1144

Item 1144

DESIGN: Dragonfly ~ Power Train - Bearing - Initial Gearbox - Load Calculations

Overview:

This page is used to;

Calculate the Loads from the Crown & Pinion Gear Set, which can be found at; DESIGN: Dragonfly ~ Power Train - Reduction - Initial - Gear Selection

Calculate the loads on the bearings.

Below are two methods of calculating these loads. They are to serve as a check on each other. One is Fafnir p. Eng/54 and the other is MDD p.89 & 141

Concerns:

Will the two crown-gear shaft bearings 'fight' each other because of the large diameter of one?

Calculations from; FORM: PT - Bevel Gear Forces:

	Load:
	Horsepower	50
	Speed	4500
	Pitch Diameter	2.25
	Tangent Load	742 lb-force
	Bevel Gear:
	Tooth Pressure Angle	20º
	Helix Angle	35º
	Ratio	2:1
	Pitch Cone Angle	26.565º
	Rotation of driving member (pinion)	CW
	Helix Direction of driving member (pinion)	Left-hand
	Radial Gear Load (separating force) - Driving Side. ~ Pinion	63 lb-force
	Parallel Shaft Load (axial load) - Driving Side. ~ Pinion	613 lb-force
	Radial Gear Load (separating force) - Driven Side. ~ Crown	613 lb-force
	Parallel Shaft Load (axial load) - Driven Side. ~ Crown	63 lb-force

Notes:

The crown gear can never be the driving member, due to the overrunning clutch.

Pinion Bearings:

FORM: Bearing Load Distribution: Input Shaft:
Am not currently using above form at present. Have just done it roughly.

Distance between gear and bearing 1"

Distance between bearing and bearing 2"

Nearest to Pinion:

Radial load: 63 * 1.5 = 95 lb-force

Axial load: = 613 lb-force

Furthest from Pinion:

Radial load: 63 * 1/2 = 32 lb-force. At approximately 100 lb-force for vibratory loads from engine. = 132 lb-force

Axial load: 0 lb-force

Crown Gear Bearings:

FORM: Bearing Load Distribution: Input Shaft: ?? Output shaft ?? or a new separate form or maybe a second view in thes form

Am not currently using above form at present. Have just done it roughly.

Distance between gear and bearing: 1"

Distance between bearing and bearing: 4"

Nearest to Crown:

Radial load: 613 * 5/4 = 766 lb-force

Axial load: 63 lb-force

Furthest from Crown:

Radial load: 613 * 1/4 = 153 lb-force

Axial load: 0 lb-force ~ Probably no axial load since bearing will float.

This may be the overrunning clutch complete with its own bearing.

Calculations from; [Source ~ MDD p.89 & 141]. Used as a check on the above calculations.

Input shaft speed (operating) = 4500 rpm.

Normal cruising input = 50 H.P. [Am using maximum power here.]

Input torque = Q = (50)(63025)/4500 = 700lb-ln [= 58 lb-ft]

Number of teeth in pinion = 18

Number of teeth in gear = 36

Tooth face = 0.8125"

P. D. pinion = 2.25"

r₁= mean pinion pitch radius

~ = 1/2 (pin. pitch dia. - tooth face * sin β)

~ = 1/2 (2.25 - 0.8125 sin 35)

~ = 1/2 (2.25 - 0.8125 * 0.5736) The book errors by showing the 2.25 as 1.125.

~ = 0.8934

Tangential Force = P = Q/r₁ = 700/0.8934 = 784 lbs. This force is 742 above. r₁is the discrepancy.

r₂ = mean gear pitch radius

~ = r₁* no..teeth in gear / no. of teeth in pinion = 0.8934 * 36/18 = 1.7868

Tooth pressure Angle = α = 20-degrees

1/2 Pinion Pitch Cone Angle = β = tan ^-1 [no. teeth pinion] / [no. teeth gear] = tan ^-118/36 = 26.56º

Spiral angle = γ = 35-degrees

Rotation of driving pinion is clockwise and the spiral angle is left hand.

Pinion thrust load = T_p = P (tan γ cos β + ((tan α sin β) / cos γ))

~ = 784 ( tan 35 cos 26.56 + ((tan 20 sin 26.56) / cos 35))

~ = 784 ( 0.5774 * 0.8945 + ((0.3640 * 0.4471) / 0.8192))

~ = 784 ( 0.5165 + 0.1987) = +561 lb.

Gear thrust load = T_g = P ((tan α cos β) / cos γ - (tan γ sin β))

~ = P ((tan 20 cos 26.56) / cos 35 - (tan 35 sin 26.56))

~ = 784 ((0.364 * 0.8945) / 0.8192 - (0.700 * 0.4471))

~ = 784 (0.3975 - 0.3130) = +66 lb.

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

The loads on the bearings are determined below, where the distances are; a = 1.0", b = 2.0" c = 1.0" and d = 4.0".

Pinion Axle Bearings:

Furthest from Pinion: (Bearing No. 1)

Radial Load due to:
P	P₁= P * a / b = 784 * 1 / 2 =	+392	lb
T_G	T_G1= T_G* a / b = 66 * 1 / 2 =	+33	lb
T_P	U₁ = T_p * r₁ / b = 561 * 0.8934 / 2	+250	lb
Total radial load =	R₁ = √(P₁² + (T_G1 - U₁)² = √ (392² - 217²) =	+326	lb

Thrust load = 0 lb..

Nearest to Pinion: (Bearing No. 2)

Radial Load due to:
P	P₂= P * (a + b / b) = 784 * 3 / 2 =	+1176	lb
T_G	T_G2= T_G* (a + b / b) = 66 * 3 / 2 =	+99	lb
T_P	U₂ = U₁ =	+250	lb
Total radial load =	R₂ = √(P₂² + (T_G2 - U₂)² = √ (1176² + 151²) =	+1186	lb

Thrust load = T_p = +250 lb.

Crown Gear Axle Bearings:

Nearest to Crown: (Bearing No. 3)

Radial Load due to:
P	P₃= P * (c + d / d)= 784 * 5 / 4 =	+980	lb
T_G	T_G3= T_G* (c + d / d) = 66 * 5 / 4 =	+83	lb
T_P	U₃ = T_p * r₁ / d = 561 * 0.8934 / 4	+125	lb
Total radial load =	R₃ = √(P₃² + (U₃ + T_G3)² = √ (980² + 208²) =	+1002	lb

Thrust load = T_g = +66 lb.

Furthest from Crown: (Bearing No. 4)

This bearing quite obviously carries very little load therefore the bearing in the overrunning clutch should suffice.

Notes:

For bearing selection from the above Load Calculations see; DESIGN: Dragonfly ~ Power Train - Bearing - Initial Gearbox - Selection

For additional information on Spiral Bevel gears see; OTHER: Mechanical - Gear - Spiral Bevel

Back to top | Dragonfly Home Page

Last Revised: January 16, 2003