WO2022247434A1 - 利用悬臂梁或外伸梁测量材料杨氏弹性模量的方法和装置 - Google Patents

利用悬臂梁或外伸梁测量材料杨氏弹性模量的方法和装置 Download PDF

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WO2022247434A1
WO2022247434A1 PCT/CN2022/083218 CN2022083218W WO2022247434A1 WO 2022247434 A1 WO2022247434 A1 WO 2022247434A1 CN 2022083218 W CN2022083218 W CN 2022083218W WO 2022247434 A1 WO2022247434 A1 WO 2022247434A1
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cantilever beam
cantilever
outrigger
reflector
young
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PCT/CN2022/083218
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English (en)
French (fr)
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周厚文
谢中
翦知渐
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常州丰智测试科技有限公司
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Publication of WO2022247434A1 publication Critical patent/WO2022247434A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/20—Investigating strength properties of solid materials by application of mechanical stress by applying steady bending forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/02—Details
    • G01N3/06—Special adaptations of indicating or recording means
    • G01N3/062—Special adaptations of indicating or recording means with mechanical indicating or recording means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/02—Details
    • G01N3/06—Special adaptations of indicating or recording means
    • G01N3/068—Special adaptations of indicating or recording means with optical indicating or recording means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014—Type of force applied
    • G01N2203/0023—Bending
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0075—Strain-stress relations or elastic constants
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
    • G01N2203/0605—Mechanical indicating, recording or sensing means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
    • G01N2203/0641—Indicating or recording means; Sensing means using optical, X-ray, ultraviolet, infrared or similar detectors

Definitions

  • the invention belongs to the technical field of measuring Young's modulus of elasticity, and in particular relates to a method and a device for measuring Young's modulus of elasticity of a material by using a cantilever beam or an overhanging beam.
  • Elastic modulus is an important characteristic quantity describing the relationship between material deformation and stress, and it is a parameter commonly used in engineering technology.
  • the external force applied in the laboratory makes the deformation of the material very small, which is difficult to observe with the naked eye.
  • the excessive load will cause the material to undergo plastic deformation, and it must be measured by amplifying the small deformation.
  • Most of the existing methods for measuring the elastic modulus are to use a universal machine to perform tension or compression experiments on the material, measure the elastic modulus of the material indirectly by measuring the propagation speed of the ultrasonic wave in the material, and measure Young's elastic modulus by beam bending method. Performing tension or compression experiments on materials has the disadvantage of low measurement sensitivity. However, the measurement by ultrasonic method requires high equipment cost and is not convenient for practical application.
  • the beam bending method to measure Young's elastic modulus is mainly reported in the laser light lever measurement method, the Hall position sensor method, the single slit diffraction method, the fiber Bragg grating measurement method, etc.
  • Their common feature is that the beam is used with two knife edges.
  • a force is applied with a knife edge (or not) in the middle of the beam to make it bend, and the Young's modulus is obtained by measuring the deflection of the beam.
  • the devices used in these methods all need knife-edge support beams, more equipment is needed to measure the deflection, the overall occupied area is also larger, and the processing accuracy and use conditions are more stringent.
  • the present invention provides a device and method for measuring Young's modulus of elasticity of a material using a cantilever beam or an overhanging beam, which has a simple structure, low cost, easy processing of samples and high accuracy of measurement results.
  • the technical scheme that the present invention adopts is: a kind of device that utilizes cantilever beam or outrigger beam to measure Young's modulus of elasticity of material, it is characterized in that: comprise laser device, cantilever beam or outrigger beam, reflecting mirror I and light spot displacement measuring device, The free end of the cantilever beam or the overhanging beam is provided with a reflector I, and the laser beam emitted by the laser can be reflected to the spot displacement measuring device through the reflector I; the reflector I is arranged parallel to or perpendicular to the bottom surface of the cantilever beam or the overhanging beam , the light spot displacement measuring device is set parallel or perpendicular to the initial state of the cantilever beam or the outrigger beam.
  • the device for measuring Young's modulus of elasticity of a material by using a cantilever beam or an outrigger beam it also includes a reflector II, and the reflector II and the light spot displacement measuring device are parallel to the initial state of the cantilever beam or the outrigger beam; the laser emitted by the laser The beam energy is reflected to the spot displacement measuring device through the mirror I and the mirror II in turn; the spot displacement measuring device adopts a spot displacement measuring device, a charge-coupled element or a photoelectric displacement sensor.
  • the above-mentioned device for measuring the Young's elastic modulus of materials by using the cantilever beam or the outrigger beam also includes a mirror III, which is set perpendicular to the initial state of the cantilever beam or the outrigger beam, and the laser beam emitted by the laser can pass through the Mirror I, mirror III, and mirror II are reflected to the spot displacement measuring device.
  • the cantilever beam includes a clamp and a rectangular cross-section beam
  • the clamp includes a rectangular parallelepiped upper clamp body and a lower clamp body, and the lower clamp body
  • the concrete upper end surface is provided with a rectangular groove, and one end of the rectangular section beam is embedded in the rectangular groove, and the upper clamp body and the lower clamp body are fixedly connected by positioning pins.
  • an operating table is also included, and the cantilever beam or outrigger beam and the reflector II are installed on the operating table, and the reflector I is installed on the cantilever
  • the upper surface of the beam or outrigger beam, the mirror II and the laser beam are located above the cantilever beam or outrigger beam.
  • the reflector 1 is arranged perpendicular to the bottom surface of the cantilever beam or the overhanging beam, and the spot displacement measuring device is perpendicular to the cantilever beam or the overhanging beam
  • the initial state is set; or the reflector I is set parallel to the bottom surface of the cantilever beam or the outrigger beam, and the spot displacement measuring device is set perpendicular to the initial state of the cantilever beam or the outrigger beam; or the reflector I is parallel to the bottom surface of the cantilever beam or the outrigger beam Setting, the light spot displacement measuring device is set parallel to the initial state of the cantilever beam or the outrigger beam.
  • the reflector 1 is installed on the cantilever beam or the overhanging beam through an optical measuring head fixture, and the optical measuring head fixture includes a clamp body, a clamp Specifically, it is a cuboid structure, and the clamp body is provided with a clamp groove with a rectangular cross section, the bottom surface of the clamp groove is parallel to the side of the clamp body, and a spring leaf is arranged in the clamp groove; the reflector 1 is attached to the top surface or side of the clamp body; The top surface of the clamp body is provided with a weight positioning block; the free end of the cantilever beam or the outrigger beam is inserted into the fixture groove, the top surface of the free end of the cantilever beam or the outrigger beam is closely attached to the top surface of the fixture groove, and the bottom surface of the fixture groove and the cantilever beam Or a spring sheet is arranged between the bottom surfaces of the
  • a method utilizing the above-mentioned device for measuring Young's modulus of elasticity of a material using a cantilever beam or an overhanging beam to measure Young's modulus of a material comprising the steps of:
  • the magnitude of the multiple applied loads is an arithmetic sequence, and the magnitude of the adjacent two applied loads is the same as the initial applied load; and measure each The position of the spot after the load is applied for the first time; then record each measurement result in a coordinate system with the number of measurements as the x-axis and the position of the spot as the y-axis, and perform linear fitting on the points in the coordinate system to obtain a fitted straight line.
