Item 0859

DESIGN: UniCopter ~ Rotor - Hub - ARR - Bearings - Pitch - Roller, Ball and Needle

Currently for 4-blade rotor only.

Outside Helicopter:

Sikorsky ABC - Rotor Blade Sleeve Assembly:

 E-mail discussing the Sikorsky ABC:

One disadvantage that I remember was a short life on the spindle bearings. This was said to be caused by the large horizontal fin generating a large nose down pitching moment in descending flight such as a steep approach or an auto rotation, likely a very fixable problem.

UniCopter:

To be similar to the ABC one above, or use thrust bearings??

Axial and Radial Forces on Pitch Bearings:

Reference only: It appears that only the centrifugal force is used when selecting the angular contact pitch bearings for convention helicopters that don't have hub springs or rigid hubs. See OTHER: Mechanical - Bearing ~ Rotor - Hub

This is my thinking; The axial (centrifugal) loading on the blade, pitch bearings and hub etc. will only increase over the 'Operating value' during the unusual situation, when the rotor's rpm is taken above its normal rotational speed. The radial load on the blade, pitch bearings, hub, power-train and fuselage etc. will constantly exceed the 'Operating value' during normal operating conditions. This high radial loading is due to the rigidity of the power-train. Therefore it may be advisable to increase the radial 'limit load factor' above the current value of 4.0.

From: DESIGN: UniCopter ~ Rotor - Disk - Blade Forces Currently 4-blade rotor only.

Ultimate axial load from a blade = 33,666 lb. (149,754 N)

Ultimate radial moment from a blade = 65,057 lbf.-in. (7,350 N-m)

Ultimate radial load on a bearing sets = 65,057 lbf.-in / 3.5"[between brgs] = 18,588 lb. (82,683 N)

The bearing furthest from the mast will be subjected to the (slightly) higher radial load.

Note that the above loads include a 4.0 [LLF - limit load factor] x 1.5 [SF - safety factor].

Drawing:

Maximum Loading on Inner Bearing(s):

Upper portion of drawing above.

The maximum axial loading is 5,611 [24,959] x (3.0 [LLF] x 1.5 [SF]) = 25,249 lb. (112,313 N)

The maximum radial loading is 10,837 [48,205] x (4 [LLF] x 1.5 [SF] = 65,022 lb.-in. / 3.5 = 18,578 lbs.

Therefore the worst case scenario on the inner bearing is a loading of 25,249 + 18,878 = 44,127 lbs. (196,286 N). Note that the LLF on the maximum axial loading has been reduced from 4 to 3 [173% RRPM] since I feel that the ability to experience maximum axial and maximum radial loads at the same time is probably impossible. Particularly with a rotor governor.

Lower portion of drawing above.

The minimum axial loading is 5,611 / 2 = 2,805 lbs top and bottom of bearing.

The maximum radial loading is 10,837 x (4 [LLF] x 1.5 [SF] = 65,022 lb.-in. / 3.4470 = 18,863 lbs.

Therefor the worst case scenario on the inner bearing is a point loading of 18,863 - 2,805 = 16,058 lbs ????

Maximum Loading on Outer Bearing(s):

Upper portion of drawing above.

This bearing is not subjected to any radial load.

Copied from above: Ultimate radial moment on a blade = 65,022 lb.-in. (289,232 N) / 3.5"[between brgs] = 18,578 lb. (82,639 N)

Lower portion of drawing above.

This bearing is not subjected to any radial load.

Copied from above: Ultimate radial moment on a blade = 65,022 lb.-in. (289,232 N) / 3"[between brgs] = 21,674 lb. (96,410 N)

Would like to go with NU 2210 below because of OD (for greater hub to blade clearance) and ID (to suit spar), but the Life rating is very low. Are my calculations in accordance with conventional rotorcraft determining????

Shock Loading:

There will not be any shock loading on the bearings since thay are only subjected to aerodynamic forces and the blades will flex slightly..

