CN103940677A - Device and method for measuring Young modulus by virtue of linear-frequency-modulation multi-beam laser heterodyne - Google Patents

Abstract

The invention relates to a device and a method for measuring Young modulus by virtue of a linear-frequency-modulation multi-beam laser heterodyne, solving the problem that the measurement accuracy is low because the indirect measurement quantity is large and data processing is complex in an existing Young modulus measurement method. According to the device and the method, to-be-measured parameter information is modulated into heterodyne signals by virtue of a linear frequency modulation technique and can be accurately acquired by demodulating laser heterodynes; when the linear expansion coefficient of a sample is measured, a plurality of frequency values including length variable quantities of metal are simultaneously obtained in a frequency domain by utilizing the method, and multiple length variable quantities are obtained after the signals are demodulated, and the accurate variable quantity of the length of the sample along with the changing of the temperature can be obtained by virtue of weighted average treatment; by taking carbon steel wire as an example to carry out a simulation experiment, the relative error of the Young modulus measurement is only 0.09%, and the measuring accuracy is remarkably improved. The device and the method are suitable for measuring the Young modulus.

Description

Linear frequency modulation multi-beam laser heterodyne is measured device and the measuring method of Young modulus

Technical field

The present invention relates to a kind of device and measuring method of measuring Young modulus.

Background technology

Young's modulus of elasticity has reflected the relation of material deformation and internal stress, when being subject to External Force Acting, material must there is deformation, its inside is stressed and the ratio of strain (being relative deformation) is called Young's modulus of elasticity, it is an important physical amount that characterizes solid material character, is important parameter when mechanical component selection in engineering.In recent years, in engineering measuring technology, feed rod thick stick method, Fiber Optical Sensor Based, CCD method, interferometric method, pulling method and the diffraction approaches etc. of adopting more, but the indirect measuring amount of these methods is more, accidental error is larger, and need carry out a large amount of data processings, therefore, the measuring accuracy of these methods is lower, cannot meet the requirement of current high-acruracy survey.

Summary of the invention

The present invention is that the indirect measuring amount of the method in order to solve existing measurement Young's modulus of elasticity is many, data processing complex causes the problem that measuring accuracy is low, thereby provides a kind of linear frequency modulation multi-beam laser heterodyne to measure device and the measuring method of Young modulus.

Linear frequency modulation multi-beam laser heterodyne is measured the device of Young modulus, and it comprises linear frequency modulation laser instrument 1, the first plane mirror 2, thin glass plate 3, the second plane mirror 4, counterweight 5, tinsel 6, convergent lens 7, photodetector 8, wave filter 9, amplifier 10, A/D change-over circuit 11 and DSP12;

One end of tinsel 6 is fixed on support, and the other end of tinsel 6 is fixedly connected with counterweight 5, and the second plane mirror 4 is posted in the bottom of described counterweight 5, and described the second plane mirror 4 parallel beneath are placed with thin glass plate 3 and have spacing;

The laser that linear frequency modulation laser instrument 1 is launched reflexes to the lower surface of thin glass plate 3 through the first plane mirror 2, be divided into reflected light and transmitted light through thin glass plate 3, described transmitted light is incident to the lower surface of the second plane mirror 4, the lower surface of this second plane mirror 4 and thin glass plate 3 will obtain No. two reflected light of multi beam after this transmitted light multiple reflections, No. two reflected light of this multi beam are after thin glass plate 3 transmissions, successively be incident to convergent lens 7 with a reflected light, and described convergent lens 7 is assembled to the photosurface of photodetector 8, the electrical signal of described photodetector 8 connects the electric signal input end of wave filter 9, the electrical signal of described wave filter 9 connects the electric signal input end of amplifier 10, the electrical signal of described amplifier 10 connects the electric signal input end of A/D change-over circuit 11, the electrical signal of described A/D change-over circuit 11 connects the electric signal input end of DSP12.

