Torsional tunable coupling for a diesel engine drive shaft

An improved coupling assembly is provided for transmitting rotary power from the working end of an internal combustion engine to a driven shaft. The crankshaft also has a free end connected to an accessory drive train. The coupling assembly comprises a low inertia flywheel having a mass so selected as to cause the node of the first crankshaft mode of torsional vibration to be located in the vicinity of the middle of the crankshaft, and a flexible coupling which interconnects the working end of the crankshaft with the driven shaft. The low inertia flywheel not only reduces the amplitude of the torsional deflection at the free end of the crankshaft, but further raises the primary torsional vibration orders of the engine which excite the coupling assembly by at least one half of an order such that the peak stresses applied to the teeth of the first gear wheel of the accessory drive train are at least halved and are further applied to at least twice as many gear teeth, thereby greatly prolonging the life of the gear wheel. Moreover, the low inertia flywheel further increases the lifetime of the flexible coupling by raising its natural frequency to a level which is substantially higher than the 0.5 engine order of torsional vibration associated with engine malfunction and governor interaction.

BACKGROUND OF THE INVENTION 
This invention generally relates to engine couplings, and is specifically 
concerned with an improved, low-inertia coupling assembly for reducing 
stress in the interface between the ends of a crankshaft and a drive 
train. 
Coupling assemblies for transmitting rotary power from the working end of a 
crankshaft of an internal combustion engine to a driven shaft are well 
known in the prior art. Such coupling assemblies generally comprise a high 
inertia flywheel in combination with a flexible coupling which 
interconnects the working end of the crankshaft with the driven shaft. The 
flexible coupling may include a resilient member formed from an 
elastomeric material. Such couplings are most typically used in diesel 
engines, and the primary purpose of the high-inertia flywheel is to smooth 
out the amplitude of the torque generated by the working end of the 
crankshaft. A secondary purpose of the flywheel is to provide a mount for 
the ring gear which engages the output gear of the starter motor of the 
engine. The flexible coupling utilized in such prior art assemblies not 
only serves the function of mechanically interconnecting the working end 
of the crankshaft with a driven shaft; the flexibility provided by the 
elastomeric material in the coupling advantageously dampens impulse 
torques which might otherwise be generated between the crankshaft and the 
driven shaft. Such unwanted impulse torques may occur, for example when 
the driven shaft is a cardan-type shaft, and the elastomeric material 
provided in such a flexible coupling allows the coupling to drive such a 
shaft for a maximum amount of time without failure. 
While such prior art coupling assemblies have performed satisfactorily in 
the past, the applicant has observed a number of shortcomings in the 
performance of such couplings as the power of diesel engines has increased 
over the years. For example, the applicant has noted that the relatively 
large inertias associated with the flywheels of prior art couplings 
(typically between 150 and 400 lbs*ft.sup.2 in diesel engines of between 
about 500 and 2000 horsepower) tend to cause the node of the first mode of 
crankshaft torsional vibration to be located in the vicinity of the 
flywheel itself. Such a location has the effect of maximizing the 
amplitude of the torsional vibration experienced by the free end of the 
crankshaft. Since the free end of the crankshaft of such diesel engines is 
typically connected to an accessory drive train such as the timing gear 
train and vehicle accessory drives, the relatively large amplitude of 
torsional movement of the free end of the crankshaft creates undesirable 
stress in this gear train which is particularly intense with respect to 
the teeth of a crank nose pinion of the gear train. 
The applicant has also observed three other major problems that come about 
as a result of the relatively large mass of the flywheels used in such 
prior art couplings. The first and most important of these problems is 
concentration of intense stress on only a few of the gear teeth of the 
gear train driven by the free end of the crankshaft. The inherent natural 
frequency of the crankshaft mode (or second system mode) of torsional 
vibration causes the crankshaft to be excited by relatively low engine 
orders (such as the second, third or fourth orders in a four, six or eight 
throw diesel crank respectively). Hence, in the case of an eight throw 
crank, the excitation of the crankshaft mode of torsional vibration in the 
engine of a prior art flywheel assembly by the fourth engine order results 
in the same four teeth (located 90.degree. apart) being subjected to very 
high torsional vibrational stresses with each revolution of the gear 
wheel. After a period of time, these stresses cause these four gear teeth 
to fail, thereby necessitating an expensive and time-consuming replacement 
of the gear wheel. A second problem associated with the use of a high 
inertia flywheel in such prior art couplings is the relatively low 
frequency it confers on the coupling mode (first system mode); i.e. 
frequencies in the range of 15 to 20 hertz. While these frequencies avoid 
major exciting orders in the engine operating speed range, the engine has 
to run through the coupling resonance speed during start-up, and can 
damage the coupling by excessive deflections at such low frequencies. 
