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Some PSRU Design Issues

This forum has hosted several discussions of various theories and intuitions
about PSRU's. On that subject, I would like to offer up some facts, based
upon the design, implementation and testing of one of the few geared PSRU's
which has demonstrated its performance and reliability, both on the test
stand and in the air.

The EPI PSRU is a part of the EngineAIR Power Systems 440 HP liquid-cooled,
turbocharged V8. That engine system powers (among others) Tom Zedaker's
Lancair-4-P which won Grand Champion at Sun n' Fun this year.

The prototype EPI PSRU has over 650 hour of flight time in Lancair-4
aircraft, driven by turbocharged engines producing up to 500 HP. It weighs 71
pounds and includes the integrated control plumbing and gear-drive for a
standard Woodward-Hartzell prop governor. It was in the aircraft which won
the Kittyhawk-to-Oshkosh race in 2000 (and which nearly won in 2001).

The subjects (briefly) addressed here are:

DESIGN SUMMARY
VIBRATION FUNDAMENTALS
ENGINE TORSIONAL VIBRATION
PSRU and PROPELLER VIBRATION
GEARS AND BEARINGS
LUBRICATION AND COOLING
GYROSCOPIC LOADS
CONCLUSIONS

(A more complete treatment of the broad subject of PSRU's, including belt,
chain and various gear reductions, will be available in a few weeks on our
website, www.epi-eng.com.)

DESIGN SUMMARY

The EPI PSRU was designed using a system approach to the problem, based on a
severe-service aircraft load model, and taking into account the following
loads:

(a) the bearing, shaft and housing loads produced by:
    torque,
    gear separation forces,
    thrust, and
    gyroscopic moments,
(b) the static gear tooth loads applied by mean engine torque,
(c) the dynamic gear tooth loads resulting from the stiffness and vibration
characteristics of the system (these can greatly exceed the static loads),
(d) the cooling load imposed by the power transmitted and
(e) the lubrication requirements.

VIBRATION FUNDAMENTALS:

Everyone knows that any piece of metal has mass. Any piece of metal also
demonstrates the properties of a spring. That is, if you apply two equal and
opposite forces to opposite sides of it, it will deflect. Sometimes that
deflection can be seen; sometimes it is so small that it can't be measured
with a micrometer. That depends on the size of the force and the size of the
piece of metal. The amount of deflection caused by a specific force
determines its "spring rate". Any system which has mass and spring rate will
vibrate at it's resonant (natural) frequency (like a tuning fork) when struck
("excited"). If it is repeatedly excited at or near its resonant frequency,
the vibrations will increase in magnitude until something breaks. As the
excitation frequency is increased beyond the resonant frequency, the
vibrations become smaller and smaller until they virtually disappear when the
excitation frequency becomes more than 6 times the resonant frequency
(frequency ratios above 6).

ENGINE TORSIONAL VIBRATION

An even-firing 8 cylinder, 4-stroke engine produces a power pulse once every
90° of crankshaft rotation. Therefore, the waveform of the instantaneous
full-throttle torque output (at the crankshaft flange) has four torque
"peaks" which are over 200% of the mean torque output (the torque which the
dyno measures), and four torque "valleys" which are approximately 25% of mean
torque. Fortunately, that waveform is approximately sinusoidal.

A crankshaft, like a plain torsion-bar, has mass and a torsional spring rate.
The things attached to the crankshaft (rods, pistons, pins, rings, etc.) add
to the apparent mass of the crankshaft. That causes the crankshaft system to
have it's own torsional resonant frequency. The torque peaks and valleys
described above cause the engine crankshaft itself to deflect forward and
backward while it is operating. When those pulses (excitations) are near the
crankshaft resonant frequency, they can cause the crank to vibrate
uncontrollably and eventually break.

The torsional resonant frequency of the crankshaft system is a function of
(1) crankshaft length;
(2) crankshaft torsional stiffness;
(3) crankshaft stroke;
(4) bobweight mass (a function of the weight of the rods, pistons, pins,
rings, bearings, oil);
(5) moments of inertia of rotating items attached to or driven by the engine.

Because of the nature of the coupling between the engine and its load, the
torsional vibration characteristics of the engine crankshaft need to be
addressed independently. If you believe that a crankshaft can live for long
without an effective torsional attenuator on the free end, look to the
experience of the Nissan folks (The crankshaft in the very early 240-Z didn't
have an effective attenuator, and therefore lasted only about 100 hours in
automotive {i.e. VERY LIGHT DUTY} service.)

Previous discussions have mentioned the vibration attenuating devices on the
free end of an engine crankshaft. Often, these are incorrectly referred to as
"DAMPERS". In most cases, they are ABSORBERS. (That's not semantics. A damper
dissipates energy, typically as heat. An absorber alternately stores and
releases energy to counteract vibration.)

