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modeling7

modeling7 - Modeling QUESTION 7 For the system shown in...

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Q UESTION 7 For the system shown in Figure 7, set up the equations in matrix form that would allow you to determine the transfer function ( 29 ( 29 L s s θ Τ . Assume the gears are massless. r 1 r 2 J 1 B K θ L (t) J L τ (t) r 4 r 3 B L Figure 7 The Free Body Diagrams are given in Figure 7.1 below and the gear with radius r 3 rotates with an angular position θ 3 . Note that the schematic between the damper and the spring is free to rotate at a unique angular position, which is denoted θ 2 . To analyze this portion, a rotational mass with inertia J 0 = 0 is inserted. For the gear set on the left the following relationship holds 2 1 1 r r τ = . For the gear set on the right the following relationships hold 3 3 4 4 3 L r r = = . Summing the torques applied to the inertia denoted J and applying the constitutive law for dampers ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 1 2 2 1 1 r J t t t t B t t r = (1) Summing the torques applied to the inertia denoted J 0 and applying the constitutive laws for springs and dampers

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modeling7 - Modeling QUESTION 7 For the system shown in...

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