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Gear Trains

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Image from JTEKT Torsen NA, Inc.

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MAE 342 – Dynamics of Machines

Variations on Gear Trains

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MAE 342 – Dynamics of Machines 3

Gear Trains

• Gear trains are used to:

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MAE 342 – Dynamics of Machines 4

Gear Trains

• Naming and labeling:

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MAE 342 – Dynamics of Machines 5

Gear Pairs

• The angle relationship is:

MAE 342 – Dynamics of Machines 6

Gear Pairs

• The “Kinematic Coefficient” is the rate at which a gear rotates with respect to the input

gear:

• The speed ratio is:

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MAE 342 – Dynamics of Machines

Gear Pairs

• Be careful with rotation directions:� For two external gears:

� For external and internal gear pair:

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ω2

ω3

ω3

ω2

N2

N2

N3

N3

ω3

N2 N3

ω2

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Gear Pairs

• The torque ratio is given by:

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MAE 342 – Dynamics of Machines 9

Parallel-Axis Gear Trains• Speed ratio calculation

• Idler gears

N2 = 8

N3 = 24 N5 = 24

N4 = 8

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Parallel-Axis Gear Trains• Speed ratio calculation

N2 = 8

N3 = 24 N5 = 24

N4 = 8

• Speed calculation

If ω2 = 120 RPM, ω5 =

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MAE 342 – Dynamics of Machines 11

Epicyclic Gear Trains

• Also called:

• Comprised of:

MAE 342 – Dynamics of Machines 12

Epicyclic Gear Trains

• These can be drawn schematically

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MAE 342 – Dynamics of Machines 13

Epicyclic Gear Trains• A variety of arrangements are possible

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Epicyclic Gear Trains� 12 possible variations

according to Lévai.

� Bevel Gear Epicyclic Trains

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MAE 342 – Dynamics of Machines 15

Epicyclic Gear Trains

• Speed ratio calculation

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Adders and Differentials• Some variations

Automobile differential

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MAE 342 – Dynamics of Machines 17

Adders and Differentials

• Chinese mechanism for tracking direction.

MAE 342 – Dynamics of Machines 18

Adders and Differentials

• Limited Slip Differential

• Worm Gear (TORSEN) Differential

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MAE 342 – Dynamics of Machines 19

Designing Gear TrainsGiven (typically):

� Overall speed ratio� Input torque� Available space� Location of input and output shafts

Solution:1. Choose gear arrangement (see tables from Gear

Handbook).2. Choose approximate gear ratios for each

reduction.3. Simultaneously choose pitch/number of

teeth/pitch circle radii/center distances.4. “Source” the gears.

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Designing Gear Trains

From Gear Handbook (Editor D.W. Dudley) McGraw Hill

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MAE 342 – Dynamics of Machines 21

Designing Gear Trains

From Gear Handbook (Editor D.W. Dudley) McGraw Hill

MAE 342 – Dynamics of Machines 22

Designing Gear Trains

From Gear Handbook (Editor D.W. Dudley) McGraw Hill