Linear frequency modulation multi-beam laser heterodyne is measured the Young modulus measuring method of the device of Young modulus, and the detailed process of this measuring method is:

Step 1, the upper end of tinsel 6 is fixed on support, counterweight 5 is fixed in lower end, the upper surface of the second plane mirror 4 is affixed on the lower surface of counterweight 5;

Step 2, stable and while making tinsel 6 in vertical direction when posting the counterweight 5 of the second plane mirror 4, thin glass plate 3 is placed in to the front 30mm of the second plane mirror 4 place, utilize two-dimentional adjustment rack to regulate thin glass plate 3, make thin glass plate 3 parallel with the second plane mirror 4;

Step 3, open linear frequency modulation laser instrument 1, make laser that linear frequency modulation laser instrument 1 sends with θ ₀angle is that incident angle is incident to thin glass plate 3;

Step 4, obtain total light field E of the laser beam that is incident to photodetector 8 _Σ(t):

E _Σ(t)＝E ₁(t)+E ₂(t)+…+E _m(t)+…；

Wherein: E ₁(t) be the reflection light field of laser beam after thin glass plate 3 lower surface reflections, and press formula

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L}{c})+k{(t-\frac{L}{c})}^2\left]\right\}$ Obtain;

Wherein: α ₁for coefficient, α ₁=γ, γ is the reflectivity of thin glass plate 3, E ₀for incident field amplitude, ω ₀for incident field angular frequency, t is the time, the rate of change that k is modulating bandwidth, and t is the frequency modulation cycle, and △ F is modulating bandwidth, and c is the light velocity, and L is the light path that arrives thin glass plate 3 lower surfaces;

E ₂(t) to E _m(t) for laser beam is after thin glass plate 3 upper surface multiple reflections and transmit the light field of thin glass plate 3 lower surfaces, and press formula

$\left\{\begin{array}{c}{E}_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+2\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+2\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{2{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\\ E_3\left(t\right)={\mathrm{\α}}_3{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+4\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+4\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{4{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\\ \·\·\·\\ E_m\left(t\right)={\mathrm{\α}}_m{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+2(m-1)\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+2(m-1)\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{2(m-1){\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\end{array}\right.$

Obtain;

Wherein: α ₂for coefficient, and α ₂=β ²γ ' ..., α _m=β ²γ ' ^m-1γ ^m-2β in formula is thin is the transmissivity of glass plate 3, γ ' is the reflectivity of the second plane mirror 4, d is the distance of glass plate 3 and the second plane mirror 4, θ is that incident light transmits the refraction angle after thin glass plate 3, n is the refractive index of medium between thin glass plate 3 and the second plane mirror 4, and the value of m is 2,3

The photosurface receiving optical signals of step 5, photodetector 8, and be translated into photocurrent, the expression formula of described photocurrent is:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}{[E_1\left(t\right)+E_2\left(t\right)+\·\·\·+E_m\left(t\right)+\·\·\·][E_1\left(t\right)+E_2\left(t\right)+\·\·\·+E_m\left(t\right)+\·\·\·]}^{*}\mathrm{ds};$

Wherein: e is electron charge, Z is the intrinsic impedance of photodetector 8 surface dielectrics, and η is quantum efficiency, and D is the area of photodetector 8 photosurfaces, and h is Planck's constant, and v is laser frequency, represents complex conjugate No. *;

The photocurrent that step 6, photodetector 8 are exported is by wave filter 9 filtering, remove DC terms, retain the photocurrent that exchanges item, be the electric current of intermediate frequency of linear frequency modulation multi-beam laser heterodyne second harmonic signal, described electric current of intermediate frequency is sent into DSP12 and is processed after amplifier 10 and A/D change-over circuit 11;

The electric current of intermediate frequency of described linear frequency modulation heterodyne signal is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))\mathrm{ds};$

After arranging, obtain:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos (\frac{4\mathrm{pknd}\cos \mathrm{\θ}}{c}t-\frac{4\mathrm{pknd}\cos \mathrm{\θ}(L+\mathrm{nd}\cos \mathrm{\θ})}{c^2});$

Wherein: p and j are positive integer;

The electric current of intermediate frequency of step 7, linear frequency modulation multi-beam laser heterodyne second harmonic signal that step 6 is obtained carries out Fourier transform, obtains the frequency f of linear frequency modulation multi-beam laser heterodyne signal _p:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d;$

