Application of GTGS-1 weak vibration tester

GTGS-1 weak vibration tester

Double grating measurement of weak vibration displacement experiment

Precision measurement has always played an important role in the field of automation control. Among them, photoelectric measurement is often used in measurement applications because of its good precision and accuracy, plus the advantages of light weight and no noise. The method of converting mechanical displacement signals into photoelectric signals, grating displacement measurement technology has been widely used in digital measurement of length and angle, motion comparison measurement, numerical control machine tools, stress analysis and other fields.

Doppler frequency shifting physical properties are also widely used, such as medical ultrasound diagnostic equipment, measuring the velocity and direction of sea currents in various depths of seawater, satellite navigation and positioning systems, tuning of musical instruments in music, etc.

The double-grating weak vibration experiment instrument is used as the tuning fork vibration analysis, micro-amplitude (displacement), measurement and light-shooting research in the mechanical experiment project.

First, the purpose of the experiment

1. Understand the principle of using the Doppler shift of light to form a light beat and use it to measure the beat frequency

2. Learn to use a method to accurately measure weak vibration displacements

3. Measuring the micro-amplitude of the tuning fork vibration using a double-grating weak vibration tester

Second, technical parameters

Experimental instruments: laser source, signal generator, frequency meter (the above instruments are integrated in the measuring instrument box)

Laser: λ = 635nm, 0 ~ 30mw

Signal generator: 120Hz ~ 950Hz, 0.1Hz fine-tuning, 0 ~ 650mw output

Frequency meter: (1Hz ~ 999.9Hz) ± 0.1Hz

Tuning fork resonant frequency: about 500Hz

Third, the experimental principle

1. Doppler shift of the displacement grating

The Doppler effect refers to the change of the frequency of the light wave received by the receiver and the frequency of the light source caused by the relative motion between the light source, the receiver, the propagation medium or the intermediate reflector. The resulting frequency change is called Doppler. Frequency shift.

Since the medium has different phase delay effects on light propagation, for the two identical monochromatic lights, if the initial time is the same phase, the same geometric path is passed, but in the medium of different refractive index, the phase of the two lights is emitted. However, for the phase grating, when the laser plane wave is perpendicularly incident, the plane wave of the incident light wave becomes the curved wavefront when the light wave is delayed due to the different optical density and the light-scattering medium portion of the phase grating. figure 1.

Figure 1 shows the curved wavefront

Figure 2 The amount of displacement of the diffracted ray in the y direction

The plane wave of the laser is incident perpendicularly to the grating. Due to the diffraction effect of each slit on the grating and the interference between each slit, the intensity of the light passing through the grating periodically changes.

In the far field, we can use the well-known grating

The diffraction equation is the equation (1) to represent the principal maximum position: dsin θ = ± kλ k = 0, 1, 2, ... (1)

Where: the integer k is the main maximum series, d is the grating constant, θ is the diffraction angle, and λ is the wavelength of the light wave.

If the grating moves at a velocity v in the y direction, the wavefront of the light emerging from the grating also moves at a velocity v in the y direction. Therefore, at different times, corresponding to the same order of diffracted light, when it exits the grating, The y direction also has a displacement of vt, as shown in Figure 2.

This displacement corresponds to the amount of change in the phase of the outgoing light wave Δφ(t)

(2)

Substituting (1) into (2):

(3)

In the middle

If the laser exits from a stationary grating; the optical vector equation is

When the laser is emitted from the corresponding moving grating, the electric wave vector equation is (4)

Obviously, the moving phase grating k-order diffracted light wave has a Doppler shift of ωa=ω0+kωd with respect to the stationary phase grating, as shown in Fig. 3.

2. Acquisition and detection of light beats

The optical frequency is very high in order to be in the optical frequency In the detection of Doppler frequency shift, the method of "shooting" must be adopted, that is, the frequency-shifted and un-shifted beams are superimposed in parallel to each other to form a light beat. Since the beat frequency is low, it is easy to measure. The Doppler shift can be detected by the beat frequency.

The method of forming a light beat in this experiment is to use two identical gratings to be in close contact with each other, one piece B is stationary, and the other piece A is relatively moved. The diffracted light formed by the laser passing through the double grating is the parallel superposition of two or more kinds of beams. The Doppler shift of the k-th order diffracted light wave formed is shown in Fig. 4.

Grating A by speed Movement, frequency shifting, and grating B is stationary, only diffracting, so the diffracted light emitted through the double grating contains two or more different frequency components and parallel beams. Due to the double grating, the laser beam With a certain width, the beam can be superimposed in parallel, thus forming a light shot directly and simply. As shown in Fig. 5.

When the diffracted light formed by the laser passing through the double grating is superimposed into a photo-shooting signal, after the photo-shooting signal enters the photodetector, the output current can be obtained by the following relationship:

Beam 1:

Beam 2: (take k=i)

Photocurrent:

(6)

Where ξ is the photoelectric conversion constant

Because the light wave frequency ω0 is very high, in the first, second and fourth terms of equation (6), the photodetector cannot react, and the third term of equation (6) is the beat frequency signal. Because the frequency is low, the photodetector can do Corresponding response. Its photocurrent

SHAPE \* MERGEFORMAT beat frequency F is:

(7)

among them For grating density, this experiment

3. Detection of weak vibration displacement

From equation (7), F beats and optical frequencies Irrelevant, and when the grating density When it is a constant, it is only proportional to the moving speed of the grating. If the grating is glued to the tuning fork, then It is periodically changed. Therefore, the frequency of the beat signal is also changed with time. The amplitude of the displacement of the weak vibration is:

(8)

Where T is the tuning fork vibration period, It indicates the number of beat waves in T/2. Therefore, as long as the wave number of the beat wave is measured, the displacement amplitude of the weak vibration can be obtained.