FORM: Rotor - Hub - Pitch Bearings ~ UniCopter Not completed

 

Inner Bearing:

 

 

 

 

Bearing:

SKF 29412 E

NTN ET- 33013 - No SKF

NTN 4T- 33113 - No SKF

 

Quantity and Type:

1 - Spherical roller thrust

1 - Tapered roller

1 - Tapered roller

 

Part number:

1048

1308

1308

 

Outer diameter:

5.1181"

3.9370"

4,3307"

 

Inner diameter:

2.3622"

2.5590"

2.5590"

 

Basic Dynamic Load Rating: [C]

345,000 N

97,500

144,000

 

Basic Static Load Rating: [Co]

915,000 N

156,000

211,000

 

Radial Load Factor for the Bearing: [X]

1.2

0.4

0.4

 

Axial Load Factor for the Bearing: [Y]

1.0

1.72

1.72

 

Actual Radial Bearing Load: [Fr]

73,398 N *

48,205 N (1)

48,205 N (1)

 

Actual Axial Bearing Load: [Fa]

303,496 N *

24,959 N(1)

24,959 N(1)

 

Dynamic Equivalent Radial Load: [Prr]

391,574 N **

62,211 N

62,211 N

 

 

 

 

 

 

Basic Rating Life (in millions of revolutions): [L10]

? ??

4

16

 

Rotor Revolutions per Minute: [nn]

10 RPM

500 RPM

500 RPM

 

Basic Rating Life (in hours): [L10h]

1,093 hrs

149 hrs

547 hrs

 

Reliability: [rr]

97 %

90 %

90 %

 

Adjusted Rating Life (in hours): [Ln]

481 hrs

149 hrs

547 hrs

 

Weight;

2.60 kg

0,73 kg

1.28 kg

NOTE (1) The actual loads do not included any LLF or SF.

_______________________

 

Outer Bearing:

 

 

 

 

 

Bearing:

B-4420

NU 2210

NU 2212

7212 BE

 

Quantity and Type:

1 - Full compliment needle

1 - Cylindrical roller

1 - Cylindrical roller

1 - Angular contact ball

 

Part number:

0139

xx

1076

xx

 

Outer diameter:

xx"

3.5433"

4.3307"

4.3307"

 

Inner diameter:

xx"

1.9685"

2.3622"

2.3622"

 

Basic Dynamic Load Rating: [C]

xx N

78,100

128,000

57,200 ***

 

Basic Static Load Rating: [Co]

xx N

88,000

153,000

45,500

 

Radial Load Factor for the Bearing: [X]

xx

1.0

1.0

1.0

 

Axial Load Factor for the Bearing: [Y]

xx

 

 

 

 

Actual Radial Bearing Load: [Fr]

xx N *

48,205 N

73,398 N

73,398 N

 

Actual Axial Bearing Load: [Fa]

xx N *

0

0

0

 

Dynamic Equivalent Radial Load: [Prr]

xx N **

48,205 N

73,398 N

73,398 N

 

 

 

 

 

 

 

Basic Rating Life (in millions of revolutions): [L10]

? ??

5

6

0 ???

 

Rotor Revolutions per Minute: [nn]

500 RPM

500 RPM

10 RPM

10 RPM

 

Basic Rating Life (in hours): [L10h]

xx hrs

166 hrs

10,640 hrs

789 hrs

 

Reliability: [rr]

xx %

90 %

97 %

97 %

 

Adjusted Rating Life (in hours): [Ln]

xx hrs

166 hrs

4,682 hrs

347 hrs

 

Weight;

xx kg

0,59 kg

1.10 kg

0.80 kg

* [Fr] must be less than 0.55 * [Fa]. This is OK.

* [P] = [Fa] + 1.2 * [Fr] = 303,496 + (1.2 * 73,398) = 391,574 N

** See SKF page 646.

*** This value looks like it can be increased by 5 to 20% by using a 30-deg bearing See Fafnir 2MM212WI

*** To reduce the OD to 3.74" 2 only NU1012's could be used for a total of 2 * 37,400 = 74,800 N, plus a reduction for the reduced moment arm length

Note that the weaker inner bearing has a much higher ratio of static to dynamic then either type of outer bearing and this application is very slow turning.

Note that the inner bearing will be under centrifugal loading constantly whereas the outer bearing will be under excessive loads occasionally.

Note that ABC will increase the blade loading somewhat. DESIGN: UniCopter ~ Rotor - Disk - Advancing Blade Concept ~ Amount of ABC

Consider using the cylindrical roller thrust bearing and the Fafnir 3MM9114WI.

