Q : Why are quartz tuning forks commonly made to vibrate at 32,768 Hz? A : 32,768 is 2^15, and digital counters are all sorts of happy about powers of 2. 32,768 Hz is
the most commonly available frequency from manufacturers.
Since we've already spent considerable effort analyzing voltage-controlled motors this
term, hopefully making an analogy between them and a piezoelectric 'motor' (of the type seen
in Problem 7.2) will be useful:
Voltage-controlled Motor
Mechanical System in RED : Inertia + damping
Electrical World in BLACK : Motor has inductance + resistance
Coupling Coefficients in BLUE : Kt must equal Ke!
Piezo-actuated Tool
Mechanical System in RED : Inertia + damping and spring_mechanical = k_beam + k_actuator
Electrical World in BLACK : capacitance across actuator
Coupling Coefficients in BLUE : Kf must equal Ki!
Common ideas are:
that we are coupling mechanical and electrical domains
that the coupling coefficients shown for each particular system must have the same values (when represented in identical units)
feedback is involved (a la 'back emf') to calculate the desired output (angular velocity or position).
Note that with either system, the feedback loop consists of the following, basic loop-pattern:
mech.sys-->coupling_coef-->elec.sys-->coupling_coef-->mech.sys-->coupling_coef-->etc, etc, etc
...and we input our additional energy at some transition-point (at some cycling arrow location above).
It's not entirely coincidental that we are inputting VOLTAGE in both cases, as this often tends
to be the easiest way to command an accurate value (i.e e_command = V(t)) into controlled systems of this type.
