The measuring of the tooth thickness

For measuring of gears there are four possibilities:

• Measuring with the tooth thickness at an adjusted tooth depth ha (see left figure).
• Measuring with the tooth depth at an adjusted tooth thickness and from this one calculates the tooth thickness (see right figure); this method we leave aside.
• Measuring the base tangent length across multiple teeth.
• The diametrically measuring about 2 pins or 2 balls.

Measuring with double toothcaliper or “Brown & Sharpe”

1.1 Straight gear

This special measuring instrument consists of a combination of two calipers, one for setting the tooth height measuring distance, one for measuring the tooth thickness (see sketch). The theoretical tooth thickness on the pitch circle is equal to the pitch (Sn) of the pitch circle arc enclosed by the two flanks of one tooth. The arc length (Sn) represents a half pitch. In practice the tooth thickness must take into account the backlash, so: practical tooth thickness= length of cord – 1/2 of backlash (see chapter backlash).

Calculating of the tooth thickness

In the next picture and with the following abbreviations:
mn = module (= ha = addendum)
= chordal height
pn = normal pitch = mn.p
d = pitch circle diameter
z = number of teeth
= ab =2.r.sinψ = d.sinψ and because d = z.m
and c’b =  of the pitch

=thus
= ab= z.m.sin

Calculating of chordal height

cc’ = m, due to ratio of reference profile, and   = cc’ + c’e
c’e = r – r.cosψ and as r =  results in:
c’e = .(1
– cosψ) = m.z.()
dus  = m + m.z.()
= m. or
= m.
In the table the values of   and  are calculated for the modules 1 and for the different tooth numbers. It suffices to multiply these numbers with the number of the used
modules. It is necessary to ensure that for the size  the theoretical value is specified and for the practical value it is necessary to reduce this number thus with ± half of the backlash.

 Z Z 10 1,564 1,062 24 1,57 1,026 11 1,565 1,056 25 1,57 1,025 12 1,566 1,051 26 1,57 1,024 13 1,567 1,047 27 1,57 1,023 14 1,567 1,044 28-29 1,57 1,022 15 1,568 1,041 30-31 1,57 1,021 16 1,568 1,038 32-33 1,57 1,02 17 1,569 1,036 34-35 1,57 1,019 18 1,569 1,034 36-37 1,57 1,018 19 1,569 1,032 38-39 1,57 1,017 20 1,569 1,031 40-42 1,57 1,016 21 1,569 1,029 43-44 1,57 1,015 22 1,569 1,028 -45 1,571 1,014 23 1,57 1,027 – – à 1,000

For the calculation of gears with internal teeth, it is necessary to subtract the arrow pitch   instead of adding. For gears with correction the half tooth angle should be increased with +

Special case

Calculation of the tooth thickness at a given radius:

If we take as a basis the tooth thickness S at the pitch circle then it is possible to calculate the tooth thickness on any radius (rp).

from rb = r.cosa = rp cosap we can calculate ap.

The tooth thickness is then

Sp = rp.

1.2 Helical gears:

The same procedure can be applied here by calculating with the virtual number of teeth:

zv =
= zv.mn.sin = mn.
for the apparently module mn = mt.cosβ. For gears
with correction the half tooth angle  should be increased with +

1.3 Straight helical teeth:

In this case one needs to measure along the side of the large module on the extreme side of the tooth.
The dimensions are the same as those of cylindrical gears with the same module but with a virtual number of teeth:

zv =
= zv.m.sin = m.

1.4 spiral bevel gears:

Given the helix angle and the arch of the gear, the measuring of the toothcaliper is not properly performed at the ends of the teeth, because at this spot one has to deal with an apparent module. Specialists measure the tooth thickness according to the real module in a specific place of the tooth ends.

1.5 Worm and wormwheels:

The same procedure can be applied here by calculating with the virtual number of teeth:

zv2

Transverse module:

Worm  = .p.mx.cosg &  =
Wormwheel  = zv2.mx.cosg.sin = mx.
For wormwheels with correction the half tooth angle  should be increased with +

Normal module:

Worm  = .p.mn

Wormwheel  = zv.mn.sin = mn.
For wormwheels with correction the half tooth angle should be increased with +