The elastomeric ("metal-ring-on-rubber-spring") devices used by the
automotive industry (as well as by Teledyne-Continental on the GTSIO-520) are
ABSORBERS which are tuned to counteract vibration at the frequency where the
particular engine generates its worst torsional excitation.  TCM and Lycoming
also use internal ABSORBERS in all their high-output engines. They consist of
pendulous counterweights attached to the crankshaft cheeks by loose pins in
hard bushings. The clearance between the pins and bushings establishes the
torsional order which each counterweight absorbs.

One aftermarket device, the Fluidampr (tm), is a viscous DAMPER which
dissipates energy by transforming it into heat by shearing action in a high
viscosity fluid. Some race car people seem to like it, but it is banned from
Winston Cup racing.

That type of damper is mildly effective over a wide range of excitations, but
contrary to intuition and hype, it is significantly LESS effective in
reducing vibration in a specific, targeted frequency range, the exact
situation you have in an aircraft engine. (There is ample research in the
engineering literature showing exactly that fact.)

PSRU and PROPELLER VIBRATION

The engineering literature is rich with information on the subject of
gearboxes. An American Gear Manufacturer's Association (AGMA) publication
summarizes the problem as follows:

"The gearbox is one component of a system comprised of a power source,
gearbox, driven equipment, and interconnecting shafts and couplings. The
dynamic response of this system depends on the distribution of the masses,
stiffnesses, and damping. In certain cases, a system may contain a torsional
natural frequency close to an excitation frequency associated with an
operating speed. Under these resonant conditions, the dynamic gear tooth
loads may be very high, and operation near a system resonance is to be
avoided."

Clearly, a PSRU cannot be treated as an isolated entity. It is one critical
component in a vibrating system having at least two natural frequencies (in
addition to the natural frequencies of major engine components such as the
crankshaft system) and two sources of excitation. Any change to any part of
the system can significantly alter the loadings imposed on the other parts of
the system.

The torsional vibration properties of the engine have already been covered.

A propeller produces torsional excitation which varies with rotational and
translational speed, flight attitude, airframe characteristics, and the
properties of the engine torsional excitation which are applied to the prop.
Worse yet, each prop blade has a resonant frequency and is especially
susceptible to destructive vibration if it is excited near that resonant
frequency. Certified prop manufacturers go through extensive analysis and
testing to be sure that a particular prop will survive the fatigue
environment produced by a particular engine. Get it wrong, and blade pieces
will be departing the aircraft.

So there is the fundamental problem: both the input and the output of a PSRU
are attached to torsional excitation machines. From that, it should be clear
that there are two primary functions of a PSRU:

    (1) reliably transmit engine power to the propeller;
                      and equally important,
    (2) isolate the gears from the engine and prop excitations and from each
other.

Most of the intuition about PSRU's suggests that substantial DAMPING is
necessary for successful operation. In fact, the exact opposite is true. The
mathematics which define the system make it abundantly clear that, if your
goal is to minimize the torsional vibration transmitted to the gearbox (and
thus to the prop), then you must minimize the TRANSMISSIBILITY. Low
transmissibility is ONLY available above the crossover frequency, and the
lowest transmissibility is achieved with ZERO damping. That is how the EPI
system is designed and implemented.

The EPI engine coupling system removes over 99% of the torsional excitation
which the engine produces at takeoff power, which makes the input to the
gearbox nearly as smooth as that of a turbine, and provides the prop with an
operating environment which is essentially devoid of engine torsional
excitation.

That is accomplished by designing the system so that the first mode resonant
frequency (with respect to engine-order excitation) is below idle speed and
the second mode resonant frequency is over four times above max RPM. That
provides a frequency ratio greater than 9.0 at cruise and a transmissibility
from engine-to-PSRU approximately 0.01. The transmissibility from
prop-to-PSRU is roughly 1.04.

As a PSRU purchaser, you should be aware that those critical resonant
frequencies undergo potentially significant change whenever any of the
following properties of the system are changed:
(1) the reduction ratio;
(2) the propeller mass moment of inertia;
(3) any property of the engine which changes its mass moment of inertia
(accessories, bore, stroke, etc.),
(4) any property of the gearbox which alters the torsional stiffness of ANY
shaft.

GEARS AND BEARINGS

The gears in the EPI PSRU are straight-cut (spur gears), made from a
specially heat-treated E-9310 (manganese-nickel-chrome-molybdenum) alloy,
which have a face width of only 1.5 inches (in the model suitable for 600
LB-FT of engine torque). The gears have special design features which greatly
improve their resistance to both hertzian and bending fatigue, as well as to
prevent the edge-loadings which are so destructive to highly-loaded gears.

