High-precision instrument for measuring extremely small elastic deformation

Abstract

The present invention is a high-precision instrument for measuring elastic minimal deformation for teaching. In the high-precision instrument for measuring elastic minimal deformation, the law of change of the double angle increase or decrease in the law of reflection of light follows the exponential function θ0=2 n+1 2-2, in the exponential function, n represents the number of reflectors, the number of times the light is reflected, and the number of times the double angle is magnified. Each plane mirror can be adjusted in two directions, horizontally and vertically. The reflectors can be n = 3, 4, 5..., and the instrument measurement formula is: Δx = [r / θnR] Δy. When r / R = 1, the formula is simplified to Δx = [1 / θn] Δy. The value of Δx can be known by measuring how many millimeters Δy is on the lens showing the light spot. The accuracy of the instrument can be increased with the increase of plane mirrors. The application of this new technical solution solves the problems of elastic deformation, 10 ‑3 Up to 10 ‑10 Millimeters and below, or even smaller changes can be measured, and changes in micrometers, nanometers, picometers and below can be accurately measured.

Description

Technical field:

[0001] The invention belongs to special equipment for teaching, in particular to special equipment for amplifying and measuring elastic micro deformation. Background technology:

[0002] At present, in the field of teaching, the equipment that can be used to see the elastic micro-deformation of the desktop is Figure 1 (1) Its demonstration effect is a qualitative demonstration rather than a quantitative demonstration, let alone a high-precision measurement. Figure 1 How does the magnification effect of the micro-deformation device come about? The book explains it this way: "Because the distance between the two mirrors is large, the light spot will move noticeably on the scale, showing the deformation of the tabletop. (2) "This is not an exact explanation or theoretical statement. (3) . Using the formula Δx=(r / θnR)Δy (4) analyze Figure 1 The related quantity is that the larger the distance between the two mirrors, the smaller the magnification effect, and the smaller the distance between the two mirrors, the greater the magnification effect. (5) This is contrary to the explanation in the book; the book also does not give the performance parameters of the device. Figure 1 Magnification (r / θn, R) ≤ 200-400 times, small deformation Δx ≥ 10 -2 Deformations smaller than this parameter will not be displayed. Figure 1 The editors also did not realize and understand the exact reason for magnifying small deformations. This is a non-obvious state of the art and application of existing technology. This is the most commonly ignored inherent logic of teaching bias for 40 years. (6) . Summary of the invention:

[0003] (1) Technical problems to be solved: Figure 1 How does the amplification principle occur? Figure 2 High-precision measurement is technically realized. Using the formula Δx=(r / θ n R)Δy analysis Figure 1 Amplification principle: the law of 2-fold angular increase or decrease in each plane mirror reflected light beam (7) The magnification effect caused by the double angle increase or decrease is that each plane mirror reflects the light beam once and magnifies the angle by 2 times. The magnification factor of the two reflections on the two mirrors is 6 times. Figure 2 Based on the 2-fold angular magnification, the exponential function θ is applied. n =2 n+1 -2 (8) The law of change, with its θ n =2 n+1-2 multiples, which is the law that the double angle increase or decrease changes according to an exponential function. This law is applied to the amplification technology of this instrument.

[0004] (2) Technical solution: A reflector having a law of change of double angle increase or decrease in the law of reflection of light applied to a high-precision instrument for measuring extremely small elastic deformation, wherein the law of change of double angle increase or decrease of the reflector follows an exponential function θ n =2 n+1 -2, in the exponential function, n represents the number of reflectors, the number of times the light is reflected, and the number of times the angle is magnified by 2 times. Each plane mirror can be adjusted in two directions, with the horizontal direction as the axis and the vertical direction as the axis, so that it has the function of pointing the reflected light beam. According to the need for accuracy, the number of reflectors can be n=3, 4, 5... Figure 2 Structure: Plane mirror A is fixed in the small frame, the small frame and the middle frame are connected by a vertical axis, there are four middle frames in the large frame, the large frame and the middle frame are connected by a horizontal axis, and the ejector pin is fixed at the vertical axis connection on the middle frame. Figure 3 Adjust the angle of the plane mirror on the vertical axis and fix the ejector pin on the edge of the large frame where the horizontal axis of the large frame and the middle frame are connected. Figure 3 Adjust the angle of rotation of the plane mirror along the horizontal axis. There are two holes with a diameter of 6 mm at 1 cm from the top and bottom of the large frame for inserting metal rods to fix the large frame, so as to increase or decrease the number of large frame combinations. Fig. 9 The middle 14 is a lens with millimeter scale, four frames on its side, and a base on the four frames. Fig.10 Support, there is a knob on the left and right sides of the four frames that emits blue light to mark the light spot displacement spacing. Figure 2 It is composed of 2 reflective surfaces, each of which is composed of one or n large frames connected in series. From one group to n groups is the number of groups of large frames connected in series according to the needs of magnification and accuracy.

