From: Epijk@aol.com
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Date: Sun, 6 May 2001 22:35:26 EDT
Subject: Alternate Engines
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Some PSRU Design Issues

This forum has hosted several discussions of various theories and intuitions=
=20
about PSRU's. On that subject, I would like to offer up some facts, based=20
upon the design, implementation and testing of one of the few geared PSRU's=20
which has demonstrated its performance and reliability, both on the test=20
stand and in the air.=20

The EPI PSRU is a part of the EngineAIR Power Systems 440 HP liquid-cooled,=20
turbocharged V8. That engine system powers (among others) Tom Zedaker's=20
Lancair-4-P which won Grand Champion at Sun n' Fun this year.=20

The prototype EPI PSRU has over 650 hour of flight time in Lancair-4=20
aircraft, driven by turbocharged engines producing up to 500 HP. It weighs 7=
1=20
pounds and includes the integrated control plumbing and gear-drive for a=20
standard Woodward-Hartzell prop governor. It was in the aircraft which won=20
the Kittyhawk-to-Oshkosh race in 2000 (and which nearly won in 2001).=20

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,=20
chain and various gear reductions, will be available in a few weeks on our=20
website, www.epi-eng.com.)

DESIGN SUMMARY

The EPI PSRU was designed using a system approach to the problem, based on a=
=20
severe-service aircraft load model, and taking into account the following=20
loads:=20

(a) the bearing, shaft and housing loads produced by:
    torque,=20
    gear separation forces,=20
    thrust, and=20
    gyroscopic moments,=20
(b) the static gear tooth loads applied by mean engine torque,=20
(c) the dynamic gear tooth loads resulting from the stiffness and vibration=20
characteristics of the system (these can greatly exceed the static loads),
(d) the cooling load imposed by the power transmitted and=20
(e) the lubrication requirements.

VIBRATION FUNDAMENTALS:

Everyone knows that any piece of metal has mass. Any piece of metal also=20
demonstrates the properties of a spring. That is, if you apply two equal and=
=20
opposite forces to opposite sides of it, it will deflect. Sometimes that=20
deflection can be seen; sometimes it is so small that it can't be measured=20
with a micrometer. That depends on the size of the force and the size of the=
=20
piece of metal. The amount of deflection caused by a specific force=20
determines its "spring rate". Any system which has mass and spring rate will=
=20
vibrate at it's resonant (natural) frequency (like a tuning fork) when struc=
k=20
("excited"). If it is repeatedly excited at or near its resonant frequency,=20
the vibrations will increase in magnitude until something breaks. As the=20
excitation frequency is increased beyond the resonant frequency, the=20
vibrations become smaller and smaller until they virtually disappear when th=
e=20
excitation frequency becomes more than 6 times the resonant frequency=20
(frequency ratios above 6).=20

ENGINE TORSIONAL VIBRATION

An even-firing 8 cylinder, 4-stroke engine produces a power pulse once every=
=20
90=B0 of crankshaft rotation. Therefore, the waveform of the instantaneous=20
full-throttle torque output (at the crankshaft flange) has four torque=20
"peaks" which are over 200% of the mean torque output (the torque which the=20
dyno measures), and four torque "valleys" which are approximately 25% of mea=
n=20
torque. Fortunately, that waveform is approximately sinusoidal.

A crankshaft, like a plain torsion-bar, has mass and a torsional spring rate=
.=20
The things attached to the crankshaft (rods, pistons, pins, rings, etc.) add=
=20
to the apparent mass of the crankshaft. That causes the crankshaft system to=
=20
have it's own torsional resonant frequency. The torque peaks and valleys=20
described above cause the engine crankshaft itself to deflect forward and=20
backward while it is operating. When those pulses (excitations) are near the=
=20
crankshaft resonant frequency, they can cause the crank to vibrate=20
uncontrollably and eventually break.=20

The torsional resonant frequency of the crankshaft system is a function of=20
(1) crankshaft length;=20
(2) crankshaft torsional stiffness;=20
(3) crankshaft stroke;=20
(4) bobweight mass (a function of the weight of the rods, pistons, pins,=20
rings, bearings, oil);=20
(5) moments of inertia of rotating items attached to or driven by the engine=
.=20

Because of the nature of the coupling between the engine and its load, the=20
torsional vibration characteristics of the engine crankshaft need to be=20
addressed independently. If you believe that a crankshaft can live for long=20
without an effective torsional attenuator on the free end, look to the=20
experience of the Nissan folks (The crankshaft in the very early 240-Z didn'=
t=20
have an effective attenuator, and therefore lasted only about 100 hours in=20
automotive {i.e. VERY LIGHT DUTY} service.)

Previous discussions have mentioned the vibration attenuating devices on the=
=20
free end of an engine crankshaft. Often, these are incorrectly referred to a=
s=20
"DAMPERS". In most cases, they are ABSORBERS. (That's not semantics. A dampe=
r=20
dissipates energy, typically as heat. An absorber alternately stores and=20
releases energy to counteract vibration.)

