324
A. Strobel et al.
3.3 Characterization of Stressing Conditions
3.3.1 Method Development
In general, grinding must be understood by the mill function and the material function.
The mill function describes the type of stressing, the transferred stress energy, and the
stress number. The material function accounts for the particles’ reaction to the applied
stress in form of breakage probability and breakage function, i.e. the size distribution
of the fragments. For modelling of comminution processes and its grinding kinetics,
knowledge about the stressing conditions applied to the particles is essential. To target
the impact velocity, i.e. the applied stress energy, and the stressing frequency in the
jet mill, a method developed to characterize the stressing conditions in wet operated
stirred media mills [45, 46] was adapted: The morphological changes of spherical,
well-characterized ductile metal probe particles are related to the relative particle
impact velocities prior to impact [33]. Briefly, single particles can be compressed
by a flat punch micromanipulator installed in a SEM. Stress-strain curves of several
100 particles can be measured and material properties such as Young’s modulus,
hardness, yields stress, and absorbed energy can be extracted [51]. The manipulation
device in the SEM, also allows to access pictures of the stressed and partly broken
particles. Surprisingly, images of compressed silica particles below their brittleductile transition (<1 μm) in the SEM and those stressed in a stirred media mill
looked very similar, indicating that compression in the SEM mimics compression
between two grinding beads. On this basis, the method was initially developed for the
case of two-sided stressing in stirred media mills. As probe particles, ductile metal
particles are used which do not break but plastically deform. The deformation is a
measure of the absorbed energy and thus can be used to extract the kinetic energy of
the milling beads. This approach provides the stress energy distribution acting in the
mill. Fundamental background information and details of the methodical procedure
are reported in two publications of Peukert et al. [45, 46].
In comparison to the method for stirred media mills, a mixture of soda-lime glass
beads and aluminium beads was used with a radio of 19:1 m/m. As can be seen in
Fig. 3a the two PSDs match perfectly. Since the two materials have a similar density,
separation during the comminution process is prevented. As shown earlier, almost no
fracture of the glass beads occurs during the first 20 s of the comminution process.
The absence of small fragments is essential for the method since they might penetrate
into the surface of the softer aluminium particles. Thus, the evaluation of the formed
dents would not be possible.
To determine the material parameters for the FEM material’s model for the aluminium spheres, single particle impact experiments with 6 mm aluminium spheres
against a steel plate were performed. In total, 108 particles were impacted in the
velocity range between 10 and 60 m s
−1 . The obtained correlation (orange dotted
line in Fig. 9a) between the velocity v prior to the impact and the resulting contact
ratio x c /x was fitted in a FEM model: Results are depicted in Fig. 9a by the blue
A. Strobel et al.
3.3 Characterization of Stressing Conditions
3.3.1 Method Development
In general, grinding must be understood by the mill function and the material function.
The mill function describes the type of stressing, the transferred stress energy, and the
stress number. The material function accounts for the particles’ reaction to the applied
stress in form of breakage probability and breakage function, i.e. the size distribution
of the fragments. For modelling of comminution processes and its grinding kinetics,
knowledge about the stressing conditions applied to the particles is essential. To target
the impact velocity, i.e. the applied stress energy, and the stressing frequency in the
jet mill, a method developed to characterize the stressing conditions in wet operated
stirred media mills [45, 46] was adapted: The morphological changes of spherical,
well-characterized ductile metal probe particles are related to the relative particle
impact velocities prior to impact [33]. Briefly, single particles can be compressed
by a flat punch micromanipulator installed in a SEM. Stress-strain curves of several
100 particles can be measured and material properties such as Young’s modulus,
hardness, yields stress, and absorbed energy can be extracted [51]. The manipulation
device in the SEM, also allows to access pictures of the stressed and partly broken
particles. Surprisingly, images of compressed silica particles below their brittleductile transition (<1 μm) in the SEM and those stressed in a stirred media mill
looked very similar, indicating that compression in the SEM mimics compression
between two grinding beads. On this basis, the method was initially developed for the
case of two-sided stressing in stirred media mills. As probe particles, ductile metal
particles are used which do not break but plastically deform. The deformation is a
measure of the absorbed energy and thus can be used to extract the kinetic energy of
the milling beads. This approach provides the stress energy distribution acting in the
mill. Fundamental background information and details of the methodical procedure
are reported in two publications of Peukert et al. [45, 46].
In comparison to the method for stirred media mills, a mixture of soda-lime glass
beads and aluminium beads was used with a radio of 19:1 m/m. As can be seen in
Fig. 3a the two PSDs match perfectly. Since the two materials have a similar density,
separation during the comminution process is prevented. As shown earlier, almost no
fracture of the glass beads occurs during the first 20 s of the comminution process.
The absence of small fragments is essential for the method since they might penetrate
into the surface of the softer aluminium particles. Thus, the evaluation of the formed
dents would not be possible.
To determine the material parameters for the FEM material’s model for the aluminium spheres, single particle impact experiments with 6 mm aluminium spheres
against a steel plate were performed. In total, 108 particles were impacted in the
velocity range between 10 and 60 m s
−1 . The obtained correlation (orange dotted
line in Fig. 9a) between the velocity v prior to the impact and the resulting contact
ratio x c /x was fitted in a FEM model: Results are depicted in Fig. 9a by the blue