In actual production, materials cannot freely leave the discharge end of the grinding mill. The discharge end of the mill has a function of inhibiting the discharge of large particles, allowing small particles to be discharged smoothly, while large particles remain in the mill for further grinding. This function is known as discharge grading. The inherent function of the mill itself affects the time materials stay within the mill, and the degree of inhibition varies with different discharge methods. For grid ball mills, the grid has a significant inhibitory effect on the discharge of large particles, even if the grid openings are large, it still prevents the discharge of some large particles. In overflow ball mills, this effect also exists but is relatively smaller compared to the grid ball mill. Neglecting this function in modeling can lead to overestimation of the large particle content in the model predictions.

To reflect this functionality, four methods can be employed for processing:

1. The model of the mill incorporates a classification function, allowing the classified sand to return directly to the mill's inlet.

2. Different axial speeds are employed for various particle sizes to represent the progression of particles within the mill, thereby equivalently returning the classified sand back to the inlet of each mixer.

3. The expression of particle breakage rate is modified. The idea is that if the expulsion of large particles is suppressed, it means that the average residence time of large particles is longer. Therefore, if the residence time of large particles is made equal to that of other particles, while the breakage rate of large particles is increased and the breakage rate of small particles is decreased, the same effect as a longer residence time for large particles can be achieved. This method is similar in thought to the pseudo-time method.

4. The system employs a non-first-order crushing rate, which increases over time. It accelerates the crushing rate for larger particles more rapidly than for smaller ones, achieving an effect similar to longer retention time for larger particles.