شبیه‌سازی گیربکس جهت مطالعه رفتار ارتعاشی در شرایط کاری مختلف

Vibration analysis of gearboxes serves as a critical metric for performance monitoring and condition assessment. This study investigates the dynamic behavior of a gearbox under varying operational conditions, with particular focus on the influence of input parameters—namely torque and rotational speed—on its vibration response. A nonlinear six-degree-of-freedom (6-DOF) dynamic model is developed for a single-stage spur gear pair. Time-varying mesh stiffness, a key contributor to gear-mesh frequency characteristics, is incorporated into the model. The mesh stiffness is formulated as a nonlinear, piecewise function, distinguishing between single- and double-tooth contact phases. To facilitate dynamic simulation, a discrete Fourier series approximation is employed to represent the periodic mesh stiffness, balancing computational efficiency and fidelity; while increasing the number of harmonics enhances accuracy, it also significantly raises computational cost and numerical complexity. The governing equations of motion are non-dimensionalized and solved numerically in state-space form using the fourth-order Runge–Kutta method (ode45). The proposed model enables precise evaluation of how mechanical load and speed variations affect key vibration features. Results demonstrate that the gearbox vibration response exhibits high sensitivity to changes in both input torque and shaft frequency. Specifically, the root-mean-square (RMS) value—a widely used diagnostic feature—increases consistently with rising torque and rotational speed. This trend is attributed to elevated tooth contact forces under higher loading, leading to amplified vibration amplitudes, which is clearly reflected in the simulation outcomes. The methodology and framework established in this work can be extended to multi-stage and planetary gear systems, offering a foundation for developing more sophisticated digital twin models in future research.