The design of the EPI system allows the gears to operate in an environment in
which the dynamic tooth loads are only slightly greater than the static
mean-torque loads, with a safety factor of over 2.0 using conservative
allowable stress levels.

(How can that be, you ask, if the engine peak torque values are over 200% of
the mean torque?? You already know the answer, because you just read the
VIBRATION sections above.)

Intuition often leads to the claim that helical gears, having a contact ratio
in excess of 2.5, would be superior to our spur gears (which have a contact
ratio of slightly over 1.6). However, most gear engineers know that contact
ratio is not the major discriminator between designs. Again, the mathematics
and engineering of gear design show that, while helicals do have a greater
contact ratio than spur gears of the same of the same pitch diameter and
diametral pitch, helicals suffer from the inherent problem of
highly-asymmetric tooth loading (edge-loading). They also produce substantial
thrust loads, but that is less of an issue. The only advantage helicals have
over similarly designed spur gears is less noise (hardly an issue in an
aircraft engine application!). The disadvantages helicals have are
significant.

Rolling element bearings which are sufficiently robust to provide
satisfactory calculated life factors in a realistic PSRU load model are
unacceptably large and heavy. The EPI PSRU does not use rolling element
bearings on either the propshaft or the input gear shaft (where the large
loads are). Therefore, the design bearing life at severe load levels is
conservatively calculated to be well over 2000 hours. In-service inspections
suggest a much longer life.

LUBRICATION AND COOLING
 
Obviously, gears and bearings must be lubricated. Intuition would suggest
that high-viscosity gear lubricant is required in a PSRU. Experience has
proven quite the opposite. However, an equally important (and often ignored)
function of the lubrication system is COOLING of the gears and bearings.
 
Why? Because involute gear tooth contact is sliding motion (not rolling
motion, as intuition suggests). The amount of power which is converted to
heat by tooth friction is approximately ½% per mesh for good quality,
well-lubricated gears. Low quality gears generate quite a bit more.

In order for a coolant to be able to carry a significant amount of heat
energy away from an object, the entry temperature of the coolant must be
substantially less than the temperature of the hot object to be cooled (high
effectiveness), or in the alternative, the coolant flowrate must be very high
(low effectiveness). The operating temperature of heat-treated, highly-loaded
gears should not get above 250°F, and the temperature of rolling element
bearings should never exceed 250°F in service.  

Those cooling requirements suggest the requirement for a continuous flow of
relatively cool oil. It should be clear that a high-power PSRU having its own
separate oil supply cannot survive without a significant oil cooling system,
which implies at least one pump and one more heat exchanger (complexity and
COOLING DRAG).

As an example, consider, a good quality two-mesh gearbox transmitting 400 HP.
The contact between the gears generates a heat load of about 10,000 BTU per
hour. Depending on the specific heat and specific gravity of the lubricating
oil and the oil temperature rise deemed acceptable, the oil flow rate
required just for cooling can exceed 3.5 GPM.

When evaluating a PSRU, ask to see test data that verify gearbox oil flowrate
as well as the entry and exit temperatures, measured after at least a
half-hour of steady-state operation at the rated power level. Also consider
that IF 3.5 GPM (or more) of oil goes into the PSRU, there must be some
suitable method to get it back out again. Gravity? Try to pour 3.5 gallons of
warm ATF through a ¾" hose in one minute.

GYROSCOPIC LOADS

The dynamic loads imposed on a PSRU come from several sources, and can be
very large. In addition to dynamic tooth contact and bending loads, gear
separation forces, and propeller thrust, it is sometimes forgotten that
gyroscopic moments can impose severe loads on not only the housing, but on
the propshaft and the bearings which support it, as well as to the engine
mounting structure and the points where it attaches to the fuselage.

As an example, when a particular (certified) 600 HP V8 turning a particular
3-blade metal prop at 2057 RPM is subjected to the FAA Part-23 gyroscopic
yaw-rate {14-CFR-23.371(a)(2)}, the propeller alone will produce over 3580
LB-FT of bending moment. That is over 5 times greater than the engine torque
and over 2.3 times greater than the propeller torque (the torque which the
engine mount is designed to handle).

With typical PSRU bearing placement, that moment alone imposes over 7000
pounds of force on each propshaft bearing. When coupled with the over-1400
pounds of gear separation force generated by 600 LB-FT of engine torque (on
20° gears), the bearing loads can be high enough to severely reduce the
expected life of a rolling element bearing. (Recall that the EPI PSRU does
not use rolling element bearings on either the propshaft or the input gear
shaft.)

Another gyroscopic-moment issue often ignored (regarding the engine mounting
structures used to install V8 engines on aircraft) is the analysis for whirl
mode. Early in the days of turboprop-powered aircraft, there were se
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