0689

Item 0689

DESIGN: UniCopter ~ Rotor - Hub - CVJ & HS - Bearings - Pitch

Forces and Moments:

The following forces are;

From one blade.
Located in the grip.
At 100% RRPM (no overspeed).
From GW at hover.
The Hub Spring contribution is arbitrarily considered to be (1.5 * thrust).

The values below come from; DESIGN: UniCopter ~ Rotor - Hub - Blade Generated Forces - Preliminary. Note that the craft has not been increased to 1320 lbs nor has the Radius been increased yet. These figures might do, at least to start, since the CVR+HS blade should be lighter than the ARR blade.

The bearing life comes from the same web page. Note that the LLF and SF have not been included.(Rightly or wrongly)

Centrifugal:

The centrifugal force is 6,600 lbs = 29.358 N. ???

Moment from Thrust:

The thrust is GW / 6 blades = (1320 / 6) = 220 lbf

The center of thrust is at 75% of disk radius = 0.75 * 120" = 90"

The hub spring contribution is = 1.5.

The moment is therefore 220# * 90" * 1.5 = 29,700 lbf-in = 3,356 N-m.

Moment from Engine Torque:

1,314 lbf-ft = 1,782 N-m per rotor divided by 6 blades = 219 lbf-ft = 2,628 lbf-in = 297 N-m.

I am adding a lead/lag rigidity factor or 3.0

The moment is therefore = 657 lbf-ft = 7,884 lbf-in = 891 N-m.

The Combined Moment from Thrust and Engine Torque:

√((29,700)² + (7,884)² ) = 30,729 lbf-in | √((3,356)² + (891)² ) = 3,472 N-m

Loads on Bearings:

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

= Centrifugal force of 6,600 lbs = 29,358.

The Radial Load on Each Bearing Set [F_r]:

Distance between bearings (d_PB) = 3.1893" [0.081 meter]

= Radial Force: = 3,472 N-m / 0.081 = 42,864 N

The combined centrifugal, thrust and torque forces (72,222 N) are approximately 1.7 times the combined thrust and torque forces (42,864 N). Therefor the angular contact bearing pair will be subjected to 1.7 times the load that the single needle bearing will.

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

Note that changing the angular contact bearings from 40º to 30 will increase their capacity slightly at the expense of axial load carrying capability. However, the axial load is always applied whereas the radial load is somewhat intermittent.

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

(Angular Contact)

Note: 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. It should be noted that even on this rotor the pre-cone removes some of the radial load during normal flight.

Therefore, the following calculations are probably slightly conservative.

Crude Comparisons, using only centrifugal force and angular contact bearings: ⁽¹⁾

	Helicopter or Bearing:	Basic Static Load Rating (for 2 brgs):	Centrifugal Force only: (3-blade rotor)	Ratio:
	Mini 500 ⁽²⁾ ~ 2 off SKF 7207 BEGAP	9337 lb-force	8810 lb-force	1.06%
	Robinson R-22		(3)
	Item 1214 \| SKF 7305BECB \| NTN 7305B	6,969 lb-force	6,600 lb-force	1.06%
	Item 1424 \| 7206BECB \| NTN 7206B	6,969 lb-force	6,600 lb-force	1.06%
⁽⁵⁾	Item 0525 \| SKF 7207BECB \| NTN 7207B	9,337 lb-force	6,600 lb-force	1.41%

(1) It is assumed that the centrifugal force to total force will be reasonably close on all helicopters but the CVJ &HS has a greater moment. Using the 30º bearings may help.

(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 SynchroLite's bearings are spaced at 2.5" versus 2" for the Mini.

(5) This is the selected bearing.

Symbols Used in the Following Algorithms:

L₁₀ = basic rating life, millions of revolutions

L_10h = basic rating life, operating hours

n = rotational speed, [rpm]

C = basic dynamic load rating

C_o = basic static load rating, [N]

C_r = basic static load rating for radial needle bearings, C_r for thrust bearings. [N]

p = exponential of the life equation; = 3 for ball bearings

P = equivalent dynamic bearing load, [N]

P_o = equivalent static bearing load, [N]

X = radial load factor for the bearing

Y = axial load factor for the bearing

F_r = actual radial bearing load, [N]

F_a = actual axial bearing load, [N]

X_o = radial load factor for the bearing | 0.5 from SKF catalog, page 292

Y_o = 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

Converted from SynchroLite to UniCopter as far as here.

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 [L_10h] should be 500 hours.