The elastomeric ("metal-ring-on-rubber-spring") devices used by the=20
automotive industry (as well as by Teledyne-Continental on the GTSIO-520) ar=
e=20
ABSORBERS which are tuned to counteract vibration at the frequency where the=
=20
particular engine generates its worst torsional excitation.  TCM and Lycomin=
g=20
also use internal ABSORBERS in all their high-output engines. They consist o=
f=20
pendulous counterweights attached to the crankshaft cheeks by loose pins in=20
hard bushings. The clearance between the pins and bushings establishes the=20
torsional order which each counterweight absorbs.

One aftermarket device, the Fluidampr (tm), is a viscous DAMPER which=20
dissipates energy by transforming it into heat by shearing action in a high=20
viscosity fluid. Some race car people seem to like it, but it is banned from=
=20
Winston Cup racing.=20

That type of damper is mildly effective over a wide range of excitations, bu=
t=20
contrary to intuition and hype, it is significantly LESS effective in=20
reducing vibration in a specific, targeted frequency range, the exact=20
situation you have in an aircraft engine. (There is ample research in the=20
engineering literature showing exactly that fact.)=20

PSRU and PROPELLER VIBRATION

The engineering literature is rich with information on the subject of=20
gearboxes. An American Gear Manufacturer's Association (AGMA) publication=20
summarizes the problem as follows:

"The gearbox is one component of a system comprised of a power source,=20
gearbox, driven equipment, and interconnecting shafts and couplings. The=20
dynamic response of this system depends on the distribution of the masses,=20
stiffnesses, and damping. In certain cases, a system may contain a torsional=
=20
natural frequency close to an excitation frequency associated with an=20
operating speed. Under these resonant conditions, the dynamic gear tooth=20
loads may be very high, and operation near a system resonance is to be=20
avoided."=20

Clearly, a PSRU cannot be treated as an isolated entity. It is one critical=20
component in a vibrating system having at least two natural frequencies (in=20
addition to the natural frequencies of major engine components such as the=20
crankshaft system) and two sources of excitation. Any change to any part of=20
the system can significantly alter the loadings imposed on the other parts o=
f=20
the system.=20

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

A propeller produces torsional excitation which varies with rotational and=20
translational speed, flight attitude, airframe characteristics, and the=20
properties of the engine torsional excitation which are applied to the prop.=
=20
Worse yet, each prop blade has a resonant frequency and is especially=20
susceptible to destructive vibration if it is excited near that resonant=20
frequency. Certified prop manufacturers go through extensive analysis and=20
testing to be sure that a particular prop will survive the fatigue=20
environment produced by a particular engine. Get it wrong, and blade pieces=20
will be departing the aircraft.

So there is the fundamental problem: both the input and the output of a PSRU=
=20
are attached to torsional excitation machines. From that, it should be clear=
=20
that there are two primary functions of a PSRU:=20

    (1) reliably transmit engine power to the propeller;=20
                      and equally important,=20
    (2) isolate the gears from the engine and prop excitations and from each=
=20
other.

Most of the intuition about PSRU's suggests that substantial DAMPING is=20
necessary for successful operation. In fact, the exact opposite is true. The=
=20
mathematics which define the system make it abundantly clear that, if your=20
goal is to minimize the torsional vibration transmitted to the gearbox (and=20
thus to the prop), then you must minimize the TRANSMISSIBILITY. Low=20
transmissibility is ONLY available above the crossover frequency, and the=20
lowest transmissibility is achieved with ZERO damping. That is how the EPI=20
system is designed and implemented.=20

The EPI engine coupling system removes over 99% of the torsional excitation=20
which the engine produces at takeoff power, which makes the input to the=20
gearbox nearly as smooth as that of a turbine, and provides the prop with an=
=20
operating environment which is essentially devoid of engine torsional=20
excitation.

That is accomplished by designing the system so that the first mode resonant=
=20
frequency (with respect to engine-order excitation) is below idle speed and=20
the second mode resonant frequency is over four times above max RPM. That=20
provides a frequency ratio greater than 9.0 at cruise and a transmissibility=
=20
from engine-to-PSRU approximately 0.01. The transmissibility from=20
prop-to-PSRU is roughly 1.04.

As a PSRU purchaser, you should be aware that those critical resonant=20
frequencies undergo potentially significant change whenever any of the=20
following properties of the system are changed:=20
(1) the reduction ratio;=20
(2) the propeller mass moment of inertia;=20
(3) any property of the engine which changes its mass moment of inertia=20
(accessories, bore, stroke, etc.),=20
(4) any property of the gearbox which alters the torsional stiffness of ANY=20
shaft.

GEARS AND BEARINGS

The gears in the EPI PSRU are straight-cut (spur gears), made from a=20
specially heat-treated E-9310 (manganese-nickel-chrome-molybdenum) alloy,=20
which have a face width of only 1.5 inches (in the model suitable for 600=20
LB-FT of engine torque). The gears have special design features which greatl=
y=20
improve their resistance to both hertzian and bending fatigue, as well as to=
=20
prevent the edge-loadings which are so destructive to highly-loaded gears.=20

The design of the EPI system allows the gears to operate in an environment i=
n=20
which the dynamic tooth loads are only slightly greater than the static=20
mean-torque loads, with a safety factor of over 2.0 using conservative=20
allowable stress levels.=20

(How can that be, you ask, if the engine peak torque values are over 200% of=
=20
the mean torque?? You already know the answer, because you just read the=20
VIBRATION sections above.)

