This video is in response to a question that we received on our question line from Amber. Amber asked us if the tolerance value for circularity can be obtained by subtracting the upper limit of diameter from the lower limit of diameter and dividing it in half. The short answer is no; that method does not provide the correct value. We will explore this issue in detail below.   

Circularity is a form constraint that measures how well the shape of a part matches a perfectly circular shape. This constraint is sometimes referred to as roundness. It is a two-dimensional tolerance control that is applied to circular cross-sections.  The circularity of each cross-section is evaluated independently.  The tolerance zone for a circularity constraint is represented by two concentric circles, while the tolerance value is the difference of the circles’ diameters.  

Going back to Amber’s question, this means that the circularity error for a given circular section is the difference in diameter between the largest circle that can be drawn inside the section (or inscribed) and the smallest circle that can be drawn outside the section (or circumscribed), while maintaining concentricity between the two circles. Since it is a diameter measurement, there is no division involved.     

Also, remember that the Geometric Dimensioning and Tolerancing Rule #1, or the envelope principle, means that size tolerances can indirectly control form. For diameter callouts, the size tolerance, and Rule #1 control circularity, unless there is a separate circularity callout. For example, consider a cylinder with a nominal diameter of 20mm and a diameter tolerance of +/- 0.5mm. The total allowed size variation is 1mm, so we would say that this example’s circularity tolerance is also 1mm. 

To further explore this example, note that the LMC, or least material condition, occurs at a diameter of 19.5mm. In contrast, the MMC, or maximum material condition, occurs at a diameter of 20.5mm.  Rule #1 requires that the part must fit within the perfect form at MMC. Therefore, our cylinder must be contained within an envelope represented by a perfect cylinder with a diameter of 20.5mm.  Note that this does not mean that the part must have perfect circularity. The part can have a maximum diameter of 20.5, perfect straightness, and a circularity error of up to 1mm.  To properly inspect this part, we would check the size and form tolerances by taking micrometer readings around the cylinder diameter at several points along the length.  Every reading should be between 19.5 and 20.5mm to ensure that size and circularity tolerances are met. We would check the part straightness for compliance with Rule #1, bypassing the cylinder through an envelope gauge with a bore of 20.5mm. 

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