An Enhanced Methodology for Estimating the Natural Frequency of Valves Using Raleigh’s Energy Principle

This paper presents a model for calculating the minimum natural frequency of valve assemblies using the Raleigh’s energy principle. Raleigh’s principle states that the point where the kinetic energy of a multi-mass system and its potential energy are equal defines the minimum natural frequency of the system. This principle was used by Ezekoye to calculate the natural frequency of valve superstructures [1]. The early Ezekoye paper provided the fundamental tools for estimating the natural frequency of valves. However, over the years, with increasing valve testing to support Generation 3 nuclear power plants requirements, where natural frequency testing is required to complement analytical predictions, it has been noted that the Ezekoye simplified model adequately addressed valves with symmetric actuators and valves with minimal center of gravity (CG) offsets but over predicts the natural frequencies of valves with large CG offset actuators. Testing experience shows that a valve’s extended structure has two fundamental natural frequencies whose values are dictated primarily by the structural flexibility in bending and torsion. This paper extends the Ezekoye model by incorporating mass inertia of the structures with the more traditional methods that are based on a lumped mass model to determine displacements. In the process, the flexibility of the extended structure (otherwise referred to as the superstructure) and the valve body itself are considered. The approach covered in this paper combines classical statics, dynamics, and strength of materials techniques to model the natural frequency of a valve assembly. The resultant natural frequencies from the enhanced model are expected to provide better predictions of the minimum natural frequencies of valve assemblies.