Stress - Fatigue Calculations

90 hp, Design Horsepower (hp) (at top of secondary)
2150 RPM of secondary
220 ft-lbfs, torque
1.625 in, Cog driver diameter
1622 lbfs, belt tension
3 in, top of bearing to centerline of cog belt drive pulley
0.184 in^4, I, second moment (stiffness of 35mm shaft)
4870 lbf-inches, bending moment at top edge of shaft-bearing interface
18,954 psi, max bending stress in shaft, Mc/I
0.35 in^4, J, Polar Moment (torsional stiffness)
5130 psi, Max torsional stress
20,250 psi, sigma prime, principal stress in part

Therefore, the stress with about 90hp being delivered out of the secondary shaft to the main rotor is near 20,250 psi.  Interestingly enough, Jack Kane's finite element analysis shows a max stress near 21,000 psi. 

Assuming the 21,000 psi, the fatigue limit for a properly designed and manufactured part made of 9310 is well above 21,000 psi, therefore it should last forever.

Some people probably hope that the engine puts out more then 90 hp to the main rotor.  The stress can be scaled to be about 225 psi per hp, so 22,500 psi for 100 hp or 28,000 psi for 125 hp.  However, data does not support horsepower output above 100hp to the main rotor.

Also, all failed shafts have shown a very small plastic zone, meaning they were loaded substantially below their strength. Another way to think about the small plastic zone is to realize that the actual stress was substantially below the ultimate stress of the part (under low stress).  Also, the variation of plastic zone sizes is small, typically less then 20% of the cross-sectional area, meaning there is good safety margin if fatigue cracks are avoided.

There is a lot of talk about the amount of pretension.  Belt manufacturers have certain recommendations about pretension, which are not used in the use of this cog belt drive.  However, Jack Kane's calculations using Gates recommendations shows the bending stress at 21,000 psi, well bell the 65,000 psi endurance limit. However, Pro-Drive does not follow Gates design and therefore has even lower pretension.

Due to the modulus of elasticity of the belt (the belt, not the individual strands of aramid fiber), the belt will stretch approximately 1/4 inch during operation.  Therefore, most of the initial pretension and any thermal shrinkage will be overcome by the stretch of the belt due to the tension in the belt.

Remember, the problem is about fretting.  Variations in stress do not matter. The culprit in the secondary shaft failure problem is the fretting caused by poor fatigue design.

Please remember that the plastic zone is the last part of the secondary shaft remaining when the shaft breaks.  The small plastic zone is the only thing holding the shaft together just before it breaks.  If the stress was too high, the plastic zone would be larger.

Steel Selection:

The selection of the secondary shaft steel is critical to ensuring a safe and long lasting secondary.  The selection of the proper steel is critical to meeting the two primary functions of the secondary.  First, the secondary shaft must be able to be hardened under the sprag clutch to Rockwell Hardness C 58 or greater.  This hardness keeps the sprag clutch elements from crushing the surface of the shaft and leaving small indentations on the surface of the secondary.  Second, the material must undergo heat treating to harden the area under the sprag clutch and still have good strength and toughness in the remaining portions of the shaft.

These two requirements, sprag clutch hardness and strength/toughness in the remaining portion of the shaft require a balancing act between these two properties.  Hardness and toughness are typically opposites; think about aluminum, it is fairly soft, but it can absorb impacts because of its ductility.  Ceramic on the other hand is very hard, yet striking ceramic with a hammer will cause it to shatter.  The fact that the ceramic shatters is because of the trade-off between hardness and toughness.

Hardness in steel is primarily controlled by carbon.  If you have a high carbon steel and heat treat it, you typically get a high hardness with a lower toughness.  In the case of the 9310 steel used in the Pro-Drive secondary, the carbon content is approximately 0.10%  (93(.10%)).  However, the trick is to locally add carbon to the surface of the secondary shaft, called carburizing.  This higher carbon content in the sprag clutch region, allows high hardness, necessary for preventing the sprag elements from damaging the surface.  Since the shaft is only carburized under the sprag clutch, the remaining areas of the shaft remain tough.  Toughness in our case is typically listed by IZOD toughness, a special method of measuring a materials toughness.  The toughness for 9310 is listed as 91 Ft-lbs.

Jack Kane talked about his material selection at Homer's, stating that the material selection is 300M.  300M is an alloy steel that is very similar to 4340.  For 300M the carbon content is around 0.40%, or about four times the amount in 9310 steel.  Therefore, when 300M is heat treated the entire secondary shaft will have much higher hardness and lower toughness.  For 4340,if it is heat treated to max hardness the toughness will be approximately 15 ft-lbs, fully six times less then 9310.  Also, a number of resources discuss the max hardness of 4340 quench and tempered is Rockwell C 53, which is signficantly below the required Rockwell C hardness of 58.

