3.1.1. Definition of Blade Vertex Angle
The angle at the vertex of the blades is denoted as β (Error! Reference source not found. ). This angle, as with a drill bit, influences numerous machining parameters such as:
The most desirable characteristic of blades is to maintain a good degree of self-alignment with the screw direction of the implant, preventing external forces, such as the thrust exerted by the operator, to deviate from the desired direction. To this end, a vertex angle β tending towards 90° has been suggested [
43].
At the same time, however, there is a need to keep the screwing torque of the implant as low as possible to facilitate insertion by the operator working in confined spaces. In fact, the lower the applied external stress, the better is the desired trajectory maintained.
Considering the limited extension of the main cutting edge of the blades, compared with a hypothetical conventional drill bit operating with the same diameter, the penetration thrust can be considered negligible. However, the resistance torque acting near the outer diameter of the blades remained relatively high. To limit the drilling torque, the use of a vertex angle β between 110° and 140° has been suggested [
42].
The increased heat produced by using any tip angle can be considered negligible in this case, as the rotation speed of the blades is very limited because the system is expected to be tightened either with a contra-angle handpiece, setting it at a low rotation speed (≤ 20 rpm), or manually with a ratchet.
Considering the standardized dimensions of the tools available on the market for blade manufacturing, a β vertex angle of 120° was chosen. This decision was made because it was considered that penetration forces are generated with sufficient intensity by the thread of the implant (even in a low-density pith), while the torque required for the blades’ action is low while maintaining a non-negligible self-aligning action.
3.1.2. Definition of the Upper Rake Angle of the Main Cutting Edge, α
Conventionally, for a drill, the variables and cutting parameters are assumed to be localized at the outermost diameter of the drill, as they may vary depending on the position chosen for their characterization because of the typical morphology of the tool.
The main cutting edge of the blades, derived from that of a traditional drill bit, has an upper face of the tool that forms an angle δ with respect to the cutting direction. With respect to the plane normal to the same cutting direction, the tool’s upper face forms an angle α, known as the top rake angle, which can be zero if it is perpendicular to the cutting direction vector (δ = 90°), positive if it forms an obtuse angle (
δ> 90°), and negative if it forms an acute angle (
δ < 90°) respect to the cutting direction (
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The rototranslation of the implant during the screwing phase produces a penetration movement of the blades according to a precise inclination, called the working direction, corresponding to the helix angle of the implant thread.
The helix angle ψ, conventionally adopted for the external thread diameter d1, is determined by
(1)
However, the action diameter of blade d3 does not necessarily coincide with the external diameter of thread d1 because it depends on the Blade Differential Diameter (BDD) interference/play to be impressed according to the desired biodynamic requirements for the cortical bone.
If, for example, a differential is to be imposed on the blades BDD = +0.05 mm at a thread diameter d1 = 3.75 mm, the diameter of the blades d3 can be determined by the following formula:
(2)
The angle of the working direction adopting d3 instead of d1 would become:
(3)
Because the blade diameter (d3) can be varied to best suit the biodynamic requirements of the cortical bone, given the negligible differences between ψ and ψ1, it is preferable to use d1, which is a constant of the implant, instead of d4, which is dependent on the BDD to be conferred.
Kalpakjian [
41] stated that if the rake angle α is small, that is, tends to 0, the chip tends to form in a discontinuous fragmented type.
Top rake angles of 8° have been use in some studies [
39,
40]. However, both provide chip formation as a function of the depth of pass (UCP) and not as a function of the rake angle.
In the blades, unlike conventional drill bits, the main cutting edge does not have a linear but a curved profile, owing to their construction method. Therefore, it is also necessary to consider the effect of blade construction geometry on the effective upper rake angle
α. Starting from the outer diameter of the blades d
3 towards the core diameter of the screw d
2, the geometric effect involves the transformation of the upper rake angle
α from positive (
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To simplify the procedure for determining the upper rake angle α without committing major approximation errors, it is advisable to use the blade helix angle
ε as a reference and then check that the ‘real’ rake angle α remains within a small geometric variation, arbitrarily set at values close to α = 0° +/- 10° in order to comply with the suggestion from other reports [
39,
40,
41].
It follows that the helix angle of the blades ε, to obtain a rake angle above the main cutting edge, α = 0°, must be equal to ψ.
It is now necessary to consider that the helix angle ε of the blades also influences the extraction of the chip from the collecting cavity (and therefore, from the osteotomy). If the helix angle is increased with respect to ψ, the filling of the collecting cavity tends to increase, conveying the chip towards the inside of the osteotomy. If it decreases, it tends to empty, driving the chip outwards. If it coincides with ψ, it tends to leave the swarf at a random filling/ejection depending on the type of swarf that the other operating conditions influence.
For the purpose of the invention, the bone chips should first fill the cavity, as this is supposed to promote the bone regeneration necessary for osseointegration [
44,
45,
46], and only then achieve their complete filling, as the collecting cavities have a volume smaller than the excavated volume.
The excess bone chip must therefore be evacuated externally, avoiding producing much compression on the walls of the osteotomy, in accordance with the objective of the blades to reduce or control compression on the cortical bone. As a result, it is preferable to give an increased angle differential ε of +9° (arbitrarily chosen) to give a slightly forced harvesting effect, because the type of continuous segmented chip (brittle), once the cavity is filled, is sufficiently “fluid” to be drained without significantly increasing the compressive effect on the bone.
As mentioned previously, the helix angle of the blades can be determined by
(4A)
This value can be approximated as an excess without appreciably affecting the desired effect at
ε =13°. The adoption of this angle results in variability (verified at CAD for simplicity) in the rake angle α between
This value falls within the previously established limits to a reasonable degree; therefore, a helix angle of ε = 13° was chosen.