# NATURAL FREQUENCY AND VIBRATION

 WHAT IS NATURAL FREQUENCY?
 The natural frequency of a system is the rate at which an object vibrates in the absence of any damping force. When the natural frequency is near or equal to the operating speed of the rotating equipment, like a pump, the system will experience high vibration amplitudes. When a pump operates at its natural frequency for an extended period of time it can drastically decrease the life.
 In a real world example, we were called out to a job site to analyze excessive vibration on several vertical turbine pumps. These pumps operated on a variable speed drive and the customer wanted to operate them down to 45 Hz. The pumps would operate in a range between 1350 and 1800 RPM.  In order to have a better understanding of the current design, our first step was to perform a finite element analysis of a solid model representing the discharge head. The model below displays how the discharge head was originally designed. You can see that it was made to be extremely rigid with both external and internal stiffeners. The natural frequency was measured to be 1500 RPM which was within the range that they intended to operate. Our options now were to either increase the rigidity of the head to bring the natural frequency up or decrease the rigidity to bring it down.

#### Original Discharge Head With Stiffeners

 In the case of this particular head, which was extremely rigid to begin with, it made more sense to look to reduce its natural frequency by removing stiffeners. We proceeded by modeling and analyzing the head in Solidworks after removal of the stiffeners. In doing so, our goal was to reduce the natural frequency to an acceptable level. Eventually we settled on the below design which removed the external stiffeners and half of the internal stiffeners.

#### Final Design With No External Stiffeners & Half Of The Internal Stiffeners

 With the final design we were able to recommend operation of the pump down to 46 Hz, or 1380RPM with a 10% safety margin.  Removing the full internal stiffeners would further reduce the critical frequency, however it was not a cost effective solution.

#### Finite Element Analsysis of Final Head Design

 When we were first called out to analyze these pumps, vibrations at pump #2 operating at 50Hz were measured to be 0.47 in/sec RMS. The Hydraulic Institute standard allows for 0.17 in/sec RMS for this size and type of pump. After modifying the discharge heads the vibration measured at 50Hz decreased significantly to 0.05 in/sec RMS.
 Strong Is Not Always Be Better
 This example displays the importance of determining the natural frequency of a pump prior to fabrication. On a vertical turbine pump, the discharge head is the ideal location to make adjustments that  change the natural frequency of the unit. We recommend avoiding cast iron heads for VFD operation since they are not as easily modifiable as a fabricated steel head.
 Smith Pump Company designs all of our fabricated steel heads in Solidworks and they go through finite element analysis to make sure the natural frequency is at least 25% away from operating speeds.
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