Wherein: K _pfor scale-up factor, and

According to the frequency f of linear frequency modulation multi-beam laser heterodyne signal _pobtain the distance d of thin glass plate 3 and the second plane mirror 4;

The quality m of step 8, change counterweight 5, the distance d of thin glass plate 3 and the second plane mirror 4 changes thereupon, obtains change of distance amount Δ d, obtains the elongation Δ l of tinsel 6, the equal and opposite in direction of the size of Δ l and Δ d according to change of distance amount Δ d;

Step 9, obtain the Young's modulus of lasticity E of tinsel 6:

$E=\frac{\mathrm{Fl}}{\mathrm{S\Δl}}=\frac{4\mathrm{mgl}}{{\mathrm{\πr}}^2\mathrm{\Δl}};$

Wherein: F is the pulling force of tinsel 6 on prolonging direction, and l represents the raw footage of tinsel 6, and S represents the sectional area of tinsel 6, and r represents the mean diameter of tinsel 6.

The invention has the beneficial effects as follows: the present invention is based on heterodyne technology, propose a kind of high-precision linear frequency modulation multi-beam laser heterodyne and measured the method for Young modulus, utilize linear frequency modulation technology that parameter information to be measured is modulated in heterodyne signal, by can accurately obtaining parameter information to be measured to the demodulation of heterodyne.

The present invention will treat that measurement information is successfully modulated in the difference on the frequency of linear frequency modulation multi-beam laser heterodyne signal by linear frequency modulation technology.In measurement linear expansion of sample coefficient process, the method has obtained multiple frequency values of the information that comprises metal length variable quantity simultaneously at frequency domain, after signal demodulation, obtain multiple length variations amounts, can obtain accurate sample length variation with temperature amount by weighted mean.Carry out emulation experiment as an example of carbon steel wire example, the relative error that Young modulus is measured is only 0.09%, has significantly improved measuring accuracy.

Compared with other measuring methods, the advantage such as linear frequency modulation multi-beam laser heterodyne method surveys Young modulus and have that high room and time resolution, measuring speed are fast, the linearity good, antijamming capability is strong, dynamic response is fast, reproducible and measurement range is large; Experimental provision is simple in structure, power consumption is little, easy to operate; Experimental result error is little, the high many-sided advantage of precision.Meanwhile, because the method experimental phenomena is obvious, experimental data is reliable, so can be widely used in the engineering design fields such as coherent laser windfinding radar.

Brief description of the drawings

Fig. 1 is the structural representation that linear frequency modulation multi-beam laser heterodyne is measured the device of Young modulus;

Fig. 2 is linear frequency modulation multi-beam laser principle of interference schematic diagram;

Fig. 3 is the Fourier transform spectrogram of linear frequency modulation multi-beam laser heterodyne signal, and horizontal ordinate is frequency, and ordinate is output amplitude;

Fig. 4 is in the different situation of counterbalance mass, the frequency spectrum that carbon steel wire length variations amount is corresponding, and wherein: wherein: curve a represents the frequency spectrum that 0.25kg counterweight is corresponding, curve b represents the frequency spectrum that 2kg counterweight is corresponding.

Embodiment

Embodiment one: present embodiment is described below in conjunction with Fig. 1, linear frequency modulation multi-beam laser heterodyne described in present embodiment is measured the device of Young modulus, and it comprises linear frequency modulation laser instrument 1, the first plane mirror 2, thin glass plate 3, the second plane mirror 4, counterweight 5, tinsel 6, convergent lens 7, photodetector 8, wave filter 9, amplifier 10, A/D change-over circuit 11 and DSP12;

One end of tinsel 6 is fixed on support, and the other end of tinsel 6 is fixedly connected with counterweight 5, and the second plane mirror 4 is posted in the bottom of described counterweight 5, and described the second plane mirror 4 parallel beneath are placed with thin glass plate 3 and have spacing;

