0206// Resultant Tolerance Zone Shape for Straightness on Unit Basis without Specified Total Length
In this topic, I will discuss about an interesting topic about Straightness. We all knowing Straightness can specify at unit basic. For example, 5 micron per 100mm to ensure smooth or no abrupt change in feature's profile. However, not everyone knowing that, if not specifying total length Straightness. That is a potential entire line elements will "bow" to one side. The effect is a result of accumulating each unit of Straightness deviation thru out the length of the line elements.
Calculating of restaurant deviation is important if you decided to don't specify total length Straightness. No worries. This is simple. You only require to know pythagoras theorem to calculate this.
First, assuming entire line elements with length L bow to one side and bend uniformly form a circle arc with radius R. Straightness specified in l unit length.
In this diagram, you can identify two triangles, one is gold triangle and another blue triangle.
Apply pythagorean theorem to these two triangles.
Rearrange the terms algebraically and isolate R from the expressions. Then, equate these 2R.
Rearrange the terms in term of Delta (aka resultant Straightness) and form a quadratic general equation. Find the Delta's roots.
There only one reasonable roots for this equation. That is the minus of square root. Positive square root will give you an unrealistic number. Yeah! We found the general equation for resultant Straightness on unit basic without specified total length Straightness.
Hope you enjoyed the beautiful of Mathematics and GD&T in this topic.
Author: WONG GUAN BOON
Published Date: 10 May 2019
