ]]> 5.023 5.980 30 31.353

[0084] Take the calibration beam b8 and use a torque wrench to determine that the torque of each bolt is 6.5 N·m. Use the same method to measure the signal again. Figure 5 As shown, the calculation is shown in Table 2, and the measured first-order frequency of free vibration is 20.194 Hz.

[0085] Table 2 Frequency calculation

[0086] frequency <![CDATA[t i (s)]]> <![CDATA[t i+j (s)]]> j f(Hz) <![CDATA[1 st ]]> 3.022 3.963 19 20.193 <![CDATA[2 nd ]]> 5.052 5.993 19 20.195

[0087] Substitute the first-order frequencies and related parameters of the two calibration beams into the support stiffness calculation equation:

[0088]

[0089]

[0090] Where:

[0091] a 1 =E a I a k a (cosh(l a k a )sin(l a k a )-cos(l a k a )sinh(l a k a )),

[0092] a 2 =E a I a k a 3 (cos(l a k a )sinh(l a k a )+cosh(l a k a )sin(l a k a )),

[0093] a 3 = -cos(l a k a )cosh(l a k a )-1,

[0094] a 4 =E a 2 I a 2 k a4 (cos(l a k a )cosh(l a k a )-1),

[0095] b 1 =E b I b k b (cosh(l b k b )sin(l b k b )-cos(l b k b )sinh(l b k b )),

[0096] b 2 =E b I b k b 3 (cos(l b k b )sinh(l b k b )+cosh(l b k b )sin(l b k b )),

[0097] b 3 = -cos(l b k b )cosh(l b k b )-1,

[0098] b 4 =E b 2 I b 2 k b 4 (cos(l b k b )cosh(l b k b )-1),

[0099] in,

[0100] k a , k b are the coefficients of calibration beam a and calibration beam b respectively,

[0101] E a 、Eb are the elastic modulus of calibration beam a and calibration beam b respectively;

[0102] l a , l b is the length of calibration beam a and calibration beam b;

[0103] is the section inertia moment of calibration beam a and calibration beam b,

[0104] A a =w a ×h a , A b =w b ×h b is the cross-sectional area of ​​the calibrated beams a and b,

[0105] w a 、w b is the width of calibration beam a and calibration beam b,

[0106] h a 、h b is the thickness of calibration beam a and calibration beam b,

[0107] ρ a , b is the density of calibration beam a and calibration beam b;

[0108] f a 、f b To measure the first-order natural frequencies of calibration beam a and calibration beam b, which are 31.355 Hz and 20.194 Hz respectively,

[0109] ω a =2πf a ,ω b =2πf b is the calibration beam circular frequency.

[0110] Solving for k 1 3.28×10 6 N / m, k 2 8.17×10 3 N / m. The calculated k 1 , k 2 Substitute it into the following formula, and the calculation equation of glass elastic modulus is:

[0111]

[0112] Where:

[0113] k g is the coefficient of the glass beam,

[0114] Eg is the elastic modulus of the glass beam, is the quantity to be solved,

[0115] k 1 The vertical stiffness of the cover plate is 3.28×10 6 N / m,

[0116] k 2 The rotational stiffness of the cover is 8.17×10 3 N / m,

[0117] l is the length of the glass beam,

[0118] is the section moment of inertia of the glass beam,

[0119] A g =w g ×h g is the cross-sectional area of ​​the glass beam,

[0120] w g is the width of the glass beam,

[0121] h g is the thickness of the glass beam,

[0122] ρ g is the density of the glass beam,

[0123] f is the measured first-order natural frequency of the glass beam,

[0124] ω=2πf is the circular frequency of the glass beam.

[0125] Take a glass beam with a length of 0.6m to be tested, and use a vernier caliper and a balance to measure the width of the glass beam to be tested to be 0.0398m, the height to be 0.0059m, and the density to be 2515.1kg / m 3 , fix the glass beam to be tested, and use a torque wrench to determine that the torque of each bolt is 6.5N·m. The free vibration signal is measured as follows Figure 6 As shown in Table 3, the calculation frequency is shown in Table 3 below. The first-order frequency of the elastic modulus is 14.045 Hz. Then the relevant parameters are substituted into formula (4). According to the solution range of [70.03 GPa, 106.9 GPa], the elastic modulus of the glass is calculated to be 73.72 GPa.

