Flatness
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Flatness Han Haitjema Mitutoyo RCE, Best, The Netherlands
Synonyms Deviation from flatness; Flatness deviation; Planeness
Definition The minimum distance separating two parallel planes between which the surface can be contained.
define the geometrical deviation are not filtered. This implies that the bandwidth can be rather small when flatness is assessed over a course grid. For example, for a square grid, this implies that surface wavelengths smaller than twice the pitch are neglected and are assumed to have a negligible influence on the flatness parameter values. Flatness Reference Planes and Parameters Flatness deviations are defined in relation to a reference plane that is defined by the assessed surface itself. It is one of the basic geometric tolerances specified in ISO 1011 (2012). The flatness tolerance is indicated by the symbol . The definitions are given in ISO 12781-1 (2011). Two reference planes are in common use, and two more are mentioned for completeness:
Theory and Application Scale of Flatness Although in theory there is no minimum or maximum, in engineering practice we take as minimum size the field of view of a microscope, even an STM type, and as a maximum the size of large telescope mirrors or very large surface plates. This means that sizes where flatness is relevant can range between a few nm2 and a few m2. A flatness deviation is a geometrical error, where this error is determined, implicitly or explicitly, for surface wavelengths from a minimum value, while all longer wavelengths that
1. Least-squares reference plane (LSPL) This plane is defined such that the sum of squares of all deviations of the surface from this plane is minimal. The advantage of this reference plane is that its calculation is straightforward and rather independent of the number of measurements, peaks, or outliers. A disadvantage is that it does not follow the definition, which leads to a higher flatness deviation than the minimum-zone plane. 2. Minimum-zone plane(s) (MZPL) The minimum-zone planes are defined as the planes with a minimum separation between
# CIRP 2016 The International Academy for Production Engineering et al. (eds.), CIRP Encyclopedia of Production Engineering, DOI 10.1007/978-3-642-35950-7_16794-2
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Flatness
which all measured surface coordinates are contained. As a single plane, either of these planes can be used or the plane in between these planes. The advantage of this plane is that it gives the minimum deviation value. Also it gives a more stable reference if there are only sharp peaks or only sharp valleys in the surface. A disadvantage is that its calculation is more complicated, its location is sensitive to measurement errors of the maximum and minimum points only, and it tends to be sensitive to the number of points taken. 3. Equal diagonal endpoints A rectangular plane can be leveled in such a way that the end-points of both diagonals have the same value. Subsequently, the minimum height of the surface can be defined as having zero height. This reference plane is used in the classical Moody (1955) m
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