- Chain-Drive PSRU Issues -
Mythology of Hy-Vo Reduction Drives Exposed
Based on current research and design projects, EPI, Inc. has determined that a PSRU with suitable reliability for aircraft applications could be implemented with Hy-Vo™ link chain. It would be substantially heavier than one of EPI's geared units for the same torque capacity, but it might be less expensive.
There are several design issues with respect to Hy-Vo chain drives to be considered. The first is determining if the capacity of the chain is sufficient to preclude failure in the projected load model for an appropriate amount of time with an appropriate factor of safety.
HY-VO FAILURE MODES
There are two primary failure modes with a link-chain drive. The first is a progressive failure which results from an apparent elongation of the chain due to wear in the link-pin joint. Failure occurs when the apparent chain elongation has reached the point that the chain begins to skip teeth. Catastrophic failure is not far behind that event.
The second, and more critical failure mode is a catastrophic failure of the chain due to tensile fatigue loading of the sideplates. This failure is sudden, complete, and potentially explosive.
One of the most frequent design errors encountered in Hy-Vo-based PSRU products is a design which, at the rated capacity, applies a tensile load to the chain which is a very high percentage of the ultimate tensile strength of the chain (explained in the next section). Unfortunately, that strategy invites the very dramatic second mode of failure described above.
HY-VO CHAIN LOADS
Chains of a specific pitch are rated by horsepower capacity per inch of width for different diameter driving sprockets at specified RPMs. That is a simplified way to take into account the fact that there are two different sources of tensile loading in the chain: applied torque and centrifugal force from rotational speed. The rated horsepower number in the chain tables combines those parameters.
Let's examine the two sources of chain load. The first is applied torque. Torque from the engine is applied to the driving sprocket. That torque produces a tension force in the tight side of the chain which is equal to the applied torque (lb-in) divided by the pitch radius of the sprocket (same as the TANGENTIAL FORCE on a gear). The chain transmits that tension force onto the driven sprocket, and that sprocket applies a torque to the output shaft which is the input torque multiplied by the tooth-count ratio of the two sprockets.
The second source of chain tensile loading is centrifugal force. The centrifugal action resulting from the chain traveling in a circular direction around the two sprockets produces a tension force which is equal throughout the entire length of chain. That force is proportional to the weight of the chain per inch and to the square of the pitchline velocity.
In the Hy-Vo chain tables, you will notice that the power rating of a given chain will increase as RPM increases, up to a point. Beyond that RPM, the power rating begins to DECREASE. That is because of the ever-increasing effect of the centrifugal loading.
The centrifugal force adds to the driving tension force on the tight side of the chain. On the slack side, the chain is still carrying the tensile force generated by the chain centrifugal action. Therefore, with a constant torque applied to the drive, the cyclic loading on a given link varies once per full travel cycle around both sprockets, from the high tensile load (driving-plus-centrifugal on the tight side) to the low tensile load (centrifugal-only on the loose side) and back to the high tensile load. If the magnitude of that varying load is too high, the side links of the chain will fracture from fatigue cycling (explained fully HERE).
The engineering people who designed the Hy-Vo chain have defined, based on millions of hours of real-life experience with all kinds of driving machinery (gasoline engines, diesel engines, electric motors, turbine motors, etc. etc.) and all kinds of driven machinery, the values of fatigue loading which a given chain can survive for 2.5 million cycles. The fatigue environment in which a given chain can survive for 2.5 million cycles is considered to be the load limit for infinite life.
As an example, a drive configuration having a 2.56 ratio and an 8.06” distance between shafts, and being driven at 4000 engine RPM, produces approximately 1493 tensile cycles per minute or about 90,000 cycles per hour. At that rate, it takes only 28 hours to apply 2.5 million fatigue cycles to the chain.
If, however, the engine torque pulses (see TORSIONAL EXCITATION BY PISTON ENGINES) are superimposed onto the chain tensile loading, not only do the tensile loads increase by a large multiple, but the cyclic frequency increases rapidly as well. For example, at 4000 RPM, an 8-cylinder engine produces 16,000 torque pulses per minute, which is over 10 times greater than the fatigue-cycling rate applied to the chain if there are no torsional pulses.
Consider an example. Suppose a PSRU with a 2.50" wide, 1/2-inch pitch Hy-Vo chain and a 23-tooth driving sprocket is used on a 450-HP 8-cylinder, spark-ignition piston engine. The engine makes a takeoff-power value of 450 HP at 4600 RPM (515 lb-ft of torque) and makes 400 cruise HP at a 4000 RPM. (530 lb-ft of torque). Also suppose that the coupling between this PSRU and the engine crankshaft provides sufficient torsional absorption so that virtually no torsional excitation is applied to the PSRU's driving sprocket (not very likely, BTW, unless it is using an EPI coupler).
In that scenario, at the takeoff power rating of 450 HP and 4600 RPM, the design life of a 2.50-wide chain (using Morse engineering data) is just under 13 hours. At the cruise rating of 400 HP at 4000 RPM, the design life is is less than 16 hours. The appropriate Hy-Vo chain for that engine, assuming good torsional attenuation, is a minimum chain width of 3.00 inches in order to have any reasonable life expectancy.
HOWEVER, if that same chain is subjected to the raw torsional pulsing of the engine, the expected life will be much lower. Depending on the amplitude and frequency of the applied torsional cyclic loading, the safe applied power level for that 3.0-inch wide, 1/2-inch pitch Hy-Vo chain would be MUCH lower than 400 HP. The wear-induced loosening of the chain is another issue entirely.
