# Dynamic Diagnostic Tests and Numerical Analysis of the Foundations for Turbine Sets

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## Abstract

**:**

## 1. Introduction

- open box foundations,
- or closed box foundations.

- m
_{i}—the proportional part of the rotating mass supported by the i-th bearing,e—the eccentricity of the mass,$\omega =2\pi f$—the cyclic frequency of the turbogenerator’s operation,f—the operating frequency (f_{0}= 50 Hz at the nominal speed of the turbine).

_{0}≤ f ≤ 1.2 f

_{0}between 40 and 60 Hz [6].

## 2. Materials and Methods

- -
- measurement of the acceleration, speed, and natural vibration amplitude of the foundation during the normal operation of the turbogenerator.

- -
- destructive tests of cores cut from the structure in order to assess the compressive strength of concrete;
- -
- -
- -
- localisation of the concrete’s reinforcement and the determination of its arrangement, its diameters, and the thickness of the concrete’s cover using a non-destructive electromagnetic method [21], followed by the comparison of the obtained results with archival documentation. Figure 2 shows a general flow chart of the analysis performed.

## 3. Dynamic Actions—A Literature Review

- -
- research on the interaction between the foundation and the soil with the determination of the displacements and internal forces of the foundation using three-dimensional viscoelastic boundary elements for the model of the upper plate of the frame foundation [23];
- -
- -
- simulation analysis for asynchronous operation capacity of the turbogenerator under excitation loss [27];
- -
- study of the superposition of vibrations and analysis of ground sensitivity [16];
- -
- -
- -
- field tests of frame foundations in terms of settlement and resistance to temperature load [33];
- -
- an investigation of the influence of the supporting structure on the dynamics of the rotor system [34]
- -
- -
- -
- -
- -
- the estimation of multiple fault parameters of a fully assembled turbogenerator system based on the least squares technique requires forced response information [46].

## 4. Case Study—A Foundation for a Turbogenerator in a Combined Heat and Power Plant

#### 4.1. Dynamic Experimental Test

#### Measurement of the Amplitude of Foundation Forced Vibrations

#### 4.2. Auxiliary Material Experimental Tests

#### 4.2.1. Assessment of the Compressive Strength of Concrete

- -
- the average value of the concrete’s compressive strength ${f}_{m\left(n\right),is}=35.06\mathrm{MPa}$,
- -
- the minimum value of the concrete’s compressive strength ${f}_{is,lowest}=29.5\mathrm{MPa}$,
- -
- standard deviation ${s}_{R}=4.34$.

- ${f}_{ck,is,cube}$—characteristic compressive strength of the concrete in the structure, which corresponds to the strength of the concrete determined on cubic samples with a side length of 150 mm;
- ${f}_{m\left(n\right),is}$—the average value of the concrete’s compressive strength in the structure obtained from n measurement results;
- ${f}_{is,lowest}$—the lowest of the determined values of the compressive strength of the concrete in the structure;k
_{n}—coefficient that depends on the number of samples n = 7, k = 2.

#### 4.2.2. Sclerometer Test of Concrete

#### 4.2.3. Measurement of the Intensity of the Carbonation Process of the Subsurface Concrete Layer

#### 4.2.4. Investigation of the Thickness of the Concrete’s Cover and the Location and Diameter of the Reinforcement

#### 4.3. Numerical Analysis of the Foundation

#### 4.3.1. Analysis of the Amplitude of the Foundation’s Vibration

- M
_{W}—the mass of the rotating part: stator rotor: 30,150 kg, turbine rotor 17,000 kg,g—acceleration due to gravity,n = 1.2.Finally assumed:${\mathrm{F}}_{\mathrm{s},\mathrm{stator}}=70.96\mathrm{kN}$,${\mathrm{F}}_{\mathrm{s},\mathrm{rotor}}=40.34\mathrm{kN}$.

