This standard specifies the test method for the material properties of piezoelectric ceramic disc thickness stretching vibration mode. This standard is applicable to the test of the material properties of piezoelectric ceramic disc thickness stretching vibration mode with a mechanical quality factor Qm greater than 50. GB/T 3389.5-1995 Piezoelectric ceramic material performance test method disc thickness stretching vibration mode GB/T3389.5-1995 Standard download decompression password: www.bzxz.net

National Standard of the People's Republic of China
Test methods fnr the properties orplczoclcctric cerarnic
Thickness extension vibration mode for disk1 Subject content and scope of application
This standard specifies the test method for piezoelectric ceramic material properties in thickness extension vibration mode GB/T3389.5—1995
Replaces GB3389.5—82
This standard is applicable to the test of material properties of piezoelectric ceramic disk thickness extension vibration mode with mechanical quality factor Q greater than 50. 2 Reference standards
GB 2413 Piezoelectric ceramic material volume density measurement method GL2414 Piezoelectric ceramic material performance test method Radial stretching vibration of disc, transverse length stretching vibration of long strip GB3389.1 Piezoelectric ceramic material performance test method Common terms and terms GB11320 Test of low mechanical quality factor piezoelectric ceramic material performance 3 Terms, symbols and codes
The terms, symbols and codes used in this standard conform to the provisions of GB 3389.1. 4 Test method
4.1 Principle of the method
Under the condition of electrical short circuit, the frequency equation of the thickness stretching vibration mode of the full-electrode piezoelectric ceramic disc is: Lgx: - X/k?
Where:, a thickness stretching vibration electromechanical coupling coefficient X
a normalized rate.
Where: w—frequency (w—2-element f), rad/s; mt—thickness of the vibrator, mt
—thickness velocity, m/s
f—fundamental or overtone frequency (1=1,3,5,7). Hz
J.—fundamental parallel resonant frequency, Hz.
Solving the transcendental equation (1), a series of roots can be obtained, each of which corresponds to a fundamental frequency. The thickness of the vibrator can be determined by the overtone ratio f%/f. The corresponding relationship between the overtone ratio ./f. and the coupling coefficient is shown in Table 1. The corresponding relationship between the ratio of the overtone frequency to the fundamental parallel resonance frequency ./f and the coupling coefficient is shown in Table 2. Approved by the State Administration of Technology on July 24, 1995 540
Implemented on April 1, 1996
WCB/T 3389.5.--1995
This standard uses the transmission line-overtone ratio method to test the material properties of the thickness stretching vibration mode of the piezoelectric ceramic vibrator, that is, the maximum transmission coefficient fmr of the vibrator is measured by a dynamic transmission network, and ff is the series resonance frequency under a certain approximation, where fm is the maximum admittance (minimum impedance) frequency and f is the series resonance frequency. The maximum conductance frequency can also be determined by the conductivity curve method (see Appendix A) to more accurately determine f. After measuring the fundamental frequency and overtone frequency, calculate the overtone ratio f./f1, determine the electromechanical coupling coefficient K+ from Table 1, and calculate other material parameters of the thickness stretching vibration of the piezoelectric ceramic disc. The symbol of the actual measured resonance frequency is uniformly represented by f in this standard. 4.2 Test conditions
4.2.1 Positive air condition
25-35'℃
4.2.2 Standard atmospheric conditions for test
25±1℃
4.3 Test chamber and its preparation
4.3.1 Sample size and requirements
Relative condensation
48%~80%
Relative humidity
48%~52%
86~-106 kPa
86 106 kPa
The sample is a thin disc, the non-parallelism of the two main planes is not greater than half of the thickness tolerance, and the two main planes are all covered with short metal layers as electrodes, and the potential thickness is polarized. The ratio of the sample diameter 4 to the thickness t should meet the requirements of the single thickness vibration model or, according to different porcelain materials, a certain sample size ratio should be selected. The sample size of general porcelain materials is 6 to 12 in the ratio of diameter d to thickness t. 4.3.2 Preparation of samples before testing
The sample should be kept clean and dry. According to the requirements of different porcelain materials, it should be stored for a certain period of time after polarization and tested after 2 hours under the environment specified in Article 4.2.