Intuition often leads to the claim that helical gears, having a contact rati=
o=20
in excess of 2.5, would be superior to our spur gears (which have a contact=20
ratio of slightly over 1.6). However, most gear engineers know that contact=20
ratio is not the major discriminator between designs. Again, the mathematics=
=20
and engineering of gear design show that, while helicals do have a greater=20
contact ratio than spur gears of the same of the same pitch diameter and=20
diametral pitch, helicals suffer from the inherent problem of=20
highly-asymmetric tooth loading (edge-loading). They also produce substantia=
l=20
thrust loads, but that is less of an issue. The only advantage helicals have=
=20
over similarly designed spur gears is less noise (hardly an issue in an=20
aircraft engine application!). The disadvantages helicals have are=20
significant.

Rolling element bearings which are sufficiently robust to provide=20
satisfactory calculated life factors in a realistic PSRU load model are=20
unacceptably large and heavy. The EPI PSRU does not use rolling element=20
bearings on either the propshaft or the input gear shaft (where the large=20
loads are). Therefore, the design bearing life at severe load levels is=20
conservatively calculated to be well over 2000 hours. In-service inspections=
=20
suggest a much longer life.

LUBRICATION AND COOLING
=20
Obviously, gears and bearings must be lubricated. Intuition would suggest=20
that high-viscosity gear lubricant is required in a PSRU. Experience has=20
proven quite the opposite. However, an equally important (and often ignored)=
=20
function of the lubrication system is COOLING of the gears and bearings.
=20
Why? Because involute gear tooth contact is sliding motion (not rolling=20
motion, as intuition suggests). The amount of power which is converted to=20
heat by tooth friction is approximately =BD% per mesh for good quality,=20
well-lubricated gears. Low quality gears generate quite a bit more.=20

In order for a coolant to be able to carry a significant amount of heat=20
energy away from an object, the entry temperature of the coolant must be=20
substantially less than the temperature of the hot object to be cooled (high=
=20
effectiveness), or in the alternative, the coolant flowrate must be very hig=
h=20
(low effectiveness). The operating temperature of heat-treated, highly-loade=
d=20
gears should not get above 250=B0F, and the temperature of rolling element=20
bearings should never exceed 250=B0F in service. =20

Those cooling requirements suggest the requirement for a continuous flow of=20
relatively cool oil. It should be clear that a high-power PSRU having its ow=
n=20
separate oil supply cannot survive without a significant oil cooling system,=
=20
which implies at least one pump and one more heat exchanger (complexity and=20
COOLING DRAG).=20

As an example, consider, a good quality two-mesh gearbox transmitting 400 HP=
.=20
The contact between the gears generates a heat load of about 10,000 BTU per=20
hour. Depending on the specific heat and specific gravity of the lubricating=
=20
oil and the oil temperature rise deemed acceptable, the oil flow rate=20
required just for cooling can exceed 3.5 GPM.=20

When evaluating a PSRU, ask to see test data that verify gearbox oil flowrat=
e=20
as well as the entry and exit temperatures, measured after at least a=20
half-hour of steady-state operation at the rated power level. Also consider=20
that IF 3.5 GPM (or more) of oil goes into the PSRU, there must be some=20
suitable method to get it back out again. Gravity? Try to pour 3.5 gallons o=
f=20
warm ATF through a =BE" hose in one minute.=20

GYROSCOPIC LOADS

The dynamic loads imposed on a PSRU come from several sources, and can be=20
very large. In addition to dynamic tooth contact and bending loads, gear=20
separation forces, and propeller thrust, it is sometimes forgotten that=20
gyroscopic moments can impose severe loads on not only the housing, but on=20
the propshaft and the bearings which support it, as well as to the engine=20
mounting structure and the points where it attaches to the fuselage.=20

As an example, when a particular (certified) 600 HP V8 turning a particular=20
3-blade metal prop at 2057 RPM is subjected to the FAA Part-23 gyroscopic=20
yaw-rate {14-CFR-23.371(a)(2)}, the propeller alone will produce over 3580=20
LB-FT of bending moment. That is over 5 times greater than the engine torque=
=20
and over 2.3 times greater than the propeller torque (the torque which the=20
engine mount is designed to handle).=20

With typical PSRU bearing placement, that moment alone imposes over 7000=20
pounds of force on each propshaft bearing. When coupled with the over-1400=20
pounds of gear separation force generated by 600 LB-FT of engine torque (on=20
20=B0 gears), the bearing loads can be high enough to severely reduce the=20
expected life of a rolling element bearing. (Recall that the EPI PSRU does=20
not use rolling element bearings on either the propshaft or the input gear=20
shaft.)

Another gyroscopic-moment issue often ignored (regarding the engine mounting=
=20
structures used to install V8 engines on aircraft) is the analysis for whirl=
=20
mode. Early in the days of turboprop-powered aircraft, there were se
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