Question

Q2 A steel shaft of different diameter carries a pulley and a motor as shown in Figure Q2. The weights of the pulley and the motor are 4 kg and 40 kg, respectively with a similar radius of gyration 0.5 m. If the shear modulus of shaft is given as G = 5 x 10$^6$ N/mm: Torsional stiffness equation is $k = \frac{\pi d^4 G}{32l}$ (a) Identify the equivalent torsional stiffness of the steel shaft between the pulley and the motor. (b) Solve the natural frequency of the system. (c) Determine the responses of the pulley, $\theta_1$ and the motor, $\theta_2$ in terms of the unknown amplitudes of $A_{11}$ and $A_{12}$, and phase angles of $\phi_1$ and $\phi_2$. 0.1 m $\theta_1$ 0.1 m * 0.1 m $\phi$ = 0.05 m $\phi$ = 0.04 m $\phi$ = 0.035 m Pulley $\theta_2$ Motor

          Q2 A steel shaft of different diameter carries a pulley and a motor as shown in Figure Q2.
The weights of the pulley and the motor are 4 kg and 40 kg, respectively with a similar
radius of gyration 0.5 m. If the shear modulus of shaft is given as G = 5 x 10$^6$ N/mm:
Torsional stiffness equation is $k = \frac{\pi d^4 G}{32l}$
(a) Identify the equivalent torsional stiffness of the steel shaft between the pulley and
the motor.
(b) Solve the natural frequency of the system.
(c) Determine the responses of the pulley, $\theta_1$ and the motor, $\theta_2$ in terms of the unknown
amplitudes of $A_{11}$ and $A_{12}$, and phase angles of $\phi_1$ and $\phi_2$.
0.1 m
$\theta_1$
0.1 m
*
0.1 m
$\phi$ = 0.05 m
$\phi$ = 0.04 m
$\phi$ = 0.035 m
Pulley
$\theta_2$
Motor

Q2 A steel shaft of different diameter carries a pulley and a motor as shown in Figure Q2.
The weights of the pulley and the motor are 4 kg and 40 kg, respectively with a similar
radius of gyration 0.5 m. If the shear modulus of shaft is given as G = 5 x 10^6 N/mm:
Torsional stiffness equation is k = (π d^4 G)/(32l)
(a) Identify the equivalent torsional stiffness of the steel shaft between the pulley and
the motor.
(b) Solve the natural frequency of the system.
(c) Determine the responses of the pulley, θ1 and the motor, θ2 in terms of the unknown
amplitudes of A11 and A12, and phase angles of ϕ1 and ϕ2.
0.1 m
θ1
0.1 m
*
0.1 m
ϕ = 0.05 m
ϕ = 0.04 m
ϕ = 0.035 m
Pulley
θ2
Motor

Added by Kayla T.

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