2.2.8. Exercise: Electromechanical Oscillation

Note: this is a new exercise, please provide feedback on errors and clarity. Objective

Design and test a mechanical oscillator pumped via electrical actuation. Overview

Physical oscillators are at the core of many machines: clocks, timers, motors, pumps, quartz crystals, washing cycles, musical instruments, and on and on. Oscillations are a product of a physical process which cycles through a set of states, with physical dynamics that determine the rate of the process. Practical oscillators lose energy over time to friction and need a source of power which delivers energy in phase to maintain the oscillation energy.

A few examples follow:

  1. A pendulum clock has a well-defined time constant based on the gravitational constant, the length of the pendulum, and (weakly) the magnitude of the motion. Energy is added via an escapement mechanism which applies force in phase with the pendulum swing. The force is provided from a descending weight which stores gravitational potential energy.
  2. An electric motor has a rotor and stator with varying magnetic fields which repel each other, precisely timed to apply torque in phase with the rotation. In a small DC motor, the stator holds permanent magnets and the rotor has an electromagnet winding with current controlled by commutation brushes which mechanically switch the current direction as a function of angle. The motor lacks the single-frequency resonance of the pendulum; the rotational rate emerge as a function of the voltage, applied load, friction, and the intrinsic parameters. Exercise Details

Creating and controlling a mechanical oscillation involves creating a device which incorporates a physical dynamic process and adding actuation to provide energy at the right time. The following exercise is framed in abstract terms to allow for many possible outcomes. But keep in mind that this can be very simple: a simple pendulum activated by solenoid or motor is perfectly fine. And try to build as little as possible: a pendulum device might comprise simply a solenoid and switch taped to a board and wired together to a power supply to make a ‘kicker’, with a pendulum formed by a weight on the end of a string. Steps and observations

  1. Choose a mechanical process which either cycles periodically or can be actuated to reset to an initial condition. Some ideas: swinging pendulum, 2D pendulum, ball rolling down track, mass rotating on a torsion spring, ball bouncing on plate, ball descending through liquid, water flowing between reservoirs.
  2. Choose a relevant intermittent actuation which can add energy to the process. Some ideas: a solenoid kicker, a winch or arm to reset object position, pumps.
  3. Choose a relevant state-based condition under which to activate the actuation. Some ideas: a particular object position, change of center of mass, liquid level. The key is that it is not based on time so that the natural time constant of the mechanical process will govern the oscillation rate.
  4. Design and construct a simple mechanism to implement the oscillator. Basic electronics are preferred but microcontrollers are permissible as long as they are not serving as a time reference.
  5. Test your mechanism. What is the frequency? Is it stable? Is is adjustable? How slow or fast can it go? Can it be dynamically modulated?