A third problem occurs if this low coupling mode frequency brings the 
half-order resonance speed within the upper speed range of the engine. 
Either a misfiring cylinder, or vigorous governor action will cause a high 
level of half-order excitation which can damage or break the coupling 
under these conditions. 
Other shortcomings associated with the use of such a high-inertia flywheel 
include the out-of-balance and bending moment forces that such a flywheel 
applies to the crankshaft which supports it, as well as the expense 
necessitated by the precision manufacture and installation of such heavy 
components in an engine. 
Clearly, there is a need for an improved coupling assembly which overcomes 
the shortcomings and problems associated with the use of high-inertia 
flywheels in such assemblies. 
SUMMARY OF THE INVENTION 
The invention is both an apparatus and a method which eliminates or at 
least ameliorates all the problems associated with prior art coupling 
assemblies that employ high-inertia flywheels which cause the node of the 
first crankshaft mode to be located in the vicinity of the flywheel. 
Specifically, the improved coupling assembly of the invention employs a 
low inertia flywheel having a mass so selected as to cause the node of the 
first crankshaft mode of torsional vibration to be located in the vicinity 
of the middle of the crankshaft, which not only reduces the amplitude of 
the torsional deflection at the free end of the crankshaft, but also 
changes the primary engine orders that excite the coupling assembly from 
whole number orders to half-orders. These two effects combine to greatly 
reduce the stress at the interface between the free end of the crankshaft 
and a drive train connected to this end. For example, where this interface 
is defined by the gear teeth of a timing gear, the changing of the primary 
exciting orders of torsional vibration by at least one half of an order 
reduces the peak stresses applied to the teeth of the gear by at least one 
half, and applies these stresses to at least twice as many gear teeth, 
thereby greatly prolonging the lifetime of the timing gear. 
The improved coupling assembly of the invention preferably includes a 
flexible coupling which employs an elastomeric element for connecting the 
working end of the crankshaft with a driven shaft. Referring to FIG. 5, 
showing a bearing supported shaft, the arrangement of this component of 
the coupling assembly increases the versatility of the assembly by 
allowing the driven shaft to be a cardan type shaft. The use of a 
low-inertia flywheel in the coupling assembly advantageously increases the 
natural frequency of the combination of the flexible coupling and the 
flywheel to a level which is substantially higher than the 0.5 engine 
order associated with governor action and engine malfunction, thereby 
eliminating or at least greatly diminishing the probability of coupling 
failure as a result of spurious excitation over the life of the engine. In 
the preferred embodiment, the flexible coupling is a shear-block coupling 
which can act as a mechanical "fuse" should the relative torque between 
the crankshaft and driven shaft exceed a predetermined safe level. 
The coupling assembly of the invention may further include a means for 
tuning or adjusting the mode of the coupling assembly formed from a 
manually removable retaining ring for facilitating the replacement of the 
elastomeric member of the flexible coupling with another elastomeric 
member having different hardness characteristics. 
The driven shaft may be a floating shaft, and the flexible coupling may 
further include a centering ring for maintaining the concentricity of one 
end of the floating shaft with the flexible coupling. Additionally, one 
edge of the centering ring may be connected to the retaining ring and the 
centering ring may circumscribe the driven member of the flexible 
coupling. The use of such a centering ring obviates the need for one of 
the bearing assemblies which normally rotatably supports such a floating 
shaft. 
Alternatively, the coupling assembly of the invention may integrally 
include a bearing assembly for rotatably supporting one end of the driven 
shaft, which would not only obviate the need for a separate bearing 
assembly to be constructed somewhere along the length of the driven shaft, 
but which would also conveniently ensure an on-center, concentric 
relationship between the coupling assembly and one end of the driven 
shaft. A housing is also preferably provided that not only encloses both 
the flywheel and the flexible coupling, but also supports the previously 
mentioned, integrally-provided bearing assembly as well.

