Question

l) For the schematic geared system shown in Figure Q1, refer all components to shaft ABP as an equivalent dynamic system, and hence derive the characteristic dynamic matrix in the form $[K][\theta]-[T]$. [6] ?) Determine the fundamental natural frequency and 'actual' inertia $I_C$ of 'UNIT C' to ensure the node position occurs at the gearbox. [7] ?) UNITS A and B are simultaneously subjected to periodic in-phase torques of the form $T_A = 1.0 \cos(2t)$ Nm, and $T_B = 2.0 \cos(2t)$ Nm respectively. Determine the actual amplitudes of the vibration $[\theta]$ of each component, ignoring any damping effects. [12] DATA: ROTATING MASS MOMENT OF INERTIA TORSIONAL STIFFNESS UNIT A $I_A = 4 \ kgm^2$ $k_A = 2 \ Nm/rad$ UNIT B $I_B = 3 \ kgm^2$ $k_B = 4 \ Nm/rad$ UNIT C $I_C = ?? \ kgm^2$ $k_C = 3 \ Nm/rad$ GEAR PINION P $I_P = 0.1 \ kgm^2$ GEAR WHEEL W $I_W = 0.4 \ kgm^2$

          l)
For the schematic geared system shown in Figure Q1, refer all components to
shaft ABP as an equivalent dynamic system, and hence derive the characteristic
dynamic matrix in the form $[K][\theta]-[T]$.
[6]
?)
Determine the fundamental natural frequency and 'actual' inertia $I_C$ of 'UNIT
C' to ensure the node position occurs at the gearbox.
[7]
?)
UNITS A and B are simultaneously subjected to periodic in-phase torques of the
form $T_A = 1.0 \cos(2t)$ Nm, and $T_B = 2.0 \cos(2t)$ Nm respectively. Determine the
actual amplitudes of the vibration $[\theta]$ of each component, ignoring any damping
effects.
[12]
DATA:
ROTATING MASS	MOMENT OF INERTIA	TORSIONAL STIFFNESS
UNIT A	$I_A = 4 \ kgm^2$	$k_A = 2 \ Nm/rad$
UNIT B	$I_B = 3 \ kgm^2$	$k_B = 4 \ Nm/rad$
UNIT C	$I_C = ?? \ kgm^2$	$k_C = 3 \ Nm/rad$
GEAR PINION P	$I_P = 0.1 \ kgm^2$
GEAR WHEEL W	$I_W = 0.4 \ kgm^2$

l)
For the schematic geared system shown in Figure Q1, refer all components to
shaft ABP as an equivalent dynamic system, and hence derive the characteristic
dynamic matrix in the form [K][θ]-[T].
[6]
?)
Determine the fundamental natural frequency and 'actual' inertia IC of 'UNIT
C' to ensure the node position occurs at the gearbox.
[7]
?)
UNITS A and B are simultaneously subjected to periodic in-phase torques of the
form TA = 1.0 cos(2t) Nm, and TB = 2.0 cos(2t) Nm respectively. Determine the
actual amplitudes of the vibration [θ] of each component, ignoring any damping
effects.
[12]
DATA:
ROTATING MASS MOMENT OF INERTIA TORSIONAL STIFFNESS
UNIT A IA = 4 kgm^2 kA = 2 Nm/rad
UNIT B IB = 3 kgm^2 kB = 4 Nm/rad
UNIT C IC = ?? kgm^2 kC = 3 Nm/rad
GEAR PINION P IP = 0.1 kgm^2
GEAR WHEEL W IW = 0.4 kgm^2

Added by Gerald B.

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