4
Y. Wang and Y. Zeng
Fig. 1.1 Mechanisms of EMM with a moving spherical tip as the tool electrode, a principles of
EMM removing process, b Schematic diagram of electric current density distribution and machined
profile by EMM, c SEM images of the tool electrode with a spherical tip
tip apex, R is the radius of the spherical tip, and k is electrolyte conductivity. The
distribution of electric current density on the workpiece is schematically illustrated
in Fig. 1.1.
Based on the Faraday’s law and Ohm’s law, the materials removal rate (v a ) is
proportional to the current density [19], as expressed in Eq. (1.2),
v a = ηωj (r )
(1.2)
where η is the electric current efficiency, ω is the electrochemical equivalent volume
of the workpiece materials. The area under the spherical tip is removed with a contour
affected by the electric current density distribution. Hence, the processed contour
by EMM with a spherical tip could be regulated by controlling the electric current
density distribution on the workpiece. According to Eqs. (1.1) and (1.2), the machined
contour could be controlled by adjusting the available parameters, such as applied
voltage, inter-electrode gap, and spherical tip diameter, in principle. By moving the
spherical tip along with a programmed trajectory, microstructures with the controlled
profiles could be directly machined on the workpiece.
In EMM with the dissolution of anodic workpiece materials, electrolytic products
on the workpiece/electrolyte interface are formed. The electrolytic products contain
metal ions (Mn
+ ) and small quantities of metal hydroxide (M(OH) n ), as shown in
Fig. 1.1. The accumulation of the electrolytic products would decrease the electrolytic conductivity, which would then reduce the electrochemical machining rate,
Y. Wang and Y. Zeng
Fig. 1.1 Mechanisms of EMM with a moving spherical tip as the tool electrode, a principles of
EMM removing process, b Schematic diagram of electric current density distribution and machined
profile by EMM, c SEM images of the tool electrode with a spherical tip
tip apex, R is the radius of the spherical tip, and k is electrolyte conductivity. The
distribution of electric current density on the workpiece is schematically illustrated
in Fig. 1.1.
Based on the Faraday’s law and Ohm’s law, the materials removal rate (v a ) is
proportional to the current density [19], as expressed in Eq. (1.2),
v a = ηωj (r )
(1.2)
where η is the electric current efficiency, ω is the electrochemical equivalent volume
of the workpiece materials. The area under the spherical tip is removed with a contour
affected by the electric current density distribution. Hence, the processed contour
by EMM with a spherical tip could be regulated by controlling the electric current
density distribution on the workpiece. According to Eqs. (1.1) and (1.2), the machined
contour could be controlled by adjusting the available parameters, such as applied
voltage, inter-electrode gap, and spherical tip diameter, in principle. By moving the
spherical tip along with a programmed trajectory, microstructures with the controlled
profiles could be directly machined on the workpiece.
In EMM with the dissolution of anodic workpiece materials, electrolytic products
on the workpiece/electrolyte interface are formed. The electrolytic products contain
metal ions (Mn
+ ) and small quantities of metal hydroxide (M(OH) n ), as shown in
Fig. 1.1. The accumulation of the electrolytic products would decrease the electrolytic conductivity, which would then reduce the electrochemical machining rate,