Method for identification of hydraulic impedance of a positive displacement pump based on pressure transfer functions estimation

Abstract

In hydraulic systems, pressure pulsations can excite structural resonances, causing unwanted vibrations and noise. A key parameter for analyzing such effects is the hydraulic impedance, as it characterizes the reflection behavior of components such as pumps and enables system-level resonance analysis. This study presents an enhanced evaluation method based on the Secondary Source Method for identifying the impedance of positive displacement pumps. A simplified one-dimensional simulation model is used to implement the method numerically, with the pump impedance represented as a Helmholtz resonator. To reduce measurement and modeling effort, the system is excited by a frequency sweep via the Secondary Source rather than by discrete pulsation frequencies as in the original presented method. This is achieved by reformulating the impedance calculation with the Transfer Matrix Method and pressure transfer functions estimated using the H₁-estimator, eliminating the need for a stationary harmonic state. The H₁-estimator improves robustness against noise, particularly near impedance minimum, while coherence serves as a quality criterion. Invalid frequency ranges are compensated by combining multiple sensor pairs, further increasing stability. The method is validated with measurement data from a vane pump, confirming its practical applicability and showing that the Helmholtz model reproduces the impedance behavior more accurately than the λ/4 model used in earlier studies. The ability to experimentally identify and model the impedance of hydraulic components enables realistic system simulations. In applications such as commercial vehicle steering systems, where pump-induced pulsations can excite resonances, the proposed method supports early-stage acoustic optimization without extensive trial-and-error or large measurement campaigns.