metrology , gear measurement

Gear tooth measurementGears are mainly used for transmission of motion & power and must be of accurate profile to obtain exact velocity ratio.

Two commonly used profiles of gear teeth are the Involute profile & the Cycloidal profile

Involute is defined as the path described by a point on an inextensible cord which is unwound from a stationary cylinder.Cycloid is defined as the curve traced by a point on the rim of a circle which rolls without slipping on a fixed straight line.

Types of gear

Spur Gear - The edge of each tooth is straight and aligned parallel to the axis of rotation.

Helical Gear - The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. The angled teeth engage more gradually than do spur gear teeth. This causeshelical gears to run more smoothly and quietly than spur gears.

Types of gear

Bevel gear - The angle between the shafts of mating gears can be anything except zero or 180 degrees. Bevel gears with equal numbers of teeth and shaft axes at 90 degrees are called miter gears..

Worm gear – Type of helical gear, but its helix angle is usually somewhat large and its body is usually fairly long in the axial direction; and it is these attributes which give it screw like qualities

Gear Tooth Nomenclature


Base circle: It is the circle from which gear teeth profiles are generated.

Pitch circle: It is an imaginary circle which by pure rolling action, would produce the same motion as the toothed wheel. The size of the gear is usually specified by the pitch circle diameter.

Pitch point: It is a common point of contact between two pitch circles of two meshing gear wheels.

Pressure angle: It is the angle between the common normal to two gear teeth at the point of contact and the common tangent at the pitch point.


Addendum: It is the radial distance from the pitch circle to the tip of the tooth.

Dedendum: It is the radial distance from the pitch circle to the root of the tooth.

Face : It is the part of the tooth surface which is above the pitch surface.

Flank : It is the part of the tooth surface which is below the pitch surface.

Circular pitch : It is the distance measured on the circumference of the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth.

Module: It is the ratio of the pitch circle diameter in millimeters to the number of teeth.

Face width: It is the width of the gear tooth measured parallel to its axis.

Gear errors1. Profile error: - The maximum distance of any point on the tooth

profile form to the design profile.2. Pitch error: - Difference between actual and design pitch3. Cyclic error: - Error occurs in each revolution of gear4. Run out: - Total range of reading of a fixed indicator with the

contact points applied to a surface rotated, without axial movement, about a fixed axis.

5. Eccentricity: - Half the radial run out6. Wobble: - Run out measured parallel to. the axis of rotation at a

specified distance from the axis7. Radial run out: - Run out measured along a perpendicular to the

axis of rotation.8. Undulation: - Periodical departure of the actual tooth surface

from the design surface.9. Axial run out: - Run out measured parallel to the axis of rotation

at a speed.10. Periodic error: -Error occurring at regular intervals

Geometrical Parameters Tooth Thickness Addendum Depth Tooth Spacing Over ‘X’ Number of teeth

Functional Parameters Pitch Variation Involute profile

Functional Parameters while meshing Runout Backlash Contact Area Noise

Following Elements are to be checked while carrying out gear measurement

Gear Measurement element

The Inspection of the gears consists of determine the following elements in which manufacturing error may be present.

1. Runout. 2. Pitch 3. Profile 4. Lead 5. Back lash 6. Tooth thickness 7. Concentricity 8. Alignment

Runout testing

It means eccentricity in the pitch circle. It will give periodic vibration during each revolution of the

gear. This will give the tooth failure in gears.

The run out is measured by means of eccentricity testers.

In this testing process, the gears are placed in the mandrel and the dial indicator of the tester posses special tip depending upon the module of the gear and the tips inserted between the tooth spaces and the gears are rotated tooth by tooth and the variation is noted from the dial indicator.

Runout testing

Pitch Measurement

There are two ways for measuring the pitch varriation .

1. Point to point measurement (i.e. One tooth point to next toot point)

2. Direct angular measurement

Pitch measurement-Point to point Measurement

Pitch measurement-Point to point Measurement

The instrument has three tips.

