There is a good article in November 92 issue of Sport Aviation by Bill Husa on "Reduction Drives an Engineering Perspective". Since I'm considering an auto (Subaru SVX) conversion for my Cozy Mark IV, I found it very interesting. The author is an engineer in the aerospace field as am I. I thought the article was well done and goes a long way to quantify some of the important issues to be addressed. I think, however, that some of the calculations use overly pessimistic assumptions.
The first area the article addresses are the gyroscopic forces generated by the propeller which have to be supported by the propeller speed reduction unit (redrive), the engine and the engine mount. Since the propeller is dynamically characterized as a weight rotating rapidly, it has very much the same properties as a gyroscope. In this case when ever the airplane pitches or yaws the propeller generates a force that is 90 degrees out of phase with the yaw or pitch motion. So, a yaw rate would generate a pitch moment and vice versa. The moment generated is proportional to the rate of the yaw or pitch motion. The yaw and pitch rates can get rather high in turbulence or during abrupt maneuvers typical of aerobatics. The other factor that determines how much force is generated by the propeller is the weight of the propeller and the distribution of that weight. This weight distribution is quantified by engineers and called inertia. The inertia is highest for a rotating body like a propeller when there is a lot of weight at the tip. In the Sport Aviation article the author uses an equation for inertia that assumes that the weight is uniformly distributed along the propeller. As you know, we all use designs that taper the blades so that they are as thin as possible at the tip. So the weight is not uniformly distributed. The equation in the article was lo =.6667xMxl2. Since the propeller is tapered in both chord and thickness, I derived an equation for a uniformly tapered rectangle in both axes, the equation for this moment of inertia is:
For the 72", presumably, aluminum blade that the article uses, the inertia should be closer to 282 sl-in2 by this formula instead of the 806 sl-in2.
The article also assumes a 360 deg/ sec yaw or pitch rate. Ibelieve this is too conservative and I would use a rate of 60deg/sec instead for a non acrobatic application. The equation for the resulting moment is:
The resulting moments are then 644 ft-lb as opposed to 11,000 in the article. It should also be noted that the inertia goes down by the cube of radius, so that a 60" prop would have 58 percent of the moment compared to a 72" prop. Further, if the prop were a wood laminate (assumed density 0.0302 b/in3) the 72" prop would have an inertia of only 87.6 sl-in2 and the resulting moment would be 200 ft-lbs. These values should be used with appropriate safety factors for the max load case. The article compares these loads to design allowables for fatigue purposes. Fatigue design allowables for aluminum are generally based on the load that material could stand for 10 million cycles. These gyroscopic maximum loads will not occur that frequently.
The article also brings up the issue of torsional vibrations. This vibration is evident many times on shut down or at very low RPM when the RPM matches the stiffness of the engine mounts and the whole airplane shutters. However a similar vibration can occur at higher RPM involving primarily the inertia of the prop, flywheel and the crankshaft. The dynamic equations for this case involve the inertia of the components, the stiffness of the shafts, and the RPM of the engine. The problem is very complex from an analytical point of view, since it is further influenced by backlash in gears, and damping from friction and viscous sources. The stiffness of the components is not a piece of cake to establish either, since the geometry is constantly changing. The point that the article makes is a good one and that is that by changing the stiffness of the drive train, as is the case with the addition of a redrive, the torsional characteristics will change. It would take a very complex analysis to determine the magnitude of this problem. This is best analyzed empirically on an engine teststand; even this is beyond more than a cursory evaluation by most small manufacturers of redrives. So, for lack of any better information the article proposes a peak torque during a resonant torsional vibration of 800 ft-lbs. This is roughly about 4 times the maximum steady state torque of a 200 HP engine. The author seems alarmed by this mismatch of loads, however, crank shafts and the shafts in perspective redrives are not and should not be designed for the operational output torque of the engine. They must be designed for the peak transient load conditions. The load of 800 ft-lbs for peak loads due to transient torsional resonance and is well within the design criteria for most crankshafts. A typical crank shaft made from high strength steel(150 ksi), 1.5" diameter is good for 8300 ft-lbs of torsion. It should not be a burden to design the redrive for at least the 800ft-lbs without excessive weight penalties. Even the smaller 1" diameter shafts in redrives are good for 2400 ft-lbs. Keep in mind also that the resonate conditions the article refers to are transient and again do not fall into a fatigue criteria.
There is another load that was not mentioned in the article that should be considered in redrive design. That is the yaw or pitch moment or combination of the two that occurs in high speed flight with a sideslip or an angle of attack. In this condition the air passes through the propeller disk at a skewed angle. If you envision the right sideslip case, the top blade (for counter clockwise rotation engines) has a reduced angle of attack while the bottom blade has an increased angle of attack. This produces a moment that is transmitted through the redrive that can be sizable. The calculations for this are complex and I don't know of a derivation for them, but I will work on it.
I think the article brings up excellent points and the design criteria of any redrive should be available to the builder/designer since these are critical issues.