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# Quality Scan: Filtering Makes Dimensional Data More Valuable

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Published Date : 2/1/2005

# Editor's Picks

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**By Jonathan J. O'HareBrown & Sharpe Inc. North Kingstown, RI**

Even the most precise machining operation imparts slight aberrations to the part, creating a surface profile that contains imperfections of varying wavelengths. Short-wavelength (high-frequency) imperfections correspond to surface roughness, and long-wavelength (low-frequency) imperfections correspond to surface waviness or form.

Because gathering dimensional data using high-speed scanning techniques collects such a large quantity of information, it also captures all frequencies. Separating the wavelengths through software filtering improves the accuracy of data analysis. Software filters work by suppressing or minimizing waves or oscillations of certain frequencies to smooth dimensional data. For example, roughness profile analysis requires removing the low frequency and leaving the high frequency. Waviness profile analysis (form) requires removing the high frequency and leaving the low frequency.

The most common approach to data filtering is using weighting functions. Such functions determine how much weight is given to a particular data point relative to its neighboring points. The simplest example of a weighting function is a uniform weighting function, known as a moving-point average. The most practical is the Gauss weighting function, which weighs neighboring points in close proximity to the adjusted point according to a statistical normal distribution. Think of a statistical bell curve of predefined width moving point-by-point through a data set. At each point, the weight of the neighbors is determined by where they fall on the bell curve relative to the center. Total weight is then used to adjust that point.

The Gauss filter is named for Carl Friedrich Gauss (1777-1855), a German mathematician and astronomer, who contributed to the understanding of normal distribution. Gauss filters are most effective for distinguishing between different error frequencies/wavelengths in a data set, and separating errors above or below a certain wavelength.

There are two types of Gauss filters: linear and polar. The linear Gauss filter is intended for applications with geometries having unidirectional errors, such as lines and planes. Polar Gauss filters are used in applications involving circular geometry. The linear filter has input units in wavelengths (distance). Cutoff wavelength is the wavelength below which the data will be eliminated when applying a linear Gauss filter. The polar filter has units in undulations per revolution (UPR), that is, waves per 360º of measurement. Cutoff frequency is the number of undulations per revolution (UPR) in the data above which the data will be reduced when applying a polar Gauss filter.

When using UPR for circular features as compared with wavelength, the benefit is that, for all circles, the number of periods for an occurring error waveform can be expressed as a function of a full 360º revolution around the circle. Most other geometries are not periodic in their nature, and therefore can only be mathematically expressed as a function of length. By expressing circular features in terms of UPR, the same cutoff input value will have the same effect in filtering, regardless of feature size.

There are other types of filters used to smooth dimensional data gathered through scanning. Spline filters work by sequentially fitting (interpolating) a finer and finer mathematical spline shape through the set of data points. A uniform filter filters data by averaging all the points in a moving window. Filter width determines the width of the window. Triangle filters filter data by a weighted moving average of all the points in a moving window. Weights are determined by a triangle function with the peak in the middle of the window. Window width is determined by filter width. The cylindrical filter option is used to filter data in a spiral or circular scan with the deviations being radial.

For features that have interrupted surfaces, such as keyways or ported holes in a bore that could limit the cutoff and cause filtering to fail, special filters can be used to connect the surfaces.

It's important to note that the function of filters is simply to smooth the peaks and valleys of the scanned data, eliminate non-essential surface noise, and allow more accurate analysis of the actual shape of the part feature. Filters are not intended to change the underlying value of data; they simply allow it be viewed more clearly. For most applications, a linear or polar Gauss filter is the best choice.

This article was first published in the February 2005 edition of *Manufacturing Engineering *magazine.

Published Date : 2/1/2005

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