Abstract:

A special hierarchical model was proposed to overcome the bottleneck on the fiber length distribution analysis by a random-beard image method, which is a new method for fiber length determination. Based on the two-end characteristic of random-beard, this model can figure out the proportion of fibers shorter than certain thresholds, and derive out a series of formulas for converting fibrogram to cumulative diagram and length frequency histogram via discontinuous point operations, avoiding the previous differential operations which magnified the measurement noise and lead to serious measurement errors. Both cotton and wool ware tested, respectively with the gauge of 2 mm and 6 mm, using these formulas and a single fiber measurement method. The histograms show that the mean differences of the weight frequencies of each length group from the two methods, are 0.31% and 0.26%, respectively, and the differences are all less than 1%, which means the measurements from the two methods have a good agreement. The new calculation method in this paper is highly precise and valuable for the data processing of fiber length measuring instruments.

Key words: length distribution, fiber measurement, random-beard, hierarchical model, histogram