Archives of Acoustics,

**6**, 2, pp. 89-110, 1981### A model of piston impact and vibration for internal combustion engine noise reduction

In this paper a mathematical model is developed to study piston impact and cylinder liner vibration in internal combustion engines. The aim of this study is to assess the effect on cylinder liner response (and, therefore on piston-- impact induced noise) of certain design modifications such as cylinder liner stiffness, -piston mass, and piston/cylinder liner running clearance. A single-mode representation of cylinder liner vibration is developed using the assumed modes method, where the cylinder liner is modeled as a thin cylindrical shell with fixed-free boundary conditions. Expressions for the kinetic and potential energy of the system, and for the generalized mass and stiffness of the system are developed. Lagrange's equation of motion is used to derive a differential equation of cylinder liner motion. The equation of motion for the piston is derived by assuming that the piston motion is pure translation. The initial conditions for cylinder liner response are developed from the conservation of momentum of the piston and the cylinder liner at impact. Experimental cylinder liner -vibration data from a diesel engine are used to verify the accuracy of the piston impact model. Agreement between the experimental data and the cylinder liner response predicted by the mathematical model is generally good, but some discrepancies do exist. A computer simulation of the model is used to study the effect of parameter changes.

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