6. Gear Measurement And Testing

Introduction • Gears are mainly used for transmission of

power and motion.

• They are used in various automobiles,

machines, equipments, electronic systems, etc.

• We already know that gears are used for

decreasing or increasing speed.

• They are also used for changing direction of

motion.

Types of Gears • Spur Gear : It is a cylindrical gear whose tooth

traces are straight lines.

• Helical Gear : It is a cylindrical gear whose tooth traces are straight helices.

• Spiral Gear : A gear whose tooth traces are curved lines.

• Straight Bevel : A gear whose tooth traces are straight line generators of a cone. It is Gear conical in form operating on intersecting axes usually at angles.

• Worm Gear Pair: The worm and mating worm wheel have their axes non-parallel and non-intersecting.

Terminology of Spur Gear

• Base Circle - It is the circle from which involute form is generated. Only the base circle on a gear is fixed and unalterable.

• Pitch Circle - It is an imaginary circle most useful in calculations. It may be noted that an infinite number of pitch circles can be chosen, each associated with its own pressure angle.

• Pitch Circle Diameter (P.C.D.) - It is the diameter of a circle which by pure rolling action would produce the same motion as the toothed gear wheel. This is the most important diameter in gears.

• Module - It is defined as the length of the pitch circle diameter per tooth. Thus if P.C.D. of gear be D and number of teeth N, then module (m) = D/N.

It is generally expressed in mm.

• Diametral Pitch - It is expressed as the number of teeth per inch of the P.C.D.

Diametral Pitch = 1/m = N/Dpitch

• Circular Pitch (CP.) - It is the arc distance measured around the pitch circle from the flank of one tooth to a similar flank in the next tooth. .-. CP. = πD/N = πm

• Addendum - This is the radial distance from the pitch circle to the tip of the tooth. Its value is equal to one module.

• Clearance - This is the radial distance from the tip of a tooth to the bottom of a mating tooth space when the teeth are symmetrically engaged. Its standard value is 0.157 m.

• Dedendum - This is the radial distance from the pitch circle to the bottom of the tooth space. Dedendum = Addendum + Clearance

= m + 0.157m = 1.157m.

• Tooth Thickness - This is the arc distance measured along the pitch circle from its intercept with one flank to its intercept with the other flank of the same tooth. Normally tooth thickness = C.P./2 = πm/2 But thickness is usually reduced by certain amount to allow for some amount of backlash and also owing to addendum correction.

• Face of Tooth. It is that part of the tooth surface which is above the pitch surface.

• Flank of Tooth. It is that part of the tooth surface which is lying below the pitch surface.

• Pressure Angle – It is the angle between path of contact and normal drawn to the line joining centers of base circle.

• Helix Angle : It is the acute angle between the tangent to the helix and axis of the cylinder on which teeth are cut.

• Lead Angle : It is the acute angle between the tangent to the helix and plane perpendicular to the axis of cylinder

• Back Lash : The distance through which a gear can be rotated to bring its non-working flank in contact with the teeth of mating gear.

Analytical Inspection of Gears

• Gear manufacturing process involves various

steps which may need in process inspection.

• A gear blank, at starting of an operation should

be checked for dimensional accuracy of face

width, bore, length, diameter, etc.

• The analytical method of gear involves

checking of various parameters of an

individual gear.

• It involves checking concentricity of gear

teeth, alignment of each tooth, hardness of

gear blank, etc.

• It also involves the factor that involves accuracy

of measurement of these parameter.

• Analytical method is tedious and it is not

preferred by industries because the values of

errors in pitch, profile cannot give the error of

overall operation of the gear.

• The analytical method is of useful for students

for study and to understand the concept.

• It will be useful for research and development

work in industries and laboratories.

Functional Method • It involves, mainly checking of gear running with

another gear during operation or at actual work.

• For testing function of gear, master gear is used in

combination of manufactured gear.

• Functional method is used for determining composite

errors in vibration, noise during working of gear.

• If the gear does not satisfy the rolling test, individual

or analytical test is carried out.

• To carry out functional test of the gear, Parkinson

gear tester or automating gear rolling machines are

used.

Rolling Test • Rolling test of gears give the composite error analysis

of gears.

• In rolling test, gear to be tested is rolled with the

master gear.

• This test reveals any errors in tooth form, pitch and

concentricity of the pitch line.

• This is the fact, economical and accurate method of

gear testing.

• Results of rolling test of gears are carefully observed

and conclusions are drawn regarding the angular

rotation per teeth, eccentricity as the error, individual

tooth error, etc.

Measurement of tooth thickness by gear tooth

vernier calliper

• It is used to measure the thickness of gear teeth

at the pitch line or chordal thickness of teeth and

the distance from the top of a tooth to the chord.

