Bending Frequency Alteration of Rotating Shafts

Rotating shafts are commonly employed in several automotive systems. An important issue when utilizing these shafts is their NVH (noise, vibration and harshness) characteristics. The resonant frequencies of these components, which can be excited externally (due, for example, to an imbalance force or vehicle external loads) or internally (due to parametric excitations, a possibility in drivelines) should be avoided for optimum NVH performance. Provided the exciting frequencies are known, one can attempt to design the shafts, or alter an existing design, to achieve this goal. In this work, which is exploratory in nature, two items are investigated. A simple shape optimization is conducted with the objective of increasing the shaft resonant frequency, which could drive it away from the range of excitations. Also a study involving an exploration of the use of functionally graded materials is presented. An existing model, which allows for changes in the material's Young's Modulus and density via three parameters, is utilized. The sensitivity of the lowest bending natural frequency to the parameters is analyzed using an assumed mode method. The study showed that the effect of the spin of the shaft was negligible. It was found that an increase of about 43% of the first bending frequency can be achieved by increasing Young's modulus by a factor of 2 and density by a factor of 1.15. In the study of shape optimization it was found that increases of the order of 5% can be obtained with realistic changes of the shape of the shaft.