RED DUNE
Red Dune · Process Engineer Toolkit

Size Analysis · Crushing & Rosin-Rammler

Enter a screen analysis to get cumulative passing and retained, mean size, d50 and P80, and a Rosin-Rammler fit. Then see the size consist after crushing to a chosen top size.

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Screen analysis

Example data loaded
FractionmmRetained onscreen, mmMass%
Total

Enter sizes from largest to smallest. Each row is the mass retained on that screen and passing the one above. Use 0 for the pan (fines). Tip: copy two columns (screen size, mass %) from Excel and paste into any size cell.

Size distribution

As received After crushing Rosin-Rammler fit

Cumulative size distribution

Method

Cumulative % retained is the running total of mass from the coarsest fraction down; % passing = 100 − % retained. Weighted mean size uses the mid-point of each fraction (the top fraction uses its screen size). d50 and P80 are read from cumulative passing by log-linear interpolation between screens.

The Rosin-Rammler fit uses R(x) = 100·exp(−(x/x′)ⁿ), fitted by linear regression of ln(ln(100/R)) on ln x, where x′ is the size at 36.8% retained and n the uniformity index.

Crushing model

All material retained at or above the chosen top size is crushed and shared out over the finer fractions in proportion to their existing mass. Finer fractions keep their shape; only their share of the total rises.

This is a quick screening model. Real crushers make more fines than it predicts, and the result depends on crusher type, gap and feed. Use it to compare options, not to guarantee a product grading.

References

  • Rosin, P. & Rammler, E. (1933). The laws governing the fineness of powdered coal. J. Inst. Fuel, 7.
  • ISO 1953:2015, Hard coal: size analysis by sieving.
  • Wills & Finch (2016). Wills' Mineral Processing Technology, 8th ed.