  • the slope of the fitting line is taken as the displacement ⁇ x of the light spot under the first applied load; 4)
  • the calculation formula of the free end rotation angle ⁇ of the outrigger beam, the calculation formula of the deflection ⁇ of the free end of the cantilever beam or the outrigger beam and the calculation formula of the moment of inertia can be used to calculate the Young's modulus of elasticity E of the material.
  • step 4 when the reflector 1 is arranged vertically to the bottom surface of the cantilever beam, and the spot displacement measuring device is set perpendicular to the initial state of the cantilever beam,
  • the calculation formula of the Young's modulus of elasticity of the material is as follows: In the formula: I is the moment of inertia of the cantilever beam, L1 is the distance between the load and the fixed end of the cantilever beam, P is the load size, D is the distance between the incident point of the laser beam on the mirror I and the spot displacement measuring device, ⁇ x is the spot displacement at the spot displacement measuring device;
  • the calculation formula of Young’s modulus of elasticity of the material is as follows: In the formula: ⁇ is the angle between the reflected beam and the horizontal direction after the laser beam is reflected by the mirror I before the load is applied, and L2 is the length of the cantilever beam;
  • the calculation formula of Young’s modulus of elasticity of the material is as follows: In the formula: ⁇ ' is the angle between the reflected beam and the vertical direction after the laser beam is reflected by the mirror I before the load is applied;
  • the calculation formula of Young’s elastic modulus of the material is as follows: In the formula, H1 is the distance between the incident point of the laser beam on the mirror I and the mirror II; H2 is the distance between the mirror II and the spot displacement measuring device;
  • the calculation formula of Young’s elastic modulus of the material is as follows :
  • the device of the present invention that utilizes a cantilever beam or an overhanging beam to measure the Young's modulus of elasticity of a material is simple in structure, compact, and low in cost; and the present invention amplifies the displacement of the free end of the cantilever beam or the overhanging beam after the load is applied through the optical principle, so , a large spot displacement can be obtained by applying a small load, which is convenient for measurement, does not cause the material to enter the plastic deformation zone, and obtains accurate results; moreover, the sample of the present invention adopts a rectangular cross-section beam structure, which is convenient for processing.
  • Figure 1 is the structural diagram of the cantilever beam with applied load
  • Figure 1(a) is the structural diagram of the rectangular cross-section beam
  • Figure 1(b) is the bending structure diagram of the cantilever beam after applying concentrated load
  • Figure 1(c) is the cantilever beam with uniform load Backbending structure diagram.
  • Figure 2 is a structural diagram of the load applied by the outrigger beam.
  • Fig. 3 is a structural diagram of a device for measuring Young's modulus of material by using a cantilever beam or an outrigger beam according to Embodiment 1 of the present invention.
  • Fig. 4 is a measurement schematic diagram of Embodiment 1 of the present invention.
  • Fig. 5 is a structural diagram of a device for measuring Young's modulus of elasticity of a material using a cantilever beam or an outrigger beam according to Embodiment 2 of the present invention.
  • Fig. 6 is a measurement schematic diagram of Embodiment 2 of the present invention.
  • Fig. 7 is a structural diagram of a device for measuring Young's elastic modulus of a material by using a cantilever beam or an outrigger beam according to Embodiment 3 of the present invention.
  • Fig. 8 is a measurement schematic diagram of Embodiment 3 of the present invention.
  • Fig. 9 is a structural diagram of a device for measuring Young's elastic modulus of a material by using a cantilever beam or an outrigger beam according to Embodiment 4 of the present invention.
  • Fig. 10 is a measurement schematic diagram of Embodiment 4 of the present invention.
  • Fig. 11 is a structural diagram of a device for measuring Young's elastic modulus of a material by using a cantilever beam or an outrigger beam according to Embodiment 5 of the present invention.
  • Fig. 12 is a measurement schematic diagram of Embodiment 5 of the present invention.
  • Fig. 13 is a structural view of the cantilever beam clamp of the present invention.
  • Fig. 14 is a structural diagram of the optical measuring head fixture of the present invention.
  • a beam with a rectangular cross-section has a thickness d, a width l, and a length L. If the thickness d of the beam is much smaller than the length of the beam, it can be regarded as a slender rod. When the bending deformation of the slender rod is small, the deflection and rotation angle of the beam can be calculated using the small deflection theory.
  • the length of the cantilever beam is L 2
  • a concentrated load P is applied at a distance of L 1 from the fixed end, the cantilever beam will bend, and its free end rotation angle ⁇ is (a section of beam from the point where the force acts to the free end no deformation):
  • E the Young's modulus of the material
  • I the moment of inertia of the cantilever beam around the z-axis
  • the deflection ⁇ at the free end of the cantilever beam is
  • the condition of the small deflection theory is that the free end rotation angle ⁇ /( ⁇ /2) ⁇ 0.2, or as long as ⁇ 18°, there is ⁇ P—the linear relationship between the two means that in the case of small deflection, the beam
  • the deformation can be directly superimposed and calculated according to the load (including the deformation caused by self-weight).
  • the E value of the material can be calculated.
  • point A is the fixed hinge support of the outrigger beam
  • point B is the support of the outrigger beam.
  • the free end rotation angle ⁇ is respectively:
  • L 3 is the distance between the fixed hinge support and the support
  • a is the distance between the support and the load application point.
  • the cantilever beam 3 and the laser 2 are respectively installed on the console through a bracket, and a spot displacement measuring device 4 is provided on the bracket of the laser 2 .
  • the free end of the cantilever beam 3 is provided with a reflector 15, and the laser beam emitted by the laser 2 can be reflected by the reflector 1 to the spot displacement measuring device 4.
  • the reflector 1 is set perpendicular to the bottom surface of the cantilever beam
  • the light spot displacement measuring device 4 is set perpendicular to the initial state of the cantilever beam 3.
  • the light spot displacement measuring device 4 adopts a scale.
  • the method for measuring Young's modulus of elasticity of material with cantilever beam or outrigger beam of the present invention comprises the steps:
  • step 1) to make the cantilever beam in this embodiment and assemble it into a device that utilizes the cantilever beam or the outrigger beam to measure the Young's modulus of elasticity of the material;
  • the device is adjusted; the laser 2 is at the same height as the center of the mirror I5, and the laser beam emitted by the laser 2 can be reflected to the spot displacement measuring device 4. Measure the initial position of the reflected light spot on the scale.
  • I is the moment of inertia of the cantilever beam
  • L1 is the distance between the load and the fixed end of the cantilever beam
  • P is the load size
  • D is the distance between the incident point of the laser beam on the mirror I and the spot displacement measuring device
  • ⁇ x is the spot displacement at the spot displacement measuring device
  • ⁇ x
  • x 2 is the scale of the spot after the load is applied
  • x 1 is the scale of the spot before the load is applied.
  • multiple loads can be applied on the cantilever near the free end to measure the position of the spot.
  • the magnitude of the multiple applied loads is an arithmetic sequence, and two adjacent The magnitude of the applied load is the same as the initial applied load; the first applied load is P, the second load is 2P, the third load is 3P... .
  • record each measurement result in the coordinate system with the measurement times as the x-axis and the spot position as the y-axis and perform linear fitting on the points in the coordinate system to obtain the fitted straight line, and calculate the slope of the fitted straight line as is the displacement ⁇ x of the light spot under the first applied load.
  • a ruler for direct reading, or use a charge-coupled device (CCD) or a photoelectric displacement sensor (PSD) as a means of detecting displacement.