One is fixed measuring tip and the second is sensitive tip, whose position can be adjusted by a screw and the third tip is adjustable or guide stop.

The distance between the fixed and sensitive tip is equivalent to base pitch of the gear.

All the three tips are contact the tooth by setting the instrument and the reading on

the dial indicator is the error in the base pitch.

Profile checking

The methods used for profile checking is 1. Optical projection method. 2. Involute measuring machine.

1. Optical projection method: The profile of the gear projected on the

screen by optical lens and then projected value is compared with master profile.

Lead checking

It is checked by lead checking instruments.

Actually lead is the axial advance of a helix for one complete turn.

The lead checking instruments are advances a probe along a tooth surface, parallel to the axis when the gear rotates.

Backlash measurement

Backlash is the distance through which a gear can be rotated to bring its nonworking flank in contact with the teeth of mating gear.

Numerical values of backlash are measured at the tightest point of mesh on the pitch circle.

There are two types of backlash 1. Circumferential backlash 2. Normal backlash

.

Measurement of tooth thickness

Measurement of tooth thickness by

Gear tooth vernier caliper. Constant chord method. Base tangent method. Measurement by dimension over pins

The tooth thickness can be very conveniently measured by a gear tooth vernier.

Since the 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. Further this is possible only when there is some arrangement to fix that position where the measurement is to be taken.

The tooth thickness is generally measured at pitch circle & is, therefore, referred to as pitch line thickness of tooth.

The gear tooth in the vernier has two vernier scales & they are set for the width ‘w’ of the tooth & the depth ‘d’ from the top, at which w occurs.

Gear tooth vernier caliper.


Considering one tooth, the theoretical values of w & d can be found which may be verified by the instrument.

Also the depth d adjusted on the instrument is slightly greater than the addendum CE, & hence the width w is called chordal thickness & d is called chordal addendum.


From the fig, w=AB=2AD,Now angle AOD = q = 360/4NWhere N is the number of teeth,w=2AD=2*AO*sinq= 2R sin (360/4N) (R=PITCH CIRCLE RADIUS)Module, m= P.C.D/number of teeth = 2R/NR=N*m/2

w=(N*m)*sin(360/4N)Also from fig, d= OC-ODOC = OE+ addendum = R+m= (N*m/2)+mOD = R * cosq= N*m/2 cos(90/N)

d = (N*m/2)+m-(N*m/2) cos(90/N)

Why constant cord method

Vernier method like the chordal thicknessand chordal addendum are dependent upon the number of teeth.

Due to this for measuring large number of gears different calculations are to be made for each gear.

So these difficulties are avoided by this constant chord method.

The Constant Chord Method

Property : - If an involute tooth is considered symmetrically in close mesh with basic rack form , then it is observed that when gear rotates and all teethes come in mesh with rack , for the given size of tooth (same module), the contact is always occur at point two points

A & F as shown in fig. i.e the distance AF remains constant and known as constant chord.

The Constant Chord Method Efficient for measuring large no of gears, each having different no of teeth but same module

The Constant Chord Method

BD=BE=arc BE =1/4circular pitch=1/4 X P.C.D/N = ¼ mIn ∆ ABD, AB=BD cos=( /4)m cos In ∆ BAC,AC=AB cos=( /4)m Cos2 C=constant cord =2AC W=C = 0.5m Cos2

Now, BC=AB sin =( /4)m cos sin h= addendum-BC h = m – 0.25mCos Sin

- pressure angle m- module

Base Tangent method

This method uses David brown tangent comparator to measure span of a Convenient no of teeth

Advantage over gear tooth vernier is:1)Measurement does not depend on 2 vernier reading, each being function of other .2)Measurement not made with an edge of measuring jaw with the face.