Therefore, the selection of a high carbon steel is detrimental to the toughness of most of the secondary shaft and the shaft may have difficulty achieving the desired hardness.  These tradeoffs will probably only be known once the system is built and tested.

Again, as stated before, the problem with the secondary shaft is not the material strength, the original secondary shafts do not show signs of insufficient strength, they show signs of reduced fatigue strength caused by fretting corrosion.  Therefore, if the material is good but the design is flawed, why change the material?

Belt Tension:

Presentations at Homer's 2004 discussed the required belt tension on a cog belt design.  It was interesting that the original Belt Tension Ratio "BTR" was discussed as 8:1, meaning that for 1600 lb belt tension the pretension would need to be 200 lbs.  Then, later in the presentation, it was discussed that Gates had raised the ration to 10:1.  In that case the 1600 lb belt tension would require a 160 lb pretension.  Jack Kane is saying that the Gates specified belt pretension is 10% of the total load.  Also, the Pro-Drive belt system is not based on the Gates design, the Belt tension ratio is even lower. 

The take home message is that the pretension is a minimal impact on the overall load on the secondary.  At Homer's John Spurling demonstrated that as torque is applied between the driving and driven pulley cause the tension on the belt to redistribute and apply the tension to the side that makes the torque.  Also, every failure seen to date is caused by high cycle fatigue, not from a excessive stress.  If the pretension in the belt were causing excessive loading, we would see failures with a significant plastic zone, indicative of overloading.  Failures are not caused by the stress level, they are caused by fretting.  Anyone saying that the problem is the 10% higher stress of the belt drive or that reducing the stress by 15% will solve the problem, is completely neglecting all of the evidence of every failure seen to date.

Centerline height of the belt/chain:

Jack Kane presented information about the difference between the load centerline between the belt and chain.  However, Jack measured the chain and belt sprockets while sitting on a table, however, owners of RotorWays will understand that the chain sprocket sits above the oil bath seal, causing the chain sprocket to sit slightly higher then required by the belt drive.  Therefore, the actual centerline between the belt and chain are nearly identical.

Changes in stress don't change the failure mode:

There is a lot of discussion about the stress in the secondary shaft.  Jack Kane shows a chain secondary shaft has a stress level of 18,000 psi and that a belt secondary shaft has a stress of 21,000 psi, a difference of about 15%.  Therefore, Jack Kane is saying that the stress of the Pro-Drive belt is about 15% higher then with a chain.  Al Behunchik states that his system is about 15% lower stress then the Pro-Drive.  Remember that the secondary shaft failures are about fretting, if the shaft frets, the shaft will fail at some point in its life.  Stress levels differences of 10%, 20%, or even 30% are not the issue, it is about fretting.

For instance, Al and Jack would have you believe that the 15% higher stress of the Pro-Drive caused the two failures of the 35mm secondary shafts.  Do you know that the star-tubes are supposed to increase horsepower by 15%?  What about variations in gross weight?  Are any ships 15% higher gross then others? The discussion of stress levels, belt tension, pulley diameters, etc. is simply rhetoric to confuse the situation away from the ONLY demonstrated failure mode for a secondary shaft, fretting corrosion.

Design Features:

  • 40 mm Shaft Diameter under bearing
  • 35mm Shaft Diameter throughout the the upper portion of the shaft.
  • Generous fillet radius in bearing - shaft interface
  • Fretting controlled by addition of fillets (addresses the RotorWay secondary shaft design flaw)
  • Entire secondary assembly will be dynamically balanced
  • Sealed SKF bearing with 40mm ID
  • L10 life of 10,000 hours (10% of bearings will have failed after 10,000 hours)
  • Surface treated for fatigue strength enhancement
  • Shaft operates well below the endurance limit, allowing infinite shaft life and a secondary system that lasts for the life of the helicopter.

RotorWay stands firm that their secondary shaft is safe for use.  However, one should consider that RotorWay has said in the past that their design was safe, even when using the 30 mm shaft.  Pro-Drive has been consistent that eliminating fretting corrosion near the bearing would improve the life of the secondary shaft.

The combination of the Pro-Drive cog belt and the Pro-Drive Secondary will finally end confusion about how to safely operate the RotorWay helicopter.  Invest in this combination and end the need for oil baths, excessive manifold pressure, and fear of an unintentional autorotation.

Pro-Drive feels that the components put into an experimental helicopter are completely up to the manufacturer of the helicopter, YOU, and that you should chose the materials and components that give you confidence to enjoy your investment.  If you have any questions about the Pro-Drive Secondary please feel free to contact Pro-Drive at 918-243-7635 or  flyapro@aol.com

Pricing:  $3200


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John Spurling, Pres.
Route 3, Box 12 C
Cleveland, OK 74020, USA
Tel. (918) 243-7635
Fax: (918) 243-7882
flyapro@aol.com
https://www.flyapro.com