  • CCD charge-coupled device
  • PSD photoelectric displacement sensor
  • the laser 2 can also be replaced by a telescope.
  • the device of the present invention that utilizes a cantilever beam or an overhanging beam to measure the Young's modulus of material is similar to the structure in embodiment 1, the difference is only that the reflector 1 is installed on the free end of the cantilever beam 3 On the top surface (set parallel to the bottom surface of the cantilever beam 3).
  • the method for measuring Young's modulus of elasticity of material with cantilever beam or outrigger beam of the present invention comprises the steps:
  • step 1) to make the cantilever beam in this embodiment and assemble it into a device that utilizes the cantilever beam or the outrigger beam to measure the Young's modulus of elasticity of the material; The device is adjusted; so that the laser beam emitted by the laser 2 can be reflected to the spot displacement measuring device 4. Measure the initial position of the reflected light spot on the scale.
  • I is the moment of inertia of the cantilever beam
  • L1 is the distance between the load and the fixed end of the cantilever beam
  • P is the load size
  • D is the distance between the incident point of the laser beam on the mirror I and the spot displacement measuring device
  • ⁇ x is the spot displacement at the spot displacement measurement device
  • ⁇ x
  • x 2 is the scale of the spot after the load is applied
  • x 1 is the scale of the spot before the load is applied
  • ⁇ is the laser beam before and after the load is applied respectively
  • L 2 is the length of the cantilever beam.
  • multiple loads can be applied on the cantilever near the free end to measure the position of the spot.
  • the magnitude of the multiple applied loads is an arithmetic sequence, and two adjacent The magnitude of the applied load is the same as the initial applied load; the first applied load is P, the second load is 2P, the third load is 3P... .
  • record each measurement result in the coordinate system with the measurement times as the x-axis and the spot position as the y-axis and perform linear fitting on the points in the coordinate system to obtain the fitted straight line, and calculate the slope of the fitted straight line as is the displacement ⁇ x of the light spot under the first applied load.
  • the device of the present invention that utilizes a cantilever beam or an overhanging beam to measure Young's modulus of material is similar to the structure in embodiment 1, and the difference is only that the reflector 1 is installed on the free end of the cantilever beam 3 On the bottom surface (set parallel to the bottom surface), the spot displacement measurement device 4 is installed on the console 1 (parallel to the initial state of the cantilever beam), the laser 2 and the cantilever beam 3 are installed on the same bracket, and the laser 2 is located below the cantilever beam 3.
  • the method for measuring Young's modulus of elasticity of material with cantilever beam or outrigger beam of the present invention comprises the steps:
  • step 1) to make the cantilever beam in this embodiment and assemble it into a device that utilizes the cantilever beam or the outrigger beam to measure the Young's modulus of elasticity of the material; The device is adjusted; so that the laser beam emitted by the laser 2 can be reflected to the spot displacement measuring device 4. Measure the initial position of the reflected light spot on the scale.
  • I is the moment of inertia of the cantilever beam
  • L1 is the distance between the load and the fixed end of the cantilever beam
  • P is the load size
  • D is the distance between the incident point of the laser beam on the mirror I and the spot displacement measuring device
  • ⁇ x is the spot displacement at the spot displacement measuring device
  • ⁇ x
  • x 2 is the scale of the spot after the load is applied
  • x 1 is the scale of the spot before the load is applied
  • ⁇ ' and ⁇ ' are the applied load respectively
  • L2 is the length of the cantilever beam.
  • multiple loads can be applied on the cantilever near the free end to measure the position of the spot.
  • the magnitude of the multiple applied loads is an arithmetic sequence, and two adjacent The magnitude of the applied load is the same as the initial applied load; the first applied load is P, the second load is 2P, the third load is 3P... .
  • record each measurement result in the coordinate system with the measurement times as the x-axis and the spot position as the y-axis and perform linear fitting on the points in the coordinate system to obtain the fitted straight line, and calculate the slope of the fitted straight line as is the displacement ⁇ x of the light spot under the first applied load.
  • the device for measuring Young's elastic modulus of materials using a cantilever beam or an overhanging beam of the present invention is similar to the structure in Example 2, the only difference is that mirror II6 is also provided, and mirror II6 is parallel Set in the initial state of the cantilever beam, the spot displacement measuring device 4 is installed on the console 1 (parallel to the initial state of the cantilever beam).
  • the method for measuring Young's modulus of elasticity of material with cantilever beam or outrigger beam of the present invention comprises the steps:
  • step 1) to make the cantilever beam in this embodiment and assemble it into a device that utilizes the cantilever beam or the outrigger beam to measure the Young's modulus of elasticity of the material;
  • the device is adjusted; so that the laser beam emitted by the laser 2 can be reflected to the spot displacement measuring device 4 through the mirror I5 and the mirror II6 in turn. Measure the initial position of the reflected light spot on the scale.
  • the cantilever beam 3 bends, the cantilever beam 3 and the mirror I rotate by the same angle ⁇ , and the reflected light spot moves to x2 .
  • the mirror I rotates by an angle ⁇
  • ⁇ x
  • I is the moment of inertia of the cantilever beam
  • L 1 is the distance between the load and the fixed end of the cantilever beam
  • P is the load size
  • ⁇ x is the spot displacement at the spot displacement measuring device
  • x 1 is the scale of the spot before applying the load
  • H 1 is the distance from the incident point of the laser beam on the mirror I to the mirror II
  • H2 is the distance between the mirror II and the spot displacement measuring device
  • ⁇ ' and ⁇ ' are the laser beam passing through the mirror I before and after the load is applied, respectively. The angle between the reflected beam and the vertical after reflection.
  • multiple loads can be applied on the cantilever near the free end to measure the position of the spot.
  • the magnitude of the multiple applied loads is an arithmetic sequence, and two adjacent The magnitude of the applied load is the same as the initial applied load; the first applied load is P, the second load is 2P, the third load is 3P... .
  • record each measurement result in the coordinate system with the measurement times as the x-axis and the spot position as the y-axis and perform linear fitting on the points in the coordinate system to obtain the fitted straight line, and calculate the slope of the fitted straight line as is the displacement ⁇ x of the light spot under the first applied load.
  • the device of the present invention that utilizes a cantilever beam or an overhanging beam to measure Young's modulus of material is similar to the structure in Example 4, the only difference being that a reflector III7 is also provided, and the reflector III7 is vertical Set in the initial state of the cantilever beam 3.
  • the method for measuring Young's modulus of elasticity of material with cantilever beam or outrigger beam of the present invention comprises the steps:
  • step 1) to make the cantilever beam in this embodiment and assemble it into a device that utilizes the cantilever beam or the outrigger beam to measure the Young's modulus of elasticity of the material;
  • the device is adjusted so that the laser beam emitted by the laser 2 can be reflected to the spot displacement measuring device 4 through the mirror I5, the mirror III7, and the mirror II6 in turn. Measure the initial position of the reflected light spot on the scale.
  • I is the moment of inertia of the cantilever beam 3
  • L1 is the distance between the load and the fixed end of the cantilever beam
  • P is the load size
  • ⁇ x is the spot displacement at the spot displacement measuring device
  • x1 is the scale of the spot before the load is applied
  • H 1 is the distance from the incident point of the laser beam on the mirror I to the mirror II
  • H 2 is the distance between the mirror II and the spot displacement measuring device
  • ⁇ ' and ⁇ ' are respectively the laser beam passing through the mirror before and after the load is applied.