4.3.3 Requirements for testing the electric field E at both ends of the sample Capacitance measurement: E≤5V/mm:
Test color and dynamic resistance: L≤30mV/mm. 4.4 Test procedure
4.4.1 Test of resonance frequency f and dynamic resistance Ri4.4.1.1 Test circuit (I)
Test circuit (I) is a voltage source transmission test circuit, as shown in Figure 1, - signal generator, - sample, ① - digital frequency meter, ① - high frequency meter RL - voltage divider resistor, R - voltage divider resistor group: RT - front end resistor, CTL, C - distributed capacitance Figure 1 Constant source transmission test circuit
W.GB/T 3389.5
The resistance of the voltage divider resistor R in the figure should match the output 1H resistance required by the signal generator. Generally, R = R, and the value of the terminal resistor Rr should correspond to the dynamic resistance R of the sample, and the reference value is 5. The distributed capacitance Cn between AB is much lower than the H of the sample. The distributed capacitance (T; the reactance of the distributed electric penetration C1C should satisfy: 1/(·()>>Rl/(-Ct)>>Rs4.4.1.2 Test circuit (-.)
Test circuit (ii) is a constant current source transmission test circuit, as shown in Figure 2. The matching resistor R limit in the figure is matched with the output impedance of the companion generator. The value of the current limiting resistor Rr should be much larger than the dynamic resistance Ri of the sample, and the reference is 1 kP.MR The distributed capacitance between the samples is far lower than that between the samples. The sample is connected to the sample through the electric field CT. Signal generator, ① a digital frequency meter, ① a commercial voltage meter! HF—Wu Xiang, Rr1…matching resistor, Rt—current limiting resistor Figure 2 Constant current source transmission test circuit
4.4.1.3 Test equipment and requirements
Signal generator: high short-term stability of the frequency to be tested, the accuracy of the frequency to be tested, the output waveform is a sine wave. Harmonic peak suppression is less than 30 dB.
Frequency meter: test error is less than +1Hz, input impedance is much larger than signal generator output impedance, and does not affect signal generator output level
Voltmeter: input impedance is greater than 1M0. Input capacitance is not greater than 40pF, frequency range is higher than the frequency to be measured, sensitivity is high. Shielding box and sample holder: The shielding box is connected to each instrument with a short shielded wire. The shielding box should be well grounded, and the connector should use a universal high-break plug. The sample holder should be clamped small, and ensure good contact between the optical device and the sample electrode surface. The diameter of the contact point is .3~1.0Im, and the clamping point is required to be close to the edge of the sample electrode surface. For example, 20×2mm is recommended. The sample clamping point is 2 away from the circular edge. tntn or so. The support should be well insulated
4.4.1.4 Measurement of fundamental frequency
Place the sample under test on the sample support and connect it to the test circuit (1) (test circuit (2)), adjust the signal generator input voltage, keep the test electric field between the two electrodes in accordance with the provisions of 4-3.3, and adjust the signal generator frequency in the frequency band corresponding to the fundamental wave of the sample thickness vibration so that the terminal voltage indicates the maximum (the terminal voltage meter indicator value of the test circuit (2) is the minimum). The frequency with the maximum response is the fundamental wave of the sample thickness extension vibration
4.4.1.5 Measurement of overtone frequency a~
After measuring the fundamental frequency, F, in 4,3.3 The regulation is that within the test electric field range, in the frequency bands near the first, fifth, and seventh waves of the sample thickness vibration, continue to adjust the signal generator frequency to make the voltage meter at the test line (I) terminal indicate the maximum value (the voltage at the test line (I) terminal indicates the minimum value) and obtain the third, fifth, and seventh overtone series resonance frequencies of the sample thickness expansion and contraction vibration modes. 4.4.1.6 Measurement of dynamic resistance R
WGB/T 3389.5—1995
In 4. 4.1. 4.4.2 Measurement of free capacitance T Using a capacitance bridge with a measurement error of no more than +1%, measure the free capacitance CT of the sample at 1 kHz and the test electric field conditions specified in 4, 3, and 3.4.4.3 Measure the sample with a ruler with an accuracy of 0.D1 mm. Measure the sample vertical diameter d and thickness t. 4.5 Calculation and evaluation of test results 4.5.1 Electromechanical coupling coefficient of buoyancy extension vibration The fundamental frequency f of the sample is measured by 4.4.1.1, and the overtone frequencies fa- and f- of the sample are measured by 4.4.1.5. Then, calculate the ratio of overtone to fundamental frequency f/fa.fs/ftfa/f. respectively: and find the corresponding coupling coefficient in Table 1. - Generally speaking, the coupling number group measurement and calculation can be obtained by using three overtone ratios of the same test pair to obtain three group values, and taking the average value can improve and ensure the accuracy of the measurement and calculation results.
