# Analysis of Vibration Plate Cracking Based on Working Stress

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## Abstract

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## 1. Introduction

- The seismic signal excited by vibroseis is controllable. Vibroseis can be used to independently choose the appropriate excitation frequency width according to the working environment, thus improving the signal excitation quality. The direction of the output force is also controllable; vibroseis can reduce the energy loss in other directions and increase the signal-to-noise ratio (SNR) of the vibroseis excitation signal.
- Vibroseis uses continuous excitation signals. According to the requirements, vibroseis can be used to control the vibrator to continuously make contact with the earth within a few seconds, and generate the required signal waveform. The repeated superposition of the signal can eliminate a large amount of random external interference, so as to obtain high-SNR data.
- Vibroseis is not destructive to the environment or organisms. Vibroseis is a low-power method which can efficiently complete the exploration of deep-stratum oil and gas reservoirs in cities, dykes, industrial areas, and other areas where it is inconvenient to use explosives.
- Vibroseis uses Combined Excitation Technology to effectively suppress the linear interference energy during operation.
- Vibroseis can be operated without drilling, which improves the mobility and reduces a lot of costs [4].

## 2. Structure and Working Principle of the KZ-28 Vibroseis Vehicle

## 3. The Vibrator Cracking Problem

## 4. Establishment of Finite Element Model for Working Stress Analysis of Vibrator Plate

- Simplify the hammer and its accessories without considering the weight of the hammer and the impact action when the hydraulic oil drives the hammer. Remove the hammer and its accessory parts in the analysis; the hammer force and dynamic hydraulic load are directly loaded into the vibrator model as the known load.
- Simplify the piston base of I-steel plate. According to the plate structure, the piston rod base is installed in the middle of the plate, which is used to connect the piston rod and I-steel plate. For the convenience of the analysis, this was simplified into solid cylindrical structure.
- The vibrator needs to be in contact with the ground during operation. Therefore, it is necessary to establish a ground model. However, the size cannot be unlimited; therefore, at the time of the earth model size selection, the size should be considered so as not to affect the deformation of the vibrator plate. Through repeated with different sizes of earth model, and considering the calculation time and accuracy, it was eventually determined that the optimal values were: diameter of the earth model, 5 m, and height, 2.5 m. The completed geometric model of the vibrator is shown in Figure 4.

- (1)
- Static load (Figure 6 shows the loading diagram of static load).

- (2)
- Dynamic load

## 5. Analysis of Working Stress of Vibrator Plate under Maximum Liquid Pressure

- In the upper half of cycle when the liquid pressure reaches the maximum, the von Mises stress on the upper surface of the plate reaches the maximum value in the area of the piston rod; the maximum value is 25.3 MPa, the larger value around the long side of columns A and C is 16.4 and 12.2 MPa, respectively, and the larger value around the short edge of columns B and D is 10.1 and 18.6 MPa, respectively.
- In the second half cycle when the liquid pressure reaches the maximum, the von Mises stress on the upper surface of the plate reaches the maximum in the area of the piston rod; the maximum value is 28.2 MPa, which presents large values on the short edges of columns A, B, C, and D of 13.6, 9.5, 8.6, and 14.6 MPa, respectively.
- Based on the analysis of Figure 9, it can be found that the stress concentration and stress peak exist when the short edge weld of the column reaches its maximum value within one cycle of liquid pressure. The location of the peak area of stress concentration exists near the area of the piston rod and the pillar. When the liquid pressure of the vertical columns B and D reached the maximum in the upper and lower half periods, they all presented large values; the post short edge weld is the part of the welding crack in practical engineering.

## 6. Analysis of Plate Deformation under Maximum Liquid Pressure

- In the upper half of the cycle, when the liquid pressure reaches the maximum value, the whole plate deforms downward on the upper surface of the plate. The maximum value of deformation is 3.2 × 10
^{−4}m near the piston rod; it deformed downward near the vertical column, showing a larger value. The edge of the plate has an upward deformation. - In the second half of the cycle, when the liquid pressure reaches the maximum value, the whole plate deforms upward on the upper surface of the plate. The maximum value of deformation is 2.2 × 10
^{−4}m near the piston rod, and the upward deformation near the vertical column presents a large value. The edge of the plate has downward deformation.

