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;

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

Loads on Bearings:

The Axial Load on the One Bearing Set [Fa]:

= 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

The Radial Load on Each Bearing Set [Fr]:

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:

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

_______________________________

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??

Note that the loads are the loading at hover.

_______________________________

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?

_______________________________

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)

 

Dynamic Equivalent Radial Load: [Prr]

 

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: 

_______________________________

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

_______________________________

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]

_______________________________

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

Additional Information:

The bearing(s) may have to be elastomeric to eliminate the problems of static friction.

OTHER: Mechanical - Bearings ~ Rotor Hub

Same Page ~ Different Craft: ~ SynchroLite (3-blade CVJ & HS) ~ SynchroLite (2-blade Teetering) ~ UniCopter

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Last Revised: November 11, 2004