The laser that linear frequency modulation laser instrument 1 is launched reflexes to the lower surface of thin glass plate 3 through the first plane mirror 2, be divided into reflected light and transmitted light through thin glass plate 3, described transmitted light is incident to the lower surface of the second plane mirror 4, the lower surface of this second plane mirror 4 and thin glass plate 3 will obtain No. two reflected light of multi beam after this transmitted light multiple reflections, No. two reflected light of this multi beam are after thin glass plate 3 transmissions, successively be incident to convergent lens 7 with a reflected light, and described convergent lens 7 is assembled to the photosurface of photodetector 8, the electrical signal of described photodetector 8 connects the electric signal input end of wave filter 9, the electrical signal of described wave filter 9 connects the electric signal input end of amplifier 10, the electrical signal of described amplifier 10 connects the electric signal input end of A/D change-over circuit 11, the electrical signal of described A/D change-over circuit 11 connects the electric signal input end of DSP12.

Embodiment two: the device that present embodiment is measured Young modulus to the linear frequency modulation multi-beam laser heterodyne described in embodiment one is further qualified, in present embodiment, the second plane mirror 4 is 30mm with the parallel distance of thin glass plate 3.

Embodiment three: the device that present embodiment is measured Young modulus to the linear frequency modulation multi-beam laser heterodyne described in embodiment one is further qualified, and in present embodiment, the length of tinsel 6 is 1m, and diameter is greater than 0.25mm and is less than 1mm.

Embodiment four: below in conjunction with Fig. 1 and Fig. 2, present embodiment is described, linear frequency modulation multi-beam laser heterodyne is measured the Young modulus measuring method of the device of Young modulus, and the detailed process of this measuring method is:

Step 1, the upper end of tinsel 6 is fixed on support, counterweight 5 is fixed in lower end, the upper surface of the second plane mirror 4 is affixed on the lower surface of counterweight 5;

Step 2, stable and while making tinsel 6 in vertical direction when posting the counterweight 5 of the second plane mirror 4, thin glass plate 3 is placed in to the front 30mm of the second plane mirror 4 place, utilize two-dimentional adjustment rack to regulate thin glass plate 3, make thin glass plate 3 parallel with the second plane mirror 4;

Step 3, open linear frequency modulation laser instrument 1, make laser that linear frequency modulation laser instrument 1 sends with θ ₀angle is that incident angle is incident to thin glass plate 3;

Step 4, obtain total light field E of the laser beam that is incident to photodetector 8 _Σ(t):

E _Σ(t)＝E ₁(t)+E ₂(t)+…+E _m(t)+…；

Wherein: E ₁(t) be the reflection light field of laser beam after thin glass plate 3 lower surface reflections, and press formula

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L}{c})+k{(t-\frac{L}{c})}^2\left]\right\}$ Obtain;

Wherein: α ₁for coefficient, α ₁=γ, γ is the reflectivity of thin glass plate 3, E ₀for incident field amplitude, ω ₀for incident field angular frequency, t is the time, the rate of change that k is modulating bandwidth, and t is the frequency modulation cycle, and △ F is modulating bandwidth, and c is the light velocity, and L is the light path that arrives thin glass plate 3 lower surfaces;

E ₂(t) to E _m(t) for laser beam is after thin glass plate 3 upper surface multiple reflections and transmit the light field of thin glass plate 3 lower surfaces, and press formula

$\left\{\begin{array}{c}{E}_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+2\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+2\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{2{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\\ E_3\left(t\right)={\mathrm{\α}}_3{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+4\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+4\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{4{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\\ \·\·\·\\ E_m\left(t\right)={\mathrm{\α}}_m{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+2(m-1)\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+2(m-1)\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{2(m-1){\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\end{array}\right.$

Obtain;

Wherein: α ₂for coefficient, and α ₂=β ²γ ' ..., α _m=β ²γ ' ^m-1γ ^m-2β in formula is thin is the transmissivity of glass plate 3, γ ' is the reflectivity of the second plane mirror 4, d is the distance of glass plate 3 and the second plane mirror 4, θ is that incident light transmits the refraction angle after thin glass plate 3, n is the refractive index of medium between thin glass plate 3 and the second plane mirror 4, and the value of m is 2,3