4.5.2 Calculation of the fundamental parallel resonance frequency of the sample, f1. The fundamental frequency of the sample is measured by 1.4.1.1, and the overtone frequency of the sample is measured by 4.1.1.5. Then, according to the coupling coefficient value obtained in 4.5.1, the corresponding value is obtained by looking up Table 2. The four parallel resonance frequency values ​​are calculated from the fundamental and overtone frequencies of the sample, f1, f2, f5, f1 and their corresponding f/f values, and the average value is taken, which is the parallel resonance frequency of the sample, f1.4.5. 3 Thickness expansion vibration frequency constant N. According to the test piece thickness t measured in 4.4.3, the parallel resonance frequency f of the test piece is calculated in 4.5.2. Then, the frequency constant N
N,= f,1
thickness expansion vibration frequency constant, Hzm;
f——fundamental parallel resonance frequency, Hz;
thickness of the test piece, m.
4.5.4 Thickness velocity VP
According to the test piece thickness t measured in 4.5.2, the thickness of the test piece is: 1.4.3, then, the thickness velocity VVu- is calculated according to formula (5). 3f,+t
thickness direction sound velocity, m/s;
F. fundamental parallel resonant frequency, Hz;
sample thickness, m.
4.5.5 Thickness stretching vibration mechanical quality factor Q (5)bzxz.net
The fundamental frequency f of the sample is measured by 4.4.1.4, the fundamental frequency dynamic resistance R of the sample is measured by 4.4.1.6, the white capacitance C of the sample is measured by 4.4.2, and the parallel resonant frequency F of the sample is obtained by 4.52. Then, the mechanical quality factor Qm is calculated by formula (6): Q
2-CT.R,.OR-)
Formula Qu-
First order stretching vibration mechanical quality factor: (6)
WJ—thickness stretching vibration fundamental frequency, Hz;
GB/T 3389.5-:1995
f—thickness stretching vibration fundamental wave parallel frequency, Hz; Ri---dynamic resistance, a,
CT—free capacitance, F.
4.5.6 White free relative dielectric constant
The free capacitance CT of the sample is measured by 4.4.2,4.4,3 After measuring the diameter d and thickness of the sample, calculate the relative dielectric constant eta according to formula (7).
Formula:
Free relative dielectric band number (a/);
Sample capacitance, F:
t——Sample thickness, m3
Sample diameter, m;
Vacuum dielectric constant + n = 8.85×10-12F/m. 4.5.7 Relative dielectric band number of clamped samples %
Measure the electromechanical coupling coefficient of the sample plane according to the method specified in GB2414. 1.5.1 Measure the coupling coefficient, 4.5.6 Measure the number of free relative dielectric bands and calculate the clamped relative dielectric constant according to formula (8): = (1 - d) + (1 - d) +
In the formula,
Relative dielectric band number (,-/);
Thickness stretching vibration electromechanical coupling coefficient
·White Relative dielectric constant
Plane electromechanical coupling coefficient.
4.5.8 Open circuit elastic stiffness constant C
The sample volume density P is measured according to the method specified in GB 2413, the sample thickness t is measured by 4.4.3, and the parallel resonance frequency f is obtained by 4.5.2. The stiffness constant C% is calculated by the formula (9): C§ -40-0-t)3
In the formula:
Parallel elastic stiffness constant, N/m
-sample volume density kg/m
fp-basic parallel resonance frequency, Hs
-sample thickness, 1.
