Lateral Vibration Analysis

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Lateral Vibration Analysis

Vertical Pump, Rotordynamics, API 610, Critical Speed, Unbalance Response, Damping

Lateral vibration analysis for vertical pump was performed. This pump is driven by induction motor with fourteen (14) pole rated at 3000 kW and 425 rpm at full load. And, it utilizes a constant speed driver and is connected to the pump shaft via flexible coupling. This analysis computes rotordynamics study, mode shapes, and unbalance response for pump shaft, which was done for test condition, nominal (new) seal clearances, and doubled (worn) seal clearance with site condition.


  1. Scope of this analysis
  2. Rotordynamics Model
  3. Design Criteria
  4. Critical Speed Analysis
  5. Damping Factor Estimation
  6. Unbalance Response Analysis
  7. Major Keywords
  8. Related Services

1. Scope of this rotordynamics  

The scope of rotordynamics includes below activities;

  • Rotordynamics model
  • Lateral vibration analysis as per API 610   
  • Vertical centrifugal pump
  • Critical speed assessment
  • Separation margin with operating speed
  • Damping factor evaluation
  • Mode shape
  • Campbell diagram
  • Unbalance response analysis
  • Clearance margin
  • Dry, Wet condition
  • Shop test and Site condition

2. Rotordynamics Model

Rotordynamic analysis of this pump was performed using FE calculation procedure, and Numerical model for the complete pump (including all important pump elements; shaft, impeller, coupling, bearings, wear-rings) was set as shown in below figure.

[Rotordynamics Model]

Dry & wet run analysis needs to be performed for two (2) pumping liquids; Test water & actual pumping fluid respectively. Altogether, below kinds of separate cases were analyzed.

  • Dry condition
  • Wet condition with 1x Clearance and test water
  • Wet condition with 1x Clearance and project pumping liquid
  • Wet condition with 2x Clearance and project pumping liquid

3. Design Criteria – lateral vibration

Lateral vibration analysis for this pump is carried out as per API 610 11th, in which the design criteria such as separation margin, damping factor, clearance margin are mentioned. It should be noted that the specific procedure in Annex I, API 610 11th is not applicable to vertical pump, which is necessary to Between bearing pump (BB) type. However, the analysis procedure and criteria is performed as per Annex I, API 610, where applicable.

  • Separation Margin: A separation margin of 10% obtained in the field conditions is typically satisfactory to avoid unacceptable vibration response amplification. 
  • Damping Factor: For both new (1x) and worn (2x) seal clearances, the damping factor versus separation margin between any lateral natural frequency and the synchronous run line shall be with the “Acceptable” region. 
Damping Factor Criteria - rotordynamics

[Damping Factor Criteria]

  • Clearance Margin: If the damping factor versus separation margin for each mode is not acceptable by specified criteria, the rotor damped response study to unbalance shall be performed.

4. Critical Speed Analysis

INERTANCE performed critical speed analysis for lateral vibration study. Campbell diagrams and mode shapes for critical speed understandings are estimated for the pump with new (1x) and worn (2x) running clearance. Excitation frequencies of concern are defined with running speed (1x), two (2) times of running speed (2x) and number of impeller vanes (5x), which each order excitation is marked in campbell diagram.

  • One times of running speed (1x)
  • Two times of running speed (2x)
  • Number (5) of impeller vane (5x)

It is found the interference point between 2nd order excitation and 3rd mode (green color) within 15% of separation margin to operating speed (425 rpm). This interference point will be carefully estimated during unbalance response analysis.

Campbell diagram - lateral vibration

[Campbell Diagram, Wet Condition, 1x Clearance, Site]

[Mode Shape, Wet Condition]

5. Damping Factor Estimation

Review of calculated damping factor according to below figure is shown for 1x Clearance and 2x Clearance together. The calculated damping factor at 1st critical speed for both clearance conditions (new & worn) are located within the unacceptable region. As this damping factor criteria is not satisfied, the damped response to unbalance is carried out as per Annex I of API 610 11th.


[Damping Factor versus Frequency Ratio Map]

6. Unbalance Response Analysis

The damped unbalance response analysis in accordance with Annex I from API 610 11th was performed, and total four (4) times of the allowable unbalance weight was applied on this analysis. See below figure for amount of unbalance applications.

[Unbalance Weight Application]

The unbalance response was calculated for new and worn clearances respectively, and below figures show responses computed throughout the entire speed range of the pump for the unbalance case 1.

[Unbalance Response Plot]

Throughout the operating speed, 425 rpm and at all analyzed cases, the results showed that the maximum response amplitude at each element are well within the acceptable region as per Annex I of API 610 11th, as they do not exceed 35% of the diametral clearance. The operating deflected shape with criteria at 425 rpm is shown in below figure.

[Deflected Shape, Wet Condition]

7. Major Keywords

  • Rotordynamics
  • Lateral vibration
  • Critical speed
  • Unbalance response
  • API 610

INERTANCE has a capability regarding noise and vibration engineering, and our experts are familiar with assessment of Lateral Vibration (Rotordynamics) Analysis. For further information, contact us at (

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