The photosurface receiving optical signals of step 5, photodetector 8, and be translated into photocurrent, the expression formula of described photocurrent is:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}{[E_1\left(t\right)+E_2\left(t\right)+\·\·\·+E_m\left(t\right)+\·\·\·][E_1\left(t\right)+E_2\left(t\right)+\·\·\·+E_m\left(t\right)+\·\·\·]}^{*}\mathrm{ds};$

Wherein: e is electron charge, Z is the intrinsic impedance of photodetector 8 surface dielectrics, and η is quantum efficiency, and D is the area of photodetector 8 photosurfaces, and h is Planck's constant, and v is laser frequency, represents complex conjugate No. *;

The photocurrent that step 6, photodetector 8 are exported is by wave filter 9 filtering, remove DC terms, retain the photocurrent that exchanges item, be the electric current of intermediate frequency of linear frequency modulation multi-beam laser heterodyne second harmonic signal, described electric current of intermediate frequency is sent into DSP12 and is processed after amplifier 10 and A/D change-over circuit 11;

The electric current of intermediate frequency of described linear frequency modulation heterodyne signal is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))\mathrm{ds};$

After arranging, obtain:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos (\frac{4\mathrm{pknd}\cos \mathrm{\θ}}{c}t-\frac{4\mathrm{pknd}\cos \mathrm{\θ}(L+\mathrm{nd}\cos \mathrm{\θ})}{c^2});$

Wherein: p and j are positive integer;

The electric current of intermediate frequency of step 7, linear frequency modulation multi-beam laser heterodyne second harmonic signal that step 6 is obtained carries out Fourier transform, obtains the frequency f of linear frequency modulation multi-beam laser heterodyne signal _p:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d;$

Wherein: K _pfor scale-up factor, and

According to the frequency f of linear frequency modulation multi-beam laser heterodyne signal _pobtain the distance d of thin glass plate 3 and the second plane mirror 4;

The quality m of step 8, change counterweight 5, the distance d of thin glass plate 3 and the second plane mirror 4 changes thereupon, obtains change of distance amount Δ d, obtains the elongation Δ l of tinsel 6, the equal and opposite in direction of the size of Δ l and Δ d according to change of distance amount Δ d;

Step 9, obtain the Young's modulus of lasticity E of tinsel 6:

$E=\frac{\mathrm{Fl}}{\mathrm{S\Δl}}=\frac{4\mathrm{mgl}}{{\mathrm{\πr}}^2\mathrm{\Δl}};$

Wherein: F is the pulling force of tinsel 6 on prolonging direction, and l represents the raw footage of tinsel 6, and S represents the sectional area of tinsel 6, and r represents the mean diameter of tinsel 6.

In present embodiment, electric current of intermediate frequency by the linear frequency modulation heterodyne signal in step 6 can be found out, the photocurrent expression formula that photodetector 8 is exported can be seen linear frequency modulation multi-beam laser heterodyne signal frequency crest after Fourier transform on frequency spectrum, by measuring heterodyne signal frequency, just can measure the distance d between thin glass plate 3 and the second plane mirror 4, in the time that d changes, just can be according to the frequency f of the linear frequency modulation multi-beam laser heterodyne signal of step 7 _pmeasure the variation delta d of corresponding d, just can calculate according to the formula in step 9 the Young modulus of tinsel 6 according to Δ d.

Utilize carbon steel wire to verify the accuracy of young modulus measuring device of the present invention and method below.

Utilize MATLAB software simulation to measure former long l=(800.3 ± 0.5) mm, measure the Young modulus of the carbon steel wire of diameter r=0.732mm with screw-thread micrometer, and verify the feasibility of linear frequency modulation multi-beam laser heterodyne measuring method.Gravity acceleration g=9.8m/s ²; Between plane mirror and thin glass plate, the refractive index of medium is got n=1 under normal circumstances; Linear frequency modulation laser wavelength is 1.55 μ m, frequency modulation cycle T=1ms, modulating bandwidth △ F=5GHz.In experimentation, require in elastic limit, institute adds counterbalance mass and is increased to gradually about 2kg according to certain step-length by 0, records not the numerical value Δ l of length variations amount and the quality m of corresponding counterweight in the same time simultaneously.