4.5.9 Short-circuit elastic stiffness constant C5
The open-circuit elastic stiffness constant is measured by 4.5.8 of this standard (+ the electromechanical coupling coefficient k measured by 4.5.1. After the number of clamped relative dielectric strips s is measured by 4.5.7, the short-circuit elastic stiffness constant C is calculated according to formula (10): C = CR(I - )
Where: C-
Short-circuit elastic stiffness constant, N/m\,
Open-circuit elastic stiffness constant + N/m
-Thickness telescopic perturbation electromechanical coupling coefficient
4.5.10 Piezoelectric stress constant e:3
The coupling coefficient k is obtained from 4.5.1. The relative dielectric constant g is obtained from 4.5.7. 8 After obtaining the open circuit elastic constant C, the piezoelectric stress constant ea:es
Nea.Cp..co
W Formula eaa
GB/T 3389.5—1995
Piezoelectric stress constant, N/V·or C/m,
Thickness stretching vibration electromechanical coupling coefficient:
…．-Relaxed relative dielectric constant
0, 004
Open circuit elastic stiffness constant, N/m
Vacuum dielectric band number, m=8.85×10-12F/m. Table 1/f, relationship table with
3: 000 1
3. 4200.8
3- 002 4
5, 002 | 82 | |tt | 0
5, 072 3
CB/T 3389.5—1995
Building Table 1
7. Non-84 2
3, 049 G
5. 07 points 6
7,117 3
Standard Search Network 0o. 224
. 3.065 4
GB/T 3389.5—1995
continuation table 1
W point
0- 282
GB/T3389.5-1995
continuation table 1
3, 111 5
5. 2411 5
7, 808 6
7. 5319 0.
W0.336
2, 850
3. 1412 3.
CB/T 3389.5
Continued Table 1
: 3. 167 5
Fai/at
5,32 1 0
7-444 6
W2 Calculation of the fundamental parallel resonant frequency, f, of the sample The fundamental frequency of the sample is measured by 1.4.1.1, and the overtone frequency of the sample is measured by 4.1.1.5. Then, according to the coupling coefficient value obtained in 4.5.1, the corresponding value of f/f is obtained by looking up Table 2. Four parallel vibration frequency values ​​are calculated from the fundamental and overtone frequencies of the sample, f1, f2, f5, f1 and their corresponding f/f values, and the average value is taken, which is the parallel resonant frequency, f, of the sample. 4.5.3 Thickness stretching vibration frequency constant N. The thickness t of the sample is measured by 4.4.3, and the parallel resonant frequency f of the sample is calculated by 4.5.2. Then, the frequency constant N
N,= f,1
Thickness expansion and contraction vibration constant, Hzm;
f——fundamental parallel resonant frequency, Hz;
Thickness of sample, m.
4.5.4 Thickness velocity VP
According to 4.5.2, the fundamental parallel resonance frequency of the sample is obtained, and the thickness of the sample is measured in 1.4.3: after that, the thickness velocity VVu is calculated according to formula (5): -3f,+t
Thickness velocity of sound, m/s;
F. Fundamental parallel resonant frequency, Hz;
Thickness of sample, m.
4.5.5 Thickness expansion and contraction vibration quality factor Q (5)
According to 4.4.1.4, the fundamental frequency of the sample is obtained, and the fundamental frequency dynamic resistance R of the sample is measured in 4.4.1.6. After the parallel resonance frequency F of the sample is obtained by measuring the capacitance C\ of the sample, the mechanical quality factor Qm is calculated by formula (6): Q
2 yuan-CT.R,.OR-)
Formula Qu-
First order stretching vibration mechanical quality factor: (6)
WJ-thickness stretching vibration fundamental wave, Hz;
GB/T 3389.5-:1995
f-thickness stretching vibration fundamental wave parallel resonance frequency, Hz; Ri---dynamic resistance, a,
CT-free capacitance, F.
4. 5. 6 White free relative dielectric constant
The free capacitance CT of the sample is measured by 4. 4. 2,4. 4,3 After measuring the diameter d and thickness of the sample, calculate the relative dielectric constant eta according to formula (7).
Formula:
Free relative dielectric band number (a/);
Sample capacitance, F:
t——Sample thickness, m3
Sample diameter, m;
Vacuum dielectric constant + n = 8.85×10-12F/m. 4.5.7 Relative dielectric band number of clamped samples %
Measure the electromechanical coupling coefficient of the sample plane according to the method specified in GB2414. 1.5.1 Measure the coupling coefficient, 4.5.6 Measure the number of free relative dielectric bands and calculate the clamped relative dielectric constant according to formula (8): = (1 - d) + (1 - d) +
In the formula,
Relative dielectric band number (,-/);
Thickness stretching vibration electromechanical coupling coefficient
·White Relative dielectric constant
Plane electromechanical coupling coefficient.
