Figure 1: Gear Tooth Vernier Caliper.
The gear tooth thickness measuring vernier is as shown in Fig. 1. It measures the thickness of the tooth on pitch circle i.e. chordal thickness.
Construction and Working of Gear Tooth Vernier Caliper
Gear Tooth Vernier Caliper consists of two beams which are in square with each other. There are two sliding vernier scales which moves along the beams of main scale. The tooth thickness on the pitch circle is measured as the distance between a fixed jaw and a movable jaw by fixed adjustable jaw of vertical vernier beam. In other words it is a combination of two vernier with a common jaw.
Working Principle of Gear Tooth Vernier Caliper
Figure 2: Working Principle of Gear Tooth Vernier Caliper
Gear tooth thickness is measured at pitch circle, and it is also called as pitch line thickness (See Figure 2). In the above sketch ‘d’ is chordal addendum, which can be calculated as,
\[\text{d = }\frac{\text{Nm}}{\text{2}}\left[ \text{1 + }\frac{\text{2}}{\text{N}}-\text{cos}\left( \frac{\text{90}}{\text{N}} \right) \right]\]
Where,
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. ‘W’ can be verified by,
\[\text{W = N}\text{.m sin}\left( \frac{\text{90}}{\text{N}} \right)\]
Procedure for Measurement using Gear Tooth Vernier Caliper
- Find chordal addendum by using by using Equation (Fig. 3).
\[\text{h = }\left( \frac{\text{mN}}{\text{2}} \right)\left[ \frac{\text{2}}{\text{N}}+1-\text{cos}\frac{\text{90}}{\text{N}} \right]\]
- Set height ‘h’ on vertical vernier by using fine adjustment screw.
- Apply vernier to gear tooth as shown in Fig. 4.16.3, so that the fix jaw can touch the flank of tooth.
- Push movable jaw of horizontal vernier and lock it.
- This gives the gear tooth thickness ‘W’.