Can see by emulation, the Fourier transform frequency spectrum of the linear frequency modulation multi-beam laser heterodyne signal obtaining through signal processing as shown in Figure 3, wherein solid line is in laser oblique incidence situation, the Fourier transform frequency spectrum of corresponding linear frequency modulation multi-beam laser heterodyne signal while measuring carbon steel wire length variations amount Δ l; Dotted line is in laser normal incidence situation, the Fourier transform frequency spectrum of corresponding linear frequency modulation multi-beam laser heterodyne signal while measuring carbon steel wire length variations amount Δ l.

From Fig. 3, can also see, in experiment, provide the theoretical curve in the situation of normal incidence, object is: in Linear Frequency Modulation multi-beam laser heterodyne signal spectrum figure, the numerical value of the centre frequency of theoretical curve when the centre frequency of first main peak of linear frequency modulation multi-beam laser heterodyne signal spectrum and normal incidence can simultaneously obtain oblique incidence time, like this, be easy to the ratio of two centre frequencies that obtain: ζ=cos θ;

In the situation that obtaining centre frequency, can calculate the size of laser refraction angle θ after thin glass plate by ζ=cos θ, the thickness of thin glass plate is ignored, and can obtain incidence angle θ according to refraction law ₀size be: pass through try to achieve K _pnumerical value, finally obtain the value of change of distance amount Δ d between thin glass plate and plane mirror, due to Δ d=Δ l, thereby according to $E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L}{c})+k{(t-\frac{L}{c})}^2\left]\right\}$ Can calculate the Young modulus of carbon steel wire in any incident angle situation.

Simultaneously, emulation has obtained in different counterbalance mass situations, while measuring carbon steel wire length variations amount corresponding linear frequency modulation multi-beam laser heterodyne signal Fourier transform frequency spectrum is as shown in Figure 4 for linear frequency modulation multi-beam laser heterodyne, as can be seen from Figure 4, along with the increase of counterbalance mass, the relative position of frequency spectrum moves the i.e. increase frequency along with quality to low frequency direction and reduces.Reason is: in the situation that carbon steel wire Young modulus is constant, counterbalance mass and carbon steel wire length variations amount are proportional, the distance that carbon steel wire length increases between thin glass plate and the second plane mirror thereupon in the time that counterbalance mass increases reduces thereupon, due to frequency f _pand the pass of the distance d between the second plane mirror and lens is f _p=K _pd, K _pin constant situation, frequency f _pbe linear spectrum with d, therefore, when the distance d between the second plane mirror and lens reduces, frequency also reduces the increase along with quality thereupon, and the relative position of frequency spectrum moves to low frequency direction, and Fig. 4 has verified the correctness of theoretical analysis above well.It should be noted that due to heterodyne detection it is a kind of detection mode of nearly diffraction limit, detection sensitivity is high, and therefore the signal to noise ratio (S/N ratio) of the linear frequency modulation multi-beam laser heterodyne signal of Fig. 3 and Fig. 4 is very high.

In theoretical derivation, the impact of the reflected light that thickness of having ignored thin glass plate do not consider device rear surface on linear frequency modulation multi-beam laser heterodyne signal, but in fact the thickness of thin glass plate is the 1mm that is generally less than existing, for overcoming this impact, the frequency distribution of the linear frequency modulation multiple beam heterodyne signal that the reflected light of thin glass plate rear surface produces, near the zero-frequency of frequency spectrum, has added the interference that wave filter just can filtering low frequency heterodyne signal in experiment light path.Utilize above-mentioned linear frequency modulation multi-beam laser heterodyne mensuration, eight groups of data of continuous coverage, have obtained the simulated measurement result of carbon steel wire length variations amount to be measured in different counterbalance mass situations, as shown in table 1.

