Chapter No. 9 Measurement of Spur Gear

Prof. S.S.SHINDE

Learning Objectives Introduction

Basic Terminology of Spur Gear

Elements to be measure

Measurement of individual elements

Introduction Gears are mainly used for transmission of power and

motion. In order that the rotary motion of the driven shaft be perfectly uniform relative to the driving shaft, it is essential that both gears be of perfect geometrical form and be perfectly mounted on perfect shafts running in perfect bearings. It is thus obvious that a big factor which decides the accuracy of gearing is the precision with which gears are manufactured. For closer control over the accuracy of manufacture, precision measurement of gears plays a vital role

Gear Terminology

Gear TerminologyPitch 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. Diametral Pitch. It is expressed as the number of teeth per inch of the P.C.D. P = N/DCircular 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. p= πD/N = πmBase Pitch. It is the circular pitch measured around the base circle = Cp cos()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 toothspace.Dedendum = Addendum + Clearance = m + 0.157 m = 1.153 m.Blank Diameter. This is the diameter of the blank from which gear is cut out. It is equal to P.C.D. plus twice the addenda.Blank diameter = P.C.D. + 2m = m N + 2m = m(N + 2).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.

Gear Measurement Following Elements are to be checked while

carrying out gear measurement 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

Tooth Thickness Measurement :1. Chordal thickness : by gear tooth calliper

2.Constant Chord Method3. Base tangent Method4. Dimension over the wires

Thickness of the gear tooth measured at the

pitch line ( Chordal Thickness)

W = 2 AB = 360/4N = 90/N as W = 2 AB : W =NM sin (W is the chord AC)tooth thickness is specified as an arc ADC

Chordal Thickness Tooth thickness at the Pitch Line.

W = 2 AB = 360/4N = 90/N as W = 2 AB : W =NM sin (W is the chord AC) tooth thickness is specified as an arc

ADC

Height at the pitch line

Height h = OE - OB h is the distance EB which is greater than the addendum EDh = 1/2NM (1 + 2/N – cos ) orh = 1/2NM + M – 1/2NM Cos

Tooth Thickness Measured by a vernier

Chordal thickness example at the pitch line

Spur gear that has a module of 5 and 30 teeth 

W = 30 x 5 Sin (90/30) = 7.85mm

h = 1/2NM + M – 1/2NM Cos h = 0.5 x 30 x 5 + 5 – 0.5 x 30 x 5 cos

90/30 = 5.1mm

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.

Constant Chord cont.

W = 0.5M Cos2 h = M – 0.25M Cos Sin

Measurement Over Rollers 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 with the gear between centresgear between centres using a comparator.

Measurement over Rollers

Measurement Over Rollers cont.OA = ¼ M cos (OA= radius of

rollers) Gauging Radius: Rg = ½ NM + ¼ M

cosDimensions over a pair of Rollers in

opposite tooth spaces :Dg = M(N + ½ cos )

Example   A 8 module gear has 20 teeth with a pressure angle

of 20. Calculate the distance over a pair of appropriate rollers spaced 6 teeth apart. 

Reference dia = MN = 8 x 20 = 160 mm Roller dia. = ½ M cos = ½ x 8 cos 20 = 11.8

mm Rg = ½ NM + ¼ M cos = 0.5 x 160 x 0.951 =

76.08 mm Distance over rollers = 2 x 76.08 + 11.8 = 163.96 mm

Base Tangent Method = Pressure angleS =Number of tooth spaces contained

in W W = arc AB + arc BC

Base Tangent Method cont. 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)

Span measurement over a number of

teeth with a vernier calliper

David Brown Tangent Comparator

Example Calculate the value of W over 4 teeth of a spur gear,

which has the following specifications.  M = 3   = 14.5 N = 44 As there are four teeth S = 3  14.5 x 2 / 360 = 0.2531 & tan 14.5 = 0.2586  (tan - ) = 0.0055 

W = NM cos ((tan – )+ /2N + S/N) W = 44 x 3 x cos 14.5( 0.0055 + / 2 x 44 + 3 / 44) W = 32.6389 mm

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.

BASE PITCH MEASUREMENT

Circular Pitch Measuring Machine.

This instrument is used for checking the circular pitch of gear tooth. The two measuring contact tips are applied on the same sides of adjacent teeth of the gear. The left-hand tip is first set up to the required module by means of some suitable arrangement. The right hand tip is a two armed lever whose one contacts the gear tooth and the other one actuates the contact point of the dial indicator. Two guide points are also provided for the stability of the instrument.

Pitch variation measuring m/c

Schematic arrangement of a pitch checking instrument.

Runout Measurement Runout. Runout means the eccentricity in the reference or

pitch circle.

Gears that are eccentric tend to have a vibration per revolution. A badly eccentric tooth may cause an abrupt gear failure. The runout in the gears is measured by employing gear eccentricity testers. The gear is held on a mandrel in the centers and the dial indicator of the tester possesses the special tip depending upon the module of gear being checked. The tip is inserted in between the tooth spaces. The gear is rotated tooth by tooth. The maximum variation is noted from the dial indicator reading and it gives the runout of the gear. The runout is twice the eccentricity. 

Backlash Measurement

Backlash in the gears is the play between the mating tooth surfaces. For the purposes of measurement and calculations, backlash is defined as the amount by which a tooth space exceeds the thickness on an engaging tooth. Backlash in the gear teeth results on account of errors in profile, pitch thickness of teeth etc. It is measured by mounting the gears in specified position. Backlash should be measured at the tightest point of the mesh. The pinion is held solidly against rotation and a rigidly mounted dial indicator is placed against the tooth at the extreme heel perpendicular to the surface. The backlash is determined by moving the gear back and forth. The backlash variation is measured by locating the points of maximum and minimum backlash in the pair and obtaining the difference. For precision gears the variation should not exceed 0.02 to 0.03 mm.

Composite Method of Gear Checking (Metrology) Composite testing of gears consists in measuring the variation

in centre distance when a gear is rolled in tight mesh (double flank contact) with a specified or master gear.

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 thesliding 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.