[0005] Instrument measurement should be calculated using the formula: Δx=(r / θ n R)Δy, when r / R=1, the formula is simplified to Δx=(1 / θ n )ΔyAt this time, the lens with the scale should be moved to the same distance as the last reflector and the small r so that R = r. At this time, just read the light spot displacement distance Δy on the lens, that is, the distance between the two blue lights in millimeters to know the measured Δx value. The measurement accuracy of the instrument is 10 -3 Up to 10 -10 Millimeters or even smaller changes can be measured, and changes at the micrometer, nanometer, picometer level and below can be accurately measured.

[0006] (3) Beneficial effects: Compared with Figure 1 and Figure 2 Relative desktop deformation θ angle magnification parameter, Figure 1 According to the exponential function θn =2 n+1 -2 means when n=2、θ2=2 2+1 -2=6 times, Figure 2 According to the exponential function θ n =2 n+1 -2 means when n=32, θ 32 =2 32+1 -2=8589934590 times. Description of the drawings:

[0007] Figure 1 It is a device for displaying tiny deformation currently used in teaching (original text).

[0008] Figure 2 This is a schematic diagram of a high-precision instrument for measuring extremely small elastic deformation. The measurement formula Δx=(r / θ n R)Δy calculation.

[0009] Figure 3 1 indicates an automatic ejector with a spring, 2 indicates a manual ejector with a thread, and 3 indicates fixed ejectors 1 and 2. Figure 3 It is a pin for adjusting the angle of the plane mirror in two directions with the horizontal direction and the vertical direction as the axis. 301 is a top view of 3 and 302 is a side view of 3.

[0010] Figure 4 In the middle, A represents a plane mirror, 4 represents a small frame, and plane mirror A is fixed. 401 is a top view of 4, 5 represents a middle frame, and 501 is a top view of 5. The vertical axes of 4 and 5 are connected to adjust the horizontal angle of the plane mirror.

[0011] Figure 5 6 in the middle is composed of A, 1, 2, 3, 4, 5, and 7. 5 and 7 are connected by horizontal axes to adjust the vertical angle of the plane mirror. Figure 5 6 is Figure 7 An enlarged view of the plane mirror in the upper right corner of Figure 9.

[0012] Figure 6 The 7 in the middle represents a large frame, 701 is the side view of 7, and 8 is composed of four 6s forming a large frame.

[0013] Figure 7 In the figure, 9 represents the 16th reflection surface. 9 is composed of four 8s. 901 is the side view of 9 and 902 is the top view of 9.

[0014] Figure 8 10 is the short base of 9, 11 is the top view of 10, 12 is the connecting rod of 9 and 10, and 13 is the top view of 12.

[0015] Fig. 914 is a lens with millimeter scale, 15 is a four-frame frame fixing 14, 16 is a diode fixed on 18, 17 is a knob for adjusting 18 to slide up and down, 19 is a side view of 14, and 20 is a top view of 14.

[0016] : Fig.10 21 is the long base of 14, 22 is the top view of 21, 23 is the connecting rod of 14 and 21, and 24 is the top view of 23. Specific implementation method:

[0017] Figure 2 It is composed of two reflecting surfaces, each of which is composed of multiple groups of large frames connected in series. From one group of large frames to multiple groups of large frames, the number of groups of large frames connected in series is determined according to the needs of magnification and accuracy.

[0018] For example: 1 Take n = 10 lenses, according to the exponential function θ n =2 n+1 -2. There is θ 10 =2 10+1 -2 = 2046 value, i.e. θ 10 =2046, then the magnification of the tiny deformation angle θ of the desktop is 2046 times.

[0019] For example: 2 Take n = 20 lenses, according to the exponential function θ h =2 n+1 -2. There is θ 20 =2 20+1 -2 = 2097150, which is θ 20 =2097150, then the magnification of the slight deformation θ angle of the desktop is 2097150 times.

[0020] For example: 3 Take n = 30 lenses, according to the exponential function θ 30 =2 30+1 -2. There is θ 30 =2 30+1 -2 = 2147483646, which is θ 30 =2147483646, then the magnification of the tiny deformation angle θ of the desktop is 2147483646 times.