^{2}:

#### 4.3.2. Analysis of the Load-Bearing Capacity of the Foundation

- F
_{s}—the centrifugal force of the rotating part equal to 111.3 kN,${\mathsf{\phi}}_{\mathrm{M}}$—the dynamic coefficient which depends on the ratio of the natural frequency n_{e}to the frequency of the excitation forces n_{s}:

- $\zeta $—the damping coefficient, n
_{s}= 50 Hz—frequency of the exciting force.

- Δ—the logarithmic damping decrement of the foundation, which is equal to approx. 0.4 for RC frame foundations.After inserting n
_{e}= 44.01 Hz,φ_{M1}= 3.1.After inserting n_{e}= 56.23 Hz,φ_{M2}= 4.2.Finally, the following was assumed:φ_{M}= 4.2.

- ${\mathsf{\phi}}_{\mathrm{M}}$—dynamic coefficient (as above),µ—fatigue factor equal to 2,γ—calculation factor equal to 5.

_{s}= 111.3 kN.

- F
_{s,stator}= 70.96 kN, adjusted to the value of 71.0 kN,F_{s,turbine}= 40.34 kN, adjusted to a value of 40.3 kN.

- F
_{s,stator,eq}= 4.2 $\xb7$ 2 $\xb7$ 5 $\xb7$ 71 = 2982 kN,F_{s,turbine,eq}= 4.2 $\xb7$ 2 $\xb7$ 5 $\xb7$ 40.3 = 1693 kN.

- M
_{k,max}—the peak value of the moment derived from the start up and stop run up loads according to the archival documentation:

- F
_{zw}= 876.3 kN—start up and stop run up load,a = 3.69 m (spacing of fastening bolts),M_{k,max}= 3233.55 kNm,M_{k,eq}= 1.7$\xb7$3233.55 = 5497.03 kNm.

^{2}/m. The execution of the numerical calculations of the natural frequencies and mode shapes of the foundation construction was possible thanks to the research and measurements conducted. The theoretical vibration amplitude of the foundation is greater than that measured during normal operation of the turbogenerator; however, both are lower than the permissible value. The calculated values of the stresses in the concrete and reinforcing bars are lower than the permissible values.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Measurement of vibrations at the operating speed of the turbine placed on the top plate of the foundation using a piezoelectric accelerometer.

**Figure 8.**A colour template for assessing the depth and intensity of the carbonation process for the rainbow test.

**Figure 10.**The image of reinforcement scanning at the S26 and S27 measurement sites (at the bottom of the foundation body); red means bars of the main reinforcement; green means cross-bars.

**Figure 11.**The image of reinforcement scanning at the S31 measurement site (column area under the foundation body) superimposed on the tested element.

**Figure 14.**Calculation results of the foundation’s natural frequency obtained by AxisVM software: (

**a**) amplitude of foundation displacement for 26 mode shapes of frequency (44.01 Hz); (

**b**) amplitude of foundation displacement for 27 mode shapes of frequency (56.23 Hz).

**Figure 15.**Maximum amplitude of foundation displacement for forced vertical vibrations obtained by the AxisVM software.

**Figure 16.**Bottom and top reinforcement of the top plate in the horizontal direction (main direction) obtained by the AxisVM software.

**Figure 17.**Bottom and top reinforcement of the top plate in the vertical direction (main direction) obtained by the AxisVM software.

**Table 1.**Results of the vibration acceleration measurement, vibration velocity, and foundation displacement (average value).

Measurement No. | Amplitude Spectrum RMS m/s ^{2} | Amplitude Spectrum RMS mm/s | Amplitude Spectrum RMS mm | ||||||
---|---|---|---|---|---|---|---|---|---|