  • I is the angle between the reflected beam and the vertical direction after reflection.
  • multiple loads can be applied on the cantilever near the free end to measure the position of the spot.
  • the magnitude of the multiple applied loads is an arithmetic sequence, and two adjacent The magnitude of the applied load is the same as the initial applied load; the first applied load is P, the second load is 2P, the third load is 3P... .
  • record each measurement result in the coordinate system with the measurement times as the x-axis and the spot position as the y-axis and perform linear fitting on the points in the coordinate system to obtain the fitted straight line, and calculate the slope of the fitted straight line as is the displacement ⁇ x of the light spot under the first applied load.
  • the cantilever beams 3 in Examples 1-5 can all be replaced by outrigger beams, and the Young's modulus of elasticity of the material can be calculated according to formula (4) or formula (5) by obtaining the rotation angle of the outrigger beam after the load is applied.
  • the cantilever beam 3 of the present invention includes a rectangular cross-section beam and a clamp, as shown in Figure 13, the clamp includes a rectangular parallelepiped upper clamp body 81 and a lower clamp body 82, and the upper clamp body 81 of the lower clamp body The end face is provided with a rectangular groove 84 , and one end of the beam with a rectangular cross section is embedded in the rectangular groove 84 , and the upper clamp body 81 and the lower clamp body 82 are fixedly connected by a positioning pin 83 .
  • the fixture is fixed on the console 1 through the vise on the console 1 .
  • the mirror I5 of the present invention is installed on the cantilever beam 3 or the outrigger beam through the optical measuring head fixture, as shown in FIG. 14 .
  • the optical measuring head clamp includes a clamp body 88, which is a rectangular parallelepiped structure.
  • the clamp body 88 is provided with a clamp groove 89 with a rectangular cross section.
  • the bottom surface of the clamp groove is parallel to the side of the clamp body, and a spring is arranged in the clamp groove.
  • Sheet 86; reflector 15 is affixed on the top surface of clip body 88, what this figure represents is that reflector 15 is parallel to the situation of cantilever beam 3 or outrigger beam bottom surface, when reflector 15 is perpendicular to cantilever beam 3 or outrigger beam On the bottom surface, the reflector 15 is attached to the side of the clamp body 88.
  • the top surface of the clamp body 88 is provided with a weight positioning block 87 .
  • spring leaf 86 is set between the bottom surface of fixture groove 89 and the bottom surface of cantilever beam 3 or outrigger beam (or between the top surface of fixture groove 89 and the top surface of cantilever beam 3 or outrigger beam Spring leaf 86) is set.

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Abstract

一种利用悬臂梁（3）或外伸梁测量材料杨氏弹性模量的方法及装置，装置包括激光器（2）、悬臂梁（3）或外伸梁、反射镜I（5）及光斑位移测量装置（4），悬臂梁（3）或外伸梁的自由端设有反射镜I（5），激光器（2）发出的激光束能经反射镜I（5）反射至光斑位移测量装置（4）；反射镜I（5）平行或垂直于悬臂梁（3）或外伸梁底面设置，光斑位移测量装置（4）平行或垂直于悬臂梁（3）或外伸梁的初始状态设置。利用悬臂梁（3）或外伸梁测量材料杨氏弹性模量的装置结构简单、紧凑，成本低；而且通过光学原理，放大了施加载荷后悬臂梁（3）或外伸梁自由端的位移，施加载荷较小，不会使得材料进入塑性变形区，得到的结果精确；而且样品采用的是矩形截面梁结构，便于加工。

Description

利用悬臂梁或外伸梁测量材料杨氏弹性模量的方法和装置 技术领域
本发明属于杨氏弹性模量测量技术领域，具体涉及一种利用悬臂梁或外伸梁测量材料杨氏弹性模量的方法及装置。
背景技术
