Bellcrank Mechanisms For Stirling ...

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BELLCRANK MECHANISMS FOR STIRLING E,NGINES
James
R.
Senft
University
of
Wisconsin
-
R.F.
River Falls, WI
54022
Victor J. Senft
University of Minnesota
Minneapolis,
MN 55455
ABSTRACT
This paper describes a family of linkage drive systems for
Stirling engines containing several new members. These
mechanisms are adaptable to all three configurations of Stirling
engine, impose minimal side loads on pistons and displacer rods,
and include compact forms suitable for pressurized high
performance engines. This group of drive systems is generated
by
a
simple common scheme. Near sinusoidal motion
is
taken
from a crankshaft carrying a single crankpin by two connecting
rods each driving a bellcrank. The stationary pivots of the
bellcranks are located
so
that their oscillatory motion has the
phase angle separation required between the piston and displacer.
The bellcranks are further configured to bring the third pin
motion to a location suitable for coupling with the piston or
displacer of the engine in a way which minimizes side loading.
The paper presents a number
of
new linkage drives from the
dual bellcrank family and indicates how they are embodied in
beta and alpha type Stirling engines. The paper includes a design
for a small multipurpose engine incorporating
one
of the subject
mechanisms.
CUNNECTING
FLYWHEEL
CRANKSHAFT
BELLCRANK
INTRODUCTION
Figure 1 schematically illustrates a single-cylinder piston-
displacer
or
"beta" type Stirling engine with a dual bellcrank
drive system. A single crankpin is linked to two ternary links
or
bellcranks by ordinary connecting rods. Both bellcranks are
pivoted to the engine frame at one end. The upper bellcrank
drives the displacer via a binary link to the displacer rod. The
lower bellcrank is similarly linked to the piston.
As the crank rotates, the bellcranks oscillate and impart near
sinusoidal motion to the piston and displacer at a phase angle
of
FIG.
1
A NEW TWIN BELLCRANK DRIVE MECHANISM
60"
which is typical for a beta type engine.
shows the
FOR A SINGLE-CYLINDER PISTON-DISPLACER OR BETA
sequence
of
motion of the engine over
a
complete cycle.
TYPE STIRLING ENGINE;.
1325
0-7803-3547-3-7116 $4.00
0
1996
IEEE
FIG.
2
MOTION OF THE TWIN BELLCRANK MECHANISM OFFIG.
1
OVER A COMPLETE CYCLE.
UNDERLYING PRINCIPLES
To understand how this mechanism was conceived and why it
produces an appropriate motion for a Stirling engine, consider a
simple crank and connecting rod drive. In such a drive system, as
schematically indicates, the rotary motion of the crankshaft
is coupled to approximately sinusoidal reciprocating motion of a
slider acting along a line through the center of the crankshaft.
we"crank
1,
\
Fixed
Connecting
Rod,
FIG.
3
A CRANK AND CONNECTING ROD DRIVE
PRODUCES NEAR SINUSOIDAL MOTION ALONG A LINE
THROUGH THE CENTER OF THE CRANKSHAFT.
FIG.
5
BELLCRANKS CAN BRING TWO SINUSOIDAL
MOTIONS TO ACT ALONG A COMMON LINE.
Of course the motion of a bellcrank point is oscillatory along an
arc rather than exactly linear, but the connecting rods will
accommodate this and links between the bellcranks and the piston
and displacer rod allow for the small deviation from linearity
without
imposing significant side loads. If the bellcrank arms are
relatively long or the oscillation angle is relatively small, then the
motion is linear enough to see that the motion of the piston and
displacer will still be near sinusoidal. The phase separation is
180
-
a
because the piston and displacer motions are taken from
the bellcranks in opposing senses in this mechanism.
By adding another connecting rod to the same crankpin,
simultaneous reciprocation can be produced along a second line
as Fig. 4 depicts, and the two motions will be out of phase
according to the angle
a
between the lines.
/
i
FIG. 4
CAN BE TAKEN OFF A SINGLE CRANKPIN.
OTHER DUAL BELLCRANK MECHANISMS
This approach can be applied in various ways as Figs. 6
-
9
show. Each figure represents only the basic geometry of a
Stirling engine mechanism for a beta type engine. Figure
6
again
depicts the engine already discussed to illustrate how these
diagrams represent a mechanism. The diagrams show the
crankpin circle in correct size and two bellcranks in correct size
and location. The stationary pin of each bellcrank
is
indicated by
the largest pivot circle; the smaller circle shows the location of
the little end of the connecting rod. Connecting rods are not
1326
Substituting bellcranks for the sliders as in Fig.
5,
both
reciprocating motions can be brought to act more or less along a
common line coinciding with the center axis of the piston and
displacer of the engine.
SINUSOIDAL MOTIONS DIFFERING IN PHASE
 shown
in
these diagrams. Connecting rod length is such that the
midstroke position of the bellcrank is that shown
in
the diagram.
Thus the connecting rods are of equal length and oscillate more or
less equally on either side
of
the dotted lines which indicate the
lines along which sinusoidal oscillation is taken from the
crankpin. The centerline shown in each diagram indicates the
axis of the engine cylinder.
Although in these diagrams the bellcranks are both shown in
their mid position, they never occupy these positions
simultaneously once connccting rods are fitted. Note that one
arm
of
the bellcrank is perpendicular to the dotted line; the other
arm is perpendicular to the line of motion of the piston and
displacer. The angle between the dotted lines in these diagrams is
120". Since the bellcranks are reversed in sense, the phase angle
difference between the piston and displacer that results
is
180
-
120
=
60".
