# Investigation on the influence of unbalanced shaft component in gearbox on displacement using the Newmark-β method

## TL;DR

This paper presents a new numerical method to analyze how unbalanced shaft components in gearboxes affect displacement and torsional deformation.

## Contribution

The integration of a variable time-step algorithm with the Newmark-β method improves accuracy and speed in dynamic analysis.

## Key findings

- The model shows less than 6% deviation in displacement compared to experimental data below critical speed.
- The method enables rapid convergence and reliable predictions for system dynamics.
- Parametric analysis reveals the impact of rotational speed, trial mass, and phase angle on system behavior.

## Abstract

This study introduces an enhanced numerical approach for analyzing the dynamic behavior of a rotor-bearing system subjected to unbalanced excitation from a gearbox drive shaft. The Newmark-β method with the integration of a variable time-step algorithm was used, allowing the system to be solved rapidly and accurately without compromising stability. This technique enables a precise computation of displacement and torsional deformation of the rotating shaft during its operational cycle. The proposed computational model is validated against experimental data, showing deviations of displacement in normal operation below the critical speed of about 6%. A comprehensive parametric analysis is conducted to evaluate the influence of rotational speed, trial mass, and initial phase angle on the system dynamics. The findings confirm that our enhanced numerical approach yields rapid convergence and reliable predictions, making it a valuable tool for dynamic analysis of rotating systems.