Item 1133

DESIGN: Dragonfly ~ Rotor - Hub - Bearings - Pitch

Thoughts for consideration: July 7, 2003

1. Having the spindle inserted into the yoke housing from the rear means that the only fastening device between the yoke and the blade grip will be a highly visible one between the spindle and the grip.
2. The yoke will be larger at the root end than the blade end, therefor consider having a larger diameter pitch bearing(s) at the root end. Insert the bearings down the flap - lead/lag hole and insert the spindle from the root end. May get away with one bearing at the root end to take the axial and radial loads. Seriously consider 7305BE
3. The larger flap - lead/lag hole will allow for a larger diameter lead/lag bushing.
4. The axial load from centrifugal force will be taken closer to the mast on the yoke housing and this housing can be lighter

Lubrication:

1. How are the bearings to be lubricated.
2. Seals: note that most other teetering rotors are enclosed at the outboard end of the spindle.
3. The incorporation of elastomeric bearings will eliminate this problem.

Forces:

The following forces are;

• Located in the yoke, at the intersection of the feathering axis of the blade and the vertical axis of the drag and flapping hinges.
• At 100% RRPM (no overspeed).
• From GW at hover.

The values below all originate at; DESIGN: Dragonfly ~ Rotor - Hub - Blade Forces - Preliminary

Centrifugal:

The centrifugal force is 3,577 lbs [15.911 N].

Note: It appears that only the centrifugal force is used when selecting the angular contact pitch bearings. See OTHER: Mechanical - Bearing ~ Rotor - Hub

Moment from Thrust:

The thrust is GW / 6 blades = (550 / 6) = 92 lbf

The center of thrust is at 75% of disk radius = 0.75 * 96" = 72"

The distance from the yoke to the center of thrust is 72' - 13.5' = 58.5"

The moment is therefore 92 * 58.5 = 5,382 lbf-in = 608 N-m.

Moment from Engine Torque:

The maximum torque from the engine, per blade is 63 lbf-ft = 756 lbs-in = 85 N-m.

The center of drag is at 75% of disk radius = 0.75 * 96" = 72"

Therefore the drag is 756 lbs-in / 72" = 10.5 lbf

The distance from the yoke to the center of drag is 72' - 13.5' = 58.5"

The moment is therefore 10.5 * 58.5 = 614 lbf-in = 69 N-m.

The Combined Moment from Thrust and Engine Torque:

√((608)2 + (69)2 ) = 612 N-m

= Centrifugal force of 15.911 N.

Note: It appears that only the centrifugal force is used when selecting the angular contact pitch bearings. See OTHER: Mechanical - Bearing ~ Rotor - Hub

Distance between bearings (dPB) = 2.5" {0.0635 meter]

= Radial Force: = 612 N-m / 0.0635 = 9,638 N

The combined centrifugal, thrust and torque forces (25,549 N) are approximately 2.65 times the combined thrust and torque forces (9,638 N). Therefor the angular contact bearing pair will be subjected to 2-1/2 times the load that the single deep groove bearing will.

Note that the radial loads on both bearings can be varied by changing the distance between the bearing sets.

Symbols Used in the Following Algorithms:

• L10 = basic rating life, millions of revolutions
• L10h = basic rating life, operating hours
• n = rotational speed, [rpm]
• C = basic dynamic load rating
• Co = basic static load rating, [N]
• p = exponential of the life equation; = 3 for ball bearings
• P = equivalent dynamic bearing load, [N]
• Po = equivalent static bearing load, [N]
• Y = axial load factor for the bearing
• Fa = actual axial bearing load, [N]
• Xo = radial load factor for the bearing | 0.5 from SKF catalog, page 292
• Yo = axial load factor for the bearing | 0.26 from SKF catalog, page 292
• s0 = static safety factor, | 0.4 from SKF catalog, page 53, table 9

Outer Bearing Selection ~ to Handle Centrifugal, Thrust and Torque Forces:

Note: It appears that only the centrifugal force is used when selecting the angular contact pitch bearings. See OTHER: Mechanical - Bearing ~ Rotor - Hub

The following calculations (for the outer bearing set only) need to be revised to take this into account. ~ Good

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Dynamic Equivalent Load: Calculations are from SKF catalog, pages 28, 52 & 292.