4.5.8 Open circuit elastic stiffness constant C
The sample volume density P is measured according to the method specified in GB 2413, the sample thickness t is measured by 4.4.3, and the parallel resonance frequency f is obtained by 4.5.2. The stiffness constant C% is calculated by the formula (9): C§ -40-0-t)3
In the formula:
Parallel elastic stiffness constant, N/m
-sample volume density kg/m
fp-basic parallel resonance frequency, Hs
-sample thickness, 1.
4.5.9 Short-circuit elastic stiffness constant C5
The open-circuit elastic stiffness constant is measured by 4.5.8 of this standard (+ the electromechanical coupling coefficient k measured by 4.5.1. After the number of clamped relative dielectric strips s is measured by 4.5.7, the short-circuit elastic stiffness constant C is calculated according to formula (10): C = CR(I - )
Where: C-
Short-circuit elastic stiffness constant, N/m\,
Open-circuit elastic stiffness constant + N/m
-Thickness telescopic perturbation electromechanical coupling coefficient
4.5.10 Piezoelectric stress constant e:3
The coupling coefficient k is obtained from 4.5.1. The relative dielectric constant g is obtained from 4.5.7. 8 After obtaining the open circuit elastic constant C, the piezoelectric stress constant ea:es
Nea.Cp..co
W Formula eaa
GB/T 3389.5—1995
Piezoelectric stress constant, N/V·or C/m,
Thickness stretching vibration electromechanical coupling coefficient:
…．-Relaxed relative dielectric constant
0, 004
Open circuit elastic stiffness constant, N/m
Vacuum dielectric band number, m=8.85×10-12F/m. Table 1/f, relationship table with
3: 000 1
3. 4200.8
3- 002 4
5, 002 | 82 | |tt | 0
5, 072 3
CB/T 3389.5—1995
Building Table 1
7. Non-84 2
3, 049 G
5. 07 points 6
7,117 3
Standard Search Network 0o. 224
. 3.065 4
GB/T 3389.5—1995
Continuation Table 1
W point
0- 282
GB/T3389.5-1995
Continuation Table 1
5. 2411 5
7, 808 6
7. 5319 0.
W0.336
2, 850
3. 1412 3.
CB/T 3389.5
Continued Table 1
: 3. 167 5
Fai/at
5,32 1 0
7-444 6
W2 Calculation of the fundamental parallel resonant frequency, f, of the sample The fundamental frequency of the sample is measured by 1.4.1.1, and the overtone frequency of the sample is measured by 4.1.1.5. Then, according to the coupling coefficient value obtained in 4.5.1, the corresponding value of f/f is obtained by looking up Table 2. Four parallel vibration frequency values ​​are calculated from the fundamental and overtone frequencies of the sample, f1, f2, f5, f1 and their corresponding f/f values, and the average value is taken, which is the parallel resonant frequency, f, of the sample. 4.5.3 Thickness stretching vibration frequency constant N. The thickness t of the sample is measured by 4.4.3, and the parallel resonant frequency f of the sample is calculated by 4.5.2. Then, the frequency constant N
N,= f,1
Thickness expansion and contraction vibration constant, Hzm;
f——fundamental parallel resonant frequency, Hz;
Thickness of sample, m.
4.5.4 Thickness velocity VP
According to 4.5.2, the fundamental parallel resonance frequency of the sample is obtained, and the thickness of the sample is measured in 1.4.3: after that, the thickness velocity VVu is calculated according to formula (5): -3f,+t
Thickness velocity of sound, m/s;
F. Fundamental parallel resonant frequency, Hz;
Thickness of sample, m.
4.5.5 Thickness expansion and contraction vibration quality factor Q (5)
According to 4.4.1.4, the fundamental frequency of the sample is obtained, and the fundamental frequency dynamic resistance R of the sample is measured in 4.4.1.6. After the parallel resonance frequency F of the sample is obtained by measuring the capacitance C\ of the sample, the mechanical quality factor Qm is calculated by formula (6): Q
2 yuan-CT.R,.OR-)
Formula Qu-
First order stretching vibration mechanical quality factor: (6)
WJ-thickness stretching vibration fundamental wave, Hz;
GB/T 3389.5-:1995
f-thickness stretching vibration fundamental wave parallel resonance frequency, Hz; Ri---dynamic resistance, a,
CT-free capacitance, F.
4. 5. 6 White free relative dielectric constant
The free capacitance CT of the sample is measured by 4. 4. 2,4. 4,3 After measuring the diameter d and thickness of the sample, calculate the relative dielectric constant eta according to formula (7).