For comparison, all the mechanisms shown in figs.
6
-
9 are scaled to produce the same stroke when linked to the
piston and displacer.
Other variations are possible in which both bellcranks are
connected to the piston alnd displacer in the same sense.
An
example
is
shown
in
Fig.
IO.
Here the phase angle between the
piston and displacer is equiil to the angle between the lines along
which motion is taken from the crank, which is 60" in the figure.
I Q
/
I
\
I
FIG.7
FIG. 10 A DIFFERENT FORM OF BELLCRANK DRIVE
FOR BETA TYPE STIRLING ENGINES.
\
I
REDUCTION TO PRACTICE
Dual bellcrank linkages can be employed in Stirling engines
intended for virtually any application, but they have special
advantages for small sizes ;and moderate power densities. This is
because dual bellcrank linkages offer compactness and low piston
side loading. A compact linkage system makes pressurized
crankcase engines practical. In most forms the bellcrank arms
that drive the piston and displacer can be made long relative to
the oscillation angle; this imposes only light side loading on the
piston and displacer even when relatively short connecting links
are used. This makes dry crankcase engines practical at moderate
power densities.
As an example of such im engine,
shows a complete
design for a small multipurpose beta type Stirling. The linkage
embodies the exact geomelry shown in
The connecting
rods are
of
"bent" form for clearance and certain members of the
linkage are forked or paired to present balanced loading on the
piston and displacer. Specifically,
the
piston bellcrank and the
displacer connecting rod arc: forked, and there are dual links to the
piston and to the displacer Iod end.
Named the "Timberline SOO"
,
the engine is suitable for firing
with solid wood fuel. The compact form of this mechanism
allows the crankcase to be pressurized and serve as the buffer
space. When charged with air to a mean working pressure of 2.5
atmospheres, the engine is capable of
500
Watts brake output at
800
rpm.
following gives further specifications for the
engine
(V.
SENFT, 1993).
I
/
I
I
I
I
FIG.
8
I
FIG. 9
FIGS.
6
-
9
DUAL BELLCRANK DRIVE MECHANISMS
FOR BETA TYPE STIRLING ENGINES
1327
I
 FLYWHEEL
"IN
LINK TO PISTON
Fl
REGENERATOR
INSUL
II
FIREBOX
FIG.
11
THE "TIMBERLINE
500"
STIRLING ENGINE
TABLE
1
TIMBERLINE
500
SPECIFICATIONS
Shaft Power:
500
W
Design Speed: 800 rpm
Working Fluid: air
Mean Pressure: 2.5 atm.
Fuel: Wood
Hot End Temperature:
600
C
Piston Diameter:
12.7
cm
Piston Stroke:
7.62
cm
Piston Swept Volume:
966
cc
Seals: Rulon
J
Bearings: Sealed rolling element
Phase Angle:
60"
Internal Heater: Corrugated copper fins
External Heater: Brazed copper fins
Internal Cooler: Aluminum fins
External Cooler: Cast aluminum fins
Regenerator: Wire screen, 70% void volume
1328
 VARIATIONS
In this linkage diagram,
oine
of the bellcranks partially hides the
other,
so
each bellcrank was drawn slightly offset
for
better
visibility. The two centerlines in the diagram are the axes
of
the
hot and cold cylinders. To obtain easy clearance, each bellcrank
together with its connecting links
can
be placed in
a
separate
plane which also contains the associated cylinder axis. The phase
angle depicted in this diagram is 116".
Another interesting variation of bellcrank drive for parallel
Rider type alpha engines is that shown in Fig.
15
which was
independently devised by
J.
David Kirk (1988). This diagram is
based on a phase angle
or
90" and is scaled to yield the same
stroke as the mechanism in
Many variations or alternate forms of dual bellcrank
mechanisms are possible besides those illustrated above. This
paper focused on the beta engine because it presents the most
challenging form of the "mechanism problem" for Stirling
engines
(J.
R. Senft, 1993). However, the same concepts can be
adapted and applied
to
the other types of Stirling engine. For
example,
12 shows the linkage form of
with a
separation angle
of
105" instead of 120"
FIG.
12
A VARIATION OF THE DUAL BELLCRANK
LINKAGE OF
shows this linkage embodied in
an
actual engine design
devised at Philips (Rinia
&
DuPre, 1946). At high operating
temperatures, this phase angle is nominally optimal for the
opposed piston alpha type engine.
7
FIG. 15 TWIN BELLCRANK LINKAGE FOR A RIDER TYPE
ENGINE INVENTED BY IKIRK.
All of the linkages in Figs;. 6-9 can be used for this and other
alpha type engines with the appropriate separation angle. Dual
bellcrank linkages also can be used in the gamma
or
split cylinder
configuration.
Non-symmetric forms
of
dual bellcrank linkage drives are also
possible and worthy of consideration.
To
illustrate, we conclude
with a linkage drive which Robert Stirling himself could have
used in his first engine.
represents the linkage form in
the abstract and Fig.
17
shows how the very first Stirling engine
would have looked with this mechanism.
FIG. 13 THE PHILIPS "W" LINKAGE ENGINE.
For alpha type engines with side-by-side parallel cylinders, the
dual bellcrank mechanism represented by the diagram in
is suitable.
I
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i
FIG 14 MECHANISM FOR A PARALLEL CYLINDER
RIDER TYPE ALPHA ENGINE.
FIG 16 A NON-SYMMETRIC FORM OFTWIN BELLCRANK
LINKAGE FOR
A
BETA TYPE STIRLING ENGINE.
1
329
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