In the different counterbalance mass situations of table 1, the simulated measurement result of Young modulus

Measure number of times	1	2	3	4	5	6	7
								m(kg)	0.25	0.50	0.75	1.00	1.25	1.50	1.75
Δl(×10 -5m)	2.337857	4.675710	6.963858	9.301719	11.639581	3.977442	16.315297
								E(×10 11N/m 2)	2.025785	1.995551	2.005528	1.995551	2.001525	1.995551	1.999815

Due to the theoretical value E of carbon steel wire Young modulus ₀=2 × 10 ¹¹n/m ², relative error:

$\mathrm{\η}=\frac{|E_0-\stackrel{\‾}{E}|}{\stackrel{\‾}{E}}\×100\%=\frac{|2.001857-2|\×{10}^{11}}{2\×{10}^{11}}\×100\%=0.09\%$

From measurement result, the order of magnitude of this experimental technique error is 10 ^-4, and the degree of accuracy that optical lever method is measured only has 1mm; From experimental data, the relative error of experimental result is 0.09% left and right, realistic conclusion, and the method, compared with few 2 of the indirect measuring amount of optical lever method, has reduced accidental error, has improved measuring accuracy.As can be seen here, the method for utilizing linear frequency modulation multiple beam process of heterodyning to survey Young modulus is feasible.

Claims (4)

1. linear frequency modulation multi-beam laser heterodyne is measured the device of Young modulus, it is characterized in that: it comprises linear frequency modulation laser instrument (1), the first plane mirror (2), thin glass plate (3), the second plane mirror (4), counterweight (5), tinsel (6), convergent lens (7), photodetector (8), wave filter (9), amplifier (10), A/D change-over circuit (11) and DSP (12);

One end of tinsel (6) is fixed on support, the other end of tinsel (6) is fixedly connected with counterweight (5), the second plane mirror (4) is posted in the bottom of described counterweight (5), and described the second plane mirror (4) parallel beneath is placed with thin glass plate (3) and has spacing;

The laser that linear frequency modulation laser instrument (1) is launched reflexes to the lower surface of thin glass plate (3) through the first plane mirror (2), be divided into reflected light and transmitted light through thin glass plate (3), described transmitted light is incident to the lower surface of the second plane mirror (4), the lower surface of this second plane mirror (4) and thin glass plate (3) will obtain No. two reflected light of multi beam after this transmitted light multiple reflections, No. two reflected light of this multi beam are after thin glass plate (3) transmission, successively be incident to convergent lens (7) with a reflected light, and described convergent lens (7) is assembled to the photosurface of photodetector (8), the electrical signal of described photodetector (8) connects the electric signal input end of wave filter (9), the electrical signal of described wave filter (9) connects the electric signal input end of amplifier (10), the electrical signal of described amplifier (10) connects the electric signal input end of A/D change-over circuit (11), the electrical signal of described A/D change-over circuit (11) connects the electric signal input end of DSP (12).

2. linear frequency modulation multi-beam laser heterodyne according to claim 1 is measured the device of Young modulus, it is characterized in that: the second plane mirror (4) is 30mm with the parallel distance of thin glass plate (3).

3. linear frequency modulation multi-beam laser heterodyne according to claim 1 is measured the device of Young modulus, it is characterized in that: the length of tinsel (6) is 1m, and diameter is greater than 0.25mm and is less than 1mm.

4. the linear frequency modulation multi-beam laser heterodyne based on claim 1 is measured the Young modulus measuring method of the device of Young modulus, it is characterized in that: the detailed process of this measuring method is:

Step 1, the upper end of tinsel (6) is fixed on support, counterweight (5) is fixed in lower end, and the upper surface of the second plane mirror (4) is affixed on the lower surface of counterweight (5);

Step 2, stable and while making tinsel (6) in vertical direction when posting the counterweight (5) of the second plane mirror (4), thin glass plate (3) is placed in to the front 30mm of the second plane mirror (4) place, utilize two-dimentional adjustment rack to regulate thin glass plate (3), make thin glass plate (3) parallel with the second plane mirror (4);

Step 3, open linear frequency modulation laser instrument (1), make laser that linear frequency modulation laser instrument (1) sends with θ ₀angle is that incident angle is incident to thin glass plate (3);

Step 4, obtain total light field E of the laser beam that is incident to photodetector (8) _Σ(t):

E _Σ(t)＝E ₁(t)+E ₂(t)+…+E _m(t)+…；

Wherein: E ₁(t) be the reflection light field of laser beam after the reflection of thin glass plate (3) lower surface, and press formula

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L}{c})+k{(t-\frac{L}{c})}^2\left]\right\}$ Obtain;