L₁₀ = L_10h * ((60 * n) / 1000000) = (500 * (60 * 650)) / 1000000 = 19.5

P = XF_r + YF_a = 0 .35 * 18,125 + 0.57 * 15,000 = 14,894 N

L₁₀ = (C / P)^p; Therefor C = ₃√L₁₀ * P = 2.692 * 14,894 = 40,094 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 * 40,094 = 66,824 N Is this the value we really want to use??

Note that the loads are the loading at hover. Also, note that they do not take into account that the (pre-cone / coning angle) will have significantly reduced the radial load.
_______________________________

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

P_o = X_oF_r + Y_oF_a= 0.5 * 18,125 + 0.26 * 15,000 = 12,962 N

C₀ = s₀ * P₀ = 0.4 * 12,962 = 5,185 N

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

If 2 Item 0987 is not strong enough then use 2 NTN 7206 (with NTN BL305 for radial only bearing)


Bearing: [SKF number given]	NTN 7204B; SKF 7204 BECB page 300, Item 0988	NTN 7205B; SKF 7205 BECB page 300, Item 0987	NTN 7206B; SKF 7206 BECB page 300, Item 1424	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	2 - 40º angular contact	1 - 40º angular contact	2 - 40º angular contact
Outer diameter:	47 mm., 1.8504"	52 mm., 2.0472"	62 mm., "	62 mm., 2.4409"	62 mm., 2.4409"
Inner diameter:	20 mm., 0.7874"	25 mm., 0.9842"	30 mm., "	25 mm., 0.9842"	25 mm., 0.9842"
Width (for 2)	28 mm., 1.1024"	30 mm., 1.1811"	32 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	39,000 N, 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	31,000 N, 6,969 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	0.35
Axial Load Factor for the Bearing: [Y]	0.57	0.57	0.57	0.57	0.57
Actual Radial Bearing Load: [Fr]	20,158 N ⁽¹⁾	20,158 N ⁽¹⁾	20,158 N ⁽¹⁾	20,158 N ^{(1) (4)}	20,158 N ⁽¹⁾
Actual Axial Bearing Load: [Fa]	15,000 N ⁽¹⁾	15,000 N ⁽¹⁾	15,000 N ⁽¹⁾	15,000 N ⁽¹⁾	15,000 N ⁽¹⁾
Dynamic Equivalent Radial Load: [Prr]	14,894 N	14,894 N	14,894 N	12,894 N	11,789 N

Basic Rating Life (in millions of revolutions): [L10]	3	4	16	5	20
Rotor Revolutions per Minute: [nn]	500 RPM	500 RPM	500 RPM	500 RPM	500 RPM
Basic Rating Life (in hours): [L10h]	105 hrs	139 hrs	520 hrs	154 hrs	664 hrs
Reliability: [rr]	90 %	90 %	90 %	90 %	90 %
Adjusted Rating Life (in hours): [Ln]	105 hrs	139 hrs ⁽²⁾	520 hrs ⁽²⁾	154 hrs ⁽²⁾	664 hrs ⁽²⁾

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

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

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.

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

Problem if considering bearing Item 1214. Its large diameter will interfere with the hub to X-outer hinge.

Outer Bearing Selection ~ to Handle Thrust and Torque Forces:

Deep Groove and Cylindrical Roller:

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


Bearing: [NTN number given]	NTN BL205, Item 1196	NTN BL3/22, Item 1423	NTN BL305, Item 1425	NTN NU205E
Quantity and Type:	1 - Deep groove	1 - Deep groove	1 - Deep Groove	1 - Cylindrical Roller
Outer diameter:	52 mm., 2.0472"	56 mm., 2.2047"	62 mm., 2.4409"	52 mm., 2.0472"
Inner diameter:	25 mm., 0.9842"	22 mm., 0.8661"	25 mm., 0.9842"	25 mm., 0.9842"
Width	15 mm., 0.5905"	16 mm., 0.6299"	17 mm., 0.6693"	15 mm., 0.5905"
Basic Dynamic Load Rating: [C]	17,000 N, 3,800 lbf	23,300 N, 5,250 lbf	26,900 N, 6,050 lbf	29,300 N, 6,600 lbf
Basic Static Load Rating [Co]	10,500 N, 2,360 lbf	13,200 N, 2,980 lbf	15,600 N, 3,500 lbf	27,700 N, 6,250 lbf
Radial Load Factor for the Bearing: [X]	1.0	1.0	1.0	1.0
Axial Load Factor for the Bearing: [Y]	0.0	0.0	0.0	0.0
Actual Radial Bearing Load: [Fr]	18,125 N, 4.075 lbf	18,125 N, 4.075 lbf	18,125 N, 4.075 lbf	18,125 N, 4.075 lbf
Actual Axial Bearing Load: [Fa]	0	0	0	0
Dynamic Equivalent Radial Load: [Prr]	18,125 N	18,125 N	18,125 N	18,125 N

