## G W

introduction

A free-piston Stirling engine is a machine in which the motion of the reciprocating elements to accomplish the thermodynamic cycle are effected by lluid forces and by the dynamical, lluidic interaction of the components. There are no mechanical linkages coupling the pistons or displaccrs.

Such machines offer advantages of simplicity, freedom from leakage (since they can be hermetically sealed), low cost, self-starting, and very long life. I hey are being developed for use as thermally activated heat pumps, solar-electric converters, remote-area power generators, total energy systems, and water pumps.

Ibis chapter is intended to give an elementary description of free-piston Stirling-engine dynamics, to give examples of some of the many possible configurations, and to discuss the present state of development and areas of research. The viewpoints given here are those of the author developed with the assistance of many helpful discussions within his own design group at Sunpower Inc.. with the M i l Stirling engine team, and from the publications cited in the text. Since the field is a very active one, the interested reader should view this chapter as no more than an introduction to the subject and should consult the literature frequently for new developments.

description ol pr ice-piston engine dynamics

In order to describe the action of free-piston engines, it is useful to assume harmonic motion of the components, which is often nearly true, and to recall that such motions may be described not only as sine waves, but also by the projections on a horizontal or vertical axis of rotating

FREE-PISTON STIRLING ENGINES h

FREE-PISTON STIRLING ENGINES h

A+H

Work component

-Displacement Spring component

Cycle work— n AD sin •/. Work component of li— li sin-/-Spring component ol~ B—B cos <}>

Fto. Ill (n) Vector representation of ;i sine wave, (li) Sum of two sine waves as a vector sum. (c) Vector work.

vectors. Readers who wish to refresh their memory on the rotating vector method of representation are referred to any standard textbook on mechanical vibrations! in which all of what is given below is clearly developed in a simple and convincing manner.

To summarize the vector representation of harmonic motions:

(a) A sine wave A sin o>t may be represented as the vertical component of a vector of magnitude A rotating at angular velocity <*> radians/second (Fig. 11.1).

(b) The sum of two sine waves A sin oil and Bsin(o»H-<M may be represented by a rotating vector equal to the vector sum of A and B leading A by the angle «/>.

(c) The work of a sinusoidal force A sin(w/ + </>) upon a displacement B sin ¡at is represented by the product of the component of the

I" For example. Den I lartog—Mechanical Vibrations, McGraw Hill.

force vector normal to the displacement vector with that displacement vector. If the force vector leads the displacement, work is done on the displacement. If the force vector lags the displacement. work is done hy the displacement. The magnitude of the work done is ttAB sin <{> per cycle or the power is:

cycle second \2tt/ 2

This can also be interpreted to mean that only the component of the force normal to the displacement does work, or that only the component of the force parallel to the velocity does work. (Note that the velocity is always 90° in advance of the displacement so that a force normal to velocity is parallel to displacement.)

The mass-sp ring-dam per system of Fig. I 1.2 illustrates the statements made above. Note that lite damping force points down, representing a

,0vJ(sin ut + ?r | Newton's second l«w: .summation of forces — mass X acceleration

X — cos w/ — .V„ <•> (sin u»/ t n ) X—aq^siii ut

## Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

Get My Free Ebook