Item 1204

DESIGN: Dragonfly ~ Power Train - Reduction - Initial - Calculations - Preliminary

Based on the calculations from the 'Auxiliary Drives' section of 'Mechanical Design and Description'. [Source ~ MDD p.89-93]

This page has been OK for calculating the loads at the four bearings, but use the program in Access for selecting the appropriate angular contact and deep groove bearings. Perhaps the bearing selection here can be used to select the appropriate hours.

Input shaft speed (operating): 4,500 rpm

Normal cruising input: 34 hp

Input torque: Q = (34 * 63025) / 4500 = 476 in-lb

No. of teeth in pinion: 16

No, of teeth in gear: 24

Tooth face: 0.675"

P.D. pinion: 2.286"

Tangential force: = P = Q / r1 = 476 / 0.9557 = 498 lbs.

r1 = mean pinion pitch radius = 1/2 (pinion pitch diameter - tooth face * sin (β) = 1/2 ( 2.286" - 0.675 * sin(33.7)) = 0.9557

r2 = mean gear pitch radius = r1 * (no. of teeth in gear/ no. of teeth in pinion) = 0.9557 * (24 / 16) = 1.4336

Tooth pressure angle = α = Arrow is 20º

1/2 Pinion Pitch Cone Angle = β = tan -1 (no. teeth pinion / no. teeth in gear) = tan -1 * (16 / 24) = 33.7º

Spiral angle = γ = Arrow is 35º

Roration of the driving pinion is ???-clockwise and the spiral angle is ??-hand. Based upon the Unicopter configuration.

Pinion thrust load = Tp = P * (tan (γ) * cos (β) + (( tan (γ) * sin (β)) / cos(γ)) = 498 * (tan (35º) * cos (33.7º) + (( tan (35º) * sin (33.7º)) / cos(35º)) = 498 * (0.7002 * 0.8320) + ((0.7002 * 0.5548) / 0.8192) = 498 * (0.5826) + (0.4742) = 138 lbs.

Gear thrust load = Tg = P * ((tan (γ) * cos (β) / cos(γ)) - (( tan (γ) * sin (β)) = 498 * (tan (35º) * cos (33.7º)) / cos(35º)) - (( tan (35º) * sin (33.7º)) = 498 * (0.7002 * 0.8320) / 0.8192) - ((0.8320 * 0.5548) = 498 * (0.0711) + (0.4616) = 16 lbs.

Positive sign (+) indicates thrust direction away from center and negative sign (-) indicates thrust direction toward center.

The loads on the bearings are determined below where a = 1", b= 1.5", C = 1" and d = 2". These dimensional values are approximate for now, and the sketch of them can be seen on page 141 of MDD.

Bearing No. 1:

 

Radial load due to

Loads on bearing 1 (furthest from pinion)

 

P

P1 = P * (a / b) = 498 * (1 / 1.5) = 332 lbs

 

TG

TG1 = TG * (a / b) = 16 * (1 / 1.5) = 11 lbs

 

Tp

U1 = Tp * (r1 / b) = 138 * (0.9557 / 1.5) = 88 lbs.

 

Total radial load

= R1 = sq rt( p12 + (tG1 - U1)2) = sq rt( 3322 + (11 - 88)2) = 323 lbs

The pinion thrust (axial) is carried on Brg. 1 = Tp = 138 lbs

The bearing used at this point is a narrow type deep groove MCR 104???.

Equivalent radial load according to MCR catalog will be 2/3 radial + thrust = __________________ = _________ lbs

Catalog rating for 1500 rpm is 350 lbs and for 2000 rpm is 310 lbs. For 4500 rpm the radial rating will be ______________ lbs.

Life factor = ____________ / _______________ = _____________

Mininum life = _________________________ = ______ hrs

Average life = _______________________ = ________ hrs.

Bearing No. 2:

 

Radial load due to

Loads on bearing 2 (closest to pinion)

 

P

P2 = P * ((a + b) / b) = 498 * ((1 + 1.5) / 1.5) = 830 lbs

 

TG

TG2 = TG * ((a + b) / b) = 16 * ((1 + 1.5) / 1.5) = 27 lbs

 

Tp

U2 = U1 = 88 lbs.

 

Total radial load

= sq rt( p22 + (TG2 - U2)2) = sq rt( 8302 + (27 - 88)2) = 828 lbs

Thrust (axial) load on Brg. 2 = 0

The bearing used is the same as Brg. 1. I.e. MRC-104

Rated capacity for 4500 rpm is ______ lbs.

Life factor = ____________ / _______________ = _____________

Minimum life = _________________________ = ______ hrs

Average life = _______________________ = ________ hrs.

Bearing No. 3:

 

Radial load due to

Loads on bearing 3 (closest to gear)

 

P

P3 = P * (d / (c + d)) = 498 * (2 / (1 + 2)) = 332 lbs

 

TG

U3 = TG * (r2 / (c +d) = 16 * (1.4336 / (1 +2) = 0.4779 lbs

 

Tp

Tp3 = Tp * (d / (c + d)) = 138 * (2 / (1 + 2)) = 92 lbs.

 

Total radial load

= sq rt( p32 + (U3 + Tp3)2) = sq rt( 3322 + (0.4779 + 92)2) = 345 lbs

Thrust (axial) load = 16 lbs.

Bearing No, 3 is also an MRC-104, operative at 16/24 * 4500 = ___rpm.

It carries beside the ____ lb gear thrust, a thrust in the opposite direction of ____- lbs from the tail rotor, or a thrust of 101 lbs.

Equivalent radial load = _____________________________ = ____lbs.

Catalog rating for 1000 rpm = ______lbs. and for 150 rpm is __________ lbs. For 3000 rpm the radial rating will be ______________ lbs.

Life factor = ____________ / _______________ = _____________

Minimum life = _________________________ = ______ hrs

Average life = _______________________ = ________ hrs.

Bearing No. 4:

 It will be obvious that this bearing carries very little load, because in the example the brg is 6" away. A Fafnir S-10K bearing was selected because of shaft diameter rather than load capacity.

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Last Revised: June 18, 2003