DESCRIPTION OF THE PREFERRED EMBODIMENT DETAILED 
FIG. 1 shows a prior art diesel engine system of which the current 
invention can be a part. Shown in FIG. 1 is crank pinion gear 118, diesel 
engine 110, engine coupling assembly 10, and output shaft 119. Diesel 
engine 110 is a four crank throw engine of the type including four pistons 
112 connected through connecting rods 114 to engine crankshaft 116. Engine 
crankshaft 116 has a free end 115 and a flywheel end 117. A four crank 
throw diesel engine is shown in FIG. 1, but an engine of any type with any 
number of crank throws and cylinders could be used with the present 
invention. 
The free end 115 of engine crankshaft 116 is connected to crank pinion gear 
118. Typically, crank pinion gear 118 is used to drive a timing gear train 
and/or vehicle accessory drives (shown schematically in phantom). The 
flywheel end 117 of engine crankshaft 116 is connected to engine coupling 
assembly 10. Also connected to engine coupling assembly 10 is output shaft 
119. 
In FIG. 1, engine coupling assembly 10 contains flywheel 130, driving 
element 18, driving element teeth 17, flexible coupling 20, driven element 
22, and driven element teeth 23. The relationship between these components 
and their operation is discussed in detail below in conjunction with FIG. 
2, which shows the preferred embodiment of engine coupling assembly 10. 
FIG. 1 represents the prior art wherein a relatively massive flywheel 130 
forms a part of the coupling assembly 10. Such massive flywheels used with 
such coupling assemblies 10 in the prior art have relatively large 
inertias, from approximately 150 to 400 lbs*ft.sup.2. The primary purpose 
of using such a flywheel 130 of high inertia is to smooth out the 
amplitude of the torque generated by the flywheel end 117 of engine 
crankshaft 116. The large inertias of the prior art flywheels, however, 
cause the node (location of approximate zero torsional vibration 
amplitude) of the first mode of crankshaft torsional vibration, which is 
equivalent to the second system mode of torsional vibration, to be located 
in the vicinity of the flywheel, near the flywheel end 117 of engine 
crankshaft 116 in FIG. 1. As a result, the amplitude of the torsional 
vibration experienced by the free end 115 of engine crankshaft 116 is 
maximized. The large amplitude of the torsional vibration at the free end 
115 of engine crankshaft 116 places undesirable stress on the teeth of 
crank pinion gear 118. Furthermore, this stress can be transferred through 
crank pinion gear 118 to a timing gear train or vehicle accessory drive, 
thereby shortening the life of these components. 
FIG. 2 shows the preferred embodiment of engine coupling assembly 10 of the 
present invention. Included in engine coupling assembly 10 are flywheel 
housing 12, flywheel end 117 of engine crankshaft 116, low inertia 
flywheel 15, optional ring gear 16, driving element 18, driving element 
teeth 17, retaining ring 19, flexible coupling 20, driven element 22, 
driven element teeth 23, and output shaft 24. In this configuration, 
output shaft 24 would be a two bearing shaft, i.e. output shaft 24 would 
be supported by two bearings (not shown) spaced apart from each other and 
the coupling assembly 10. 
As shown in FIG. 2, low inertia flywheel 15 connects to driving element 18. 
Flywheel end 117 of engine crankshaft 116 rigidly connects to driving 
element 18 and output shaft 24 rigidly connects to driven element 22. 
Driving element 18 and driven element 22 interact through flexible 
coupling 20, which is better shown in FIG. 3. Flexible coupling 20 is held 
in place by retaining ring 19 as described in more detail below. Optional 
ring gear 16 may be connected to low inertia flywheel 15 to allow for 
cranking of the engine 110 through driving element 18 and engine 
crankshaft 116. Flywheel housing 12 preferably encloses both low inertia 
flywheel 15 and flexible coupling 20. 