^{−6}m, and the that of the upward deformation in the lower half period is 1.69 × 10

^{−4}m.

## 7. Analysis of Working Stress and Deformation of Plate at Different Frequencies under the Action of Liquid Pressure

- In the upper half of the cycle, when the liquid pressure reaches the maximum value, the von Mises stress on the surface of the plate reaches the maximum value in the piston rod area, 23.2 MPa. Larger values are presented near the long side of columns A, B, C, and D, respectively 12.9, 8.6, 7.5, and 7.8 MPa. Large values are presented at air springs A and B, respectively 4.6 and 3.8 MPa.
- In the second half of the cycle, when the liquid pressure reaches the maximum value, the von Mises stress on the upper surface of the plate reaches the maximum value in the piston rod area, 17.1 MPa, and larger values are displayed on the short edge of the vertical columns A, B, C, and D, respectively 9.4, 8.4, 10.1, and 11.9 MPa.
- Compare the stress distribution of the plate under 80 Hz liquid pressure to others. When the upper semi-periodic stress value under 50 Hz reaches the maximum, there is no stress concentration on the short edge of the column.

- In the upper half of the cycle, when the liquid pressure reaches the maximum value, the whole plate deforms downward on the upper surface. The maximum value of the deformation is 2.8 ×10
^{−5}m near the piston rod, while the downward deformation near the column presents a larger value, 8.8 × 10^{−6}m. The edge of the plate has upward deformation. - In the second half of the cycle, when the liquid pressure reaches the maximum value, on the upper surface of the plate the deformation has a maximum value near the piston rod, 1.5 × 10
^{−4}m, the upward deformation near the four vertical columns. The short edge of the plate deforms downward. - By analyzing the deformation of the whole, under the effect of liquid pressure of 50 Hz, the deformation law of the whole plate in the working process is quite similar to that under 80 Hz, and the position of the short edge weld of the column plate shows up and down deformation alternately over the whole cycle.

^{−6}m. The maximum value of the upward deformation in the second half of the cycle is 9.1 × 10

^{−5}m.

- In the upper half of the cycle when the liquid pressure reaches the maximum value, the von Mises stress on the upper surface of the plate reaches the maximum value in the piston rod area, 32.3 MPa, and the larger value is displayed near the vertical columns A, B, C, and D, respectively 10.1, 9.1, 13.4, and 9.6 MPa.
- In the second half of the cycle when the liquid pressure reaches the maximum value, the von Mises stress on the upper surface of the plate reaches the maximum value in the piston rod area, 33.6 MPa, and the larger value is shown at the long side of the vertical columns A and C, respectively 15.7 and 14.8 MPa, and the larger value is shown at the short edge of B and D, respectively 14.6 and 16.6 MPa.
- As for the stress distribution of the plate under 80 Hz liquid pressure, in the upper half of the cycle, the stress value under 100 Hz reaches the maximum. There is also a stress concentration near the column, while the stress distribution in the second half of the cycle is similar to that under 80 Hz.

- In the upper half of the cycle, when the liquid pressure reaches the maximum value, the piston rod and the column are deformed downward and the rest of the parts are deformed upward on the upper surface of the plate. The maximum deformation is 3.4 × 10
^{−5}m near the piston rod, and it is deformed downward near the vertical column, showing a larger value. - In the second half of the cycle, when the liquid pressure reaches the maximum value, on the upper surface of the plate, the deformation takes on a maximum value near the piston rod, 1.4 × 10
^{−4}m, showing a larger value near the four vertical columns. The short edge of the plate deforms downward. - According to the global deformation analysis, under 100 Hz liquid pressure, the deformation law of the whole plate in the working process is similar to that under 80 Hz, and the position of short edge weld of the column plate shows up and down deformation alternately over the whole cycle.

