A semi-analytical study on fluid-induced nonlinear dynamic behavior of the flexible robotic arms

Abstract

The accuracy and performance of a robot arm is reduced when placed in a fluid environment due to inductive vibrations caused by drag forces created by surrounding fluids. Accordingly, in this research, the fluid-induced nonlinear dynamic behavior of the robot flexible arm is investigated semi-analytically. In order to model the induced vibrations in the robot arm, the equations governing the transverse vibrations of the arm are derived using the nonlinear Euler–Bernoulli beam theory and taking into account the force due to the fluid surrounding the arm. A differential equation is used to calculate the force exerted on the arm by the surrounding fluid in terms of the frequency of the vortices and the deflection of the robotic arm. After the differential equations governing the forced dynamic behavior of the robot arm have been extracted, an appropriate numerical method will be applied to analyze the effect of system parameters such as the geometric and mechanical characteristics of the arm, fluid velocity, etc on the response of forced vibrations and natural frequencies of the robot arm. According to the results, as the fluid velocity increases, the inertial forces increase and cannot be ignored. The vibrations amplitude of the system increases abruptly at higher fluid velocity, and the oscillations of the system stabilize. When the nondimentional velocity of the fluid is equal to 2, the amplitude of the stable oscillations is equal to 0.2 of the thickness of the arm, which is higher than the amplitude of free vibrations. This range of fluid velocity is known as the lock-in zone.