a) [15 marks] stationary bearing T(t) shaft A PS B viscous fluid A cylinder A rotates about its axis inside a bearing. T

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A 15 Marks Stationary Bearing T T Shaft A Ps B Viscous Fluid A Cylinder A Rotates About Its Axis Inside A Bearing T 1 (73.11 KiB) Viewed 45 times

a) [15 marks] stationary bearing T(t) shaft A PS B viscous fluid A cylinder A rotates about its axis inside a bearing. The cylinder is hollow with all its mass concentrated in a thin shell around its circumference. The small gap between the cylinder and the bearing contains a viscous fluid. A long, thin shaft connects the cylinder to a flywheel B. The flywheel is solid and its mass is uniformly distributed within it. A time- varying tortional moment T(t) is applied to the flywheel causing the system to rotate. The shaft strains elastically due to this motion. Develop the state space equations of motion for both the cylinder and the flywheel. Assume that the damping force due the bearing fluid is proportional to angular velocity. The equations should be expressed using only of the following variables: t-time A and 0B - the angular degrees of freedom of the cylinder and flywheel A and Oв - the angular velocities of the cylinder and flywheel mA and RA - the mass and radius of the cylinder mв and Rв the mass and radius of the flywheel b- the damping coefficient of the bearing fluid k- the torsional spring coefficient of the elastic shaft T-the tortional moment