In operation, engine crankshaft 116 will supply rotary power to driving 
element 18. Driving element 18 will in turn provide rotary power to driven 
element 22 and output shaft 24 through flexible coupling 20. The mass of 
low inertia flywheel 15 is selected so as to locate the node of the first 
mode of crankshaft torsional vibration, which is equivalent to the second 
system mode of torsional vibration, approximately in the middle of engine 
crankshaft 116, as opposed to having the node located on the end of the 
engine crankshaft 116 near the flywheel 15 as would result from prior art 
flywheel systems. For example, prior art flywheel systems used with 
engines of approximately 500 to 2000 horsepower employed flywheels having 
inertias from approximately 150 to 400 lbs*ft.sup.2. The relatively large 
inertias associated with these prior art flywheels resulted in a torsional 
vibration node, having approximately zero amplitude, in the engine 
crankshaft near the junction of the crankshaft with the flywheel. 
Furthermore, such large inertias resulted in a torsional vibration having 
maximum amplitude at the free end 115 of engine crankshaft 116. 
The present invention employs a low inertia flywheel having an inertia 
approximately 5 to 10 times lower, from approximately 15 to 80 
lbs*ft.sup.2, than that of prior art flywheel systems. Due to the 
relatively large inertias associated with the internal components of high 
horsepower diesel engines, applicant has discovered that a high inertia 
flywheel is not required, and in fact is detrimental to the operation of 
engine. As a result of the use of a low inertia flywheel, the amplitude of 
the torsional vibration in engine crankshaft 116 at the free end is 
reduced by a factor of at least two. This reduction in torsional vibration 
amplitude leads to a reduction in stress at the interface between the free 
end 115 of engine crankshaft 116 and the drive train connected thereto, 
which increases the life expectancy of the drive train. Specifically, by 
reducing the amplitude at free end 115 of engine crankshaft 116, the 
stress on the teeth of crank pinion gear 118 is greatly reduced. As a 
result, the life expectancy of crank pinion gear 118 is increased. 
Furthermore, by moving the location of the node of the first mode of 
crankshaft torsional vibration to the center of engine crankshaft 116, the 
torsional stress on flywheel end 117 of engine crankshaft 116 is reduced, 
thereby increasing the life expectancy of engine crankshaft 116. 
Engine coupling assembly 10 could be an Atra-flex model A-8 coupling 
assembly manufactured by ATR Inc. The commercially available coupling is 
modified for use with the present invention to allow coupling between a 
flywheel assembly and an output shaft rather than coupling between an 
input shaft and output shaft. This modification, however, must be made 
without adding additional mass to the coupling assembly so that the 
desired low inertia assembly is achieved. 
FIG. 3 shows a cross sectional diagram of the flexible coupling 20 taken 
along line 3--3 in FIG. 2. FIG. 3 shows flexible coupling 20, retaining 
ring 19, driving element teeth 17 and driven element teeth 23. As seen in 
FIG. 3, driving element teeth 17 and driven element teeth 23 are encased 
in slots 32 of flexible coupling 20. Retaining ring 19 circumferentially 
surrounds flexible coupling 20 to maintain flexible coupling 20 in 
position during operation. 
In operation, driving element teeth 17, as a result of the connection to 
the engine crankshaft 116 through driving element 18 discussed above in 
conjunction with FIG. 2, will exert a rotational force on flexible 
coupling 20. This force will be transferred through flexible coupling 20 
to driven element teeth 23. As a result, power will be transferred to 
output shaft 24 through driven element 22 as discussed above in reference 
to FIG. 2. 
Retaining ring 19 is used to prevent flexible coupling 20 from disengaging 
with driving element teeth 17 and driven element teeth 23. During 
operation, the centrifugal force exerted on retaining ring 19 from 
flexible coupling 20 will hold retaining ring 19 in position. When the 
coupling assembly is stationary, however, retaining ring 19 can be easily 
removed to allow replacement of flexible coupling 20. To facilitate 
replacement, flexible coupling 20 is provided with a radially oriented 
slit 303, which will allow flexible coupling 20 to be, in effect, unwound 
from and easily removed from the coupling and replaced. 
Flexible coupling 20 will conform slightly due to the force applied by 
driving element teeth 17. By varying the elastomeric properties of 
flexible coupling 20 (i.e. spring constant), it is possible to fine tune 
the resonant frequency of the coupling. The particular advantages and 
methods by which this can be done are discussed further below. 
