Measuring a Chamfer Angle Using Gage Balls

Quote of the Day

The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.

— Alfred North Whitehead, Process and Reality, p. 39 [Free Press, 1979]

Introduction

Figure 1: Chamfer Angle Measurement Example Using Two Gage Balls.

One metrology operation I have had to perform a number of times is measuring a chamfer angle precisely – Figure 1 shows today's example. Many items are chamfered – even in electronics. For example, edge connectors on printed circuit boards often need to be chamfered to ensure that they do not damage the connectors they are being inserted into.

Referring to Figure 1, you might think that chamfer measurements would be easy because you have a vertical edge and horizontal edge that you should be able to measure. Unfortunately, these edges are rarely straight. They often are rounded or irregular. This makes the chamfer angle measurement non-repeatable. Using gage balls eliminates any dependence on the determining precisely the location of an edge.

Background

Equation 1 is the formula I use for determining a chamfer angle using two gage balls of different diameter.

Eq. 1

where

• M₁ is height measurement of ball 1 above the top surface.
• M₂ is height measurement of ball 2 above the top surface.
• R₁ is the radius of gage ball 1.
• R₂ is the radius of gage ball 2.

I derive Equation 1 in the analysis section.

Analysis

Symbol Definitions

Figure 2 shows the variables that I defined for the angle measurement scenario of Figure 1.

Derivation and Example Calculation

I am lazy this morning. I am sure there is a clever geometric derivation, but the quickest way to get a formula is to use Mathcad's symbolic processor to solve a simple system of equations. Figure 3 shows my derivation with Q = arctan(θ/2). I often initially do my trigonometric derivations sans trig functions because Mathcad will often generate overly complex answers, e.g. applying half-angle formulas to solve for θ.

As an example, I use Equation 1 to determine the angle in Example 1. In my function evaluation, I use the fact that the gage ball diameter, D, is 1/2 the radius, R.

Figure 3: Derivation of Equation 1 and Application to Figure 1 Example.

Conclusion

This is a relatively simple formula that is useful for precision angle measurement of a chamfer angle using two gage balls or roller gages of different diameter.

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