measurement of gear tooth thickness

INSPECTION AND MEASUREMENT OF TOOTH THICKNESS

RAJEEV U Prajeevullatt@gmail.com

GEAR MEASUREMENT

Gears are the devices meant for power transmission.For proper working the gears should be measured and inspected in each steps as:

Raw materials. Machining the blanks. Heat treatment. The cutting and finishing operations.

The accuracy depends on:

The measuring equipment available. Errors in the tooth surface finish

GEAR INSPECTION

Inspecting the dimensions and the surface for getting a designed thread.

Two types Analytical: slow process which check all

individual elements. Less preferred

Functional: carrying out running test with master and deciding. Much preferred

MEASUREMENT OF TOOTH

THICKNESS Defined as the length of an arc, which is difficult to measure

directly.

This is the most important measurement a gear should undergo.

The tooth thickness is generally measured at pitch circle and is therefore, the pitch line thickness of tooth.

Gear tooth thickness varies from the tip of the base circle of the tooth,

The instrument must be capable of measuring the tooth thickness at a specified position on the tooth.

METHODS FOR MEASUREMENT

1. GEAR TOOTH VERNIER CALLIPER.

2. CONSTANT CHORD METHOD.

3. BASE TANGENTIAL METHOD.

4. BY DIMENSION OVER PINS.

MEASUREMENT BY GEAR TOOTH VERNIER

CALLIPER It’s very conveniently measured by a gear tooth vernier caliper.

The gear tooth vernier has two vernier scales and they are set for the width (w) of the tooth and the depth (d) from the top.

Each of which is adjusted independently by adjusting screw on graduated bars.

It measures the tooth thickness at the pitch line.

It can also measure chordal addendum, the distance from top to chord.

Only used to verify the theoretical measurements.

GEAR TOOTH VERNIER CALLIPER

In fig.

w=AB=2AD

<AOD=x= 360°4N , Where N is the no.of teeth

w=2AD=2*AO.sin x=2R.sin360

4𝑁

Module m=P.C.D

no.of teeth=2R/N

Therefore

R=N.m/2

w=2N.m

2sin

360

4𝑁=N.m.sin

90

𝑁

Also d=OC-OD

But OC=OE+addendum=R+m=(Nm/2)+m

And OD=Rcos 𝑥=𝑁𝑚

2cos

90

𝑁

Therefore

d=𝑁𝑚

2+ 𝑚 −

𝑁𝑚

2cos

90

𝑁=

𝑁𝑚

21 +

2

𝑁− cos

90

𝑁

• This method is simple and inexpensive.

• However it needs different setting for a variation in number of teeth for a given pitch.

• Accuracy is limited by the least count of instrument.

• The wear during use is concentrated on the two jaws.

• The calliper has to be calibrated at regular intervals to maintain the accuracy of measurement.

ADVANTAGES AND LIMITATIONS

CONSTANT CHORD METHOD

Defined as “The chord joining those points, on opposite faces of tooth, which make contact with the mating teeth when the centerline of the tooth lies on the line of the gear centers”.

Constant chord measured where the tooth flank touches the flank of the

basic rack.

The teeth of the rack are straight and inclined to their Centre line at the

pressure angle.

Tooth thickness of rack along pitch line is equal to the arc tooth thickness of

gear round its pitch circle.

Property used :

“The gear tooth and rack space are in contact in the

symmetrical position at the points of contact of the flanks, the chord is

constant at this point irrespective of the system of gear in mesh”.

In fig.

PD=PF=arc PF=1/4*circular pitch

=1

4∗

π∗PCD

N= 1

4 ∗ π ∗ m

AP is tangential to the base circle, <CAP=x

∴ in ∆APD, AC = PD cos x = π

4 m. cos2 x

C= constant chord =2AC= π 2 mcos2x …….................→ 1

Where x→pressure angle

For helical gear , constant chord= π

2 mncos2xn

Where mn=NORMAL MODULE xn=NORMAL PRESSURE ANGLE

Now PC=APsin x= π

4 m cos x sin x

∴ d = addendum − PC = m −π

4 m cos x sin x

=m 1 −π

4cos x sin x ……………………………………………..….→2

for helical gear , d = mn 1 −π

4cos xn sin xn

Also PC=πm

4sin x cos x =

πm

8sin 2x ……………………….....→3

ADVANTAGES

For all number of teeth value of constant chord is same.

It readily lends itself to a form of comparator which more sensitive than the gear tooth vernier

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THANK YOU…