Referring now to FIG. 4, an alternate embodiment of the engine coupling 
assembly 10, which is suitable for use where precise alignment is not 
needed and quick changes are desirable, is shown. The structure of engine 
coupling assembly 10 is identical to that described above in connection 
with FIG. 2 except that retaining ring 19 shown in FIG. 2 has been removed 
and centering ring 40 has been added. With the addition of centering ring 
40, retaining ring 19 is no longer needed. The flexible coupling 20 is now 
held in place during operation by centering ring 40. As best seen in FIG. 
4, centering ring 40 is rigidly connected to driven element 22 and 
surrounds flexible coupling 20. By using centering ring 40 in this way, 
the concentricity of output shaft 24 relative to driving element 18 is 
maintained. Therefore, in this configuration, only one bearing is required 
to be used with output shaft 24, which acts as a floating shaft. Output 
shaft 24 could be connected to a flexplate assembly 401 or gear coupling 
(not shown). This coupling configuration is particularly advantageous when 
frequent quick changes are desirable and precise alignment is not 
necessary. Specific uses could include dynamometer drives and other engine 
or load test applications. 
A third embodiment of the engine coupling assembly 10 is shown in FIG. 5. 
Here, an integral bearing assembly is incorporated into engine coupling 
assembly 10. The bearing assembly contains support flanges 503, bearings 
505, and driven element 22. Support flanges 503 are rigidly connected to 
flywheel housing 12 and support driven element 22 through bearings 505. 
The bearing assembly rotatably supports output shaft 24, which obviates 
the need for a separate bearing assembly to be constructed somewhere along 
the length of the driven shaft. Additionally, the bearing assembly ensures 
that output shaft 24 will be maintained in a concentric relationship with 
engine coupling assembly 10. A bearing assembly of this type would 
typically be used to drive a cardan type shaft or single bearing 
generator. However, other possible shaft configurations could be used 
where an integral bearing assembly is advantageous. 
FIG. 6 is a Campbell, or interference, diagram showing the relationship 
between system mode frequencies, engine RPM, and engine excitation orders, 
which represent the number of vibrations occurring per revolution of the 
engine crankshaft 116. The Y-axis of the graph represents the natural 
frequency of a system mode in hertz. The X-axis of the graph represents 
the engine speed in rotations-per-minute (RPM). The engine excitation 
orders of 0.5 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 6 are plotted as lines on 
the graph. 
The natural resonant frequency of the first system mode, or coupling mode, 
of torsional vibration will be determined by the properties of the 
elastomeric coupling used in the engine coupling assembly. In particular, 
the natural frequency, f, of the first system mode of torsional vibration 
is given by equation 1 below, 
##EQU1## 
where K is the spring constant of the elastomeric coupling and I.sub.e is 
the effective inertia of the system given by equation 2, 
##EQU2## 
Where I.sub.1 represents the inertia of the engine components, flywheel, 
and coupling components attached thereto, and I.sub.2 represents the 
inertia of the driven coupling components, driven shaft, and driven load. 
Solving equation 1 and equation 2 with respect to the parameters associated 
with prior art flywheel systems yields a natural resonant frequency of the 
first system mode of torsional vibration of approximately 15-20 hertz. If 
a typical engine operating range of approximately 600 to 2400 RPM is used, 
FIG. 6 shows that the 0.5 engine excitation order will be present at a 
15-20 hertz natural frequency from approximately 1800-2400 RPM. 
The 0.5 order is typically not harmful if the engine is operating smoothly. 
The 0.5 order can, however, be excited as a result of a misfiring 
cylinder, by the action of an engine speed governor, or from any other 
occurrence that results in erratic engine operation. If this occurs, the 
resulting resonance will quickly destroy the elastomeric coupling and 
require expensive and time consuming repairs. 
By referring to FIG. 6, it can be seen that if the first system mode 
resonant frequency can be raised above approximately 20 hertz, then the 
0.5 order mode will no longer be present across the engine operating range 
from 600 to 2400 RPM. By referring to equation 1, it can be seen that the 
first system mode resonant frequency, f, can be raised in either of two 
ways: (1) by raising the spring constant, K, of the coupling, or (2) by 
lowering the effective inertia, I.sub.e, of the system. 
The first method, raising the spring constant, K, of the coupling will only 
result in minor fluctuations in the resonant frequency. This is so because 
the spring constant must be retained within certain limits in order to 
maintain the benefits of the flexible coupling. If the spring constant is 
raised to a point to advantageously effect the resonant frequency, the 
coupling will no longer be elastomeric. The elasticity of the coupling is 
required and for this reason, the natural resonant frequency of the 
coupling cannot be significantly altered by changing the spring constant 
of the coupling. 