Basic Rating Life (in millions of revolutions): [L10]	1	2	4	5
Rotor Revolutions per Minute: [nn]	500 RPM	500 RPM	500 RPM	500 RPM
Basic Rating Life (in hours): [L10h]	28 hrs	71 hrs	124 hrs	165 hrs
Reliability: [rr]	90 %	90 %	90 %	90 %
Adjusted Rating Life (in hours): [Ln]	28 hrs	71 hrs	124 hrs	165 hrs

Full Compliment Needle: Not used. If used, change the distance between inner and outer brgs to 2.25"

Symbols Used in the Following Algorithms: From Torrington - [Engineering / 75]

C_r = basic static load rating for radial needle bearings, C_r for thrust bearings. [N]

SF = Speed factor

P = Applied load

HF = Hardness factor

SF = 2.25 for speed of 500 rpm. Value of 500 from [Source ~ MDD p.17]

Moment = 1519 N-m, Distance between inner and outer bearings = 2.5" = 0.0635.

P = 1,151 N-m / 0.0635 = 18,126 N = [10,189 lbf-in / 2.5" = 4,076 lb]

HF = 1.00. From Torrington - [Engineering / 74]

L₁₀ = 2,500 required (desired). Value of 2,500 from [Source ~ MDD p.17]

Bearings: Item 0401 Full Compliment Torrington B-1416. C_r= 4,570 lbf =20,328 N

LF = C_r/ (SF * P * HF) = 10,053 / (2.25 * 18,126 N * 1.00) = [4,570 / (2.25 * 4,076 * 1)] = 0.498

If LF = 0.498 then L₁₀ = 50 hours From Torrington - [Engineering / 75]

Actually, because the pre-cone is 1º greater than the actual cone there will be a small negative loading. During hard maneuvering there will be a large positive loading. Lead/lag forces may be another story.

A higher capacity option is the Cylindrical Roller bearing with the same dimensions, NU205, page B-88. Basic Dynamic load rating is 29,300 N = 6,600 lbf

Lubrication:

How are the pitch bearings to be lubricated.

Oil is preferred, because of friction and bearing capacity, but this will require a chamber above the bearing.

Put the filling location for each blade in the crown, at a radial angle to the pitch bearing axis so that only the corroct quantity of oil can be poured it.

See pages on Mini 500 in Rotor folder.

Oil Seal:

Most other teetering rotors are enclosed at the outboard end of the spindle. The centrifugal force of the oil will place pressure on the seal. The less oil the less pressure, I think. Restrict the volume of the oil chamber. Use high temperature oil. Drill out the center of the spindle for cooling. Alternatively, The centrifugal force at this close proximity to the center of rotation may not result in much force.

The incorporation of elastomeric bearings will eliminate this problem. Or at least a radial elastomeric bearing, which is impervious to oil, at the outer location.

Currently consider a 25 ID, 52mm OD seal at the outer end. [Item 1398]

A sealed cap at the inner opening
A thought; What about a flexible cover that has a tight fit on the grip spindle, a press fit on the rotor's crown and the ability to oscillate about 30º?

Retaining Lock Nut:

The BUY drawing is 1421.dc.

Loading;

The centrifugal force is 3,371 lbf.
The Limit Load Factor is 4
The Safety Factor is 1.5.
The total is 20,026 lbf
The KTM lock nut M 25 x 1,5 [Item 1421] has a static load carrying capacity of 29,225 lbf
Ref; The Mini 500 appears to use the lighter series lock nut, which has a thickness that is 1/3 that of this series. I.e. a combined limit load and safety of 3.
Locking is by grub screw and/or it looks like the SKF locking washer MB 5 will work.

Additional Information:

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

Elastomeric pitch bearings will eliminate the potential problem of oil leakage the thereby eliminate the need for inner and outer seals.

OTHER: Mechanical - Bearings ~ Rotor Hub

Same Page ~ Different Craft: ~ Dragonfly ~ SynchroLite (2-blade teetering) ~ UniCopter

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Last Revised: January 19, 2005