ISO 9276-4:2001

Overview

ISO 9276-4:2001 - "Representation of results of particle size analysis - Part 4: Characterization of a classification process" provides the mathematical basis for describing and reporting the behaviour of particle classification and separation processes. The standard formalizes how to represent density and cumulative particle size distributions, define cut sizes, derive grade efficiency (T(x) / Tromp’s curve), and use mass/number balances to characterise classifiers such as impactors, sieves, air classifiers, centrifugal separators and hydrocyclones. Clause 3 treats the ideal (error‑free) case; Clause 4 addresses systematic errors; Annex A discusses stochastic errors.

Key Topics

• Density and cumulative distributions: representation of q(x) and Q(x) for feed, fine and coarse fractions and how weighted distributions relate to relative mass/number.
• Mass and number balances: splitting feed into fine and coarse fractions; calculation of relative amounts (v) from distribution curves when direct mass flows are not available.
• Cut size definitions:
  • Equiprobable cut size (x_e) - median of the grade efficiency curve where particles have equal chance of reporting to fine or coarse.
  • Analytical cut size (x_a) - the cut size corresponding to an experimentally observed relative amount of fine material (v) in the product.
• Grade efficiency / Tromp’s curve (T(x)): size‑selectivity function defined from fractions and feed distributions to quantify classifier performance.
• Sharpness of cut & imperfection: metrics for how well a classifier separates sizes (overlap of distributions).
• Error analysis: influence of systematic errors (e.g., splitting, incomplete dispersion, comminution within the classifier) and the effect of stochastic errors on T(x).

Applications

ISO 9276-4 is practical for:

• Particle size analysis laboratories reporting classifier performance and particle size distributions.
• Process and design engineers characterizing air classifiers, impactors, hydrocyclones and centrifugal separators.
• Equipment manufacturers validating and specifying classifier selectivity, cut size and sharpness.
• Quality control and R&D when comparing experimental results to idealized separation behaviour or when reconstructing mass balances from sampled distributions.

Who should use it

• Metrology labs, industrial testing facilities, researchers in particulate technology, and manufacturers of particle classification equipment will use ISO 9276-4 to standardize reporting, ensure consistent interpretation of Tromp’s curves and support design or optimisation based on reproducible mass/number balances.

Related standards

• ISO 9276 series (Parts 1–5) - covers graphical representation, average size calculations, curve fitting, characterization (this part) and log‑normal validation. Use ISO 9276-4 in conjunction with other parts for complete particle size analysis reporting.