It has been claimed that a chain drive is better than a gear drive because it eliminates the shaft bearing loads from the separation force which gears generate. The reality is, however, that in a chain drive, the gear force pushing the shafts apart is replaced by a similar force which is pulling the two shafts together, approximately equal to the sum of the driving tension plus twice the centrifugal force. That force increases with chain speed, and can become very large. It is applied to the bearings on both shafts.
Component temperature is an important consideration in chain drives. The manufacturer specifies a maximum of 250°F for the chain in order to stay safely away from the tempering temperature. If that temperature is reached, the tensile strength and fatigue life of the chain will be significantly reduced, as will the life expectancy of any rolling element bearings. (see LUBRICATION AND COOLING).
An interesting property of a Hy-Vo chain is the elastic elongation (stretch) which the chain experiences in response to a load. This stretch-per-unit-load (aka "spring rate") inserts an apparent torsional rate into the system, and reduces the first mode resonant frequency of the system. Typical torsional rates for a 2:1 reduction ratio implemented with 2.0, 2.5, or 3.0-inch wide chain are roughly 375, 454 and 501 lb-ft per degree respectively. (That rate varies with the tooth count of both sprockets, the chain width and the distance from the input shaft to the propshaft.)
However, this chain rate DOES NOT alter the pulse transmission characteristics of the engine-to-drive coupling. If the transmissibility of the coupling isn’t low enough, the engine pulses are still applied to the driving sprocket and to the chain, and might be amplified (see TRANSMISSIBILITY). The chain rate only diminishes the pulse amplitude applied to the output shaft and the prop.
"SELF DAMPING" ???
We have heard several sources describe a link-chain drive as being "self-damping". Let’s discuss these alleged "self-damping" characteristics.
First, recall the discussion of VIBRATION BASICS, where damping was defined as the property of energy dissipation. The dissipation of feedback energy from a system near resonance has the effect of limiting the vibration amplitude from going totally out of control. Recall that, no matter how much damping there is in a system, at resonance, there will still be amplification of the excitation forces.
Various marketeers of Hy-Vo PSRU drives claim that, because the slack side of the chain is loaded only by the centrifugal-tension force, somehow that magically introduces "damping" into the system. All it really introduces is backlash, which increases as the chain stretches through wear.
There can be an argument made that resonant vibration is less likely to go out of control because, near resonance, the entities being driven by the chain (prop and propshaft) have a difficult time feeding energy back into the vibrating system, due to the large amount of effective backlash. That effect is probably what is being incorrectly hyped as "self-damping".
In the best case, the effective backlash can somewhat attenuate the feedback of vibration energy from the prop when operating with an excitation frequency close to a resonance point. But remember, damping is only a crutch for a poorly-designed system operating near resonance (explained HERE).
However, the claim that, because of the backlash, a HyVo chain drive is somehow immune from torsional excitation problems is at best a demonstration of a profound lack of understanding of the problem, and at worst, a callous prioritization of sales over the safety of others.
The "self-damping" claim completely ignores the bigger problems, which result from the piston engine pulsing forces (a) causing destructive vibratory loads in the gears (or sprockets and chain) of a transmission unit, and (b) causing destructive blade vibration in the propeller. After all, the prop does not vibrate unless it is induced to do so by the application of an intermittent force at or near one of the resonant frequencies of the components (mainly BLADES) (see PROPELLER VIBRATION).
When the connection between the engine and gearbox does not attenuate those pulsing forces to near-zero, the pulsing of a piston engine will not only be applied to the PSRU innards, but will also be applied to the prop blades, whether or not there is feedback to the engine.
The properties of the EPI PSRU systems reduce the pulsing forces seen by the drive gear of the transmission to near-zero. That is what enables us to use 1.5-INCH WIDE GEARS to carry 450 V8 horsepower for a very long time.
To analyze it further, consider the torque waveform of a V8 engine (TORSIONAL EXCITATION BY PISTON ENGINES) applied to the driving gear in a chain reduction. Suppose a chain-PSRU is attached to the crankshaft of a V8 with a torsionally rigid coupling. As an example, let’s use our engine which produces a mean torque of 600 lb.-ft., and suppose that the driving gear in the chain PSRU has a 4" pitch diameter. Then at the mean torque (600 lb.-ft.), the tight side of the chain is carrying about 3600 pounds of driving tension force (PLUS the centrifugal component).
But remember that the torque occurs in pulses. At the instantaneous torque peak (200%), the chain carries 7200 pounds of driving tension. At the instantaneous torque valley (10%), the chain carries about 360 pounds of driving tension. So the driving tension in the tight side of the chain is varying between 360 and 7200 pounds, but never goes to zero. That cyclic loading is far beyond the life capacity of a 4" wide, 1/2-inch pitch Hy-Vo chain.
In addition, at 4000 RPM, the centrifugal tensile load in the chain is about 800 pounds. In a non-resonant condition, the centrifugal force is not enough to cause the tight side of the chain to bulge or to create any slack during the torque valleys. Clearly then, the torsional excitation which the engine produces is being transmitted very effectively onto the chain.
The elasticity of the chain (described above) will affect the pulse amplitude transmitted onto the output shaft. That amplitude could be increased or decreased, depending on the other properties of the system.
The only time decoupling (due to chain slop) can occur is if the torque waveform goes negative or if the driven entity is being excited near its resonant frequency. Because that pounding is being shared by so many teeth, the sprocket teeth are more tolerant of the abuse, but the chain takes a mighty beating. It’s no wonder the chains stretch. Notice that the elasticity of the chain does not necessarily reduce the amplitude of the excitation pulses delivered to the prop blades.