• The thickness of a tooth at pitch line and the

addendum is measured by an adjustable tongue,

each of which is adjusted independently by

adjusting screw on graduated bars.

• The effect of zero errors should be taken into

consideration.

• This method is simple and inexpensive.

• However it needs different setting for a

variation in number of teeth for a given

pitch and accuracy is limited by the least

count of instrument.

• Since 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.

• The tooth thickness is generally measured at

pitch circle and is, therefore, referred to as

pitch-line thickness of tooth.

• 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, at which w

occurs.

Considering one gear tooth, the theoretical

values of w and d can be found out which may

be verified by the instrument.

• In Fig. 15.14, it may be noted that w is a chord

ADB, but tooth thickness is specified as an arc

distance AEB.

• Also the distance d adjusted on instrument is

slightly greater than the addendum CE, w is

therefore called chordal thickness and d is

called the chordal addendum.

• In the above sketch ‘d’ is chordal addendum

which can be calculated as –

d = [(N × m)/2]×[1+(2/N)-cos(90/N)]

N – Number of teeth

M – module

• Tooth thickness can be calculated using gear

tooth vernier.

• By setting ‘d’ in vertical vernier, horizontal

vernier gives ‘w’ and can be verified by –

w = N × m sin(90/N)

Measurement of tooth thickness by Constant

Chord Method.

• In the above method, it is seen that both the

chordal thickness and chordal addendum are

dependent upon the number of teeth.

• Hence for measuring a large number of gears

for set, each having different number of teeth

would involve separate calculations, thus the

procedure becomes tedious and time-

consuming one.

• The constant chord method does away with

these difficulties.

• Constant chord of a gear is measured where

the tooth flanks touch the flanks of the basic

rack.

• The teeth of the rack are straight and inclined

to their centre lines at the pressure angle as

shown in Fig

• Also the pitch line of the rack is tangential to

the pitch circle of the gear and,- by definition,

the tooth thickness of the rack along this line is

equal to the arc tooth thickness of the gear

round its pitch circle.

• Now, since 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 position irrespective of the gear

of the system in mesh with the rack.

• The measurement of tooth thickness at

constant chord simplified the problem for all

number of teeth.

• If an involutes tooth is considered

symmetrically in close mesh with a basic rack

form, then it will be observed that regardless

of the number of teeth for a given size of tooth

(same module), the contact always occurs at

two fixed point A and B. AB is known as

constant chord.

• The constant chord is defined as the chord joining those

points, on opposite faces of the tooth, which make

contact with the mating teeth when the centre line of the

tooth lies on the line of the gear centers.

• The value of AB and its depth from the tip, where it

occurs can be calculated mathematically and then

verified by an instrument.

• The advantage of the constant chord method is that for

all number of teeth (of same module) value of constant

chord is same.

• In other words, the value of constant chord is constant

for all gears of a meshing system.

The Base Tangent Method Or David Brown

tangent comparator Or Flange Micrometer

• The purpose of tangent tester is to determine the

mean value and variation in base tangent length.

• It is measured between two parallel measuring

surfaces tangential to unlike gear teeth falnk.

• In this method, the span of a convenient number of

teeth is measured with the help of the tangent

comparator.

• This uses a single vernier caliper and has, therefore,

the following advantages over gear tooth vernier

which used two vernier scales :

(i) the measurements do not depend on two vernier

readings, each being function of the

other.

(ii) the measurement is not made with an edge of

the measuring jaw with the face. Consider a

straight generator (edge) ABC being rolled back

and forth along a base circle.

• The tangent length can be calculated as –

d = N × m – cos ø [tan ø – ø – (pia/2N) + (pia S/N)

Where, N – Number of teeth

M – module

Ø – Pressure angle

S – No. of teeth between two anvils.

• Direct values of ‘d’ are available for different

S, N and m.

• The instrument essentially consists of a fixed

anvil and a movable anvil.

• There is a micrometer on the moving anvil side

and this has a very limited movement on either

side of the setting.

N (Teeth on

Gear)

10 to 18 19 to 27 28 to 36 37 to 45 46 to 54 55 to 63

S (Teeth to be

spanned)

2 3 4 5 6 7

• The distance is adjusted by setting the fixed

anvil at desired place with the help of looking

ring and setting tubes.

• The movable anvil can be also locked by using

slip gauges for setting proper calculate

distance.

• Difference of reading which is set and

measured can be calculated using micrometer.

Parkinson’s Gear Tester

• The principle of this device is to mount a

standard gear on a fixed vertical spindle and the

gear to be tested on another similar spindle

mounted on a sliding carriage, maintaining the

gears in mesh by spring pressure.