Formula:
Free relative dielectric band number (a/);
Sample capacitance, F:
t——Sample thickness, m3
Sample diameter, m;
Vacuum dielectric constant + n = 8.85×10-12F/m. 4.5.7 Relative dielectric band number of clamped samples %
Measure the electromechanical coupling coefficient of the sample plane according to the method specified in GB2414. 1.5.1 Measure the coupling coefficient, 4.5.6 Measure the number of free relative dielectric bands and calculate the clamped relative dielectric constant according to formula (8): = (1 - d) + (1 - d) +
In the formula,
Relative dielectric band number (,-/);
Thickness stretching vibration electromechanical coupling coefficient
·White Relative dielectric constant
Plane electromechanical coupling coefficient.
4.5.8 Open circuit elastic stiffness constant C
The sample volume density P is measured according to the method specified in GB 2413, the sample thickness t is measured by 4.4.3, and the parallel resonance frequency f is obtained by 4.5.2. The stiffness constant C% is calculated by the formula (9): C§ -40-0-t)3
In the formula:
Parallel elastic stiffness constant, N/m
-sample volume density kg/m
fp-basic parallel resonance frequency, Hs
-sample thickness, 1.
4.5.9 Short-circuit elastic stiffness constant C5
The open-circuit elastic stiffness constant is measured by 4.5.8 of this standard (+ the electromechanical coupling coefficient k measured by 4.5.1. After the number of clamped relative dielectric strips s is measured by 4.5.7, the short-circuit elastic stiffness constant C is calculated according to formula (10): C = CR(I - )
Where: C-
Short-circuit elastic stiffness constant, N/m\,
Open-circuit elastic stiffness constant + N/m
-Thickness telescopic perturbation electromechanical coupling coefficient
4.5.10 Piezoelectric stress constant e:3
The coupling coefficient k is obtained from 4.5.1. The relative dielectric constant g is obtained from 4.5.7. 8 After obtaining the open circuit elastic constant C, the piezoelectric stress constant ea:es
Nea.Cp..co
W Formula eaa
GB/T 3389.5—1995
Piezoelectric stress constant, N/V·or C/m,
Thickness stretching vibration electromechanical coupling coefficient:
…．-Relaxed relative dielectric constant
0, 004
Open circuit elastic stiffness constant, N/m
Vacuum dielectric band number, m=8.85×10-12F/m. Table 1/f, relationship table with
3: 000 1
3. 4200.8
3- 002 4
5, 002 | 82 | |tt | 0
5, 072 3
CB/T 3389.5—1995
Building Table 1
7. Non-84 2
3, 049 G
5. 07 points 6
7,117 3
Standard Search Network 0o. 224
. 3.065 4
GB/T 3389.5—1995
continuation table 1
W point
0- 282
GB/T3389.5-1995
continuation table 1
3, 111 5
5. 2411 5
7, 808 6
7. 5319 0.
W0.336
2, 850
3. 1412 3.
CB/T 3389.5
Continued Table 1
: 3. 167 5
Fai/at
5,32 1 0
7-444 6
W6 The fundamental frequency dynamic resistance R of the sample is measured. 4. 4. 2 The white capacitance C\ of the sample is measured. After the parallel resonance frequency F of the sample is obtained by 4.52, the mechanical quality factor Qm is calculated using formula (6): Q
2-CT.R,.OR-)
Formula Qu-
First order stretching vibration mechanical quality factor: (6)
WJ—thickness stretching vibration fundamental frequency, Hz;
GB/T 3389.5-:1995
f—thickness stretching vibration fundamental parallel resonance frequency, Hz; Ri---dynamic resistance, a,
CT—free capacitance, F.
4.5.6 Free relative dielectric constant
After measuring the free capacitance CT of the sample by 4.4.2, the diameter d of the sample by 4.4.3, and the thickness ±, the relative dielectric constant eta is calculated according to formula (7).
Formula:
Free relative dielectric band number (A/);
Free relative dielectric constant of the sample, F:
t——sample thickness, m3
sample diameter, m;
Vacuum dielectric constant + n=8.85×10-12F/m. 4.5.7 Relative dielectric band number of clamped material %
Measure the plane electromechanical coupling coefficient of the sample according to the method specified in GB2414. The coupling coefficient is measured in 1.5.1, and the free relative dielectric band number is measured in 4.5.6. The clamped relative dielectric constant is calculated according to formula (8): = (1 - ) + (1 - ) +
Where,
relative dielectric band number of clamped material (, -/);
thickness stretching vibration electromechanical coupling coefficient
·white relative dielectric constant
plane electromechanical coupling coefficient.