[0021] appendix

[0022] (1) Full-time senior high school textbook (compulsory) High School Physics Volume 1 is (published by People's Education Press, second printing in Heilongjiang in June 2003) Figure 1 On page 6 ( Figure 1-10 ).

[0023] (2) and (1) are both on page 6 ( Figure 1-10 ) Experimental explanation full text citation " Figure 1-10It is a device that can display tiny deformations. It can magnify tiny deformations to the point where they can be seen directly. Two plane mirrors M and N are placed on a large table. A beam of light is reflected by the two mirrors in turn and finally hits a scale to form a light spot. Press the tabletop hard and the mirror will tilt in the direction indicated by the arrow. Due to the large distance between the two mirrors, the light spot will move significantly on the scale, showing the deformation of the tabletop.

[0024] (3) Figure 1 The reason for magnifying small deformations is θ n R is determined by the angle θ twice. n =2 n+1 The product of -2 is not caused by r, which is the reason stated in the book: the distance between the two mirrors is large.

[0025] (4) This is a formula I derived, and the formula can be used to accurately analyze Figure 1 and Figure 2 characteristics of change.

[0026] (5) Measurement calculation formula Δx = (r / θnR) Δy

[0027] Δx in the formula: represents the small change in the desktop

[0028] Δy: Right Figure 1 is the displacement of the light spot on the scale; Figure 2 It is the displacement of the light spot on the lens with a millimeter scale, that is, the distance between the two blue lights.

[0029] r: Yes Figure 1 is half the distance between the two plane mirrors; Figure 2 It is half the length of the distance between the two reflecting surfaces composed of 16 plane mirrors.

[0030] R: Yes Figure 1 is the distance from the second plane mirror to the scale; Figure 2 It is the distance from the plane mirror that reflects the light beam for the last time to the lens with a millimeter scale showing the light spot.

[0031] θ n : is an exponential function θ n =2 n+1 The value of -2 is the deflection of the nth reflection angle of the plane mirror and the magnification of the angle θ relative to the desktop deformation. This is also the magnification parameter of the high-precision instrument for measuring the minimum elastic deformation and the general formula for the high-precision instrument for measuring the minimum elastic deformation. 2 is the increase or decrease of the 2-fold angle in each plane mirror's reflected light beam. 2 n+1 The change in the angle of deflection of the light reflected by the n+1th plane mirror is twice the change in the angle follows the exponential function θ n =2 n+1-2 Regularly changing quantity.

[0032] Measurement calculation formula: Δx=(r / θnR)Δy. By deforming the measurement calculation formula, we can see that: Δx / Δy=r / θnR. There is an inverse relationship between r and Δy, that is, the greater the distance between the two mirrors, the smaller the magnification effect. There is also an inverse relationship between Δx and θnR, that is, the greater the magnification, the more it can show tiny deformations. n =6 is constant. When the desktop deformation is less than one hundredth of a millimeter, R must be increased, otherwise the desktop deformation cannot be seen.

[0033] (6) Senior High School Textbook (Trial) Physics (Type A) Volume 1, published by People’s Education Press, first edition in November 1983, reprinted by Heilongjiang People’s Publishing House, second edition in April 1985, Figure 1 On page 14.

[0034] (7) The law of change of the double angle increase or decrease in the law of reflection of light: if the incident angle of light increases or decreases by one angle unit, the sum of the incident angle and the reflection angle will increase or decrease by two angle units.

[0035] (8) Exponential function θ n =2 n+1 -2 is the general formula, which is the known magnification parameter and exponential function θ before measuring the minimum deformation of the desktop n =2 n+1 θ in -2 n , 2, 2 n+1 , respectively represent the multiples of the deflection angle of the light reflected by the nth plane mirror relative to the minimum deformation angle θ of the desktop, 2 is the increase or decrease of the double angle in the light beam reflected by each plane mirror, and 2 n+1 The increase or decrease of the angle twice the deflection angle of the light reflected by the n+1th plane mirror follows the exponential function θ n =2 n+1 -2 is a regular variation of the quantity.

[0036] Measurement calculation formula Δx = (r / θnR) Δy; general formula for the magnification of high-precision instruments for measuring extremely small elastic deformation θ n =2 n+1 -2The derivation process is as follows:

[0037] (1): Based on the law of reflection of light and the arc length formula, the measurement calculation formula is derived. Let ΔX = aΔY. If it holds, then a can be calculated.

[0038] ΔX represents the change in the slight deformation of the desktop

[0039] ΔY represents the change in the displacement of the light spot on the scale

[0040] a represents the substitution coefficient

[0041] Arc length L = αR, Δx and Δy can be understood as the change in arc length

[0042] Therefore, Δx=1=α`r, Δy=L=αR

[0043] r represents half the distance between the two plane mirrors.

