Roundness

Measure of how closely the shape of an object approaches that of a circle

Roundness is the measure of how closely the shape of an object approaches that of a mathematically perfect circle. Roundness applies in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft or a cylindrical roller for a bearing. In geometric dimensioning and tolerancing, control of a cylinder can also include its fidelity to the longitudinal axis, yielding cylindricity. The analogue of roundness in three dimensions (that is, for spheres) is sphericity. Roundness is dominated by the shape's gross features rather than the definition of its edges and corners, or the surface roughness of a manufactured object. A smooth ellipse can have low roundness, if its eccentricity is large. Regular polygons increase their roundness with increasing numbers of sides, even though they are still sharp edged. In geology and the study of sediments (where three dimensional particles are most important), roundness is considered to be the measurement of surface roughness and the overall shape is described by sphericity.

The ISO definition of roundness is the ratio of the radii of inscribed and circumscribed circles, i. e. the maximum and minimum sizes for circles that are just sufficient to fit inside and to enclose the shape.

Having a constant diameter, measured at varying angles around the shape, is often considered to be a simple measurement of roundness. This is misleading. Although constant diameter is a necessary condition for roundness, it is not a sufficient condition for roundness: shapes exist that have constant diameter but are far from round. Mathematical shapes such as the Reuleaux triangle and, an everyday example, the British 50p coin demonstrate this.

Roundness measurement is very important in metrology. It includes measurement of a collection of points. For this two fundamental methods exist: intrinsic or extrinsic.

The round object is placed over a flat plate and the point of contact is taken as the datum point. Again a dial gauge is placed over the round object and the object is rotated keeping the datum at constant position. Thus the error in roundness can be directly known by comparing the peak height as measured by the dial gauge. Alternatively a V shaped base can be used instead of a flat plate. Two datum points will exist instead of one since the base is V shaped. The error in roundness can be measured similar to the previous method. Also a cylindrical body can be clamped between two axle centres. Here also the dial gauge is mounted over the cylindrical body and thus the roundness is measured by similar procedure as above.

The intrinsic method is limited to small deformations only. For large deformations extrinsic method has to be followed. In this case the datum is not a point or set of points on the object, but is a separate precision bearing usually on the measuring instrument. The axis of the object or part of the object to be measured is aligned with the axis of the bearing. Then a stylus from the instrument is just made to touch the part to be measured. A touch sensor connected to the tip of the stylus makes sure that the stylus just touches the object. A minimum of three readings are taken and an amplified polar plot is drawn to get the required error.