The second method of raising the first system mode resonant frequency, by 
lowering the effective inertia of the system, can be used effectively. 
From equation 2, it can be seen that the effective inertia can be lowered 
by lowering either I.sub.1 or I.sub.2. I.sub.2, however, is determined by 
the load components and is usually beyond the control of the engine 
manufacturer. Therefore, it is necessary to lower I.sub.1, the inertia of 
the engine components, flywheel, and coupling components attached thereto. 
The present invention recognizes this deficiency in prior art systems and 
solves the problem by providing a low inertia flywheel and coupling 
assembly. In the system of the present invention, the first system mode 
resonant frequency is raised to approximately 22-25 hertz, thereby 
avoiding the 0.5 order mode over the entire operating range of the engine. 
This is accomplished by selecting a mass for the flywheel assembly such 
that the inertia of the system results in a frequency, f, of between 
approximately 22 and 25 hertz as determined from equations 1 and 2 above. 
Furthermore, the present invention uses the first method discussed above, 
that of raising the spring constant of the elastomeric coupling, to fine 
tune the resonant frequency. Slight changes in the spring constant can 
result in minor alterations to the resonant frequency without effecting 
the advantages of the flexible coupling, thereby allowing a fine tuning of 
the coupling resonant frequency. With the improved coupling assembly, the 
0.5 order is eliminated across the entire normal operating range of the 
engine. Therefore, coupling failure as a result of erratic engine 
operation exciting the 0.5 order is completely avoided with the present 
invention. 
A third advantage of the present invention can be seen by reference to 
FIGS. 6 and 7. By reducing the mass of flywheel 15, the primary engine 
orders are changed from whole number orders to fractional orders, 
preferably odd multiples of 0.5 i.e. 0.5, 1.5, 2.5, 3.5, etc. The primary 
engine vibration orders include second, third, fourth and sixth orders for 
a four, six, eight and twelve throw crank respectively. The change in the 
primary engine vibration orders is particularly advantageous because it 
causes the stress at the free end 115 of engine crankshaft 116 to be 
distributed over at least twice as many gear teeth of crank pinion gear 
118. In conjunction with the reduction in torsional vibration amplitude 
that results from a crank center node, this reduces the stress on the gear 
teeth of crank pinion gear 118 by at least four times. 
For example, referring to FIG. 6, if an engine is operating at a 
synchronous speed of 1800 RPM, and the first mode of crankshaft torsional 
vibration (second system mode of vibration) has a natural frequency of 120 
hertz, the engine will experience fourth order vibrations. This results in 
exactly four vibration pulses, spaced 90 degrees apart, per revolution of 
engine crankshaft 116. Each vibration pulse will occur at exactly the same 
location (0, 90, 180 and 270 degrees) during each revolution. This causes 
undesirable vibrational stresses to be concentrated on the same gear teeth 
during each revolution, which leads to earlier failure of these gear 
teeth. The present invention, however, by reducing the mass of engine 
flywheel 15, will cause the engine orders to be changed from whole orders 
to half orders. As a result, the fourth order of the above example changes 
to 3.5 and 4.5. This results in 3.5 and 4.5, respectively, vibration 
pulses per revolution of engine crankshaft 116. It will now require two 
complete revolutions before the vibration pulses will occur on the same 
gear teeth, thereby distributing the stress over twice as many gear teeth. 
With a 3.5 primary engine excitation order, the vibration pulses will 
occur approximately every 102.9 degrees (3.5 pulses per 360 degree 
revolution equals 1 pulse every 102.9 degrees). With a 4.5 primary engine 
excitation order, the vibration pulses will occur every 80 degrees (4.5 
pulses per 360 degree revolution equals 1 pulse every 80 degrees). The 
resulting distribution of stress over twice as many gear teeth will result 
in much longer component life. 
