ENGR216 2021 Dynamics Q A1 (ENGR5004)

ENGR216 2021 Dynamics Q A1Past paperOld spec ENGR2162:218 marks22 min

ENGR216 Summer 2021 Dynamics Q A1[PARTIAL] Left out: Part (d) (static and dynamic balancing of rotating machinery) is not in the ENGR5004 syllabus.

Figure A1 shows the drive mechanism from an industrial machine, whereby motor M drives geared shaft D via rotation of gear S. For a short time, gear S rotates with an angular acceleration of $\alpha_S = (250\,t^2 + 50)\ \mathrm{rad/s^2}$ , where $t$ is in seconds.

Figure A1: motor M drives gear S (radius 60 mm) meshing with the gear on shaft D (radius 150 mm).

Formulas you may need

Fixed-axis rotation: $\omega = \omega_0 + \int_0^t \alpha\,dt$ , $\theta = \theta_0 + \int_0^t \omega\,dt$ (learn this)
Meshing gears (no slip at the pitch point): $r_S\,\omega_S = r_D\,\omega_D$ , $r_S\,\theta_S = r_D\,\theta_D$ , $r_S\,\alpha_S = r_D\,\alpha_D$ (learn this)
Point on a rotating body: $v = \omega r$ , $a_t = \alpha r$ (learn this)

(a)
Determine the angular velocity of shaft D when $t = 2$ s, starting from rest.
omega_D =rad/s
[4]
(b)
Determine the angular displacement of shaft D when $t = 2$ s, starting from rest.
theta_D =rad
[4]
(c)
State any assumptions that you have made, explaining your reasoning
[4]Third
(d)
Write brief notes explaining why dynamic and static balance should be considered when designing and commissioning rotating machinery.
[6]