The number of waveforms consists of the complete waveform number, the first number of waves, and the mantissa of the wave. According to the display on the oscilloscope, the fractional part of the waveform is not the first and last digits of a complete waveform, but at both ends of the wave group. Can be converted by inverse sine function

The fractional part of the waveform, that is, the number of waveforms = the number of integer waveforms + the first and last digits of the wave, 1/2 or 1/4 or 3/4 of the waveform fraction +

Where a and b are the ratio of the amplitude of the first and last amplitudes of the wave group and the amplitude of the complete waveform at that location. The wave group refers to the waveform within T/2, and if the number of fractional waveforms is 1/2 or more, the waveform is 0.5. The waveform is 0.25, and the full 3/4 waveform is 0.75.

Figure 6 (a) single trace display of the beat wave

Figure 6 (b) Double trace shows the beat wave and tuning fork drive wave

Example: As shown in Fig. 7, in T/2, the number of integer waveforms is 4, and the fractional fraction is full 1/4 waveform, b=h/H=0.6/1=0.6.

and so

According to Equation 8, the amplitude A is obtained as:

Similarly, in Figure 6(b), the number of beat frequency waveforms is 21.5, and the amplitude can be obtained.

Fourth, the experimental device

X—trigger signal output, Y2—excitation waveform output, Y1—beat frequency waveform output

Figure 8 experiment panel

Figure 9 Experimental platform

Fifth, the experimental content

1. Preview "Application of Oscilloscope", familiar with the use of dual-track oscilloscope.

2. Connect the Y2 and X external triggers of the oscilloscope to the output sockets of Y1 and X of the dual-grating weak vibration tester to turn on the respective power supplies.

3. Geometric light path adjustment.

Carefully remove the "static grating frame", (non-erasable grating) slightly loosen the locking handwheel on the top of the laser, carefully move the laser up and down and left and right by hand, let the light beam pass through the center of the hole where the static grating frame is mounted. Adjust the photocell Hold the handwheel so that a certain level of diffracted light falls into the small hole in front of the photocell. Lock the laser.

4. Double grating adjustment.

Carefully install the “static grating frame”. The static grating should be as close as possible to the moving grating. Be careful not to let them touch each other! (Pitch 1mm or so) Use a white paper as the observation screen, place the light spot on the front of the photocell holder, slowly rotate the grating frame, and carefully observe the adjustment so that the two beams overlap as much as possible. Remove the observation screen and gently tap the tuning fork to adjust The oscilloscope, in conjunction with adjusting the laser output power, should see a very beautiful beat wave.

5. Tuning fork resonance adjustment.

First place the “Power” knob near 4-5 o'clock, adjust the “Frequency” coarse adjustment knob, (500Hz), then adjust the “Frequency” fine adjustment knob to make the tuning fork resonate. When adjusting, gently press the top of the tuning fork. Find the adjustment direction. If the tuning fork resonance is too strong, turn the "power" knob to the small clock point, so that the wave number of the T/2 internal light shot seen on the oscilloscope is about 15. Record the vibration frequency of the tuning fork at this time. The number of complete waves on the screen, the first and last values ​​of a complete waveform, and the amplitude values ​​corresponding to the complete waveform.

6. Measure the resonance curve when the external force drives the tuning fork.

Fix the position of the “power” knob. In the vicinity of the tuning fork resonance point, carefully adjust the “frequency” knob to measure the vibration frequency of the tuning fork and the corresponding signal amplitude. The frequency interval can be 0.1HZ, for example, 8 points can be selected to measure the corresponding The number of waves, from equation (8), calculates their respective amplitudes A.

7. Keep the signal output power unchanged, stick the plasticine to the effective mass of the tuning fork one by one, and adjust the “frequency” fine adjustment knob to study the changing trend of the resonance curve.

8. The laser power is generally adjusted to the middle, and it does not need to be adjusted frequently.

Sixth, data processing

1. Find the average frequency of the beat signal when the tuning fork is resonant;

2. Find the displacement amplitude of the tuning fork when it is weakly vibrating at the resonance point;

3. Draw the frequency-amplitude curve of the tuning fork on the coordinate paper;

4. Make the harmonic curve of the tuning fork with different effective mass, and qualitatively discuss its changing trend.

Seven, complete set

1. Instruction manual 1 copy

2. Product certificate 1 copy

3. Power cord 1

4.Q9 seat line 2

5. Headphones 1 pair

6. Fuse (0.5A/220V) 2

Eight, after-sales service

Under the conditions of product use, within 12 months after arrival, the factory is responsible for free maintenance and replacement of the product due to product quality problems. After 12 months, the machine is faulty or improperly used, resulting in damage. The factory will still give good service.

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