弹性模量是描述材料形变与应力关系的重要特征量，是工程技术中常用的一个参数。在实验室施加的外力使材料产生的变形相当微小，难以用肉眼观察，同时过大的载荷又会使得材料发生塑形变形，还必须要通过将微小变形放大的方法来测量。现有的测量弹性模量的方法大都是采用万能机对材料进行拉伸或压缩实验，通过测量超声波在材料中的传播速度间接测量材料的弹性模量及梁弯曲法测量杨氏弹性模量。对材料进行拉伸或压缩实验，具有测量灵敏度低的缺陷。而超声波法进行测量，则所需设备成本高，不便于实际应用。
梁弯曲法测量杨氏弹性模量，见于报道的主要有激光光杠杆测量法、霍尔位置传感器法、单缝衍射法、光纤布拉格光栅测量法等，它们共同的特点是将横梁用两个刀口支撑，在横梁中间位置用刀口(或不用)施加作用力使其产生弯曲，通过测量梁的挠度来获得杨氏模量。这些方法所使用的装置都需要刀口支撑横梁，测量挠度需用的器材较多，整体的占用面积也较大，加工精度、使用条件较为苛刻。
发明内容
为了解决上述技术问题，本发明提供一种结构简单，成本低，使得样品便于加工且测量结果精确度高的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置及方法。
本发明采用的技术方案是：一种利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，其特征是：包括激光器、悬臂梁或外伸梁、反射镜I及光斑位移测量装置，所述的悬臂梁或外伸梁的自由端设有反射镜I，激光器发出的激光束能经反射镜I反射至光斑位移测量装置；反射镜I平行或垂直于悬臂梁或外伸梁底面设置，光斑位移测量装置平行或垂直于悬臂梁或外伸梁的初始状态设置。
上述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置中，还包括反射镜Ⅱ，反射镜Ⅱ和光斑位移测量装置平行于悬臂梁或外伸梁的初始状态；激光器发出的激光束能依次经反射镜I、反射镜Ⅱ反射至光斑位移测量装置；光斑位移测量装置采用的是光斑位移测量装置、电荷耦合元件或光电位移传感器。
上述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置中，还包括反射镜Ⅲ，反射镜Ⅲ垂直于悬臂梁或外伸梁的初始状态设置,激光器发出的激光束能依次经反射镜I、反射镜Ⅲ、反射镜Ⅱ反射至光斑位移测量装置。
上述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置中，所述的悬臂梁包括夹具和矩形截面梁，所述的夹具包括长方体形的上夹具体和下夹具体，下夹具体的上端面设有矩形凹槽，矩形截面梁的一端嵌装在矩形凹槽内，上夹具体与下夹具体通过定位销固定联接。
上述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置中，还包括操作台，所述的悬臂梁或外伸梁和反射镜Ⅱ安装在操作台上，反射镜I安装在悬臂梁或外伸梁上表面，反射镜Ⅱ和激光束位于悬臂梁或外伸梁上方。
上述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置中，所述的反射镜I垂直于悬臂梁或外伸梁的底面设置，光斑位移测量装置垂直于悬臂梁或外伸梁初始状态设置；或反射镜I平行于悬臂梁或外伸梁的底面设置，光斑位移测量装置垂直于悬臂梁或外伸梁初始状态设置；或反射镜I平行于悬臂梁或外伸梁的底面设置，光斑位移测量装置平行于悬臂梁或外伸梁初始状态设置。
上述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置中，反射镜I通过光学测量头夹具安装在悬臂梁或外伸梁上，所述的光学测量头夹具包括夹具体，夹具体为长方体结构，夹具体上设有截面为矩形的夹具槽，夹具槽的底面平行于夹具体的侧面，夹具槽内设有弹簧片；反射镜I贴在夹具体的顶面或侧面上；夹具体顶面设有砝码定位挡片；悬臂梁或外伸梁的自由端插入夹具槽，悬臂梁或外伸梁的自由端的顶面与夹具槽顶面贴紧，夹具槽底面和悬臂梁或外伸梁的底面之间设置弹簧片；或悬臂梁或外伸梁的自由端的底面与夹具槽底面贴紧，夹具槽顶面和悬臂梁或外伸梁的顶面之间设置弹簧片。
一种利用上述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置的利用悬臂梁或外伸梁测量材料杨氏弹性模量的方法，包括如下步骤：
1)将材料加工成矩形截面梁，然后利用矩形截面梁制成悬臂梁或外伸梁；利用悬臂梁或外伸梁组装利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置；
2)开启激光器，调试标尺位置；测量反射光斑在标尺上的初始位置；
3)然后在悬臂梁或外伸梁接近自由端处施加荷载，再测量反射光斑在标尺上的位置，得到光斑的位移Δx；
或在悬臂梁或外伸梁接近自由端处多次施加荷载，多次施加的荷载的大小为等差数列，且相邻的两次施加的荷载的大小与初次施加的荷载相同；并测量每次施加载荷后光斑位置；然后在以测量次数为x轴，以光斑位置为y轴的坐标系内记录每次的测量结果，对坐标系内的点进行线性拟合，得到拟合直线，求取拟合直线的斜率即为第一次施加的荷载下光斑的位移Δx；4)根据光斑的位移Δx计算悬臂梁或外伸梁每次施加载荷后的自由端转角θ，进而根据悬臂梁或外伸梁自由端转角θ的计算公式、悬臂梁或外伸梁自由端挠度δ的计算公式及惯性矩计算公式，计算得到材料的杨氏弹性模量E。
上述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的方法中，步骤4)中：当反射镜I垂直于悬臂梁的底面设置，光斑位移测量装置垂直于悬臂梁初始状态设置时，材料杨氏弹性模量的计算公式如下：
Figure PCTCN2022083218-appb-000001
式中：I为悬臂梁的惯性矩，L 1为载荷距离悬臂梁固定端的距离，P为载荷大小，D为激光束在反射镜I上的入射点与光斑位移测量装置之间的距离，Δx为光斑位移测量装置处光斑位移；
当反射镜I平行于悬臂梁的底面设置，光斑位移测量装置垂直于悬臂梁初始状态设置时，材料杨氏弹性模量的计算公式如下：
Figure PCTCN2022083218-appb-000002
式中：α为施加载荷前，激光束经反射镜I反射后的反射光束与水平方向的夹角,L 2为悬臂梁的长度；
当反射镜I平行于悬臂梁的底面设置，光斑位移测量装置平行于悬臂梁初始状态设置时，材料杨氏弹性模量的计算公式如下：
Figure PCTCN2022083218-appb-000003
式中：α'为施加载荷前，激光束经反射镜I反射后的反射光束与竖直方向的夹角；
当反射镜I平行于悬臂梁的底面设置，反射镜Ⅱ和光斑位移测量装置平行于悬臂梁的初始状态时，材料杨氏弹性模量的计算公式如下：
Figure PCTCN2022083218-appb-000004
式中H 1为激光束在反射镜I上的入射点道反射镜Ⅱ的距离；H 2为反射镜Ⅱ与光斑位移测量装置之间的距离；
当反射镜I平行于悬臂梁的底面设置，反射镜Ⅱ和光斑位移测量装置平行于悬臂梁的初始状态,反射镜Ⅲ垂直于悬臂梁的初始状态时，材料杨氏弹性模量的计算公式如下：
Figure PCTCN2022083218-appb-000005
与现有技术相比，本发明的有益效果是：
本发明的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置结构简单、紧凑，成本低；而且本发明通过光学原理，放大了施加载荷后悬臂梁或外伸梁自由端的位移，因此，施加载荷较小载荷即可获得较大的光斑位移，便于测量，不会使得材料进入塑性变形区，得到的结果精确；而且本发明的样品采用的是矩形截面梁结构，便于加工。
附图说明
图1是悬臂梁施加载荷的结构图；图1(a)为矩形截面梁结构图，图1(b)为悬臂梁施加集中载荷后弯曲结构图；图1(c)为悬臂梁施加均匀载荷后弯曲结构图。
图2是外伸梁施加载荷的结构图。
图3是本发明实施例1的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置的结构图。
图4是本发明实施例1的测量原理图。
