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 difference 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.[1] [2]
Having a constant diameter, measured at varying angles around the shape, is often considered to be a simple measurement of roundness. This is misleading.[3]
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 does not describe radial displacements of a shape from some notional centre point, merely the overall shape.
This is important in manufacturing, such as for crankshafts and similar objects, where not only the roundness of a number of bearing journals must be measured, but also their alignment on an axis. A bent crankshaft may have perfectly round bearings, yet if one is displaced sideways, the shaft is useless. Such measurements are often performed by the same techniques as for roundness, but also considering the centre position and its relative position along an additional axial direction.
A single trace covering the full rotation is made and at each equally spaced angle,
\thetai
Ri
\hat{R}=
| 1 | |
| N |
| N | |
| \sum\limits | |
| i=1 |
Ri
\hat{a}=
| 2 | |
| N |
| N | |
| \sum\limits | |
| i=1 |
Ri\cos{\thetai}
\hat{b}=
| 2 | |
| N |
| N | |
| \sum\limits | |
| i=1 |
Ri\sin{\thetai}
The deviation, sometimes referred to as noncircularity, is then measured as:
\hat{\Delta}=Ri-\hat{R}-\hat{a}\cos{\thetai}-\hat{b}\sin{\thetai}
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 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.
A common definition used in digital image processing (image analysis) for characterizing 2-D shapes is:
Roundness = . This ratio will be 1 for a circle and greater than 1 for non-circular shapes. Another definition is the inverse of that:
Roundness =, which is 1 for a perfect circle and goes down as far as 0 for highly non-circular shapes.