Bone material is a finely engineered composite exhibiting anisotropy, as depicted in
Figure 1. It primarily consists of two layers: cortical and trabecular bone. Cortical bone includes the osteon units, also known as the Haversian system, situated between the inner and outer circumferential lamellae [
15]. These units are the fundamental structural components of the skeletal core. Trabecular bone, on the other hand, features a spongy structure located inside the inner circumferential lamellae. It is composed of numerous bone trabeculae interwoven into a sponge-like structure, offering a combination of porosity, strength, and lightness [
16].
During the bone drilling process, common wear mechanisms include abrasion, adhesion, and oxidation. Abrasion occurs due to the relative motion between the drill bit and the bone tissue, leading to gradual material wear on the surface. Adhesion refers to the bonding between the drill bit material and the bone tissue, which not only increases the wear of the drill bit but may also degrade the quality of the drilled hole. Additionally, the frictional heat generated by the high-speed rotation of the drill bit in contact with bone tissue can cause oxidation reactions. The resulting oxides can further affect the performance of the drill bit and the integrity of the bone tissue.
Compared to other metal drilling materials, bone material may have lower hardness and density, but the drilling process cannot utilize effective cooling fluids. This inability prevents timely expulsion of bone chips from the hole. The bone chips, in contact with the continuously rotating drill bit, generate substantial friction. Moreover, as bone material is semi-brittle, flank wear becomes the predominant form of tool wear during the drilling process.
2.2. Primary Cutting Edge Mechanical Model
During the bone drilling process, the use of medical-grade stainless steel for drill bits, which has a lower hardness compared to the tools used in metal material drilling, results in severe wear on the main cutting edges and the flank face [
22].
The wear process alters the contour of the main cutting edges from a curved shape to a new shape. Therefore, the worn main cutting edges are simplified to an elliptical arc, as shown in
Figure 4b. Based on geometric characteristics, the contact area between the worn main cutting edges and the bone material is divided into three parts: the rake face area 1, the area beneath the elliptical arc cutting edge 2, and the area beneath the flank face 3, as illustrated in
Figure 5.
In Region 1 on the rake face, brittle fracture occurs at the cross-section of the bone unit fibers and the inter-bone plate matrix due to the shearing and compressive actions on the rake face, leading to the formation of chips. Since the rake face wear in bone drilling is typically not severe, the cutting force generated by the worn rake face is similar to that produced by a new rake face. Referring to the cutting force model for orthogonal cutting with a new tool, the basic cutting forces
and
along the
x-axis and
z-axis in Region 1 can be expressed as:
The subscript 1 in and denotes Region 1, is the shear strength of the fibers, is the shear strength of the matrix, is the rake angle of the tool, is the friction angle between the chip and the rake face, is the shear plane angle, is the cutting depth, is the length of the main cutting edge element, and is the fiber orientation angle.
Based on the geometric relationships in
Figure 6, the fundamental cutting forces
and
in Region 1 can be further calculated as follows:
Due to the presence of a fiber angle
between the bone unit fiber direction and the cutting speed during the cutting process,
Figure 7 illustrates the variation of the fiber angle at different positions relative to the bone unit fiber along the main cutting edge. The fiber angle
can be expressed as a function of the radial distance
.
where
is the fiber angle when the radial distance
is equal to the drilling radius
.
In Region 2, tool wear causes the cutting edge to become elliptical, thereby pushing the cutting material downward. Based on Hertzian contact theory and assuming a cylindrical model, the indentation depth is approximated as the length of the minor axis
of the workpiece. The normal force
derived from this can be related to Young’s modulus
perpendicular to the bone unit fiber direction and the average length of the minor axis
. The expression for the normal force is as follows:
where
is the Young’s modulus of the bone material perpendicular to the bone unit fiber direction, and
is the average length of the minor axis along the entire main cutting edge.
The friction force is controlled by the friction coefficient
,
and can be calculated based on the principles of tribology.
Assuming the major axis
increases linearly with the radial distance
, the fundamental cutting forces along the
x-axis and
z-axis in Region 2 can be calculated as follows:
In Region 3, the contact between the flank face and the cutting material surface is caused by the rebound of the cutting material. This process can be approximated as an elastic half-space contact based on Hertzian contact theory. Assuming that the rebound height is linearly related to the average minor axis length
, the normal force
in the drilling Region 3 can be obtained from the following equation:
where
is the coefficient, the friction force
between the flank face and the machined surface is given by
, and
is the tool’s relief angle.
Therefore, the fundamental cutting forces
and
along the
x-axis and
z-axis in Region 3 can be expressed as follows:
By summing all the cutting forces from the three regions, the total cutting forces and along the x-axis and z-axis along the worn main cutting edge can be calculated as follows: , .
The cutting forces defined above are in the orthogonal coordinate system
, as shown in
Figure 8. To obtain the vertical downward thrust generated by the drill bit, the cutting forces
and
are first resolved in the inclined coordinate system
. Then, the resulting components
,
, and
are resolved in the actual drilling coordinate system
. Finally, by summing all the cutting forces along the
-axis, the axial force
generated by the drill bit during the drilling process can be expressed as:
By integrating the thrust
of all the components, the thrust
generated by the two main cutting edges can be expressed as:
where
is the angle between the chisel edge and the main cutting edges.
The thrust generated by the chisel edge can be expressed as
after a transformation:
By superimposing the thrusts
and
of the main cutting edges and the chisel edge, respectively, the axial force
, considering the effect of wear, can be expressed as:
In summary, the feed rate, spindle speed, and geometric parameters of the tool significantly influence the axial force in drilling. Tool wear leads to the degradation of the performance of the main cutting edges, thereby affecting the axial force, making it a reliable indicator for evaluating tool wear. As wear progresses, not only does the axial force change, but the forces in the horizontal direction also vary accordingly [
23]. Therefore, an effective monitoring strategy should include an analysis of the changes in horizontal forces. Due to the periodic variation of the unit fiber angle during the drilling process, performing time–frequency domain analysis on the collected signals is a feasible method for monitoring tool wear in the drilling process of bone materials.