Time-Domain Substructure Transient Vibration Transfer Path Analysis Based on Time-Varying Frequency Response Functions under Operational Excitations

Rong He,Hong Zhou

doi:10.1155/2019/2030326

Abstract

The time-domain substructure inverse matrix method has become a popular method to detect and diagnose problems regarding vehicle noise, vibration, and harshness, especially for those impulse excitations caused by roads. However, owning to its reliance on frequency response functions (FRFs), the approach is effective only for time-invariable linear or weak nonlinear systems. This limitation prevents this method from being applied to a typical vehicle suspension substructure, which shows different nonlinear characteristics under different wheel transient loads. In this study, operational excitation was considered as a key factor and applied to calculate dynamic time-varying FRFs to perform accurate time-domain transient vibration transfer path analysis (TPA). The core idea of this novel method is to divide whole coupled substructural relationships into two parts: one involved time-invariable components; normal FRFs could be obtained through tests directly. The other involved numerical computations of the time-domain operational loads matrix and FRFs matrix in static conditions. This method focused on determining dynamic FRFs affected by operational loads, especially the severe transient ones; these loads are difficult to be considered in other classical TPA approaches, such as operational path analysis with exogenous inputs (OPAX) and operational transfer path analysis (OTPA). Experimental results showed that this new approach could overcome the limitations of the traditional time-domain substructure TPA in terms of its strict requirements within time-invariable systems. This is because in the new method, time-varying FRFs were calculated and used, which could make the FRFs at the system level directly adapt to time-varying systems from time to time. In summary, the modified method extends TPA objects studied in time-invariable systems to time-varying systems and, thus, makes a methodology and application innovation compared to traditional the time-domain substructure TPA.

Highlights

In the beginning of the 1980s, classical transfer path analysis (TPA) methods were developed; after decades of development, TPA has become a useful tool for load identification and contributes to investigation in the field of noise and vibration [1–3]. ere are three major limitations regarding traditional TPA
Several new approaches, such as operational TPA (OTPA), have been developed in the last two decades, aimed at overcoming these limitations [10–20]. ese methods attract some attention as they only require operational data measured at the path and reference locations under certain conditions [21]. us, they avoid testing frequency response functions (FRFs) and a considerable amount of testing time
During the 2010s, several researchers started to study substructure inverse matrix TPA (IMTPA) methods [20, 34–36]. ese methods have some advantages over traditional TPA and operational path analysis with exogenous inputs (OPAX) [1–3, 6–8, 37, 38]. e classical TPA is more time-consuming owing to the requirement of system disassembly, and OPAX is not a suitable method for transient loads

Summary

Introduction

In the beginning of the 1980s, classical transfer path analysis (TPA) methods were developed; after decades of development, TPA has become a useful tool for load identification and contributes to investigation in the field of noise and vibration [1–3]. ere are three major limitations regarding traditional TPA. Us, they avoid testing FRFs and a considerable amount of testing time Despite saving time, these approaches suffer from problems regarding the setting of appropriate paths and reference locations. E core idea of OPAX is a combination of the necessary minimal FRFs and operational data for a compromise between results accuracy and tests, consuming via parametric models for the load identification [10, 11, 20, 24]. In the 2010s, a time-domain substructure transient vibration TPA method was studied by several researchers. E classical TPA is more time-consuming owing to the requirement of system disassembly, and OPAX is not a suitable method for transient loads. The traditional substructure inverse matrix method based on FRFs has one main limitation; the whole system should be considered as a stable unit, and its transfer characteristics are not likely to be changed by loads.

Methods

Experimental Validation