# Comprehensive Evaluation Method for High-Performance
## 2 Materials and Methods  
An attempt was made to develop a method for evaluating the high-performance milling of Inconel 718. This method should involve a comprehensive, multi-dimensional analysis of the process and allow for the comparison of various machining types, regardless of their kinematics or tool path. The primary assumptions of the proposed evaluation method are as follows:  
* the method pertains only to roughing operations;
* the compared processes must use tools with the same geometry (i.e., the same diameter and number of cutting edges, or in the case of assembled tools with interchangeable inserts, the same tool body or the same number of cutting edges in the tool);
* the cutting speed must be the same in the compared processes;
* the cutting trials must be conducted on the same machine tool;
* The cutting trials must use material from the same heat of steel. Additionally, the research plan must be designed to take place under accelerated wear conditions. Beyond the economic rationale, this approach allows for a more detailed analysis of a greater number of parameters. Based on studies [34] regarding minimum quantity lubrication (MQL) and other lubrication methods, it has been established that even minimal lubrication affects tool life in the milling process of Inconel alloys. For this reason, to accelerate tool wear, dry machining was chosen, allowing for the achievement of results related to accelerated wear. A key aspect of the method is to observe the accelerated wear mechanism in order to accurately calculate tool life until the VBBmax wear is reached. Based on the literature analysis presented in the introduction, it was assumed that a comprehensive evaluation of the high-performance milling of Inconel 718 requires the investigation of the following process parameters:  
* components of cutting forces \(\mathrm  
Equation (2) is used, while for parameters where the values should be maximized (e.g., Q and Gmax), Equation (3) is applied. \[x_{i}^{*}(k)=\frac{\max x_{i}(k)-x_{i}(k)}{\max x_{i}(k)-\min x_{i}(k)} \tag{2}\]  
\[x_{i}^{*}(k)=\frac{x_{i}(k)-\min x_{i}(k)}{\max x_{i}(k)-\min x_{i}(k)} \tag{3}\]  
where i = l,..., m; k = l,..., n, m is the number of experimental data points, and n is the number of responses; x\({}_{i}\)(k) represents the original sequence, x\({}_{i}\)*(k) represents the sequence after initial data processing, and max x\({}_{i}\)(k) denotes the maximum value of x\({}_{i}\)(k). Next, the grey relational coefficient \(\xi_{i}\)(k) is calculated from the previously normalized values. The relationship between the actual and normalized measured values is determined using Equation (4). \[\xi_{i}(k)=\frac{\Delta_{\min}+\xi\Delta_{\max}}{\Delta_{0i}(k)+\xi\Delta_{ \max}} \tag{4}\]  
where \(\Delta_{0i}\) is calculated using Equation (5):  
\[\Delta_{0i}=\left\|x_{0}(k)-x_{i}(k)\right\| \tag{5}\]  
where \(\Delta_{\min}\) is the smallest value of \(\Delta_{0i}\) (k), and \(\Delta_{\max}\) is the largest value of \(\Delta_{0i}\) (k) among all the compared values. \(\xi\) is the distinguishing or identification coefficient, and its value ranges from 0 to 1. \(\xi\) is typically set to 0.5. The next step is the analysis of the grey relational grade (GRG). This is a multi-output feature analysis based on grey relational assessment. The result of this analysis transforms multiple responses into a single numerical value. The GRG (\(\gamma\)) is calculated using Equation (6), and its value ranges between 0 and 1. \[\gamma_{i}=\frac{1}{n}\sum_{k=1}^{n}\xi_{i}(k) \tag{6}\]  
where \(\gamma_{i}\) is the required grey relational grade for the i-th set of parameters, and n is the number of process responses. In this work, the responses are the volumetric material removal rate (Q), the volume of material predicted to be removed during the tool's life cycle (Gmax), the average maximum power consumption (P\({}_{c}\)), and the average maximum component of cutting forces (F\({}_{2}\)).