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Output shaft

Housing

Lube Nozzle Bearings

Bearings

Input Gear

Bolts

PMC face-gears

RCM Face-gear

RCM Face-gear

PMC face-gears

Output face-gears

Pericyclic Transmission Components

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Static Stress Analysis using Clamp-Pin condition provides a

relationship between shaft diameter and thickness to minimize

weight.

Note: K=0 for solid shaft, K=.9 for very thintube

=250rpm

P =200HP

Dp=

5.5in

Output Shaft Load Capacity

Output Shaft

Light and small

OD

Ft Ft

Ax

Ay ByBx

MxAz

a b

My2 2

Btotal x yM M M= +

63000tP

M

=

3 2 2

4

16( ) ( )

(1 )o b b t t

s

d K M K M s K

= +

Static Shaft Model Reaction Momentsare Calculated

Power TransmissionShafting Equation

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FEA Validation of Shaft Model

Solidworks FEA model substantiates Analytical model within 15%

in all cases.

Bearing

Condition

Tangential and Radial

Forces, Ft & Fr

Stress Concentration

Clamped

Support

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

K (ID/OD)

%

errorfrom

analytica

lmode

l

Dp=5.5, 200HP

Dp=7.0, 200HP

Dp=8.5, 200HP

Clamped Support

Light and small

OD

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Light and small

OD

AxAyMx

Az

My

Bx By

M1 M2

Frr Frr

Ftr FtrFar Far

FroFro

FaoFto Fto

a b c

7 Unknowns:

Mx, My, Ax, Ay, Az, Bx, By

6 Equilibrium Equations & 1 Deflection Eq:

Fx, Fy, Fz, Mx, My, Mz, EIv(x)

Input Shaft/Carrier Analysis

3 2 2

416 ( ) ( )

(1 )o b b t t

s

d K M K M s K

= +

Mb, Mt known. By having load and Shaft

ID specified(= Bearing OD), OD is found

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Input and Output Bearing Selection

Radial Bearing Forces, calculated in shaft analysis, are combined,

run through Load-Life Calculations, and a bearing is selected

Of the bearings

that support

the load and

big enough ID

(=Dmp), find

the lightest The lightest

bearing for this

application

Output

Cp, modified bearing load is known

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Inputs

Power (HP)

out (rpm) Reduction Ratioi, o, (deg)

Tooth Bending Stress

Calc Min Dmp Allowable

Dmp

Static Analysis

Overturning Moment, Torque

Tooth Forces,

PMC Bearing Analysis

Can PMC Bearing support this PMC gear?

yes

Gear WeightUse geometry to find Weight

(PMCx2, RCMx2, Output)

PVT Design Space

Tooth Count Calculation

N1, N2, N3, N4

Output Shaft

Min Weight and OD

OD, K, Weight

Output Bearings

Timken Table Lookup

Np, OD, Weight

Output Shaft OD = Bearing Bore

Input Shaft

Min Weight and OD, K

OD, K, Weight

PMC Bearings

Modified Life Calc, tables

Weight, T, OD

Dmp = PMC Bearing Bore

PMC Bearing OD

= Input Shaft ID

Transmission Weight Breakdown(Figure to the Right)

Expanding the PVT Design Code Yields Transmission Weight

Breakdown by Component

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The Code chooses the minimum Gear Dmp based on Bending

Stress, then checks it with Contact Stress

The minimum allowable Gear

Diameter is found in tooth

bending stress, then checked in

contact stress

Based on this Dmp, other

parameters such as Weight and

OD are calculated

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Transmission Weight and Diameter are plotted as a function

of Torque to be compared to other Transmission Designs

Note: casing, lube system, input shaft bearings, and ancillariesnot included

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Continuation of the Research

Variable Speed Mechanism:

Clutches

Traction Drives

Torque Converters

Alternative Input Shaft (carrier) Analysis

Does large diameter, small length beam behave differentlythan static beam analysis?

Comparison of PVT Weight Plots versus other transmissions

What are the physical limitations of

each type?