# Effect of Impeller Diameter on Dynamic Response of a Centrifugal Pump Rotor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Modeling

_{n}is the generalized coordinate and Q

_{nc}represents non-conservative forces that are not directly related to the potential energy of the system. So, to derive the governing equations of motion using Equation (1), one must calculate the kinetic and potential energy of the system.

#### Ball Bearing Model

## 3. Numerical Solution

#### Bearing Stiffness of P-502B

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Calculated response at impeller diameter = 0.254 m for API unbalance, normal bearing clearance.

**Figure 7.**Calculated response at impeller diameter = 0.281 m for API unbalance, normal bearing clearance.

**Figure 8.**Calculated response at impeller diameter = 0.31 m for API unbalance, normal bearing clearance.

Parameter | Value |
---|---|

Material | AISI4140 |

Length (m) | 0.7 |

Equivalent diameter (m) | 0.036 |

Young’s modulus (N/${\mathrm{m}}^{2}$) | 2.10 × 10^{11} |

Density (kg/${\mathrm{m}}^{2}$) | 7850 |

Mass (kg) | 5.6 |

Polar inertia of mass (kg-${\mathrm{m}}^{2}$) | 0.000939 |

Diametric inertia of mass (kg-${\mathrm{m}}^{2}$) | 0.2373 |

Moment of inertia $\left({\mathrm{m}}^{4}\right)$ | 8.24 × 10^{8} |

Parameter | Value |
---|---|

Material | GG25 |

Type | closed |

Equivalent thickness (m) | 0.12 |

Diameters (m) | 0.254–0.281–0.31 |

Density (kg/${\mathrm{m}}^{2}$) | 7150 |

Mass (kg) | 4.3–5.2–6 |

Polar inertia of mass (kg-${\mathrm{m}}^{2}$) | 0.03467–0.05231–0.06153 |

Diametric inertia of mass (kg-${\mathrm{m}}^{2}$) | 0.017338–0.02422–0.03283 |

SKF6307 | SKF7308 | |
---|---|---|

Parameter | Value | value |

${D}_{m}$ (mm) | 57.5 | 65 |

${D}_{b}$ (mm) | 13.5 | 15 |

Z | 8 | 8 |

g (mm) | 0.051 | 0.053 |

${r}_{i}{r}_{o}$ (mm) | 41.2 | 46.35 |

$\gamma $ | 0.23 | 0.23 |

${f}_{i}$ | 3.05 | 3.08 |

${f}_{o}$ | 3.05 | 3.08 |

$\sum}{\rho}_{i$ (${\mathrm{mm}}^{-1}$) | 0.31 | 0.28 |

$\sum}{\rho}_{o$ (${\mathrm{mm}}^{-1}$) | 0.24 | 0.22 |

$\mathrm{F}{\left(\rho \right)}_{i}$ | 0.216 | 0.215 |

$\mathrm{F}{\left(\rho \right)}_{o}$ | 0.212 | 0.211 |

${\delta}_{i}^{*}$ | 0.9865 | 0.9866 |

${\delta}_{o}^{*}$ | 0.9869 | 0.9871 |

${k}_{pi}$ ($\mathrm{N}/{\mathrm{mm}}^{1.5}$) | $3.940\times {10}^{5}$ | $4.146\times {10}^{5}$ |

${k}_{po}$ ($\mathrm{N}/{\mathrm{mm}}^{1.5}$) | $4.472\times {10}^{5}$ | $4.673\times {10}^{5}$ |

${k}_{pio}\left(\mathrm{N}/{\mathrm{mm}}^{1.5}\right)$ | $1.301\times {10}^{5}$ | $1.342\times {10}^{5}$ |

Limited Speed (RPM) | 12,000 | 10,000 |

Diameter of Impeller (mm) | Amplitude of Vibration (m) | Critical Speed (Backward) (Rpm) | Critical Speed (Forward) (Rpm) |
---|---|---|---|

254 | 0.198 | 13,480 | 14,646 |

281 | 0.380 | 12,909 | 14,437 |

310 | 0.401 | 12,493 | 14,184 |

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**MDPI and ACS Style**

Shooshtari, A.; Karimi, M.; Shemshadi, M.; Seraj, S.
Effect of Impeller Diameter on Dynamic Response of a Centrifugal Pump Rotor. *Vibration* **2021**, *4*, 117-129.
https://doi.org/10.3390/vibration4010010

**AMA Style**

Shooshtari A, Karimi M, Shemshadi M, Seraj S.
Effect of Impeller Diameter on Dynamic Response of a Centrifugal Pump Rotor. *Vibration*. 2021; 4(1):117-129.
https://doi.org/10.3390/vibration4010010

**Chicago/Turabian Style**

Shooshtari, Alireza, Mahdi Karimi, Mehrdad Shemshadi, and Sareh Seraj.
2021. "Effect of Impeller Diameter on Dynamic Response of a Centrifugal Pump Rotor" *Vibration* 4, no. 1: 117-129.
https://doi.org/10.3390/vibration4010010