Asymptotic analysis of self-excited and forced vibrations of a self-regulating pressure control valve

Abstract

Pressure vibrations in hydraulic systems are a widespread problem and can be caused by external excitation or self-exciting mechanisms. Although vibrations cannot be completely avoided in most cases, at least their frequencies must be known in order to prevent resonant excitation of adjacent components. While external excitation frequencies are known in most cases, the estimation of self-excited vibration amplitudes and frequencies is often difficult. Usually, numerical studies have to be executed in order to elaborate parameter influences, which is computationally expensive. The same holds true for the prediction of forced oscillation amplitudes. This contribution proposes asymptotic approximations of forced and self-excited oscillations in a simple hydraulic circuit consisting of a pump, an ideal consumer and a pressure control valve. Two excitation mechanisms of practical interest, namely pump pulsations (forced vibrations) and valve instability (self-excited vibrations), are analyzed. The system dynamics are described by a singularly perturbed third-order differential equation. By separating slow and fast variables in the system without external excitation, a first-order approximation of the slow manifold is computed. The flow on the slow manifold is approximated by an averaging procedure, whose piecewise defined zero-order solution maps the valve’s switching property. A modification of the procedure allows for the asymptotic approximation of the system’s forced response to an external excitation. The approximate solutions are validated within a realistic parameter range by comparison with numerical solutions of the full system equations.

An alternative approach to averaging in nonlinear systems using classical probability density

“…To obtain the CPD of 𝑔(𝑡), the analytic formula (79) cannot be used anymore since the inverse of the function cannot be given by a closed formula. In addition, the motion is not periodic, implying the assembly of infinitely many terms in Equation (7). If one wants to sample 𝑔(𝑡) starting at 𝑡 = 𝑎 and ending at 𝑡 = 𝑏, the resulting CPD would depend on the values of 𝑎 and 𝑏.…”

“…It is an essential tool for analyzing and synthesizing such systems, as it enables the effective representation of the underlying dynamics. The technique has been extensively studied and applied in various fields, including physics [1][2][3][4], engineering [5][6][7][8], and biology [9].…”

Assessment of units vibration state and water supply path of Amuzang-2 pumping station

“…The main reasons for the unsteady pulsating flow are inherent in the very nature of the centrifugal pump, its design features, and the physical processes that occur when water flows through the elements of the flow path [10][11][12][13][14][15][16][17][18][19].…”

Nonlinear dynamics and safety aspects of pressure relief valves

“…Because of the possibly rare opening, the dashpot aiming to provide additional damping can get stuck, which could have catastrophic consequences; external viscous damping carries high safety risks and maintenance requirements. Still, the magnitude of damping becomes relevant when valve vibrations occur [1,2]. These vibrations can be detected by the harsh noise which often includes the sound of the impacts between the valve disc and the valve seat.…”