The criteria as given by OTHER: Mechanical - Bearing ~ Rotor Hub talks about an average life of 2500 hours at 500 rpm. The SKF catalog, pages 27 says "The median life is approximately five times the calculated basic rating life." Assuming that average life and median life are the same, then the calculated basic rating life [L10h] should be 500 hours.

L10 = L10h * ((60 * n) / 1000000) = (500 * (60 * 650)) / 1000000 = 19.5

P = XFr + YFa = 0 .35 * 9,638 + 0.57 * 15,911 = 12,442 N

L10 = (C / P)p; Therefor C = 3√L10 * P = 2.692 * 12,442 = 33,495 N

OTHER: Mechanical - Bearing ~ Rotor Hub says "For a light series bearing, 60 percent of this calculated capacity may be used as the allowable operating load to which it should be subjected." Therefore the allowable operating load: 100/60 * 35,763 = 55,826 N Is this the value we really want to use??

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Static Equivalent Load: Calculations are from SKF catalog, pages 52 & 292.

Po = XoFr + YoFa = 0.5 * 9,638 + 0.26 * 15,911 = 8,956 N

C0 = s0 * P0 = 0.4 * 8,956 = 3,582 N

Ultimate Static Equivalent Load: 3,582 N * Limit load factor of 4 * Safety factor of 1.5 (1) = 21,494 N [Source ~ MDD p.10]

(1) Should the limit load factor stay at 4, but the safety factor be reduced to 1.0 or 1.25 from 1.5?

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Comparisons, using only centrifugal force: (1)

 Helicopter or Bearing: Basic Static Load Rating (for 2 brgs): Centrifugal Force only: Ratio: Mini 500 (2) ~ 2 off SKF 7207 BEGAP 9337 lb-force 8810 lb-force 1.06% Robinson R-22 (3) 7204BECB 3,732 lb-force 3,577 lb-force 1.04% 7205BECB~ 0.572 lb. 4,586 lb-force 3,577 lb-force 1.28% 7305BECB 6,969 lb-force 3,577 lb-force 1.95% 7305BE ~ 0.506 lb. 3,507 lb-force 3,577 lb-force 0.98% (4) 7306BE ~ 0.748 lb. 4,766 lb-force 3,577 lb-force 1.33%

(1) It is assumed that the centrifugal force to total force ratio will be reasonably close on all helicopters.

(2) For information on the Mini 500 see; DESIGN: SynchroLite ~ Rotor - Hub - Bearing - Pitch

(3) The centrifugal force can probably come from earlier PPRuNe thread and be double checked against the known Robinson pre-cone angle; if the information on the bearings becomes available.

(4) The change that was made to the Mini-500 pitch bearings was to the radial bearing, not the angular contact bearings. The offset hub on the Dragonfly will result in proportionally greater moments, but the Dragonfly's bearings are spaced at 2.5" versus 2" for the Mini. Therefor the slightly proportionally smaller ratio 'might' not be a problem