Wherein: α ₁for coefficient, α ₁=γ, γ is the reflectivity of thin glass plate (3), E ₀for incident field amplitude, ω ₀for incident field angular frequency, t is the time, the rate of change that k is modulating bandwidth, and t is the frequency modulation cycle, and △ F is modulating bandwidth, and c is the light velocity, and L is for arriving the light path of thin glass plate (3) lower surface;

E ₂(t) to E _m(t) for laser beam is after thin glass plate (3) upper surface multiple reflections and transmit the light field of thin glass plate (3) lower surface, and press formula

$\left\{\begin{array}{c}{E}_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+2\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+2\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{2{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\\ E_3\left(t\right)={\mathrm{\α}}_3{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+4\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+4\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{4{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\\ \·\·\·\\ E_m\left(t\right)={\mathrm{\α}}_m{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+2(m-1)\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+2(m-1)\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{2(m-1){\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\end{array}\right.$

Obtain;

Wherein: α ₂for coefficient, and α ₂=β ²γ ' ..., α _m=β ²γ ' ^m-1γ ^m-2β in formula is thin is the transmissivity of glass plate (3), γ ' is the reflectivity of the second plane mirror (4), d is the distance of glass plate (3) and the second plane mirror (4), θ is that incident light transmits the refraction angle after thin glass plate (3), n is the refractive index of medium between thin glass plate (3) and the second plane mirror (4), and the value of m is 2,3

The photosurface receiving optical signals of step 5, photodetector (8), and be translated into photocurrent, the expression formula of described photocurrent is:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}{[E_1\left(t\right)+E_2\left(t\right)+\·\·\·+E_m\left(t\right)+\·\·\·][E_1\left(t\right)+E_2\left(t\right)+\·\·\·+E_m\left(t\right)+\·\·\·]}^{*}\mathrm{ds};$

Wherein: e is electron charge, Z is the intrinsic impedance of photodetector (8) surface dielectric, and η is quantum efficiency, and D is the area of photodetector (8) photosurface, and h is Planck's constant, and v is laser frequency, represents complex conjugate No. *;

The photocurrent of step 6, photodetector (8) output is by wave filter (9) filtering, remove DC terms, retain the photocurrent that exchanges item, be the electric current of intermediate frequency of linear frequency modulation multi-beam laser heterodyne second harmonic signal, described electric current of intermediate frequency is sent into DSP (12) and is processed after amplifier (10) and A/D change-over circuit (11);

The electric current of intermediate frequency of described linear frequency modulation heterodyne signal is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))\mathrm{ds};$

After arranging, obtain:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos (\frac{4\mathrm{pknd}\cos \mathrm{\θ}}{c}t-\frac{4\mathrm{pknd}\cos \mathrm{\θ}(L+\mathrm{nd}\cos \mathrm{\θ})}{c^2});$

Wherein: p and j are positive integer;

The electric current of intermediate frequency of step 7, linear frequency modulation multi-beam laser heterodyne second harmonic signal that step 6 is obtained carries out Fourier transform, obtains the frequency f of linear frequency modulation multi-beam laser heterodyne signal _p:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d;$

Wherein: K _pfor scale-up factor, and

According to the frequency f of linear frequency modulation multi-beam laser heterodyne signal _pobtain the distance d of thin glass plate (3) and the second plane mirror (4);

The quality m of step 8, change counterweight (5), the distance d of thin glass plate (3) and the second plane mirror (4) changes thereupon, obtain change of distance amount Δ d, obtain the elongation Δ l of tinsel (6) according to change of distance amount Δ d, the equal and opposite in direction of the size of Δ l and Δ d;

Step 9, obtain the Young's modulus of lasticity E of tinsel (6):

$E=\frac{\mathrm{Fl}}{\mathrm{S\Δl}}=\frac{4\mathrm{mgl}}{{\mathrm{\πr}}^2\mathrm{\Δl}};$

Wherein: F is the pulling force of tinsel (6) on prolonging direction, and l represents the raw footage of tinsel (6), and S represents the sectional area of tinsel (6), and r represents the mean diameter of tinsel (6).