^{−5}m, and that of upward deformation in the lower half period is 1.83 × 10

^{−4}m.

- The stress on the welding seam of the vertical column is mostly tensile stress, but is compressive stress in a small period.
- The maximum transverse stress and maximum longitudinal stress of the vertical welding seam of the vertical column increased with the rise in frequency, among which the tensile stress was clearly higher than the compressive stress.
- The peak value and variation amplitude of the deformation of the welding seam increased with the rise in liquid pressure frequency, and the deformation became more obvious with the rise in frequency.

## 8. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 9.**Stress distribution of plates. (

**a**) plate stress distribution at the maximum of upper half cycle; (

**b**) plate stress distribution at the maximum of lower half cycle.

**Figure 12.**Schematic diagram of stress change at the mid-point of weld. (

**a**) longitudinal stress. (

**b**) transverse stress.

**Figure 13.**Schematic diagram of plate deformation. (

**a**) plate deformation distribution at the upper half cycle maximum. (

**b**) plate deformation distribution at the lower half cycle maximum.

**Figure 15.**Distribution of plate stress under 50 Hz. (

**a**) plate stress distribution at the maximum of upper half cycle. (

**b**) plate stress distribution at the maximum of lower half cycle.

**Figure 16.**Variation of mid-point stress under 50 Hz. (

**a**) longitudinal stress. (

**b**) transverse stress.

**Figure 17.**Deformation diagram under 50 Hz. (

**a**) plate deformation distribution at the upper half cycle maximum. (

**b**) plate deformation distribution at the lower half cycle maximum.

**Figure 19.**Distribution of plate stress under 100 Hz. (

**a**) plate stress distribution at the maximum of upper half cycle. (

**b**) plate stress distribution at the maximum of lower half cycle.

**Figure 20.**Variation of mid-point stress of welding seam under 100 Hz. (

**a**) longitudinal stress. (

**b**) transverse stress.

**Figure 21.**Deformation under 100 Hz. (

**a**) plate deformation distribution at the upper half cycle maximum. (

**b**) plate deformation distribution at the lower half cycle maximum.

Parts | Materials | Density (kg/m^{3}) | Elastic Modulus (Pa) | Poisson’s Ratio | Yield Strength (MPa) |
---|---|---|---|---|---|

Above-slab structure | 45 steel | 7890 | 2.09 × 10^{11} | 0.269 | 355 |

Tablet | 16 Mn | 7850 | 2.12 × 10^{11} | 0.310 | 345 |

Ground | rock | 2600 | 5.5 × 10^{10} | 0.270 | -- |

50 Hz | 80 Hz | 100 Hz | |
---|---|---|---|

Maximum transverse tensile stress (MPa) | 4.8 | 8.9 | 10 |

Maximum transverse compressive stress (MPa) | 0.9 | 6.4 | 7.43 |

Maximum longitudinal tensile stress (MPa) | 9.8 | 15.5 | 18.6 |

Maximum longitudinal compressive stress (MPa) | 2.4 | 5.5 | 10 |

Maximum positive displacement (×10^{−5} m) | 9.1 | 16.9 | 18.3 |

Maximum negative displacement (×10^{−5} m) | 0.53 | 0.77 | 1.9 |

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**MDPI and ACS Style**

Kang, Z.; Li, G.; Wang, F.; Zhang, H.; Su, R. Analysis of Vibration Plate Cracking Based on Working Stress. *Machines* **2018**, *6*, 51.
https://doi.org/10.3390/machines6040051

**AMA Style**

Kang Z, Li G, Wang F, Zhang H, Su R. Analysis of Vibration Plate Cracking Based on Working Stress. *Machines*. 2018; 6(4):51.
https://doi.org/10.3390/machines6040051

**Chicago/Turabian Style**

Kang, Zeyu, Gangjun Li, Fujun Wang, Huan Zhang, and Rui Su. 2018. "Analysis of Vibration Plate Cracking Based on Working Stress" *Machines* 6, no. 4: 51.
https://doi.org/10.3390/machines6040051