Base Tangent method

= Pressure angle S =Number of tooth spaces

contained in W W = arc AB + arc BC

And when S tooth spaces are considered, arc BC = 2/N x S x NM/2 cos AC =NM/2 cos (tan - ) = /2N radians Arc CD =Rp cos /2N = NM/2 cos /2N AB = NM cos ( tan – ) + /2N Total arc length for S spaces,

W = NM cos ((tan – )- /2N + S/N)

Base Tangent method

Base Tangent method

David Brown Tangent Comparator – The distance(w) for S no of teeth Calculated and set with the help of slip gauges. The distance w theoretical and actual is verified for any difference.

Measurement of concentricity

In setting of gears the centre about which the gear is mounded should be

coincident with the centre from which the gear is generated.

It is easy to check the concentricity of the gear by mounting the gear between

centres and measuring the variation in height of a roller placed between the

successive teeth. Finally the variation in reading will be a

function of the eccentricity present.

Measurement of concentricity

Allignment checking

It is done by placing a parallel bar between the gear teeth and the gear being mounted between centres.

Finally the readings are taken at the two ends of the bar and difference in reading is the misalignment

Geometric measurement mc

GEOMETRIC MEASUREMENTPOINT MEASUREMENT : Free point, peak point, constant intersection, mid point (between elements of measured data)

LINE MEASUREMENT :Line, Tangent line, Perpendicular line

CIRCLE MEASUREMENT : Circle (Multipoint), Centre & radius.DISTANCE, ANGLE :Distance, Step, Pitch & angle.

Gear measuring instrument

It can accomplish a variety of gear measuring tasks including the inspections of tooth data on cylin- drical gears ( external spur and helical gears: standard measuring module ), shaping and shaving cutters, as well as on gear and worm hobs (optional). In addition, the range of application also extends to inspection of worm and worm gear, spiral, straight and helical bevel gears (optional). These gear measuring centres are widely used in automobile, machine tool, instrument industries, as well as inspection laboratory and modern factory environ- ment.

Test Plug Method for checking pitch diameter and tooth spacing

A roller is placed between a pair of teeth so that the its centre lies on the pitch circle as shown on slide.

For a gear with an odd number of teeth a radial measurement is taken with the gear between centres using a comparator.


OA = ¼ M cos (OA= radius of rollers)

Gauging Radius: Rg = ½ NM + ¼ M cos

Dimensions over a pair of Rollers in opposite tooth spaces :

Dg = M(N + ½ cos )

Procedure Two pins of equal dia are placed on either

side of tooth and reading compared with calculated value of M.

M=(m X nX Cos )/cos m x cos 90/N + d M-Required size over wire ‘m – module, d-dia of wire, -pressure

angle, m – pressure angle at centre of pin(m formula given in book)


PARKINSON GEAR TESTER


The master gear is fixed on vertical spindle and the gear to be tested is fixed on similar spindle which is mounted on a carriage.

The carriage which can slide either side and these gears are maintained in mesh by spring pressure.

When the gears are rotated, the movement of sliding carriage is indicated by a dial indicator and these variations arc is measure of any irregularities in the car under test. Fig

The variation is recorded in a recorder which is fitted in the form of a waxed circular chart.


In the gears are fitted on the mandrels and are free to rotate without clearance and the left mandrel move along the table and the right mandrel move along the spring-loaded carriage

The two spindles can be adjusted so that the axial distance is equal and a scale is attached to one side and vernier to the other, this enables center distance to be measured to within 0.025mm

If any errors in the tooth form when gears are in close mesh, pitch or concentricity of pitch line will cause a variation in center distance from this movement of

carriage as indicated to the dial gauge will show the errors in the gear test.

The recorder also fitted in the form of circular or rectangular chart and the errors are recorded.

Limitations of Parkinson gear tester: 1. Accuracy±0.001mm 2. Maximum gear diameter is 300mm 3. Errors are not clearly identified: 4. Measurement dependent upon the master gear. 5. Low friction in the movement of the floating carriage.


metrology , gear measurement

Documents

pitch point

gear tooth

pitch surface

pitch error

design pitch

pitch circle diameter

pitch circles

circular pitch