Validation of the Accuracy of Approximation in a Design Formula for an Air Spring by Using Numerical Analysis

Abstract

Previously, the authors proposed an approximation formula for designing an air spring that consists of two air tanks connected by a long pipe. The analysis was based on a linear approximation, so there is no amplitude dependency in the amplitude ratio for the sinusoidal vibration of a system with an the air spring. However, according to the experiment, it was found that there is remarkable amplitude dependency in a system with this type of air spring, so the frequency response curves for the system change with the magnitude of the input amplitude. It became clear that the approximation formula is in agreement with the limit value when the input amplitude approaches zero. We consider that the deviation between the approximation formula and the experimental results are caused by the various assumptions which used in the analysis. As we remove these assumptions one by one, we perform the numerical analysis based on the finite difference method for this air spring. As a result, it was found that the effects of the turbulent flow in the pipe and the pressure loss at the inlet and outlet of the pipe are very small. A major influence is attributed in the connector that connects the pipe to the air chamber. The flow is throttled and disturbed at the connector whose inner diameter is smaller than the inner diameter of the pipe.