lec 9 gear.ppt

7/27/2019 Lec 9 Gear.ppt

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Circular pitch: Distance

measured along the

circumference of the pitch

circle from a point on one tooth

to the corresponding point on

the adjacent tooth

Width of space: Tooth space

along the pitch circle

Addendum: Radial height of a

tooth above the pitch circle(normally 1 module)

Dedendum: Radial depth of

tooth below the pitch circle(normally 1.25 module)

Clearance: Radial difference between the addendum and the dedendum of a tooth

Tooth thickness: Tooth thickness measured along the pitch circle

Top land: Surface of the top of the tooth

Bottom land: Surface of the bottom of the tooth between the adjacent fillets

Face: Tooth surface between the pitch circle and the top land

Flank: Tooth surface between the pitch circle and the bottom land including filletFillet: Curved portion of the tooth flank at the root circle

T

dp


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Base circle: Imaginary circle from

which the involute curve of the tooth

profile is generated.

Pressure line/Line of action: Common

tangent to the base circles of mating

gears. It is also common normal at the

point of contact of the mating gears

Force is transmitted from the driving

gear to the driven gear on this line

Pressure angle: Angle between the pressure line and the common

tangent the pitch circles

Backlash: Clearance between mating teeth measured at the pitch

circle

Involute: Locus of apoint on a straight

line which rolls

without slipping on

the circumference of

a circle

Curve generated by unwrapping a taut string from a cylinder


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Arc of Contact: Locus of a point

on the pitch circle from the

beginning to the end of engagement

of two mating gears

Arc of Approach: Portion of the

arc of contact from the beginning ofengagement to the pitch point

Arc of Recess: Portion of the arc of

contact from the pitch point to the

end of engagement

Module(m) : Ratio of pitch diameter in mm to the number of teeth

Diametral pitch (P): Number of teeth per unit lengths of the pitch circle diameter in inches

Velocity ratio(VR): Ration of angular velocity of the driven to the angular velocity of driver

d

TP

T

dm

2

1

2

1

1

2

1

2

T

T

d

d

N

NVR

d1, d2: Pitch diameter of driver and driven

T1,T2: Number of teeth of driver and driven

N1,N2: Angular velocity(rpm) of driver and driven

1,2: Angular velocity (rad/s) of driver and driven

2211 NdNd

2

2

1

1

T

d

T

d

p


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4

Principles of Transmission and Conjugate Action

When a pair of mating gear teeth act against each other, rotary motion is produced which is

transmitted from the driver to the driven gear

If such a pair of gears have tooth profiles which are so designed that a constant angular

velocity ratio is produced and maintained during meshing, the two gears are said to have

conjugate action and the tooth profiles are said to have conjugate curves

In other words, conjugate action is assured if constant

where 1: angular velocity of the driver component of the mating pair

2: angular velocity of the driven component of the mating pair

If the tooth profile of one member of the pair is given, it is possible to construct the tooth

profile of the other member in order to have conjugate action when the gears mesh.

However the mostly commonly used curves are the family ofinvoluteand cycloidalcurves

2

1


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5

Law of Gearing:In order to have a constant angular velocity ratio, the tooth curves must be so

shaped that the common normal to the tooth profiles at the point of contact will always pass

through the pitch point, irrespective of the position of the contact during the course of action

Figure shows two curved surfaces which are

in contact with each other.

Body 1 with centre at O1 and having

angular velocity of1 is pushing body 2 of

which the centre is at O2. This produces

rotary motion and body 2 rotates with an

angular velocity of2 . The point of contact

at this instant is at Q where the two surfacesare tangent to each other.

The common tangent to the curves is T-T

and the transmission of forces takes place

along the common normal N-N which is

also called the line of action

Circles drawn through P, having centers atO1 and O2 are termed as pitch circles

For producing constant angular velocity

ratio, the cur ved profi les of the mating

teeth must be such that the law of gear ing

is satisf ied


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6

In case of involute profile, all points of contact takes place on the same straight line(line N-N in figure)

which means that the point Q which is the instantaneous point of contact at any position , moves up and

down along the line N-N

In figure, the lines QM1 and QM2 represent the

linear velocity vectors of the two gears at the

instantaneous point Q. Since the two bodies are

rigid, the common point Q can have only one

velocity component on the line of action N-N

and this is represented by Qn.

When resolved QM1 and QM2 have

components Qt1 and Qt2 respectively on the

common tangent T-T. The vector difference Qt1

and Qt2 gives the relative sliding velocity

When the contact takes places at the pitch point P,

QM1 = QM2, hence t1 - t2 = 0 . i.e for pure rolling

motion, the point of contact lie on the line of center

)( 2121 PQQtQt


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7

QO

QM

QO

QM

2

22

1

11 ,

1

1

2

2

1

2

QM

QO

QO

QM

From similar triangles QM1n and O1QR

ROQn

QOQM

11

1

From similar triangles QM2n and O2QS

SO

Qn

QO

QM

22

2

SO

RO

Qn

RO

SO

Qn

2

11

21

2

Again O1PR and O2PS are similar triangle, from

which we have

2

1

2

1

2

1

1

2

r

r

PO

PO

SO

RO

Inferences:

When a pair of curved surfaces are in direct contact transmitting

conjugate motion, the angular velocities of the two bodies are inversely

proportional to the segments into which the line of centers is cut by the

common normal

To produce constant angular velocity ratio, the common normal mustintersect the line of centers at a particular, immovable point

lec 9 gear.ppt

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