Neural network based prediction of the efficacy of ball milling to separate cable waste materials

Material recycling technologies are essential for achieving a circular economy while reducing greenhouse gas emissions. However, most of them remain in laboratory development. Machine learning (ML) can promote industrial application while maximising yield and environmental performance. Herein, an asynchronous-parallel recurrent neural network was developed to predict the dynamic behaviour when separating copper and poly(vinyl chloride) components from the cable waste. The model was trained with six datasets (treatment conditions) at 3600 epochs. High accuracy was confirmed based on a mean-square error of 0.0015–0.0145 between the prediction and experimental results. The quantitative relationship between the input features and the separation yield was identified using sensitivity analysis. The charged weight of cables and impact energy were determined as the critical factors affecting the separation efficiency. The ML framework can be widely applied to recycling technologies to reveal the process mechanism and establish a quantitative relationship between process variables and treatment outputs.


Supplementary Notes 1 Introduction of Cu and PVC recovery from cable waste by ball milling
As shown in Figure S1, the developed separation process for cable waste first involved de-plasticizing the PVC cover using organic solvents (such as diethyl ether), which can dissolve plasticizers but not PVC 1,2 .Cables was put into a Soxhlet-extractor filled by 150 mL of diethyl ether, which were heated at 75 ºC.Soxhlet-extraction was carried out for the maximum 300 min.The same number of cables were immersed in diethyl ether at room temperature for a maximum of 60 minutes in order to create a sample with a low extraction yield.Flexible electric cables become brittle by extracting plasticizers from covering PVC, and the de-plasticized PVC coverings can be crushed into scraps by ball milling and separated from the Cu core.The ball milling treatment of de-plasticized cables with different Yext was carried out using a stainless-steel ball mill reactor made by (15cm in diameter, PM-001, AS ONE Co., Japan)) with tungsten carbide balls (AS ONE Co., Japan).The grinding balls have diameters of 10, 15, and 20 mm and weigh 7.8, 26.0, and 62.0 g/ball, respectively.In order to assess the size distribution of the crushed samples, the crushed cables were divided into 12 parts between 100 m and 4.75 mm using an electromagnetic sieve shaker (3000/min vibration, 1.8mm amplitude, AS200Basic, AS ONE Co., Japan).Separation yield (Ysep) of cable was defined by Equation (S1): where ms [g] is the amount of separated cable; m0 [g] is the amount of all the cables after ball milling.

Supplementary Notes 2 Mechanism of cable separation by ball milling
Based on our previous experimental investigation and analysis by discrete element method 2 , the mechanism of cable separation by ball milling is depicted in Figure S2.It was found that the cable hardness increased and its elasticity reduced when the plasticizer was removed from the flexible PVC covering.Cracks from the edge to the center of the PVC covering can be formed due to inelastic collisions between the balls and cables.Thicker cables need more impact energy to create a crack.As the number of cracks accumulates, the Cu wrapped in the cables can slide out from the crushed PVC covering.Longer cables and larger numbers of cables will increase the required more time to accumulate cracks before complete separation.Because kinetic energy is conserved during elastic collisions, the impact energy from small balls cannot be utilized for crushing cables as it only imparts kinetic energy to the other balls and cables.Despite the greater impact energy from larger ball sizes and higher rotational speeds than moderate conditions, the increased impact energy will be partially wasted; thus, the time efficiency cannot be improved in this way.In addition, unnecessary collisions on separated PVC and Cu may produce finer particles, which will degrade the separation accuracy.In summary, moderate conditions of ball size, moderate rotational speed, and shorter cable lengths provide benefits for crushing a specific type and diameter of cables.

Supplementary Notes 3 The quantitative relation between IM and ball diameter
In our previous study, the IM was calculated based on the simulation of ball milling process including the motions of grinding balls and charged cables.The simulation was carried out by a discrete element method in Multiphase Flow with Interphase eXchanges 16,17 .During the simulation, the impact energy was calculated according to the collision intensity between the grinding balls and cables as follows:   for quantifying c.The number of layer parameters can be found in Table S2.Table S2.The properties of each hidden layers in NNk and NNc.

Name of hidden layer Input number of feature dimension
Output number of feature dimension

Figure S1 .
Figure S1.Schematic diagram of Cu and PVC recovery from the separation of de-plasticized

Figure S2 2 .
Figure S2 2 .Schematic diagram showing the mechanism of crushing cables by ball milling.
IM [J/s] is the sum of impact energy of the ball-to-cable collisions per second; m [g] is the mass of the grinding balls; and vbc [m/s] represents the relative velocity between the ball and cable at the time of the collision.When the size of mill and other mechanical conditions are fixed, a linear relation can be assumed between IM and m.In consequence, a cubic function can be used to model IM by the ball diameter (d) as shown in Equation (S3).
fitting based on the d vs. IM for different types of cables, the quantitative relation can be derived in FigureS3.

Figure S3 .Supplementary Notes 4
Figure S3.Fitted cubic relation between ball diameter (d) and impact energy (IM) for different

Figure S4 .
Figure S4.Network structures including input, output, hidden layers, and activations functions

Figure S5 .
Figure S5.Ysep-exp and the predicted Ysep for all experimental conditions (a-f) based on the

Table S1 .
Literature review on the recent advance in the material recycling by cable separation.