GEARS Classification of gears – Gear tooth terminology - Fundamental Law of toothed gearing and...

GEARS Classification of gears – Gear tooth

terminology - Fundamental Law of toothed gearing and involute gearing – Length of path of contact and contact ratio - Interference and undercutting - Gear trains – Simple, compound and Epicyclic gear trains - Differentials

104/19/23 S.K.AYYAPPAN,LECT.MECH

2

Spur Gears

Gears: Gears are machine elements that transmit motion by means of successively engaging teeth. The gear teeth act like small levers.


3

Power transmission systems

Belt/Rope Drives - Large center distance of the shafts

Chain Drives - Medium center distance of the shafts

Gear Drives - Small center distance of the shafts


4

Friction Discs


5

Spur Gears animation


6

Bevel Gears animation


7

Conveyor/Counting Gear train

Gear PumpWatch gear wheels


8

Industrial Applications

Printing machinery parts

Rotary die cutting machines

Blow molding machinery

Agricultural equipment

Boat out drives

Hoists and Cranes

Automotive prototype and reproduction

Diesel engine builders


9


Newspaper Industry Plastics machinery Motorcycle Transmissions Polymer pumps

Automotive applications

Commercial and Military operations

Special gear box builders


10


Heavy earth moving vehicles

Canning and bottling machinery builders

Special machine tool builders

Book binding machines Marine applications

Injection molding machinery

Military off-road vehicles Stamping presses


11

Classification

Gears may be classified according to the relative position of the axes of revolution. The axes may be parallel, intersecting and neither parallel nor intersecting.

1. Gears for connecting parallel shafts

Spur Gears: External contact Internal contact


12

Helical gears

Parallel Helical gears Heringbone gears (Double Helical gears)


13

Bevel gears2. Gears for connecting intersecting shafts – Bevel Gears


Bevel gears

14

Spiral bevel gears Straight bevel gears


15

3. Gears for neither parallel nor intersecting shafts.

Crossed-helical gears Worm & Worm Wheel


16

Rack and Pinion


17

Worm and Worm Wheel


18

Hypoid Gear


19

Hypoid Gear


20

Gear Box


21

Terminology

Spur Gears


22

Terminology


23

Definitions

Addendum: The radial distance between the Pitch Circle and the top of the teeth. Arc of Action: Is the arc of the Pitch Circle between the beginning and the end of the engagement of a given pair of teeth. Arc of Approach: Is the arc of the Pitch Circle between the first point of contact of the gear teeth and the Pitch Point. Arc of Recession: That arc of the Pitch Circle between the Pitch Point and the last point of contact of the gear teeth. Backlash: Play between mating teeth.


24

Definitions

Base Circle: The circle from which is generated the involute curve upon which the tooth profile is based. Center Distance: The distance between centers of two gears. Chordal Addendum: The distance between a chord, passing through the points where the Pitch Circle crosses the tooth profile, and the tooth top. Chordal Thickness: The thickness of the tooth measured along a chord passing through the points where the Pitch Circle crosses the tooth profile. Circular Pitch: Millimeter of Pitch Circle circumference per tooth.


25

Definitions

Circular Thickness: The thickness of the tooth measured along an arc following the Pitch Circle Clearance: The distance between the top of a tooth and the bottom of the space into which it fits on the meshing gear.

Contact Ratio: The ratio of the length of the Arc of Action to the Circular Pitch. Dedendum: The radial distance between the bottom of the tooth to pitch circle. Diametral Pitch: Teeth per mm of diameter.


26

Definitions

Face: The working surface of a gear tooth, located between the pitch diameter and the top of the tooth. Face Width: The width of the tooth measured parallel to the gear axis.

Flank: The working surface of a gear tooth, located between the pitch diameter and the bottom of the teeth Gear: The larger of two meshed gears. If both gears are the same size, they are both called "gears".

Land: The top surface of the tooth.


27

Definitions

Line of Action: That line along which the point of contact between gear teeth travels, between the first point of contact and the last. Module: Millimeter of Pitch Diameter to Teeth. Pinion: The smaller of two meshed gears. Pitch Circle: The circle, the radius of which is equal to the distance from the center of the gear to the pitch point. Diametral pitch: Teeth per millimeter of pitch diameter. Pitch Point: The point of tangency of the pitch circles of two meshing gears, where the Line of Centers crosses the pitch circles.


