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## Defining Linearity

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Assuming a properly calibrated feeder (a calibration scaling process resulting in measured and requested feed rate being equal at a specified operating rate), a feeder’s linearity measurement quantifies how well it delivers, on the average, the targeted discharge rate throughout the feeder’s complete operating range.

Perfect linearity is represented by a straight-line correspondence between the setpoint and measured average feed rate throughout the feeder’s specified turndown range from its design full-scale operating rate.

To perform a linearity measurement, several groups of timed catch samples must be taken from the feeder’s discharge stream. Typically, ten consecutive catch samples are obtained and weighed at each of the following flow rates: 5%, 25%, 50%, 75% and 100% of full scale. Ten samples at each rate are statistically sufficient to compute a reliable average. The smallest tested flow rate should be at the feeder’s maximum turndown—in this case the feeder’s assumed 20:1 turndown converts to 5%.

For each of the five data sets the average sample weight is calculated, and the difference between the computed average and the desired sample weight is taken. (Note that when a group’s average sample weight is less than the desired sample weight, the difference will be negative.) These weight-based errors may then be expressed in terms of percent of desired rate by dividing each difference by its respective targeted sample weight and multiplying by 100. The result is a set of five error values, reflecting average feed rate performance over the unit’s operating range.

To reduce this set of five error values to a single number that characterizes the feeder’s linearity performance, the range of the error set is computed. The result expresses the feeder’s linearity performance in percent of operating rate.

A complete expression of a linearity statistic must contain a +/- percentage error value and sampling criteria. For example, a linearity performance statement might take the following form: +/-0.04% of set rate based upon ten consecutive samples of one minute, one pound, one belt revolution, or thirty screw revolutions, whichever is greater, over a range of 20:1 from full scale.

Note that the issue of timescales previously introduced is not applicable to linearity measurement since the statistic seeks to quantify average rate accuracy over the feeder’s full range of operation.