Fig. 1. Nonlinear spring oscillator model
Fig. 2. Sweep signal
Fig. 3. Sweep result
Fig. 4. Results of excitation at LDR frequency
Fig. 5. Results of excitation far away from LDR frequency
Fig. 6. Results of excitation at 2 times LDR frequency
Fig. 7. Detection experiment. (a) Detection circuit; (b) specimen to be tested
Fig. 8. Excitation results of specimen 6 at LDR frequency
Fig. 9. Excitation results of specimen 6 far away from LDR frequency
Fig. 10. Excitation results of specimen 6 at 2 times LDR frequency
Fig. 11. Amplitude of each component in echo response (excitation frequency is 40 kHz and excitation voltage is 1-90 V)
Fig. 12. Amplitude of each component in echo response (excitation frequency is 31.5 kHz and excitation voltage is 1-90 V)
Fig. 13. Comparison of preset and estimated damage equivalent radius of each group of specimens
Damage shape | LDR frequency /kHz |
---|
Equivalent damage radius of 0.5 mm | Equivalent damage radius of 0.75 mm | Equivalent damage radius of 1 mm | Equivalent damage radius of 1.5 mm | Equivalent damage radius of 2 mm |
---|
Average value | 464.6 | 195.2 | 116.8 | 60.3 | 31.0 | Circular | 466.8 | 198.7 | 120.1 | 63.0 | 31.5 | Irregular shape | 458.7 | 200.2 | 126.0 | 58.8 | 29.9 | Triangle | 450.6 | 188.6 | 109.3 | 60.6 | 29.6 | Square | 482.2 | 193.1 | 111.7 | 58.9 | 33.0 |
|
Table 1. LDR frequency of each specimen with different damage sizes
Parameter | Simulated value | Experimental value |
---|
Not at LDR | At LDR | Not at LDR | At LDR |
---|
| 0.3 | 0.663 | 0.24 | 0.54 | | 7.4 | 15.5 | 2.6 | 5.8 | Growth rate of | | 121% | | 125% | Growth rate of | | 109% | | 123% |
|
Table 2. Simulated and experimental results under different detection conditions
Group number | Preset equivalent damage radius /mm | Estimated equivalent damage radius /mm |
---|
1 | 0.5 | 0.521 | 2 | 0.75 | 0.803 | 3 | 1 | 1.039 | 4 | 1.5 | 1.446 | 5 | 2 | 2.020 |
|
Table 3. Preset and estimated damage equivalent radius of each group of specimens