图5是本发明实施例2的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置的结构图。
图6是本发明实施例2的测量原理图。
图7是本发明实施例3的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置的结构图。
图8是本发明实施例3的测量原理图。
图9是本发明实施例4的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置的结构图。
图10是本发明实施例4的测量原理图。
图11是本发明实施例5的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置的结构图。
图12是本发明实施例5的测量原理图。
图13是本发明的悬臂梁的夹具的结构图。
图14是本发明的光学测量头夹具的结构图。
具体实施方式
下面结合附图和实施例对本发明做进一步的说明。
测量原理
利用悬臂梁测量杨氏弹性模量的原理如下：
如图1(a)所示，矩形截面梁，厚度为d，宽度为l，长为L。如果梁的厚度d相对于梁的长度小很多，则可看作是一根细长杆，当细长杆的弯曲变形较小时，可利用小挠度理论来计算梁的挠度和转角。
如图1(b)，悬臂梁的长度为L 2，在距离固定端L 1处施加集中载荷P，悬臂梁将产生弯曲，其自由端转角θ为(从力的作用点至自由端的一段梁不变形)：
Figure PCTCN2022083218-appb-000006
其中E为材料的杨氏模量，I为悬臂梁绕z轴的惯性矩，其表达式为：
Figure PCTCN2022083218-appb-000007
悬臂梁自由端的挠度δ为
Figure PCTCN2022083218-appb-000008
小挠度理论成立的条件是自由端转角θ/(π/2)<0.2，或者说只要θ<18°，就有θ∝P——二者的线性关系意味着，在小挠度的情形，梁的变形可以根据载荷直接叠加计算(包括自重引起的形变)。
在测出一定荷载P下悬臂梁自由端转角θ的基础上，再结合公式(1)即可计算出材料的E值。
考虑到实际施加载荷时，很难保证载荷是作用在某一点的集中载荷，这里给出在某一区域施加均匀载荷q的情形，如图1(c)所示，悬臂梁自由端转角θ的计算公式成为：
Figure PCTCN2022083218-appb-000009
比较式(1)和式(3)可以发现，如果加载区域比较小，可以将小区域的均匀载荷看作是加载在荷载区域中心位置(a+b/2处)的集中载荷，则(1)和式(3)的差别极小。例如b≈a/10时，相对误差只有7.6×10 -4。可以忽略不计，在实际测量或计算时，可直接采用式(1)计算θ。
利用外伸梁测量杨氏弹性模量的原理如下：
如图2所示，A点为外伸梁的固定铰支座，B点为外伸梁的支座，当在C点(外伸梁的自由端)施加载荷P之后，自由端转角θ和挠度δ分别为：
Figure PCTCN2022083218-appb-000010
Figure PCTCN2022083218-appb-000011
L 3为固定铰支座与支座之间的距离，a为支座与载荷施加点之间的距离。同样，如果能测出一定荷载P下外伸梁的自由端转角θ，带入式(4)可计算出材料的E值。
实施例1
如图3、4所示，本发明的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，包括操作台1、激光器2、悬臂梁3、反射镜I5及光斑位移测量装置4，悬臂梁3及激光器2分别通过支架安装在操作台上，激光器2的支架上设有光斑位移测量装置4。所述的悬臂梁3的自由端设有反射镜I5，激光器2发出的激光束能经反射镜I反射至光斑位移测量装置4。反射镜I垂直于悬臂梁底面设置，光斑位移测量4装置垂直于悬臂梁3的初始状态设置。光斑位移测量装置4采用的是标尺。
本发明的用悬臂梁或外伸梁测量材料杨氏弹性模量的方法，包括如下步骤：
1)将材料加工成矩形截面梁，然后利用矩形截面梁制成悬臂梁3；
2)利用步骤1)制成本实施例中的悬臂梁组装成利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置；并对利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置进行调节；使得激光器2与反射镜I5的中心同高，且使得激光器2发出的激光束能够反射到光斑位移测量装置4处。测量反射光斑在标尺上的初始位置。
3)然后在悬臂梁或外伸梁接近自由端处施加荷载，再测量反射光斑在标尺上的位置，得到光斑的位移Δx；
4)根据光斑的位移Δx计算悬臂梁或外伸梁每次施加载荷后的自由端转角θ，进而根据悬臂梁或外伸梁自由端转角θ的计算公式、悬臂梁或外伸梁自由端挠度δ的计算公式及惯性矩计算公式，计算得到材料的杨氏弹性模量E。
如图4所示，因为激光束在反射镜I上的入射点与光斑位移测量装置之间的距离D很长，悬臂梁自由端转角θ很小，所以2θ≈Δx/D。根据公式(1)，θ＝PL 1 2/(2EI)，可得：
Figure PCTCN2022083218-appb-000012
式中：I为悬臂梁的惯性矩，L 1为载荷距离悬臂梁固定端的距离，P为载荷大小，D为激光束在反射镜I上的入射点与光斑位移测量装置之间的距离，Δx为光斑位移测量装置处光斑位移，Δx＝|x 2-x 1|，x 2为施加载荷后光斑所在的刻度，x 1为施加载荷前光斑所在的刻度。
为了获得更精确的施加载荷P下的光斑的位移，可以在悬臂梁上接近自由端处多次施加荷载进行测量光斑位置，多次施加的荷载的大小为等差数列，且相邻的两次施加的荷载的大小与初次施加的荷载相同；第一次施加载荷为P，第二次载荷为2P，第三次载荷为3P……。然后在以测量次数为x轴，以光斑位置为y轴的坐标系内记录每次的测量结果，对坐标系内的点进行线性拟合，得到拟合直线，求取拟合直线的斜率即为第一次施加的荷载下光斑的位移Δx。然后再按步骤4)计算即可得到E。
测量光斑位移，可以放置标尺直接读数，也可采用电荷耦合元件(CCD)或光电位移传感器(PSD)作为检测位移的手段。激光器2还可以采用望远镜替代。
实施例2
如图5、6所示，本发明的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置与实施例1中的结构相似，区别仅仅在于反射镜I安装在悬臂梁3的自由端的顶面上(平行于悬 臂梁3的底面设置)。
本发明的用悬臂梁或外伸梁测量材料杨氏弹性模量的方法，包括如下步骤：
1)将材料加工成矩形截面梁，然后利用矩形截面梁制成悬臂梁3；
2)利用步骤1)制成本实施例中的悬臂梁组装成利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置；并对利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置进行调节；使得激光器2发出的激光束能够反射到光斑位移测量装置4处。测量反射光斑在标尺上的初始位置。
3)然后在悬臂梁或外伸梁接近自由端处施加荷载P，再测量反射光斑在标尺上的位置，得到光斑的位移Δx；
4)根据位移Δx计算悬臂梁或外伸梁每次施加载荷后的自由端转角θ，进而根据悬臂梁或外伸梁自由端转角θ的计算公式、悬臂梁或外伸梁自由端挠度δ的计算公式及惯性矩计算公式，计算得到材料的杨氏弹性模量E。
如图6所示，光斑移动距离表达式为：
Figure PCTCN2022083218-appb-000013
调试好实验装置后，在L 1位置加上荷载P，测出载荷P所对应的Δx，可得：
Figure PCTCN2022083218-appb-000014
式中：I为悬臂梁的惯性矩，L 1为载荷距离悬臂梁固定端的距离，P为载荷大小，D为激光束在反射镜I上的入射点与光斑位移测量装置之间的距离，Δx为光斑位移测量装置处光斑位移，Δx＝|x 2-x 1|，x 2为施加载荷后光斑所在的刻度，x 1为施加载荷前光斑所在的刻度，αβ分别为施加载荷前后激光束经反射镜I反射后的反射光束与竖直方向的夹角，L 2为悬臂梁的长度。