FORM: Rotor - Hub - Pitch Bearings ~ UniCopter / Dragonfly

 Current choice. Bearing: [SKF number given] NTN 7204B; SKF 7204 BECB page 300, Item 0988 NTN 7205B; SKF 7205 BECB page 300, Item 0987 NTN 7305; SKF 7305 BE page 294, Item 1214 NTN 7305B; SKF 7305 BECB page 300, Item xxxx Quantity and Type: 2 - 40º angular contact 2 - 40º angular contact 1 - 40º angular contact 2 - 40º angular contact Location: Outer Outer Inner Outer Outer diameter: 47 mm., 1.8504" 52 mm., 2.0472" 62 mm., 2.4409" 62 mm., 2.4409" Inner diameter: 20 mm., 0.7874" 25 mm., 0.9842" 25 mm., 0.9842" 25 mm., 0.9842" Width (for 2) 28 mm., 1.1024" 30 mm., 1.1811" 17 mm., 0.6693" 34 mm., 1.3386" Basic Dynamic Load Rating: (for 2) [C] 22,900 N, 5,148 lb-force 25.100 N, 5,643 lb-force 26,000 N, 5,845 lb-force 42,300 N, 9,509 lb-force Basic Static Load Rating:(for 2) [Co] 16,600 N, 3,732 lb-force 20,400 N, 4,586 lb-force 15,600 N, 3,507 lb-force 31,000 N, 6,969 lb-force Radial Load Factor for the Bearing: [X] 0.35 0.35 0.35 0.35 Axial Load Factor for the Bearing: [Y] 0.57 0.57 0.57 0.57 Actual Radial Bearing Load: [Fr] 12,045 N (1) 12,045 N (1) 9,638 N (1) (4) 12,045 N (1) Actual Axial Bearing Load: [Fa] 15,911 N (1) 15,911 N (1) 15,911 N (1) 15,911 N (1) 11,789 N 12,443 N 11,789 N Basic Rating Life (in millions of revolutions): [L10] 10 9 ?? 46 Rotor Revolutions per Minute: [nn] 500 RPM 500 RPM 500 RPM Basic Rating Life (in hours): [L10h] 225 hrs 304 hrs 1154 hrs Reliability: [rr] 90 % 90 % 90 % Adjusted Rating Life (in hours): [Ln] 225 hrs (2) 304 hrs (2) 1154 hrs (2) Weight; for single or pair 0.204 K, 0.450 lb. 0.258 K, 0.568 lb 0.23 K, 0.506 lb 0.46 K, 1.012 lb
1. [Fr] must be less than 0.55 * [Fa]. This is OK.
2. This is way too low. [Source ~ MDD p.17] says that the bearing(s) should be selected and its rate thrust capacity calculated for an average life of 2500 hours at 500 rpm. It also says that for a light series, 60 percent of this calculated capacity
3. It looks like a pair of NTN 7305B bearing will give 467 hours. They have the same ID as the 7025B and a larger OD but they should not offer any mounting difficulties.
4. Reduced because of the greater distance between the bearing sets.

Note: It looks like this two bearing set might have to have a light pre-load. See information on Mini 500 on 0767.html

Inner Bearing Selection ~ to Handle Thrust and Torque Forces:

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Dynamic Equivalent Load: Calculations are from SKF catalog, pages 28, 52 & 292.

L10 = (C / P)p =

P = XFr + YFa = 1.0 * 12,045 + 0.0? * 15,911 = 12,045 N

Note that the loads are the loading at hover. Also, the light series 60% has not been taken into account (it may be only applicable to dynamic load. Also see; OTHER: Mechanical - Bearing ~ Rotor Hub

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Static Equivalent Load: Calculations are from SKF catalog, pages 52 & 292.

Po = 0.6Fr + 0.5Fa = 0.6 * 12,045 + 0.5 * 0 = 7,227 N

C0 = s0 * P0 = 0.4 * 7,227 = 2,890 N

2,890 N * Limit load factor of 4 * Safety factor of 1.5 = 17,345 N [Source ~ MDD p.10]

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This may be changed to Access table as above

 Current choice. Deep groove: Deep groove: Deep groove: Maximum capacity (full) type Deep groove: Maximum capacity (full) type NTN 6204; SKF 6204 page 188, Item xx NTN 6205; SKF 6205 page 300, Item xx NTN BL205 page B-28, Item 1196 NTN BL205 page B-28, Item xx ID = 20 mm., 0.7874" 25 mm., 0.9842" 25 mm., 0.9842" 25 mm., 0.9842" OD = 47 mm., 1.8504" 52 mm., 2.0472" 52 mm., 2.0472" 62 mm., 2.4409" Width = 14 mm., 0.5512" 15 mm., 0.5905" 15 mm., 0.5905" 17 mm., 0.693" Mass = 0.11 K, 0.24 lb 0.13 K, 0.286 lb 0.142 K, 0.312 lb 0.258 K, 0.569 lb Basic Load Ratings ~ Dynamic = 12,700 N, 2,855 lb-force 14,000 N, 3147 lb-force 17,000 N, 3800 lb-force 26,900 N, 6047 lb-force ~ Static = 6,550 N, 1,472 lb-force 7,800 N, 1,754 lb-force 10,500 N, 2,360 lb-force 15,600 N, 3,507 lb-force