[0126] Table 3 Frequency calculation

[0127] frequency <![CDATA[t i (s)]]> <![CDATA[t i+j (s)]]> j f(Hz) <![CDATA[1 st ]]> 5.051 5.977 13 14.040 <![CDATA[2 nd ]]> 10.037 10.962 13 14.050

[0128] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A dynamic glass elastic modulus measurement method, characterized in that: The measuring method adopts a dynamic glass elastic modulus measuring device for measurement, wherein the measuring device comprises a base, a support, a cover plate, a base bolt, a cover plate bolt, a glass beam, a calibration beam and a torque wrench. The support is fixed to one end of the base with foot bolts, and one end of the calibration beam is fixed between the cover plate and the support with the cover plate bolts using a torque wrench; The measuring method comprises the following steps: S1: Select two calibration beams, denoted as calibration beam a and calibration beam b; S2: Use a torque wrench to fix one end of the calibration beam a between the cover plate and the support; S3: Apply an initial displacement to the free end of the calibration beam a to make the calibration beam a vibrate freely and measure the first-order natural frequency f of the calibration beam a. a ; S4: Measure and calibrate the first-order natural frequency f of beam b according to S2 and S3 b ; S5: Calculate the vertical stiffness k1 and rotational stiffness k2 of the cover plate according to the first-order natural frequency of the calibration beam a and the calibration beam b; S6: Use a torque wrench to fix the glass beam to be tested between the cover plate and the support, and measure the first-order natural frequency f of the glass beam to be tested according to S3; S7: Calculate the elastic modulus E of the glass beam based on the first-order frequency of the glass beam g ; The calculation process of the vertical stiffness k1 and the rotational stiffness k2 of the cover plate in S5 is as follows: Where: a1=E a I a k a (cosh(l a k a )sin(l a k a )-cos(l a k a )birth a k a )), a2=E a I a k a 3 (cos(l a k a )sinh(l a k a )+cosh(l a k a )sin(l a k a )), a3=-cos(l a k a )cosh(l a k a )-1, a4=E a 2 I a 2 k a 4 (cos(l a k a )cosh(l a k a )-1), b1=E b I b k b (cosh(l b k b )sin(l b k b )-cos(l b k b )birth b k b )), b2=E b I b k b 3 (cos(l b k b )sinh(l b k b )+cosh(l b k b )sin(l b k b )), b3=-cos(l b k b )cosh(l b k b )-1, b4=E b 2 I b 2 k b 4 (cos(l b k b )cosh(l b k b )-1), in, E a 、E b are the elastic modulus of calibration beam a and calibration beam b respectively; l a , l b is the length of calibration beam a and calibration beam b; I a ,I b are the section inertia moments of calibration beam a and calibration beam b respectively, A a , A b are the cross-sectional areas of the calibration beams a and b, respectively, A a =w a ×h a , A b =w b ×h b ; w a 、w b is the width of calibration beam a and calibration beam b, h a 、h b is the thickness of calibration beam a and calibration beam b, ρ a , b is the density of calibration beam a and calibration beam b; f a 、f b To measure the first-order natural frequency of calibration beam a and calibration beam b, ω a ,ω b is the calibration beam circular frequency, ω a =2πf a ,ω b =2πf b ; k a , k b are the coefficients of calibration beam a and calibration beam b respectively, The calculation process of the glass elastic modulus in S7 is as follows: E g I g k g (cosh(lk g )sin(lk g )-cos(lk g )birth g ))k1+E g I g k g 3 (cos(lk g )birth g )+cosh(lk g ) sin(lk g ))k2-(cos(lk g )cosh(lk g )+1)k1k2+E g 2 I g 2 k g 4 (cos(lk g )cosh(lk g )-1)=0 Where: E g is the elastic modulus of the glass beam, which is the quantity to be solved; k1 is the vertical stiffness of the cover plate, k2 is the cover plate rotation stiffness, l is the length of the glass beam, I g is the section moment of inertia of the glass beam, A g is the cross-sectional area of ​​the glass beam, A g =w g ×h g ; w g is the width of the glass beam, h g is the thickness of the glass beam, ρ g is the density of the glass beam; f is the measured first-order natural frequency of the glass beam, ω is the circular frequency of the glass beam, ω=2πf; k g is the coefficient of the glass beam, 2. The dynamic glass elastic modulus measurement method according to claim 1, characterized in that: The vertical height reserved between the belly of the cover plate and the support is used to place the calibration beam, and the vertical height is not greater than the thickness of the calibration beam.

3. The dynamic glass elastic modulus measurement method according to claim 1, characterized in that: The glass beam has the same thickness as the calibration beam, and the glass beam can replace the calibration beam and be placed between the cover plate and the support.

4. The dynamic glass elastic modulus measurement method according to claim 1, characterized in that: The E g The solution range is [E c ,1.5E c ],in 5. The dynamic glass elastic modulus measurement method according to claim 1, characterized in that: In S2, S4 and S6, the torques of the cover plate bolts used to fix the calibration beam a, the calibration beam b and the glass beam to the cover plate are the same.

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