The normalised Kumaraswamy breakage function: A simple model for wheat roller milling

A simplified model describing wheat breakage during roller milling is presented. Previous work introduced the breakage equation describing First Break roller milling of wheat in terms of a breakage function that incorporated relevant input and processing parameters such as roll gap, kernel diameter and kernel hardness. The resulting empirical function, based on polynomial fits, was sufficiently flexible to describe the range of particle size distributions encountered in typical milling operations, but contained a high number of coefficients, making the interpretation of the physical significance of the coefficients difficult and requiring an excessive amount of experimental data. The current work simplifies the breakage function by normalising the output particle size distribution against the milling ratio raised to a power. The Kumaraswamy probability distribution function is then used to describe the normalised data obtained following First Break milling of a wide range of wheat at different roll gaps under both Sharp-to-Sharp and Dull-to-Dull roll dispositions. Using this approach, the effects of roll gap and kernel diameter on wheat breakage can be described using just four parameters. This simplified equation is more practical and versatile for implementation in process integration strategies for the purpose of design and optimisation of cereal processes for food and non-food uses.