topic angular momentum kinetic energy 3d equations of motion 2 a hybri

Question

Topic: Angular Momentum, Kinetic Energy/3D Equations of Motion 2. A hybrid car combines and controls the power flows from an internal combustion engine ICE and two high speed motor/generators, MG1 and MG2, connected to a battery using a planetary gear set (ie Toyota Hybrid System) as shown. The planetary gear set has three inputs, (S)un, planet (C)arrier and (R)ing gears, such that the ICE rotation rate, ce, may be optimized to achieve highest efficiency at any car speed through the planetary gear set by electronically controlling the speed of MG1, GI (ie electronic continuously variable transmission).Note the rotation rates, @@GI, CE, and of the sun, planet carrier and ring of the planetary gear system are given by: N₁s+N₁-(Ns. N₂) =0 where N₁, Ng are the number of gear teeth on the sun and ring gears,respectively. Ng/N₁=2.6. The rotation rates, G2, Ow, of the motor/generator MG2 and the wheels, respectively, are given by G2-GR 2R, Ow=GRwO, GR-3.1, GRW 0.3.LICE, IMG 0.6 MG2-0.17 w where Ix is the spin axis rotational inertia of the ICE, MG1, MG2 and one wheel,respectively. All spinning components can be modelled as axisymmetric and with transverse rotational inertia's of 50% of the spin axis values. M is the total mass of the car and r,-0.63m is the wheel radius. Assume the hybrid car is travelling straight at steady speed in electric vehicle mode ie ce-0.(a) Determine the angular momentum components of the MG1 and MG2, as a ratio of one wheel's spin axis component. Comment on how negotiating a corner will change the components in the xyz directions.[6 mks](b) Determine the rotational kinetic energy of the MG1, MG2 as a ratio of one wheel's. Comment on the magnitudes. [4 mks](c) MGI develops an unbalanced shaking moment with measured amplitude 1.5 N m at 100km/hr. Calculate the depth of two drill holes of diameter 5mm at radius 60mm, on the MGI steel rotor of half-thickness 65 mm, that are required for balance. Prescribe the locations of the drill holes. {Hint: for simplicity align peak shaking moment with a body fixed axis)[8 mks]