A Smart Helmholtz Resonator

Helmholtz resonators are commonly used for tuning of acoustic systems such as industrial processes, vehicle exhaust, engine intake manifold systems and more. Past efforts resulted in limited tuning capability and significant mechanical complexity. The work presented here considers a system that modifies the acoustic response of a system continuously, online, allowing optimum performance over a range of operating conditions in contrast to discrete points. The system consists of a static Helmholtz resonator designed to enforce a nominal resonance and an active control of an audio speaker that provides a variable acoustic impedance. The combination of the nominal impedance of the resonator and the differential impedance of the control speaker results in a active controlled, variable frequency Helmholtz resonator, named for simplicity the “Smart Helmholtz Resonator.” The system is modeled using bond graph methods and state space formulation is used to analyze the frequency response. INTRODUCTION The Helmholtz resonator (HR) is an ideal, simple acoustic device that has applications in acoustic systems. In acoustic system design, a HR is often used to modify the acoustic response. For example, internal combustion engine intake manifold systems are designed so that the acoustic response enhances the engine performance, increases fuel economy and reduces emissions (Kong, Woods, 1992). When design considerations such as space and material limitations cause the acoustic response to degrade engine performance and/or create excessive noise, the solution is often to add a designed HR to the system, thus improving the response. Tuning of engine intake manifold systems is commonly used in the automobile industry. Engine performance can be greatly improved by designing the dimensions of the intake manifold system to improve the engine “breathing” (Jameson, Hodgins, 1990). More recently, efforts have been made to change the acoustic response of the intake manifold system on-line. The GM 4.3L V6 engine uses a butterfly valve to change the manifold acoustic response between two configurations at a given engine speed (Grahm et al., 1992). The result is an engine that is tuned at two speeds, instead of one, and thus has greater performance and higher fuel economy. Another model, the engine in the Mazda Wankel engine powered car changes the length of the acoustic space in the intake manifold continuously as the engine speed changes using a unwinding coiled acoustic duct (Garret, 1992). The result is an engine that can be tuned at a range of frequencies and thus improved performance over a range of engine speeds. However the complex mechanism used to control and link the coil duct to the engine adds significant complexity to the manifold design. This paper considers the solution of using active control to modify the acoustic response of a HR in real time. A successful working model of the Smart HR could be used in engine intake manifold systems to continuously tune the engine over a range of operating speeds and thus improve engine performance over a wide range of operating speeds. This system would function as a self-contained device with few moving parts and integrate smoothly with the manifold system, thus eliminating the complexity of changing the physical dimensions of the acoustic system during operation. MODEL DEVELOPMENT The model of the Smart Helmholtz Resonator (SHR) consists of an ideal HR, with a complex impedance boundary condition. A controller is used to implement the boundary condition and bond graph modeling and frequency response is used to analyze the resulting system. An ideal HR is an acoustic resonant system whose volumetric flow ua, to input pressure, Pin relationship can be represented by a second order transfer function. The HR consists of a rigid-wall cavity and at least one short and narrow orifice thorough which the fluid filling it communicates with the external medium (Temkin, 1936) as shown in Figure 1. Cross Section Area, S