7 - lecture seven mech2305

7/28/2019 7 - Lecture Seven Mech2305

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LECTURE SEVEN

GEARS

Common Gear Types

Spur

Helical

Bevel

Worm

Common Gear Types Uncommon Gear Types

Spur Gears

SPUR GEARS are usedwhen shafts must rotatein the same plane.

The teeth are straightand parallel to the shaft.The pinion is the smallerof a gear pair.

All forces are in the gearplane.

Pinion

Helical gears

HELICAL GEAR hascurved teeth at anangle to the shaft.

These teeth grip withless noise thanstraight teeth.

A thrust force isproduced by the mesh.


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Herringbone Gears

HERRINGBONE

GEAR has teeth thatare V-shaped, like adouble helical gear.

No thrust force.

Bevel gears

This type of gear is

used when the shaftsto be turned meet atan angle.

Spiral and hypoidbevel gears are usedin the automotiveindustry.

Spiral Bevel Hypoid

Worm Gear

It is a high-wear gearmesh. Replaced byspiral bevel andhypoid gears in mostmodern machinery.

Requirements

Minimise sliding at the gear mesh tominimise wear

The speed ratio must be constantthrough all rotational angles

Teeth have to be cut to a specialprofile (involute profile)

Frictional Clutch

R1 R2

1

2

A frictional clutchsatisfies all theseconditions.

But it has limitedtorque transmissioncapacity.

Required Gear Tooth Geometry

Two teeth in a mesh

O1

O2

Rotation centres for the two gearsContact Point

C

Speed Ratio 1 2

2 1

r

r

=

For R1/R2 to stay constant,P should remain fixed.

R1

R2

P

From Geometry1 1

2 2

r R

r R=

r1

r2

1

2

Contact Speed

Vc = 1 r1 = 2 r2


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Conjugate Action Summary

The same normal velocity at Contact

Angular speed ratio is r1

/r2

or R1

/R2

The point P is called the pitch point.

For R1/R2 to stay constant, P shouldremain fixed

In other words, the line of actionshould cross the line connecting therotation centres at the same point atevery instant and at any possibleconfiguration of the rotating bodiesover the entire 360o rotation of eithershaft.

This is satisfied by an involute profile

Involute Profile

An involute profile can begenerated by unwrappingstring that is wrappedaround a cylinder.

The trajectory of any pointon that string is an involuteprofile.

The perimeter of thecylinder is called the basecircle.

The "unwrapped string" iscalled the generating line.

Two Gears in Contact

The involute generated byunwrapping one stringfrom one gear andwrapping it onto anotheras the gears rotate

Pressure Line (Generating Line)

The line of action, thegenerating line, or thepressure line are differentnames for the involutegenerating string. The

pressure angle is the anglebetween that line and thetangent to the pitch circles.

The Pitch Radius :cos

p Rr

=

Gear Tooth Parameters Spur Gear Mesh


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Ft

Fs

N : No of teethr : Gear radius, mm : Angular speed, rad/s : Pressure Angle, deg

Principal Parameters

GEAR MODULEm = D/N mmm1 = m2

D2D1

Principal Parameters

Standard Gear Modules

GEAR MODULE

m = D/N

Typical Values are

2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50

Standard Gear Modules

Conversion

M=25.4/P

P

Standard Gear Modules Standard Gear Modules


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N2N3

N4

N5

5 1 3 4 1 3

1 2 4 5 2 5

N N N N Ne

N N N N N

= =

The idler cancels out

Gear Reduction Ratio

DrivingGearse

DrivenGears=

N2

N1

=

Gear Reduction RatioExample Two

Hunting Tooth

21:40

31:60

20:40

30:60

Are these all good ratios ? Whichones are to be preferred? Why?

Bonus Point

90o

35 Teeth

Module = 6

= 20o 45T

65T

A

B

C

3kW

600 RPM

Idler

Driven

Gear

What is the torque on shaft C ?

Motor

Motor

Motor

Motor

Drum 2 m

23T

23T

23T

23T

132T

132T 29T

29T

152T

140 t

AA

BB

Bonus Point

What is thetorque on each

motor ?

Contact Forces - Spur gear

Ft

Fs

Gear

Pinion

rg

rp

orp g

t t

p p p g g g

T TW WF F

r r r r = = = =

& &

Fn

Face Width


6/8

Contact Forces - Helicalgears

Ft

Fs

Fa

rp

Fs and Ft are as in spur

gears.

Axial force is given by

tana tF F =

Bonus Point

90o

35 Teeth

Module = 6

= 20o 45T

65T

A

B

C

3kW

600 RPM

Idler

Driven

Gear

What is the resultant force on the idler shaft bearings?

A B C D

How to calculate the speeds ?

The wheels will have the same linear speed at thepitch circle contact points

Drawing Environment

Drawing Environment Drawing Environment


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Drawing EnvironmentWalter Christie - 1900s

Engine

Friction clutches

Front wheels

Why the Friction Clutches ?

Why do we need a diff?

Velocity Differential

diff

avg

tV

R=

t

Speed Differential

The speed differential is only aproblem for driven wheels

The undriven but steered frontwheels will not need a differential

The driven unsteered rear wheels willneed a differential

Two slotted discsDiscs rotating at different

speeds


8/8

Replace lever with a lump ofsteel

What is a planet gear

Planets rotate around the sun

Planets rotate around their own axesof rotation

44

3

44

33333333333333333333

11111111

25

2

1

2

1 Sun Gear2 Planet Gear3 Planet Carrier / Output Shaft4 Ring Gear / Brake Ring5 Clutch Pack

CST Clutch on Longwall AFC Drives We can do this with a planetgear ?

A rotates around itsaxisIt also rotatesaround the axis of B& C

Open Differential Bonus Point

Tooth Numbers

Ni=16; Nc=57Np=12; No=17

Jack the right wheel up andrev the engine up. The diffinput is 1500 RPM.

What is the left wheel speed ?

What is the speed of the free-rotating right wheel?

7 - lecture seven mech2305

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