• Movements of the sliding carriage as the gears

are rotated are indicated by a dial indicator, and

these variations are a measure of any

irregularities in the gear under test; alternatively

a recorder can be fitted, in the form of a waxed

circular chart and records made of the gear

variation in accuracy of mesh.

Construction • One fixed spindle and other movable spindle is

mounted on flat base.

• The movable spindle moves along with base

by rolling action on the main base plate as

shown in figure.

• A master gear is mounted on the fixed spindle

whereas a gear to be tested is mounted on a

movable spindle.

• The dial gauge is set to note the errors whose

pointer touches the floating body.

Working • When master gear is rotated slowly, a gear to

be tested will also get rotation movement

because of their meshing.

• Errors in the manufactured gear cause the gear

to move away from the centerline of spindle.

• When the on test moves, the floating body also

moves by the same distance. Because of

displacement of floating body, dial gauge gives

displacement.

• The variations in the readings can be observed

and platted in the graphical format.

Limitations • Maximum 300 mm diameter gears can be

tested.

• The floating body is very sensitive and hence

readings are to be taken very carefully.

• Accuracy up to 1µm can be possible while

measurement.

• Only composite errors in the gears can be

checked not individual one.

• Measurement depends upon the master gear.

Involute Measurement

• Involute is a curve plotted by a point on a

straight line which rolls around a circle

without slipping.

• Involute measurement is done by –

1) By profile projector

2) By Involute measuring machine

Involute Measuring Machine

• The basic principle of working is that if a straight

edge is rolled around a base circle without slipping,

the stylus of the dial gauge attached as above, gives

a involute.

• The gear to be tested is mounted on a mandrill.

• The circular disc of the same size as that of PCD is

also to be mounted on the same mandrill.

• The straight edge on the disc, which is tangent rolls

around the disc, generates a involute and the

variation is recorded by dial gauge.

• A electronics plotter can be used instead of dial

gauge for recording purpose.

Pitch Measuring Machine

• This instrument has three tips.

• One is the fixed measuring tip, other one is the

sensitive tip whose position can be adjusted by a

screw and the further movement of it is

transmitted through a leverage system to the dial

indicator and the third tip is the supplementary

adjustable stop which is meant for the stability of

the instrument and its position can also be

adjusted by a screw.

• The distance between the fixed and sensitive tip

is set to be equivalent to the base pitch of the

gear with the help of slip gauges.

• The properly set-up instrument is applied to

the gear so that all the three tips contact the

tooth profile.

• The reading on dial indicator is the error in the

base pitch.

Procedure of Measurement • The distance between tip (1) and (2) is set to a

standard using slip gauges when dial gauge is

showing a readings considered as zero.

• The machine is then applied to the gear under

test.

• All three tips are made contact to gear under

test.

• Reading of dial indicator shows the variation

in pitch.

• Repeat the procedure for next pair of gear

tooth.

Errors in Gear • Following are various gear errors that can be

checked while analytical inspection is carried out.

1) Profile 2) Spacing 3) Pitch 4) Run out 5) Gear

Tooth Thickness 6) Lead 7) Backlash.

The Errors are –

1) Cumulative pitch error

2) The tooth thickness error

3) Cyclic error

4) Run out

5) Radial Run out

6) Backlash

• Cumulative pitch error - It is defined as the

actual length between corresponding flanks of

teeth not adjacent to each other.

• The tooth thickness error – It is the difference

in actual tooth thickness and required tooth

thickness.

• Cyclic error - An error occurring during each

revolution of the element under consideration.

• Run out - It is the total range of reading of a

fixed indicator with the contact point applied to a

surface rotated, without axial movement about a

fixed axis.

• Radial Run out - It is the run-out measured

along a perpendicular to the axis of rotation.

• Backlash – It is the play between the matting

tooth surfaces i.e. the distance through which a

gear can be rotated to bring its nonworking

flank in contact to teeth of mating gear.

• Axial run-out (wobble) - It is the run-out

measured parallel to the axis of rotation, at a

specified distance from the axis.

? MSBTE QUESTIONS

• Describe with a neat sketch the use of Vernier

gear tooth caliper to measure the chordal

thickness of gear tooth on the pitch circle.

• Describe with neat sketch Parkinson gear tester.

• Explain principle of measurement of gear tooth

thickness using a gear tooth vernier.

• State and explain any four types of errors in

gear.

• Explain how will you check the involute profile

of a spur gear using involute measuring

machine.

• Explain following errors in gears

i) Backlash ii) Run out

Explain constant chord method for measuring tooth thickness of gear.