## 1 Introduction
By designing the material used and the uncoated cutting insert, we aimed to minimize the effects of degraded machinability of the various materials and the effects of the properties of the cutting insert structures. [PERSON] and [PERSON] et al. point out the effects of cutting the cutting edge of a sintered carbide tool when milling steel C45 to eliminate tool wear and achieve the required surface quality [24; 25]. Is the application of a laser beam suitable for checking the quality parameters of the machined surface of products (e.g., diameter deviation) after the end of the cutting process? Based on the experience of machining different materials, we have chosen C45 steel specimens and sintered carbide inserts for dry turning and under the important condition that the vibrations of the machine tool comply with the values certified for the machine tool. Therefore, in order to eliminate negative phenomena in product control, we proposed to review the application of the new generation LTS to measure the deviation of cylindrical surface diameter (\(\Delta_{d}\)) and evaluate the effects of flank wear (\(VB_{B}\) value according to ISO 3685) of the sintered carbide insert on this parameter under different cutting conditions. Optimization of Input Factors Using the GRA Method and Analysis of the Significance of Factors According to ANOVA  
When processing data from technological processes with different response parameters, the mutual relationships are complex and very often incomprehensible. We refer to this relationship as grey. For processing selected results from our research, we proposed a method based on GRA [26]. When optimizing with the method GRA we followed Lin [27]. The following values and parameters must be calculated as part of the procedure. Calculation of the data for the methodology and the smaller the better according to Equation (1):  
\[x_{i}^{*}(k)=\frac{max\ x_{i}^{0}(k)-x_{i}^{0}(k)}{max\ x_{i}^{0}(k)-min\ x_{i}^{0 }(k)} \tag{1}\]  
where:  
\(i=1,\ldots,\) m \(k=1,\ldots,\) n,  
\( \begin{array}{ll}\text{in}&\text{is the number of experimental data,}\\ x_{i}^{0}(k)&\text{is the number of response characteristics,}\\ x_{i}^{*}(k)&\text{indicates the original sequence,}\\ x_{i}^{*}(k)&\text{indicates a sequence after data processing,}\\ max\ x_{i}^{0}(k)&\text{highest value of }x_{i}^{0}(k),\\ min\ x_{i}^{0}(k)&\text{lowest value of }x_{i}^{0}(k),\\ x_{i}^{0}&\text{is the required value of }x_{i}^{0}(k).\end{array} \)  
GRC \(\xi_{i}(k)\) according to Equation (2):  
\[ \begin{array}{ll}\xi_{i}(k)=\frac{\Delta_{min}+\zeta_{i}\Delta_{max}}{\Delta _{ii}(k)+\zeta_{i}\Delta_{max}}\\ \Delta_{oi}(k)=\left|x_{o}^{*}(k)-x_{i}^{*}(k)\right|\\ \Delta_{max}=1.00\ \Delta_{min}=0.00\end{array}  \tag{2}\]  
where:  
\(\Delta_{ii}(k)\)  
\(\Delta_{min}\), \(\Delta_{max}\)  
are the minimum and maximum values of the absolute differences (\(\Delta_{oi}\)),  
\(\xi\)  
is an identification coefficient, and is defined in scope \(0\leq\xi\leq 1\) and  
depends on the needs of the system. Usually, the value of (\(\xi\)) is 0.5. GRG calculation according to Equation (3):  
\[\gamma_{i}=\frac{1}{n}\sum_{k=1}^{n}\xi_{i}(k) \tag{3}\]  
where:  
\(\gamma_{i}\) is the GRG required for the \(i\) experiment,  
\(n\) number of response characteristics. Calculation of the expected value of the optimal GRG level according to Equation (4). \[\hat{\gamma}=\gamma_{m}+\sum_{i=1}^{s}(\gamma_{i}-\gamma_{m}) \tag{4}\]  
where:  
\(\gamma_{m}\) is the total mean of GRG,  
\(\gamma_{i}\) is the mean of GRG at the optimal level of each factor,  
\(s\) is the number of significant process factors. Many authors have used the GRA method, the Taguchi method, and the ANOVA method to present the results of their research. [PERSON] et al. and [PERSON] et al. optimized the process factors in their study and used the Taguchi L27 orthogonal array [28; 29], [PERSON] et al. and [PERSON] et al. solved the optimization of parameters in the machining process, using the Taguchi method--GRA [30; 31]. [PERSON] et al.