SPUR GEAR MEASUREMENT

A. Basic parameters of a Spur gear : 1. Module = m : It indicates the size of the gear; its units are mm.2. No. of teeth = z 3. Pressure angle = α; standard pressure angle of most of the gears is 20 degrees

B. Derived parameters of a standard spur gear: 1. Pitch circle diameter (PCD) = m.z

Pitch circle is an imaginary circle between the tip circle and root circle of the gear. On the pitch circle width of the gear tooth = width of the gap between consecutive teeth.

2. Addendum = 1mAddendum is the radial distance between tip circle and pitch circle.

3. Outside diameter = tip circle diameter = pcd + 2.addendum = m.z + 2.m = m(z+2) 4. Dedendum = radial distance between pitch circle and root circle = 1.25m5. Root diameter = PCD – 2.dedendum = m.z – 2.5z = m(z-2.5)6. Base circle diameter (BCD ) = m.z.cosα7. Base pitch = π.BCD/z = π.m.cosα8. Circular pitch = π.PCD/z = π.m9. Diametral pitch (DP) = one inch/m = 25.4/m

Standard DP’s are rational numbers like 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16The larger the DP, the smaller is the gear tooth.

10. Chordal width = m.z.sin(90/z)11. Common tangent measurement across ‘n’ number of teeth =

m.cosα {(n-0.5)π + z. invα}the value of n depends on z and this should be read from tables ( for z=40, n=5)The value of invα can be read from tables or calculated (invα = tanα – α, α in radians)For α = 20 degrees, invα = 0.0149

Procedure:

a) Count the number of teeth z and measure OD of the gear.b) From the above two values, using the formula at B.3 above, calculate module m.c) Using the formula at B.9, calculate DPd) Theoretical value of DP should be a round figure as given at B.9, correct ite) Find out the theoretical value of m from the corrected value of DP in the previous step.f) Compute the percentage of error in the measured value of m.g) Compute theoretical value of chordal width from B.10h) Measure chordal width using gear tooth callipers setting it to the correct (theoretical)

value of m.i) Compute the percentage of error in the measurement of chordal width.j) Calculate the theoretical value of base pitch and circular pitch from B.7 and B.8k) Calculate length of common tangent from B.11 l) Measure length of common tangent over n teeth from B.11m) Compute the error in measurement of common tangentn) Tabulate all the above theoretical values and the measured values.

Terminology of spur gears

Diametral pitch (DP )...... The number of teeth per one inch of pitch circle diameter.

Module. (m) ...... The length, in mm, of the pitch circle diameter per tooth.

Circular pitch (p)...... The distance between adjacent teeth measured along the are at the pitch circle diameter

Addendum ( h a )...... The height of the tooth above the pitch circle diameter.

Circular tooth thickness (ctt)...... The width of a tooth measured along the arc at the pitch circle diameter.

Chordal width (ctt)...... The width of a tooth measured along the chord at the pitch circle diameter.

Dedendum ( h f )...... The depth of the tooth below the pitch circle diameter.

Outside diameter ( OD )...... The outside diameter of the gear.

Base Circle diameter ( BCD ) ...... The diameter on which the involute teeth profile is based.

Pitch circle dia ( pcd ) ...... The diameter of the pitch circle.

Pressure angle ...... The angle between the tooth profile at the pitch circle diameter and a radial line passing through the same point.

Whole depth...... The total depth of the space between adjacent teeth.