4.5.8 Open circuit elastic stiffness constant C product
Measure the sample volume density P according to the method specified in GB 2413, measure the sample thickness t by 4.4.3, and obtain the parallel resonance frequency f by 4.5.2. The stiffness constant C% is calculated by the connected formula (9): C§ - 40 -0-t)3
wherein:
parallel elastic stiffness constant, N/m
-sample volume, kg/m
fp-basic parallel resonant frequency, Hs
-sample thickness, 1.
4.5.9 Short-circuit elastic stiffness constant C5
The open-circuit elastic stiffness constant is measured by 4.5.8 of this standard (+ the electromechanical coupling coefficient k measured by 4.5.1. After the number of clamped relative dielectric strips s is measured by 4.5.7, the short-circuit elastic stiffness constant C is calculated according to formula (10): C = CR(I - )
Where: C-
Short-circuit elastic stiffness constant, N/m\,
Open-circuit elastic stiffness constant + N/m
-Thickness telescopic perturbation electromechanical coupling coefficient
4.5.10 Piezoelectric stress constant e:3
The coupling coefficient k is obtained from 4.5.1. The relative dielectric constant g is obtained from 4.5.7. 8 After obtaining the open circuit elastic constant C, the piezoelectric stress constant ea:es
Nea.Cp..co
W Formula eaa
GB/T 3389.5—1995
Piezoelectric stress constant, N/V·or C/m,
Thickness stretching vibration electromechanical coupling coefficient:
…．-Relaxed relative dielectric constant
0, 004
Open circuit elastic stiffness constant, N/m
Vacuum dielectric band number, m=8.85×10-12F/m. Table 1/f, relationship table with
3: 000 1
3. 4200.8
3- 002 4
5, 002 | 82 | |tt | 0
5, 072 3
CB/T 3389.5—1995
Building Table 1
7. Non-84 2
3, 049 G
5. 07 points 6
7,117 3
Standard Search Network 0o. 224
. 3.065 4
GB/T 3389.5—1995
continuation table 1
W point
0- 282
GB/T3389.5-1995
continuation table 1
3, 111 5
5. 2411 5
7, 808 6
7. 5319 0.
W0.336
2, 850
3. 1412 3.
CB/T 3389.5
Continued Table 1
: 3. 167 5
Fai/at
5,32 1 0
7-444 6
W6 The fundamental frequency dynamic resistance R of the sample is measured. 4. 4. 2 The white capacitance C\ of the sample is measured. After the parallel resonance frequency F of the sample is obtained by 4.52, the mechanical quality factor Qm is calculated using formula (6): Q
2-CT.R,.OR-)
Formula Qu-
First order stretching vibration mechanical quality factor: (6)
WJ—thickness stretching vibration fundamental frequency, Hz;
GB/T 3389.5-:1995
f—thickness stretching vibration fundamental parallel resonance frequency, Hz; Ri---dynamic resistance, a,
CT—free capacitance, F.
4.5.6 Free relative dielectric constant
After measuring the free capacitance CT of the sample by 4.4.2, the diameter d of the sample by 4.4.3, and the thickness ±, the relative dielectric constant eta is calculated according to formula (7).
Formula:
Free relative dielectric band number (A/);
Free relative dielectric constant of the sample, F:
t——sample thickness, m3
sample diameter, m;
Vacuum dielectric constant + n=8.85×10-12F/m. 4.5.7 Relative dielectric band number of clamped material %
Measure the plane electromechanical coupling coefficient of the sample according to the method specified in GB2414. The coupling coefficient is measured in 1.5.1, and the free relative dielectric band number is measured in 4.5.6. The clamped relative dielectric constant is calculated according to formula (8): = (1 - ) + (1 - ) +
Where,
relative dielectric band number of clamped material (, -/);
thickness stretching vibration electromechanical coupling coefficient
·white relative dielectric constant
plane electromechanical coupling coefficient.
4.5.8 Open circuit elastic stiffness constant C product
Measure the sample volume density P according to the method specified in GB 2413, measure the sample thickness t by 4.4.3, and obtain the parallel resonance frequency f by 4.5.2. The stiffness constant C% is calculated by the connected formula (9): C§ - 40 -0-t)3
wherein:
parallel elastic stiffness constant, N/m
-sample volume, kg/m
fp-basic parallel resonant frequency, Hs
-sample thickness, 1.