为了获得更精确的施加载荷P下的光斑的位移，可以在悬臂梁上接近自由端处多次施加荷载进行测量光斑位置，多次施加的荷载的大小为等差数列，且相邻的两次施加的荷载的大小与初次施加的荷载相同；第一次施加载荷为P，第二次载荷为2P，第三次载荷为3P……。然后在以测量次数为x轴，以光斑位置为y轴的坐标系内记录每次的测量结果，对坐标系内的点进行线性拟合，得到拟合直线，求取拟合直线的斜率即为第一次施加的荷载下光斑的位移Δx。然后再按步骤4)计算即可得到E。
实施例3
如图7、8所示，本发明的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置与实施例1中的结构相似，区别仅仅在于反射镜I安装在悬臂梁3的自由端的底面上(平行于底面设置)，光斑位移测量装置4安装在操作台1上(平行于悬臂梁的初始状态)，激光器2和悬臂梁3安装在同一支架上，激光器2位于悬臂梁3下方。
本发明的用悬臂梁或外伸梁测量材料杨氏弹性模量的方法，包括如下步骤：
1)将材料加工成矩形截面梁，然后利用矩形截面梁制成悬臂梁3；
2)利用步骤1)制成本实施例中的悬臂梁组装成利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置；并对利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置进行调节；使得激光器2发出的激光束能够反射到光斑位移测量装置4处。测量反射光斑在标尺上的初始位置。
3)然后在悬臂梁或外伸梁接近自由端处施加荷载，再测量反射光斑在标尺上的位置，得到光斑的位移Δx；
4)根据位移Δx计算悬臂梁或外伸梁每次施加载荷后的自由端转角θ，进而根据悬臂梁或外伸梁自由端转角θ的计算公式、悬臂梁或外伸梁自由端挠度δ的计算公式及惯性矩计算公式，计算得到材料的杨氏弹性模量E。
如图8所示，光斑移动距离表达式为：
Figure PCTCN2022083218-appb-000015
调试好实验装置后，在L 1位置加上荷载P，测出载荷P所对应的Δx，可得：
Figure PCTCN2022083218-appb-000016
式中：I为悬臂梁的惯性矩，L 1为载荷距离悬臂梁固定端的距离，P为载荷大小，D为激光束在反射镜I上的入射点与光斑位移测量装置之间的距离，Δx为光斑位移测量装置处光斑位移，Δx＝|x 2-x 1|，x 2为施加载荷后光斑所在的刻度，x 1为施加载荷前光斑所在的刻度，α'、β'分别为施加载荷前后激光束经反射镜I反射后的反射光束与竖直方向的夹角，L 2为悬臂梁的长度。
为了获得更精确的施加载荷P下的光斑的位移，可以在悬臂梁上接近自由端处多次施加荷载进行测量光斑位置，多次施加的荷载的大小为等差数列，且相邻的两次施加的荷载的大小与初次施加的荷载相同；第一次施加载荷为P，第二次载荷为2P，第三次载荷为3P……。然后在以测量次数为x轴，以光斑位置为y轴的坐标系内记录每次的测量结果，对坐标系内的点进行线性拟合，得到拟合直线，求取拟合直线的斜率即为第一次施加的荷载下光斑的位移Δx。然后再按步骤4)计算即可得到E。
实施例4
如图9、10所示，本发明的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置与实施例2中的结构相似，区别仅仅在于还设置了反射镜Ⅱ6，反射镜Ⅱ6平行于悬臂梁的初始状态设置，光斑位移测量装置4安装在操作台1上(平行于悬臂梁的初始状态)。
本发明的用悬臂梁或外伸梁测量材料杨氏弹性模量的方法，包括如下步骤：
1)将材料加工成矩形截面梁，然后利用矩形截面梁制成悬臂梁3；
2)利用步骤1)制成本实施例中的悬臂梁组装成利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置；并对利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置进行调节；使得激光器2发出的激光束能够依次经反射镜I5、反射镜Ⅱ6反射到光斑位移测量装置4处。测量反射光斑在标尺上的初始位置。
3)然后在悬臂梁或外伸梁接近自由端处施加荷载，再测量反射光斑在标尺上的位置，得到光斑的位移Δx；
4)根据位移Δx计算悬臂梁或外伸梁每次施加载荷后的自由端转角θ，进而根据悬臂梁或外伸梁自由端转角θ的计算公式、悬臂梁或外伸梁自由端挠度δ的计算公式及惯性矩计算公式，计算得到材料的杨氏弹性模量E。
如图10所示，原点O设为激光束在反射镜I上的入射点作垂线与操作台的交点，x 1＝(H 1+H 2)tanα'。在悬臂梁3上施加荷载P之后，悬臂梁3弯曲，悬臂梁3和反射镜I转动相同 的角度θ，反射光斑移到了x 2处。反射镜I转动角度θ，则反射光方向转动角度2θ，即β’＝α’-2θ。因此有：
Δx＝|x 2-x 1|＝(H 1+H 2)(tanβ'-tanα')＝-2(H 1+H 2)(1+tan 2α')θ+O(θ 2)。
据公式(1)可知，θ＝PL 1 2/(2EI)，得：
Figure PCTCN2022083218-appb-000017
式中：I为悬臂梁的惯性矩，L 1为载荷距离悬臂梁固定端的距离，P为载荷大小，Δx为光斑位移测量装置处光斑位移，x 1为施加载荷前光斑所在的刻度，H 1为激光束在反射镜I上的入射点道反射镜Ⅱ的距离；H 2为反射镜Ⅱ与光斑位移测量装置之间的距离，α'、β'分别为施加载荷前后激光束经反射镜I反射后的反射光束与竖直方向的夹角。
为了获得更精确的施加载荷P下的光斑的位移，可以在悬臂梁上接近自由端处多次施加荷载进行测量光斑位置，多次施加的荷载的大小为等差数列，且相邻的两次施加的荷载的大小与初次施加的荷载相同；第一次施加载荷为P，第二次载荷为2P，第三次载荷为3P……。然后在以测量次数为x轴，以光斑位置为y轴的坐标系内记录每次的测量结果，对坐标系内的点进行线性拟合，得到拟合直线，求取拟合直线的斜率即为第一次施加的荷载下光斑的位移Δx。然后再按步骤4)计算即可得到E。
实施例5
如图11、12所示，本发明的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置与实施例4中的结构相似，区别仅仅在于还设置了反射镜Ⅲ7，反射镜Ⅲ7垂直于悬臂梁3的初始状态设置。
本发明的用悬臂梁或外伸梁测量材料杨氏弹性模量的方法，包括如下步骤：
1)将材料加工成矩形截面梁，然后利用矩形截面梁制成悬臂梁3；
2)利用步骤1)制成本实施例中的悬臂梁组装成利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置；并对利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置进行调节；使得激光器2发出的激光束能够依次经反射镜I5、反射镜Ⅲ7、反射镜Ⅱ6反射到光斑位移测量装置4处。测量反射光斑在标尺上的初始位置。
3)然后在悬臂梁或外伸梁接近自由端处施加荷载，再测量反射光斑在标尺上的位置，得到光斑的位移Δx；
4)根据位移Δx计算悬臂梁或外伸梁每次施加载荷后的自由端转角θ，进而根据悬臂梁或外伸梁自由端转角θ的计算公式、悬臂梁或外伸梁自由端挠度δ的计算公式及惯性矩计算公式，计算得到材料的杨氏弹性模量E。
如图12所示，光斑移动距离表达式为：
Figure PCTCN2022083218-appb-000018
据公式(1)可知，θ＝PL 1 2/(2EI)，得：
Figure PCTCN2022083218-appb-000019
式中：I为悬臂梁3的惯性矩，L 1为载荷距离悬臂梁固定端的距离，P为载荷大小，Δx为光斑位移测量装置处光斑位移，x 1为施加载荷前光斑所在的刻度，H 1为激光束在反射镜I 上的入射点道反射镜Ⅱ的距离；H 2为反射镜Ⅱ与光斑位移测量装置之间的距离，α'、β'分别为施加载荷前后激光束经反射镜I反射后的反射光束与竖直方向的夹角。
为了获得更精确的施加载荷P下的光斑的位移，可以在悬臂梁上接近自由端处多次施加荷载进行测量光斑位置，多次施加的荷载的大小为等差数列，且相邻的两次施加的荷载的大小与初次施加的荷载相同；第一次施加载荷为P，第二次载荷为2P，第三次载荷为3P……。然后在以测量次数为x轴，以光斑位置为y轴的坐标系内记录每次的测量结果，对坐标系内的点进行线性拟合，得到拟合直线，求取拟合直线的斜率即为第一次施加的荷载下光斑的位移Δx。然后再按步骤4)计算即可得到E。
