# Torsional Vibration Analysis

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## Torsional Vibration Analysis

### Vertical Pump, Torsional Natural Frequency (TNF), API 610, Critical Speed, Torque Response, Transient Analysis

Torsional vibration analysis for vertical pump was performed. This pump is driven by induction motor, and, it utilizes a constant speed driver and is connected to the pump shaft via flexible coupling. This analysis computes torsional critical speed, mode shapes, torque response and transient analysis for train shaft.

## 1. Scope of this Torsional Vibration Study

The scope of this torsional vibration analysis includes below activities;

• Rotordynamics model
• Torsional vibration as per API 610
• Vertical centrifugal pump
• Torsional Natural Frequency (TNF)
• Torsional Critical speed
• Separation margin with operating speed
• Torque Response Analysis
• Mode shape
• Campbell diagram (Torsional interference diagram)
• Dry and wet condition
• Transient Analysis
• Modified Goodman Diagram Analysis
• S-N Curve Estimation
• Coupling Torque Assessment

## 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 and motor elements; shaft, impeller, coupling, bearings, driver core, etc.) was set as shown in below figure.

Dry & wet run analysis needs to be performed for rotordynamics model, and the analysis was carried out with consideration of fluid inertia inside of pump impeller for wet condition. Altogether, below kinds of separate cases were analyzed.

• Dry condition: Torsional critical speed analysis
• Wet condition: Torsional critical speed analysis, Torque response analysis, Transient analysis

## 3. Design Criteria

Torsional vibration analysis for this pump is carried out as per API 610 11th and HI 9.6.8-2014, in which the design criteria such as separation margin are mentioned.

• Separation Margin: A separation margin of 10% obtained in the field conditions is typically satisfactory to avoid unacceptable torque response amplification.
• Torque Response: In case torsional resonance are estimated to fall within the separation margin (+/-10%) of operating speed, the steady state torque response and transient analysis shall be performed to demonstrate that the potential resonance have no adverse effect.

## 4. Critical Speed Analysis

The torsional vibration analysis computes undamped critical speeds and mode shapes. The critical speeds were estimated for both wet and dry conditions. Excitation of torsional natural frequencies can come from many sources, which might be a function of running speed and should be considered in this analysis. The torsional excitation forces considered consist of;

• One times of running speed (1x)
• Two times of running speed (2x)
• Number (five, 5) of impeller vane (5x)
• Number (nine, 9) of Impeller volute frequency (9x)
• 50 Hz, Line frequency (7.06x)
• Two times of Line frequency (14.12x)
• Motor pole pass frequency (14x)

The result shows the critical speed analysis for dry condition simply in above figure. Dry run analysis relates to undamped torsional critical speed calculations taking in account only the rotor model. Undamped (dry) natural frequency are shown versus rotor speed in below figure, and, for example, the cross point between 1st undamped torsional natural frequency with the run line (synchronous 2x line) is defined as the 1st dry critical speed. In above figure, it is found some interference points on torsional mode 1, 2 and 3. Then, Undamped mode shapes has been estimated for torque response analysis.

## 5. Torque Response Analysis

The steady state torque response analysis was done for wet condition, and total three (3) torque application cases were considered in order to realize the worst case of torsional vibration as results of mode shape analysis. A torque excitation corresponding to 1.0% of full load torque was applied at specified location. Based on mode shape analysis, the amount of torque amplitude is applied in order to excite the torsional modes of the train rotor in a worst case scenario. The amount of torque is oriented relative to each other in the worst possible configuration so as to produce the greatest possible torsional deflection as shown in below figure.

This addresses the possibility that the pump is operated continuously right at this critical speed. A conservatively estimated damping ratio of 1% was assigned to the mode. For this case, the phases of the torques are applied in a worst case configuration according to the mode shape. Hence, total response is determined by combining all of the individual response amplitudes calculated for in-phase applied loads at each forcing station.

The calculated steady state torque and dynamic torque are used to compute torsional shear stresses for comparison to material limits. This is done in a Goodman diagram analysis, where the goal is to show that predicted fatigue life is infinite.

The predicted alternating torques in the coupling are well below peak torque limit, which data was provided from Manufacturer. It is believed that the coupling can accommodate the predicted dynamic torque without failure.

## 6. Transient Torsional Vibration

Transient torsional analysis is similar to a steady state torque response analysis, except that it is done for the transient condition. Its results are cyclic torques and stresses as functions of time. This chapter includes definition of applied loads, calculation of response loads and performance of the stress analysis of the weakest shaft elements.

Four (4) different operating conditions has been examined to determine maximum torsional stress in train shaft, when the complete system is dynamically excited.

• Two phase short circuit torque
• Three phase short circuit torque
• Reclosing torque
• Accelerating torque

Driver manufacturer specified the corresponding excitation torques of induction motor in form of adequate equations for two phase short circuit torque as shown in below figure. This torque load was applied at the position of the motor core location to the loaded shaft.

In below figures, Transient torque responses are showing the simultaneous results on each shaft element for two phase short circuit torque, in which maximum torque amplitude will be compared with torque limitation.

Peak torque response loads occurring at shaft train were compared to the permissible torque load. Below figure contains a summary and evaluation of calculated torsional torque from transient analysis, and it is confirmed that all torque amplitudes for all cases are within acceptable limits. For all components of this pump, a safe operation can be expected.

## 7. Major Keywords – Torsional Vibration Analysis

• Rotordynamics
• Torsional vibration
• Critical speed
• Torque Response
• Torsional Stress
• Campbell Diagram

INERTANCE has a capability regarding noise and vibration engineering, and our experts are familiar with assessment of Torsional Vibration Analysis.