The 0.5 order change that results from the present invention can be better 
seen in FIG. 7. FIG. 7 depicts the resulting engine orders for a prior art 
near flywheel node and for the crank center node resulting from the 
present invention for four, six and eight throw crankshafts. For example, 
an eight throw crankshaft employing a prior art flywheel system in which a 
torsional vibration node occurs at or near the flywheel results in 
prominent fourth and eighth orders of torsional vibration. As a result, 
the stress on a crank pinion gear will be concentrated on the same four or 
eight teeth respectively. However, if a low inertia flywheel is employed, 
that results in a crank center node of torsional vibration, FIG. 7 shows 
that the prominent engine orders become 2.5, 5.5 and 6.5. The resulting 
stress on a crank pinion gear will therefore be distributed over 5, 10, or 
12 teeth respectively. 
The following table illustrates the above effect: 
TABLE I 
______________________________________ 
Natural Vibrational Torque 
Resonant By Engine Order 
Inertia Frequency (In-Lbs.) 
Coupling 
(In-Lb-Sec.sup.2) 
(Hertz) 3.5 4.0 4.5 
______________________________________ 
Heavy 105 14.5 6825 25611 8285 
DCB 834.5 
Prior Art 
Light 18 24.6 10394 7218 22320 
Atra A-8 
Present 
Invention 
______________________________________ 
Table I illustrates the changes that occur in inertia, natural resonant 
frequency, and vibrational torque for 3.5, 4, and 4.5 engine excitation 
orders when a low inertia flywheel of the present invention is used in 
place of a high inertia flywheel of a typical prior art system. As seen in 
Table I, the inertia of the system of the present invention is 18 
inch-pound-second.sup.2 ; almost a factor of 6 times smaller than the 105 
inch-pound-second.sup.2 inertia of a typical prior art system. 
Furthermore, Table I shows that the natural resonant frequency of the 
improved coupling assembly increases from 14.5 Hertz to 24.6 Hertz. 
The change of the primary engine excitation orders from whole orders to 
half orders is clearly illustrated by Table I. With a high inertia 
coupling, as used in the prior art, the torque due to the fourth order is 
25,611 inch-pounds, while that of the 3.5 and 4.5 orders is 6,825 and 
8,285 inch-pounds respectively. With the low inertia flywheel of the 
present invention, the respective torque for the 3.5, 4, and 4.5 orders is 
10,394, 7,218, and 22,320 inch-pounds. As described above, Table I shows 
that the fourth excitation order has reduced by approximately 18,000 
inch-pounds, while the 3.5 order has increased by approximately 3,500 
inch-pounds and the 4.5 order has increased by approximately 14,000 
inch-pounds. Table I also shows that the peak torque of 25,611 inch-pounds 
present in the fourth order of a prior art flywheel system is reduced to 
22,320 inch-pounds in the present invention. Therefore, not only is the 
torque spread out over more teeth of a driven gear, but the peak torque 
value is reduced. 
Raising the natural resonant frequency of the coupling mode (first system 
mode) is also particularly advantageous during engine start-up and shut 
down. During engine start-up, the rotational speed of the engine will 
increase from zero to the idle speed. When this occurs, the engine will be 
required to pass through the primary order of torsional vibration at the 
resonant frequency of the coupling assembly. Ideally, it is desirable to 
have the engine RPM associated with the primary excitation order and 
coupling resonant frequency to be close, within 50 RPM, but below the 
engine low-idle speed. This is so because the magnitude of the deflections 
resulting from the primary order are inversely related to the square of 
the engine RPM. 
For example, in an eight throw crank engine the primary exciting order is 
the fourth order. If the low-idle speed of the engine is 400 RPM, then it 
is desirable to have the engine RPM associated with the coupling resonant 
frequency and the fourth excitation order to be between approximately 350 
and 400 RPM, and preferably between 390 and 400 RPM. From FIG. 6, it can 
be seen that at a coupling resonant frequency typical of prior art systems 
of 16 hertz, the engine speed for a fourth order excitation is 
approximately 240 RPM. If the coupling resonant frequency is increased to 
25 hertz, the engine speed for a fourth order excitation increases to 
approximately 380 RPM. Therefore, the magnitude of the deflection, which 
is proportional to the square of the inverse of this difference in RPM 
will be approximately 2.5 times less in a system with a coupling resonant 
mode frequency of 25 hertz than in a system with a resonant frequency of 
16 hertz. This reduction in magnitude of the deflection will in turn 
result in a reduction in the stresses that occur on the coupling assembly 
during engine start-up.