MODELING THE SHAFT MOTION IN THE BEARING OF AN INTERNAL GEAR PUMP USING FRACTIONAL DERIVATIVES
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DOI:
https://doi.org/10.34238/tnu-jst.12953Abstract
In the process of designing and calculating the internal gear pumps, the lubricant film is modeled by a spring-damper system. Previous studies have been based on the assumption that the force generated by the lubricant film is a linear function of displacement and velocity. This paper proposes a new model using fractional-order derivatives, in which the lubricant film force depends nonlinearly on the velocity. The paper also establishes a method for calculating the stiffness and damping coefficients in the model, as well as determining the trajectory of the shaft motion. Numerical simulations are performed with the fractional derivative order ranging from 0.7 to 1.0. The results show that the stiffness coefficients converge rapidly and are less dependent on the value of , while the damping coefficients decrease quickly to zero as decreases. When the order approaches 1, the computational results converge to the linear case. The study demonstrates the potential of applying fractional calculus to solve practical engineering problems.Downloads
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