## 2 Materials and Methods
### Mesh Geometry Refinement for Finite Element Analysis (FEA)
Thus, the parameters of the drilling regime with a \(d=\)O2 mm drill are presented:  
Feed-\(f\) (mm/rev)--the distance that a drill advances into the bone in one complete rotation,  
\(f=K_{f}\times C_{f}\times d^{0.6}\), mm/rev,  
\(f=0.85\times 0.055\times 2^{0.6}=0.071\) mm/rev,  
where \(K_{f}\) is a correction coefficient depending on the hole depth \(h\) and its diameter \(h>3d\) (10 mm > 3 \(\times\) 2 mm); \(K_{f}=0.85\); \(C_{f}\) is the feed coefficient based on the bone hardness and drilling precision; \(C_{f}=0.055\); \(d\) is the drill diameter. Feed ratio speed--\(V_{f}\) (mm/min)  
\(V_{f}=f\cdot n\), mm/min,  
\(V_{f750}=0.071\times 750=53.3\) mm/min,  
\(V_{f1200}=0.071\times 1200=85.2\) mm/min,  
where \(n\) is the rotational speed required for drilling (values considered between 750 rev/min and 1200 rev/min depending on the bone condition and on the area where the hole will be positioned). We noticed that the maximum safe rotational speed should be up to 1800-2000 rev/min. Cutting speed--\(V_{c}\) (m/min)  
\(V_{c}=\pi\times d\times n/1000\), mm/min,  
\(V_{c750}=\pi\times 2\times 750/1000=4.71\) m/min,  
\(V_{c1200}=\pi\times 2\times 1200/1000=7.53\) m/min. Axial cutting force--\(F_{fu}\) (N)  
\(F_{fu}=C_{F1}\cdot d^{xx}\cdot g^{fx}\cdot Hb^{nft}\cdot K_{F}\), (N), where \(C_{F1}\) is experimentally determined based on the bone hardness, \(C_{F1}=1.6\); \(xF\) and \(yF\) are experimentally determined correction coefficients depending on the hardness of the mandible bone and on the drilling conditions (the drill tool is guided or not, the drilling process is with or without cooling), \(xF=\)1, \(yF=\)0.7; \(f=0.071\) mm/rev; HB--mean value of the mandible bone hardness, HB = 56 HB; \(nF\) is an experimentally determined coefficient that depends on the drill's type and on the hardness of the mandible bone, \(nF=0.75\); \(K_{F}\) is a correction coefficient of the drilling force, determined by: \(K_{F}=K_{af}\times K_{afF}\times K_{xf}\times K_{nf}\), where: \(K_{afF}\) is a correction coefficient depending on the sharpening method of the drill, \(K_{afF}=1\); \(K_{afF}\) is a correction coefficient experimentally determined based on the manual advancement of the drill, \(K_{afF}=0.97\); \(K_{xf}\) is a correction coefficient depending on the value of the angle of the drill tip (2\(\times\)0), \(K_{xf}=0.98\); \(K_{nfF}\) is a correction coefficient depending on the relative thickness of the drill core \(\eta\), and its diameter, \(d=\) 02 mm, \(\eta=0.18\), \(K_{nfF}=1.19\). So, \(K_{F}=1\times 0.97\times 0.98\times 1.19=1.13\), and \(F_{fu}=1.6\times 2^{1}\times 0.071^{0.7}\times 56^{0.75}\times 1.13=11.62\) N  
Cutting torque--\(M_{W}\) (N\(\cdot\)m)  
\(M_{W}=C_{M1}\times d^{xM}\times g^{M}\times HB^{nM}\times K_{yM}\), N\(\cdot\)m, where \(C_{M1}\) is a coefficient experimentally determined based on the bone hardness, \(C_{M1}=0.0163\); \(d=\) 02 mm; \(xM\) and \(yM\) are correction coefficients experimentally determined based on the bone hardness and drilling conditions (guided, with/without cooling), \(xM=1.3\), \(yM=\)0.93; HB = 56 HB; \(nM\) is a coefficient experimentally determined based on the drill's type and on the bone hardness, \(nM=0.54\); \(K_{yM}\) is the correction coefficient of the cutting torque, \(K_{yM}=1.1\)  
\(M_{W}=0.0163\times 2^{1.3}\times 0.071^{0.93}\times 56^{0.54}\times 1.1=0.033\) N\(\cdot\)m  
Total cutting power--\(P_{c}\) (W)  
\(P_{c}=P_{F}+P_{M}\), (W), where \(P_{F}\) is the power derived from the feed and \(P_{M}\) is the power derived from the cutting torque. \(P_{c}=V_{f}\times F_{fu}+M_{W}\times n\times 2\pi/60=0.02+4.14=4.16\) W.  
At the base of the guide, certain areas are carefully established, considering that they are in contact with neighboring teeth, and specific constraints are applied to fix the guide. The areas fixed in this manner will not present displacements following the FEA simulation (Figure 5).