Analysis of Low Free Vibration Modes Large Branched Gear Mechanisms Using Dqds Algorithm

The main impartial of this paper is to propose a new empirical process for computing the most dominant vibration modes of a large branched gearing mechanism in a lathe. This method utilizes the algorithm, which is derived from the LR algorithm and is particularly effective for finding the eigenvalues of large matrices. The gearing mechanism in question consists of multiple gears, resulting in numerous dynamic parameters that need consideration. To simplify the dynamic modelling process, the system is divided into subsystems. However, even the stiffness matrices derived for these subsystems are quite large, making it complex and time-consuming to compute the vibration modes from these matrices. To address these difficulties, the algorithm is employed to calculate the vibration modes of each subsystem. Typically, most systems operate within the mid-frequency range. As a result, this empirical method allows for the effective exclusion of less dominant vibration modes associated with high-frequency ranges. This simplifies the system model and reduces computational complexity significantly. This reduction method offers several advantages, including a simplified system model and reduced computational demands