 

Friction:

General Information:

Ball bearings have a lower friction than tapered roller bearings. Consider tandem, or more, arraignment.

SKF spherical roller thrust bearings are recommended to be operated in oil not grease.

Algorithms for Friction at Pitch Bearings:

The force transmitted to the cyclic stick, by the friction in the teetering bearings and the seals:

Bearings:

Information and algorithms for bearings are from SKF General Catalogue, p 56.

Estimation of Frictional Moment:

M = 0.5 * μ * F * d

where:

M = frictional moment, [Nmm]

μ = coefficient of friction for the bearing;

Deep grove ball bearing = 0.0015 (unsealed bearing)

Angular contact ball bearing (single row) = 0.0020

Needle roller bearing = 0.0025

Spherical roller bearing = 0.0018

Needle roller thrust bearing = 0.0050

F = bearing load, [N]

d = bearing bore diameter, [mm]

More Accurate Calculation of Frictional Moment:

M = M0 + M1

Remainder of information and algorithms can be found in SKF General Catalogue, p 58.

Seals:

Information and algorithms can be found in SKF General Catalogue, p 62.

M3 = ((d + D) / f3 )2 + f4

where:

M3 = frictional moment of 2 seals, [Nmm]

d = bearing bore diameter, [mm]

D = bearing outside diameter, [mm]

f3 = a factor [table 6]

f4 = a factor [table 6]

Estimate of Friction at Pitch Bearings:

1Nmm = 0.008857 in-lb (I think)

Axial load:

Consider ballscrew bearings for axial. 60° contact angle Fafnir p. 42

 

Bearing:

Static (N)

Dynamic: (N)

Dynamic Thrust (lbs)

Weight: (lbs)

 

3MM9107WI

12900

20200

 

0.35

 

MM9311 WI 3H QUH

 

 

17000

2 for 2.16

9,357 pounds = 41,622 N

M0 = 0.5 * μ * F * d

M0 = 0.5 * 0.0020 * 41,622 * 35

M0 = 1,457 Nmm = 12.9 in-lbs

Radial load:

 

Bearing:

Static (N)

Dynamic: (N)

 

Weight: (lbs)

 

22206 CJ

13800

13100

 

0.64

4,107 pounds = 18,269 N

M2 = 0.5 * μ * F * d

M2 = 0.5 * 0.0018 * 18,269 * 30

M2 = 493 Nmm = 4.37 in-lbs

* locations = 8.74 in-lbs

Seals:

M3 = ((d + D) / f3 )2 + f4

M3 = ((30 + 72) / 20 )2 + 10

M3 = 36 Nmm = 0.32 in-lbs

Total Frictional Moment:

M = M0 + M2 + M3

M = 12.9 + 8.74 + 0.32 = 21.96 say 22 in-lbs

Note: Prouty says "most modern helicopters with a floor mounted cyclic stick have a longitudinal force gradiant of 1 to 4 lb/in, with the lateral system being somewhat less".

Lubrication:

Lubricate with oil, not grease, to minimize friction. Oil will require seals with higher friction. May need reservoir, sit gauge (or side fill hole). How does oil get to upper portion of bearings?

Note that this bearing set (the pitch bearings) should be an ideal candidate for elastomeric bearings. The friction of the bearings should be considerably less and there will not be any seals to add to the friction.

See: DESIGN: UniCopter ~ Rotor - Hub - Pitch Bearing - Elastomeric

Consider: ~ March 13, 2003

See: OTHER: Mechanics - Bearing - Crossed Cylindrical Roller

Consider: ~ February 24, 2004

2 larger angular contact ball bearings at the very root and a smaller full compliment ball (or roller) bearing outboard.

Consider: ~ November 24, 2006

The use of needle bearing for radial loads to keep the rotorhub's drag as low as possible. The control will be by power, therefor a higher friction should not be a problem. Consider a tension-torsion strap for the axial load, particularly if there are 4 blades per rotor.

Same Page ~ Different Craft: ~ SynchroLite (3-blade CVJ w/ HS) ~ SynchroLite (2-blade teetering) ~ Dragonfly

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Last Revised: November 24, 2006