Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations (external excitation source) matches the system's natural frequency of vibration than it does at other frequencies. Mechanical resonance may cause violent swaying motions (large vibrational displacements) and even catastrophic failure (1).

External items in large vertical pumps that could excite a natural frequency are:

• Rotational unbalance
• Impeller exit pressure pulsations
• Gear couplings misalignment

Natural frequencies of a vertical pump and motor are calculated by performing a modal analysis using the Finite Element Method (FEM). The common name to refer to this kind of analysis is Finite Element Analysis (FEA). Typical software tools used at the Flowserve Santa Clara business unit for the analysis are ANSYS and Pro/ENGINEER. The primary reason for conducting an FEA is to obtain an acceptable separation margin between the unit operating speed and the individual structural natural frequencies.

FEA is based on a numerical method that some authors define as Galerkin's Method [Reddy, 1984]. A domain is divided into n number of subdomains, the elements, and equations of n grade are used to approximate the solutions of each subdomain. The accuracy of this numeric method depends on the number of subdomains into which the domain has been divided and the boundary conditions.

As associated with solving a differential equation, the accuracy of the FEA performed on a vertical pump and motor depends on the nature of the elements (in FEA software a considerable number of options are available for the analyst to select from depending on the purpose) and the boundary conditions applied to the model.

The element selection is not complex for an analyst with knowledge of the FEA software. Software like ANSYS, the one used by the Flowserve Santa Clara business unit, describes each element by the degrees of freedom, its particular properties, and its behavior and outputs.

On the other hand, the proper application of boundary conditions for a model requires knowledge and experience by the analyst. The analyst must not only possess the skills and knowledge about how to run the FEA software, but must also understand the behavior of the system modeled. In addition, an analyst must understand the significance of various actions and decisions that must be taken while modeling and running the analysis.

Background

During the spring of 2009, two large vertical pumps installed in a power generating plant experienced mechanical vibration problems associated with structural resonance.

The initial vibration amplitude of the pumps was found to be above the user's allowable vibration level. Preliminary solutions to the vibration problem affected the natural frequency values of the pump system, and a mechanical resonance condition appeared.

When the pumps were initially installed at the site, vibration readings were taken and a discrepancy was reported between the contractual limit of 0.157 in/s peak-to-peak and the measured vibration amplitude.

Before evaluating possible solutions to the problem, the pumps were bump tested to determine their structural natural frequency. Without water in the suction pit, the first structural natural frequency was 5.5 Hz, and the second natural frequency was 10.5 Hz. The second natural frequency is 23 percent higher than the operating speed of 514 rpm (8.5 Hz). As the suction pit was filled with water, the natural frequency values were reduced, since the water adds mass to the system. With the suction pit filled with water, a subsequent bump test showed a natural frequency at 8.5 Hz, which indicated that structural resonance was a contributing factor to the high mechanical vibration recorded when the pumps were operated.

The manufacturer proposed several different alternatives to shift the structural resonance and reduce the amplitude of the operating vibration. Since the second natural frequency coincided with the operating speed, a possible solution involved increasing the flexibility of the pump discharge head. Two methods to accomplish this task were evaluated-removing the external ribs from the discharge head or adding an external mass at the top of the motor.

Figure 1. Discharge head with external ribs available on original design. Cutting the external ribs was a proposed solution for increasing flexibility of the discharge head.

Figure 2. 3-D model of the pump.

The first step in the problem-solving process was to modify the FEA so that it agreed with the site bump test results. Cutting the external ribs would reduce the stiffness of the discharge head to mounting plate connection, which would lower the natural frequency value. The model was updated to simulate removal of the external ribs, and the analytical results showed that the natural frequency value decreased. Unfortunately, the reduction was not sufficient to provide the desired separation margin between the pump operating speed and the pump system natural frequency.

The next step was to model adding an external mass at the top of the motor. The pump manufacturer's standard is to procure motors capable of having external weight added to the top of the motor that is equal to 20 percent of the motor weight without affecting the structural integrity of the mechanical operation of the motor.

The pump motor's manufacturer was aware of this requirement and approved the installation of a 2,000-lb. weight at the top of the motor.