4.5.9 Short-circuit elastic stiffness constant C5
The open-circuit elastic stiffness constant is measured by 4.5.8 of this standard (+ the electromechanical coupling coefficient k measured by 4.5.1. After the number of clamped relative dielectric strips s is measured by 4.5.7, the short-circuit elastic stiffness constant C is calculated according to formula (10): C = CR(I - )
Where: C-
Short-circuit elastic stiffness constant, N/m\,
Open-circuit elastic stiffness constant + N/m
-Thickness telescopic perturbation electromechanical coupling coefficient
4.5.10 Piezoelectric stress constant e:3
The coupling coefficient k is obtained from 4.5.1. The relative dielectric constant g is obtained from 4.5.7. 8 After obtaining the open circuit elastic constant C, the piezoelectric stress constant ea:es
Nea.Cp..co
W Formula eaa
GB/T 3389.5—1995
Piezoelectric stress constant, N/V·or C/m,
Thickness stretching vibration electromechanical coupling coefficient:
…．-Relaxed relative dielectric constant
0, 004
Open circuit elastic stiffness constant, N/m
Vacuum dielectric band number, m=8.85×10-12F/m. Table 1/f, relationship table with
3: 000 1
3. 4200.8
3- 002 4
5, 002 | 82 | |tt | 0
5, 072 3
CB/T 3389.5—1995
Building Table 1
7. Non-84 2
3, 049 G
5. 07 points 6
7,117 3
Standard Search Network 0o. 224
. 3.065 4
GB/T 3389.5—1995
continuation table 1
W point
0- 282
GB/T3389.5-1995
continuation table 1
3, 111 5
5. 2411 5
7, 808 6
7. 5319 0.
W0.336
2, 850
3. 1412 3.
CB/T 3389.5
Continued Table 1
: 3. 167 5
Fai/at
5,32 1 0
7-444 6
W3
From 4.5.1, the combined coefficient k is obtained, from 4.5.7, the dielectric constant g is obtained, and from 4.5.8, the open circuit elastic stiffness constant C is obtained. Then, the piezoelectric stress constant ea is calculated according to formula (11):es
Nea.Cp..co
W Formula eaa
GB/T 3389.5—1995
Piezoelectric stress constant, N/V·or C/m,
Thickness stretching vibration electromechanical coupling coefficient:
…．-Relativistic dielectric constant
0, 004
Open circuit elastic stiffness constant, N/m
Vacuum dielectric band number, m=8.85×10-12F/m. Table 1/f, relationship table with
3: 000 1
3. 4200.8
3- 002 4
5, 002 6
Standard search network 0.056
fas/fa
5,0128
GB/T 3389.5—1995
Continued table 1
5. 4119 6
7. 4122 6
W0. 112
.3.0182
GR/T 3389.5—1995
Continued table 1
7. 04:5 9
. 032 2 | |tt | 282 | |tt | . 1412 3.
CB/T 3389.5
Continued Table 1
: 3. 167 5
Fai/at
5,321 0
7-444 6
W3
From 4.5.1, the combined coefficient k is obtained, from 4.5.7, the dielectric constant g is obtained, and from 4.5.8, the open circuit elastic stiffness constant C is obtained. Then, the piezoelectric stress constant ea is calculated according to formula (11):es
Nea.Cp..co
W Formula eaa
GB/T 3389.5—1995
Piezoelectric stress constant, N/V·or C/m,
Thickness stretching vibration electromechanical coupling coefficient:
…．-Relativistic dielectric constant
0, 004
Open circuit elastic stiffness constant, N/m
Vacuum dielectric band number, m=8.85×10-12F/m. Table 1/f, relationship table with
3: 000 1
3. 4200.8
3- 002 4
5, 002 6
Standard search network 0.056
fas/fa
5,0128
GB/T 3389.5—1995
Continued table 1
5. 4119 6
7. 4122 6
W0. 112
.3.0182
GR/T 3389.5—1995
Continued table 1
7. 04:5 9
. 032 2 | |tt | 282 | |tt | . 1412 3.
CB/T 3389.5
Continued Table 1
: 3. 167 5
Fai/at
5,321 0
7-444 6
W
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