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Prediction of High Frequency Response Characteristics of Hydraulic Mounts

The major objectives of this study are to identify the source(s) of high frequency resonance(s), suggest a method to effectively estimate mount parameters and propose both linear and nonlinear models capable of predicting the high frequency characteristics. First, a lumped parameter linear model is derived and the resonances controlled by decoupler, fluid column and rubber element are examined. By using a simplified mechanical model, typical parameters are estimated from measured dynamic stiffness data. Estimations correlate well with experiments and provide quantitative evaluation of the physical parameters, some of which (such as the decoupler damping) are otherwise difficult to measure by using conventional experimental techniques. A nonlinear time domain model for a free decoupler mount is proposed to predict both the inertia track and decoupler resonances. Both nonlinear and linear models match well with high frequency measurements. INTRODUCTION MOTIVATION AND LITERATURE REVIEW Hydraulic engine mounts are designed to provide superior amplitude-sensitive and spectrally-varying properties over the lower frequency regime (typically up to 50 Hz) [1]. However, at relatively higher frequencies (say from 50~300 Hz), the decoupler induced resonance could be dominant which would worsen their performance from the vibration isolation perspective. Singh et al. [1] developed linear time-invariant lumped parameter models for both free and fixed decoupler mounts. They suggested a multi degree of freedom (MDOF) fluid model. Ushijima et al. [2] suggested an analogy between mechanical and fluid elements in order to investigate the fluid resonance effect at higher frequencies. Lee et al. [3] modeled a hydraulic mount using the bond graph method, which was shown to be an efficient approach in developing the multi-disciplinary model equations. Colgate et al. [4] proposed two linear models for large amplitude and small amplitude excitations respectively though both models could be combined using piecewise functions. Geisberger et al. [5] examined the volume column effect within the decoupler regime and suggested a MDOF decoupler model as a remedy to the high frequency resonance. A “bell chamber” was also examined as an alternate way to suppress the decoupler resonance [6]. They proposed a decoupler model with exponential smoothening “stop” resistance to characterize the decoupler switching mechanism. Tiwari et al. [7-8] described a series of laboratory experiments to characterize various nonlinearities of fixed and free mounts. They also suggested a multi-staged switching model over the lower frequency regime (up to 50 Hz) to predict the transient behavior of the decoupler switching mechanism. PROBLEM FORMULATION Dominant inertial and standing wave effects may occur at higher frequencies (f) [11]. Further, prediction of higher frequency responses may demand a distributed parameter formulation along with a true nonlinear time domain model. However, simplifications can still be made depending on the frequency range of interest and the amplitude sensitivity of the particular mount design. Accordingly, key assumptions of this article are as follows. 1. The displacement excitation amplitude (X) is small (< 0.1 mm) over the higher frequency regime; this is due to the test machine limitations and low displacements found in vehicles at higher f. 2. For a free (or floating) decoupler hydraulic mount, the decoupler gap is assumed to remain open all the time and the governing system should be almost linear. 3. In this article, the hydraulic mount with a free decoupler is chosen although similar treatment could be extended to membrane type hydraulic mount. When an elastic membrane is used instead of a floating decoupler structure [2], the compliant membrane could accumulate the displaced fluid under small amplitude excitations. Thus, the inertia track is “decoupled” (or removed) from the system. 4. The driving point dynamic stiffness could be approximated by the measured cross point dynamic stiffness, especially at lower f [9]; this has been confirmed by the experimental work of Lee et al. [10]. The nonlinear lumped model suggested earlier by Adiguna et al. [8] is extended, in this article, to cover the higher frequency regime. Predictions of the resulting linear MDOF model will be verified. PROBLEM FORMULATION PHYSICAL MODEL Figure 1 shows the inner structure of a typical hydraulic mount (designated here as G). The rubber decoupler is placed between two inertia track plates with a small gap d g . Also the working thickness around the decoupler center is 5.0 mm, which makes the decoupler plate relatively rigid (with low compliance d C ). These design features make the dynamic stiffness relatively insensitive to the displacement excitation amplitude X (peak to peak), as shown by the measured data of Figure 2. Fig.1 Schematic of free decoupler mount G. Fig. 2 Measured dynamic stiffness of mount G up to 300 Hz. MDOF FLUID SYSTEM MODEL We develop a MDOF fluid model of a free decoupler mount by considering several control volumes as shown in Figure 3. The Voight visco-elastic formulation is used to characterize the rubber element in terms of dynamic stiffness kr and damping br that are weakly dependent on f and X.