Determination of Kinematic and Dynamic Characteristics of Oscillating Conveyor Mechanism

This research focuses on the dynamic analysis of an oscillating conveyor mechanism using numerical methods to solve nonlinear differential equations that govern its motion. The system under study is modeled by a second-order differential equation of the form R(t)dω1dt+Q(t)ω12(t)=W(t), where R(t), Q(t), and W(t) are time-dependent functions representing system parameters such as resistance, damping, and external driving forces. To solve these equations, we employed a numerical approach based on Euler’s method, which discretizes the time domain into small steps h and approximates the derivatives of angular velocity and angular displacement. The angular velocity ωk+1 and angular displacement φk+1 are updated iteratively using the formulas ωk+1=ωk+h(WkRk−QkRkωk2) and φk+1=φk+hωk, respectively. Initial conditions, with ω0=0 and φ0=0, were specified, and the system was simulated over a specified time range divided into N time steps. In the simulation, key parameters such as A(t), B(t), D(t), E(t), F(t), H(t), N(t), M(t), Q(t), R(t), and W(t) were evaluated at each time step based on the system’s geometry and the angular displacements. Due to the complexity of the system, analytical solutions were impractical, so the Runge–Kutta method was employed for higher accuracy in the integration process. The results from the numerical simulations were validated by comparing them with theoretical expectations, and the system’s dynamic behavior was visualized using time-series and 3D plots. The simulation demonstrated that the system’s stability and accuracy were highly dependent on the time step h, with smaller values providing more precise results at the cost of increased computational time. The research confirms the applicability of numerical methods in solving complex nonlinear differential equations for dynamic systems and provides insights into the system’s behavior under various operating conditions.