X | Y | Z | X | Y | Z | X | Y | Z | |

1 | 0.027–24 | 0.08 | 0.061 | 0.18 | 0.57 | 0.4 | 0.002 | 0.046 | 0.003 |

2 | 0.016–25 | 0.0058 | 0.05 | 0.11–12 | 0.032 | 0.4 | 0.002 | 0.0024 | 0.005 |

3 | 0.014–32 | 0.019 | 0.003 | 0.11 | 0.10 | 0.09 | 0.002 | 0.002 | 0.005 |

4 | 0.014–50 | 0.063 | 0.03 | 0.05 | 0.085 | 0.095 | 0.001 | 0.005 | 0.002 |

5 | 0.006–50 | 0.003 | 0.006 | 0.04 | 0.025 | 0.02 | 0.002 | 0.001 | 0.001 |

6 | 0.0022–18 | 0.0045 | 0.016 | 0.03 | 0.03 | 0.09 | 0.002 | 0.002 | 0.005 |

7 | 0.038–50 | 0.025–23 | 0.04 | 0.11 | 0.16 | 0.25–25 | 0.004 | 0.002 | 0.004 |

8 | 0.017–22 | 0.022 | 0.35–17 | 0.12 | 0.15 | 0.33–18 | 0.002 | 0.001 | 0.003 |

Localisation | Measurement Point | Drilling Diameter [mm] | Compressive Strength [MPa] |
---|---|---|---|

Foundation | O1 (F1) | 100 | 34.00 |

O2 (F2) | 100 | 34.60 | |

O3 (F3) | 100 | 43.20 | |

O4 (F4) | 100 | 37.50 | |

O5 (F5) | 100 | 32.20 | |

O6 (F6) | 100 | 29.50 | |

O7 (F7) | 100 | 34.40 |

Site | Angle | Readings | L_{i} | L_{i} − L_{av} | (L_{i} − L_{av})^{2} |
---|---|---|---|---|---|

[Deg] | |||||

1 | 90 | 45 44 47 47 44 44 46 46 47 | 45.6 | −2.67 | 7.11 |

2 | 90 | 52 52 49 49 51 50 49 49 49 | 50 | 1.78 | 3.16 |

3 | 90 | 48 47 47 48 47 48 48 49 49 | 47.9 | −0.33 | 0.11 |

4 | 90 | 50 52 52 49 49 50 52 52 52 | 50.9 | 2.67 | 7.11 |

5 | 90 | 44 44 46 46 48 46 47 48 48 | 46.3 | −1.89 | 3.57 |

6 | 90 | 48 49 50 49 48 48 48 49 49 | 48.7 | 0.44 | 0.2 |

Site | Angle | Readings | L_{i} | L_{i} − L_{av} | (L_{i} − L_{av})^{2} |
---|---|---|---|---|---|

[Deg] | |||||

1 | 90 | 51 51 50 52 50 50 51 50 52 | 50.8 | −1.35 | 1.83 |

2 | 90 | 52 52 52 50 51 52 52 50 52 | 51.4 | −0.69 | 0.47 |

3 | 90 | 51 52 54 54 52 54 52 52 52 | 52.6 | 0.43 | 0.18 |

4 | 90 | 54 52 54 54 52 53 53 54 52 | 53.1 | 0.98 | 0.96 |

5 | 90 | 54 54 52 52 52 52 54 53 53 | 52.9 | 0.76 | 0.58 |

6 | 90 | 52 52 52 52 54 51 52 51 52 | 52 | −0.13 | 0.02 |

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**MDPI and ACS Style**

Szolomicki, J.; Dmochowski, G.; Roskosz, M.
Dynamic Diagnostic Tests and Numerical Analysis of the Foundations for Turbine Sets. *Materials* **2023**, *16*, 1421.
https://doi.org/10.3390/ma16041421

**AMA Style**

Szolomicki J, Dmochowski G, Roskosz M.
Dynamic Diagnostic Tests and Numerical Analysis of the Foundations for Turbine Sets. *Materials*. 2023; 16(4):1421.
https://doi.org/10.3390/ma16041421

**Chicago/Turabian Style**

Szolomicki, Jerzy, Grzegorz Dmochowski, and Maciej Roskosz.
2023. "Dynamic Diagnostic Tests and Numerical Analysis of the Foundations for Turbine Sets" *Materials* 16, no. 4: 1421.
https://doi.org/10.3390/ma16041421