实施例1-5中的悬臂梁3都可以采用外伸梁替代，获得外伸梁施加载荷后的转角，即可根据公式(4)或公式(5)计算得到材料的杨氏弹性模量。
为了使得测量结果更精确，本发明的悬臂梁3包括矩形截面梁和夹具，如图13所示，所述的夹具包括长方体形的上夹具体81和下夹具体82，下夹具体81的上端面设有矩形凹槽84，矩形截面梁的一端嵌装在矩形凹槽84内，上夹具体81与下夹具体82通过定位销83固定联接。构成悬臂梁3后，夹具通过操作台1上的台钳固定在操作台1上。
为了使得测量装置适应不同厚度的样品，操作更方便，本发明的反射镜I5通过光学测量头夹具安装在悬臂梁3或外伸梁上，如图14所示。所述的光学测量头夹具包括夹具体88，夹具体88为长方体结构，夹具体88上设有截面为矩形的夹具槽89，夹具槽的底面平行于夹具体的侧面，夹具槽内设有弹簧片86；反射镜I5贴在夹具体88的顶面上，此图表示的是反射镜I5平行于悬臂梁3或外伸梁底面的情况，当反射镜I5垂直于悬臂梁3或外伸梁底面时，反射镜I5贴在夹具体88的侧面上。夹具体88顶面设有砝码定位挡片87。使用时，悬臂梁3或外伸梁的自由端插入夹具槽89，悬臂梁3或外伸梁的自由端的顶面与夹具槽89顶面贴紧(或悬臂梁3或外伸梁的自由端的底面与夹具槽89底面贴紧)，夹具槽89底面和悬臂梁3或外伸梁的底面之间设置弹簧片86(或夹具槽89顶面和悬臂梁3或外伸梁的顶面之间设置弹簧片86)。

Claims (9)

  1. 一种利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，其特征是：包括激光器、悬臂梁或外伸梁、反射镜I及光斑位移测量装置，所述的悬臂梁或外伸梁的自由端设有反射镜I，激光器发出的激光束能经反射镜I反射至光斑位移测量装置；反射镜I平行或垂直于悬臂梁或外伸梁底面设置，光斑位移测量装置平行或垂直于悬臂梁或外伸梁的初始状态设置。
  2. 根据权利要求1所述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，其特征是：还包括反射镜Ⅱ，反射镜Ⅱ和光斑位移测量装置平行于悬臂梁或外伸梁的初始状态；激光器发出的激光束能依次经反射镜I、反射镜Ⅱ反射至光斑位移测量装置；光斑位移测量装置采用的是光斑位移测量装置、电荷耦合元件或光电位移传感器。
  3. 根据权利要求2所述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，其特征是：还包括反射镜Ⅲ，反射镜Ⅲ垂直于悬臂梁或外伸梁的初始状态设置,激光器发出的激光束能依次经反射镜I、反射镜Ⅲ、反射镜Ⅱ反射至光斑位移测量装置。
  4. 根据权利要求2所述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，其特征是：所述的悬臂梁包括夹具和矩形截面梁，所述的夹具包括长方体形的上夹具体和下夹具体，下夹具体的上端面设有矩形凹槽，矩形截面梁的一端嵌装在矩形凹槽内，上夹具体与下夹具体通过定位销固定联接。
  5. 根据权利要求1所述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，其特征是：反射镜I通过光学测量头夹具安装在悬臂梁或外伸梁上，所述的光学测量头夹具包括夹具体，夹具体为长方体结构，夹具体上设有截面为矩形的夹具槽，夹具槽的底面平行于夹具体的侧面，夹具槽内设有弹簧片；反射镜I贴在夹具体的顶面或侧面上；夹具体顶面设有砝码定位挡片；悬臂梁或外伸梁的自由端插入夹具槽，悬臂梁或外伸梁的自由端的顶面与夹具槽顶面贴紧，夹具槽底面和悬臂梁或外伸梁的底面之间设置弹簧片；或悬臂梁或外伸梁的自由端的底面与夹具槽底面贴紧，夹具槽顶面和悬臂梁或外伸梁的顶面之间设置弹簧片。
  6. 根据权利要求2所述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，其特征是：还包括操作台，所述的悬臂梁或外伸梁和反射镜Ⅱ安装在操作台上，反射镜I安装在悬臂梁或外伸梁上表面，反射镜Ⅱ和激光束位于悬臂梁或外伸梁上方。
  7. 据权利要求1所述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置，其特征是：所述的反射镜I垂直于悬臂梁或外伸梁的底面设置，光斑位移测量装置垂直于悬臂梁或外伸梁初始状态设置；或反射镜I平行于悬臂梁或外伸梁的底面设置，光斑位移测量装置垂直于悬臂梁或外伸梁初始状态设置；或反射镜I平行于悬臂梁或外伸梁的底面设置，光斑位移测量装置平行于悬臂梁或外伸梁初始状态设置。
  8. 一种利用权利要求1-7中任一权利要求所述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置的利用悬臂梁或外伸梁测量材料杨氏弹性模量的方法，包括如下步骤：
    1)将材料加工成矩形截面梁，然后利用矩形截面梁制成悬臂梁或外伸梁；利用悬臂梁或外伸梁组装利用悬臂梁或外伸梁测量材料杨氏弹性模量的装置；
    2)开启激光器，调试标尺位置；测量反射光斑在标尺上的初始位置；
    3)然后在悬臂梁或外伸梁接近自由端处施加荷载，再测量反射光斑在标尺上的位置，得到光斑的位移Δx；
    或在悬臂梁或外伸梁接近自由端处多次施加荷载，多次施加的荷载的大小为等差数 列，且相邻的两次施加的荷载的大小与初次施加的荷载相同；并测量每次施加载荷后光斑位置；然后在以测量次数为x轴，以光斑位置为y轴的坐标系内记录每次的测量结果，对坐标系内的点进行线性拟合，得到拟合直线，求取拟合直线的斜率即为第一次施加的荷载下光斑的位移Δx；4)根据光斑的位移Δx计算悬臂梁或外伸梁每次施加载荷后的自由端转角θ，进而根据悬臂梁或外伸梁自由端转角θ的计算公式、悬臂梁或外伸梁自由端挠度δ的计算公式及惯性矩计算公式，计算得到材料的杨氏弹性模量E。
  9. 根据权利要求8所述的利用悬臂梁或外伸梁测量材料杨氏弹性模量的方法，步骤4)中：
    当反射镜I垂直于悬臂梁的底面设置，光斑位移测量装置垂直于悬臂梁初始状态设置时，材料杨氏弹性模量的计算公式如下：
    Figure PCTCN2022083218-appb-100001
    式中：I为悬臂梁的惯性矩，L 1为载荷距离悬臂梁固定端的距离，P为载荷大小，D为激光束在反射镜I上的入射点与光斑位移测量装置之间的距离，Δx为光斑位移测量装置处光斑位移；
    当反射镜I平行于悬臂梁的底面设置，光斑位移测量装置垂直于悬臂梁初始状态设置时，材料杨氏弹性模量的计算公式如下：
    Figure PCTCN2022083218-appb-100002
    式中：α为施加载荷前激光束经反射镜I反射后的反射光束与水平方向的夹角，L 2为悬臂梁的长度；
    当反射镜I平行于悬臂梁的底面设置，光斑位移测量装置平行于悬臂梁初始状态设置时，材料杨氏弹性模量的计算公式如下：
    Figure PCTCN2022083218-appb-100003
    式中：α'为施加载荷前激光束经反射镜I反射后的反射光束与竖直方向的夹角；
    当反射镜I平行于悬臂梁的底面设置，反射镜Ⅱ和光斑位移测量装置平行于悬臂梁的初始状态时，材料杨氏弹性模量的计算公式如下：
    Figure PCTCN2022083218-appb-100004
    式中H 1为激光束在反射镜I上的入射点道反射镜Ⅱ的距离；H 2为反射镜Ⅱ与光斑位移测量装置之间的距离；
    当反射镜I平行于悬臂梁的底面设置，反射镜Ⅱ和光斑位移测量装置平行于悬臂梁的初始状态,反射镜Ⅲ垂直于悬臂梁的初始状态时，材料杨氏弹性模量的计算公式如下：
    Figure PCTCN2022083218-appb-100005
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