Structural optimization of an automobile transmission case to minimize radiation noise using the model reduction technique

Abstract

Vehicles should provide a comfortable environment for passengers. The noise from the transmission case is one of the causes of an uncomfortable environment. The transmission is composed of gears, shafts, bearing and cases. When transmission activity occurs, noise is transferred to the passengers through the transmission case. Design of the transmission case is performed in order to reduce the transmission noise. Acoustic analysis is carried out and structural optimization is utilized for the design to reduce the noise. Generally, the boundary element method (BEM) has been utilized for acoustic analysis. However, it is difficult to utilize the boundary element method in structural optimization because the cost to calculate the sensitivity information is fairly expensive. Instead, the finite element method (FEM) is employed for calculating the radiation noise of the transmission. Radiation noise is considered as the total noise from the transmission. Radiation noise is calculated at the outside of the transmission case and it can be expressed indirectly by multiplication of the velocity in the normal direction of the finite elements, the radiation efficiency and the characteristic acoustic impedance. The high frequencies are dominant for the transmission noise and the radiation efficiency is 1 at the high frequency range. Since the characteristic acoustic impedance has a constant value, the noise is the same as the norm of the velocity. The velocity of each finite element is calculated from modal analysis and the noise is expressed based on the average velocity of the vibrating structure. However, a long computation time is required to calculate the noise in a large scale structure such as a transmission. Thus, the entire model of transmission is condensed into the reduced model by the model reduction technique. The component mode synthesis (CMS) method is employed for the model reduction technique. The CMS method is an effective method for dynamic analysis of large and/or complex structures. The reduced model keeps the dynamic characteristics of the entire structure and it is used for structural optimization. In structural optimization, the design variables are the thicknesses of the groups of the transmission cases, the objective function is the mass of the structure and a constraint is imposed on the noise. An alternative formulation is made by exchanging the objective and constraint functions. The optimization results are discussed in terms of practical application.