Quote of the Day
Cost is more important than quality, but quality is the best way to reduce cost.
— Genichi Taguchi. I have much empirical evidence for the truth of his statement.
I am continuing to work through the metrology examples on this web page as part of junior machinist self-training. Today's technique shows how to use gage balls to measure the bore diameter of a cylinder (Figure 1). You can measure a bore diameter using a micrometer, but I have concerns that I might be measuring along a chord instead of a diameter – this error would result in too small of a result. The gage ball approach should eliminate that type of error.
In this post, I will work through the basic geometry associated with this measurement and will work an example.
Figure 2 shows how I defined my variables. The analysis involves solving the right triangle formed by X, Y, and the line formed by r1 and r2.
Figure 3 shows the algebra involved with the solving for the bore diameter (dB). Because I work in Mathcad, most the algebraic manipulations are hidden. If you desire, you can see the algebra worked out in my response to a question below the post.
Figure 4 shows my results after applying the values in Figure 1 to the bore diameter formula. The result is very close to the bore diameter of 4.0000 on the scale drawing.
I am almost done reviewing the use of roller gages and gage balls. A couple more examples will complete my set of canonical applications.