28

Definitions

Pressure Angle: Angle between the Line of Action and a line perpendicular to the Line of Centers. Profile Shift: An increase in the Outer Diameter and Root Diameter of a gear, introduced to lower the practical tooth number or acheive a non-standard Center Distance. Ratio: Ratio of the numbers of teeth on mating gears. Root Circle: The circle that passes through the bottom of the tooth spaces. Root Diameter: The diameter of the Root Circle. Working Depth: The depth to which a tooth extends into the space between teeth on the mating gear.


29

Formulae

pitchCircularXTeeth

pitchDiametral

TeethdiameterPitch

T

D

pitchDiametralppitchCircular c

cd pD

T

pitchCircularppitchDiametral


30

Formulae

pitchDiametral

GearonTeethpiniononTeeth

pitchCircular

GearonTeeth

piniononTeeth

cedisCenter

2

2tan

Cos Diameter Pitch Diameter Circle Base


31

Forumulae Specific to Gearswith Standard Teeth

Addendum = 1 ÷ Diametral Pitch= 0.3183 × Circular Pitch

Dedendum = 1.157 ÷ Diametral Pitch

= 0.3683 × Circular Pitch Working Depth = 2 ÷ Diametral Pitch

= 0.6366 × Circular Pitch

Whole Depth = 2.157 ÷ Diametral Pitch= 0.6866 × Circular Pitch


32

Forumulae Specific to Gearswith Standard Teeth

Clearance = 0.157 ÷ Diametral Pitch = 0.05 × Circular Pitch

Outside Diameter = (Teeth + 2) ÷ Diametral Pitch= (Teeth + 2) × Circular Pitch ÷ π

Diametral Pitch = (Teeth + 2) ÷ Outside Diameter


33

Law of Gearing

N2 is the foot of the perpendicular from O2 to N1N2.

Tooth profile 1 drives tooth profile 2 by acting at the instantaneous contact point K.

N1 N2 is the common normal of the two profiles.

N1 is the foot of the perpendicular from O1 to N1N2


34

Law of Gearing

Although the two profiles have different velocities V1 and V2 at point K, their velocities along N1N2 are equal in both magnitude and direction. Otherwise the two tooth profiles would separate from each other. Therefore, we have

1.4222111 NONO


35

Law of Gearing

2.411

22

2

1

NO

NO

We notice that the intersection of the tangency N1N2 and the line of center O1O2 is point P, and from the similar triangles

3.42211 PNOPNO


36

Law of Gearing

Therefore, velocity ratio

4.41

2

2

1

PO

PO


37

Law of Gearing

From the equations 4.2 and 4.4, we can write,

5.411

22

1

2

2

1

NO

NO

PO

PO

-ratio of the radii of the two base circles and also given by;

6.4cos

cos

222

111

PONO

andPONO


38

Law of Gearing

-centre distance between the base circles

7.4cos

coscos

2211

2211

2121

NONO

NONO

POPOOO

= pressure angle or the angle of obliquity. It is angle between the common normal to the base circles and the common tangent to the pitch circles.


39

Constant Velocity Ratio

A common normal (the line of action) to the tooth profiles at their point of contact must, in all positions of the contacting teeth, pass through a fixed point on the line-of-centers called the pitch pointAny two curves or profiles engaging each other and satisfying the law of gearing are conjugate curves, and the relative rotation speed of the gears will be constant (constant velocity ratio).


40

Conjugate Profiles

To obtain the expected velocity ratio of two tooth profiles, the normal line of their profiles must pass through the corresponding pitch point, which is decided by the velocity ratio. The two profiles which satisfy this requirement are called conjugate profiles.


41

Conjugate action

It is essential for correctly meshing gears, the size of the teeth ( the module ) must be the same for both the gears.

Another requirement - the shape of teeth necessary for the speed ratio to remain constant during an increment of rotation; this behaviour of the contacting surfaces (ie. the teeth flanks) is known as conjugate action.


04/19/23 S.K.AYYAPPAN,LECT.MECH 42

04/19/23 S.K.AYYAPPAN,LECT.MECH 43

GEARS Classification of gears – Gear tooth terminology - Fundamental Law of toothed gearing and...

Documents

Transcript of GEARS Classification of gears – Gear tooth terminology - Fundamental Law of toothed gearing and...