## 4 Experimental Section
The maximum force was reached in measurement 1--tightening to 2.5 turns generated a compressive axial force of 266 N. The region from 1.75 to 3 turns of the screw can be perceived as a risk area of 180 to 266 N. Exceeding the strength limit of the bone fragment led to the plastic deformation in the area of the thread cut in the bone and the thread was sheared. Figure 12: Two bone fragments with a force sensor connected by a headless screw. Figure 13: Axial forces during headless screw tightening. Once the thread in the bone was sheared, a sharp decline in the force was expected. This was not confirmed, which can be explained by the existence of frictional forces observed on the contact surfaces between the bone and the screw and by the development of elastoplasticity in the area of interest. The statistical evaluation of the results is shown in Figure 14. The maximum average compression force was 230.9 N and acted on the screw at 2.25 turns; after that, the thread in the bone was sheared off, and the compression force began to decrease. The highest median value of the normal compressive force (220 N) acted on the screw at 2 tightening turns. The maximum and minimum measured values of the force F formed the envelope of the course of the compressive force dependence. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measurement** & **Fmax [N]** & **n [1]** \\ \hline
**1** & 266 & 2.5 \\
**2** & 233 & 2 \\
**3** & 237 & 2.75 \\
**4** & 250 & 2.5 \\
**5** & 212 & 2.25 \\
**6** & 246 & 2 \\
**7** & 265 & 2.5 \\
**8** & 196 & 2.25 \\
**9** & 224 & 2 \\
**10** & 180 & 2.5 \\
**Min** & **180** & 2 \\
**Mean** & **204** & **2.25** \\
**Median** & **220** & **2** \\
**Standard deviation** & **28.37** & **0.26** \\
**Max** & **266** & **2.75** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum values of the measured axial force in individual measurements. Figure 14: The statistically processed association between screw tightening and axial force. We also looked for a function suitably approximating the measured data, as finding such an approximation function is advantageous for their further processing. The experimental data obtained in our experiment showed similar behavior of the compressional force as the data obtained when measuring the dependence of the force on the screw displacement when the screw was being pulled out of the bone [24], which studied the effect of elastic foundation on tearing a screw out of the bone. Based on the similarity between data reported in [24] and our findings, we can conclude that the compression forces are also influenced by elastic foundation in the case of Herbert screws. More information about the elastic foundation can be found in [21; 24]. Hence, the search for an approximation function was based on the findings in that previous study and used a similar mathematical model. The measured data were approximated by a cosine power function \(\mathrm{F}=A\ [1-\cos(B\mathrm{n})\ ]^{m}\), where \(A\), \(B\), and \(m\) are constants. which interpolated the values very well. The approximation function must satisfy the following boundary conditions:  
1. Boundary conditions for the initial point: 1. \(\mathrm{n}(0)=0\) 2. \(\mathrm{F}(0)=0\)
2. Boundary conditions for the extreme point: 1. \(\mathrm{The}\) function passes through the extreme point [\(\mathrm{n_{E}}\); \(\mathrm{F_{E}}\)]; 2. For extreme point, the derivation \(\frac{\mathrm{dF}}{\mathrm{dn}}=0\)  
Mentioned boundary conditions are shown in Figure 15.  
After the introduction of boundary conditions, the solution for the following equation was calculated:  
\[\mathrm{F}=\frac{\mathrm{F_{E}}}{2^{m}}\ [1-\cos\left(\frac{\tau\mathrm{n_{E}}}{ \mathrm{n_{E}}}\right)\ ]^{m} \tag{5}\]  
From Equation (5), it is clear that only the parameter \(m\) was unknown. This parameter can be found by regression, for example, using the Matlab software, version R 2019b (Toolbox Curve Fitting), created by The MathWorks, Inc. (Natick, MA, USA) [25]. Values from all measurements were interpolated using this function.