[0044] R is the distance from the light spot reflected by the second plane mirror to the scale.

[0045] ΔX=aΔY Transform the formula to a=ΔX / ΔY=α`r / αR

[0046] When r=R, we get a=α` / α=?

[0047] Analyze according to the law of reflection of light Figure 1 So: a = α` / α = 1 / 6

[0048] ∴ΔX=aΔY=(1 / 6)ΔY=(1 / θ6)ΔY=ΔY / θ6 This formula is the measurement calculation formula

[0049] (2): Derivation of the general formula for the magnification factor, i.e., the exponential function θ n =2 n+1 -2 According to the law of reflection of light, the recursive formula is obtained:

[0050] ∵θ1=2

[0051] Again, ∵θ n =2(θ n-1 +1), (n∈Z)

[0052] According to the recursive formula: Find the general formula θ n =?

[0053] Solution: Let θ n + k = 2 (θ n-1 +k), where k is a constant

[0054] Then θ n =2θ n-1 +k, compared with the known recursive formula, k=2

[0055] ∴The sequence {θ n +2} is a geometric number with (θ1+2)=4 as the first term and 2 as the common ratio

[0056] ∴θ n +2=4◇2 n-1 =2 n+1

[0057] ∴θ n =2 n+1 -2 This formula is the general formula; in mathematics, it is also called an exponential function

Claims

1. An exponential function θ n =2 n+1 -2 regular changes in the characteristics of the 2 times the angular increase and decrease of the reflector is used to measure the elastic minimal deformation of the high-precision instrument, the use of 2 times the angular increase and decrease of the reflector, the characteristics of the reflector The variation law of the 2-fold angular increase or decrease follows the exponential function θ n =2 n+1 -2, in the exponential function, n represents the number of reflectors, the number of times the light is reflected, and the number of times the angle is magnified by two times.

2. According to claim 1, an exponential function θ n =2 n+1 -2 regular changes are characterized by a 2-fold angular increase and decrease mirror used for measuring elastic minimal deformation high-precision instruments, characterized by The plane mirror is fixed in the small frame, and the small frame and the middle frame are connected by a vertical axis.

3. According to claim 1 or 2, according to the exponential function θ n =2 n+1 -2 regular changes in the characteristics of the 2 times the angle of the reflector used to measure the elastic deformation of the small high-precision instrument, the characteristics of which are There are 4 middle frames inside the big frame, and the big frame and the middle frames are connected by a horizontal axis.

4. According to claim 1 or 3, according to the exponential function θ n =2 n+1 -2 regular changes in the characteristics of the 2 times the angle of the reflector used to measure the elastic deformation of the small high-precision instrument, the characteristics of which are A pin (3) is fixed at the vertical axis connection position on the upper side of the middle frame to adjust the angle of rotation of the plane mirror with the vertical axis.

5. An exponential function according to claim 1 or 4 θn=2 n+1 -2 regular changes are characterized by a 2-fold angular increase and decrease mirror used for measuring elastic minimal deformation high-precision instruments, characterized by A thimble (3) is fixed on the edge of the large frame at the horizontal axis connection between the large frame and the middle frame to adjust the angle of rotation of the plane mirror along the horizontal axis.

6. A method according to claim 1 or 5 according to an exponential function θ n =2 n+1 -2 regular changes are characterized by a 2-fold angular increase and decrease mirror used for measuring elastic minimal deformation high-precision instruments, characterized by There are two holes with a diameter of 6 mm at 1 cm from the upper and lower edges of the large frame for passing metal rods to fix the large frame, so as to increase or decrease the number of groups of the large frame combination.

7. The method according to claim 1, wherein the exponential function θ n =2 n+1 -2 regular changes are characterized by a 2-fold angular increase and decrease mirror used for measuring elastic minimal deformation high-precision instruments, characterized by A lens has millimeter scales on it and four frames on its side, which are supported by a base. On the left and right sides of the four frames, there is a high-brightness diode that emits blue light to mark the spacing knob of the light spot displacement.

8. The method according to claim 1, wherein the exponential function θ n =2 n+1 -2 regular changes are characterized by a 2-fold angular increase and decrease mirror used for measuring elastic minimal deformation high-precision instruments, characterized by The high-precision instrument for measuring elastic minimal deformation consists of two reflective surfaces, each of which is composed of one or n large frames connected in series. From one group to n groups is the number of groups of large frames connected in series according to the needs of magnification and accuracy. The measurement is calculated using the formula Δx=(r / θ n R)Δy calculation.

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