1. Introduction
As is well known, metal cutting is a common way to manufacture metal parts [
1]. In the cutting process, the same parameters (tool geometric parameters and tool operating parameters) have different degrees of influence on different performance indicators. To obtain the best cutting performance, those parameters are adjusted depending on their influence degree [
2]. However, in this process, the tool geometric parameters and tool operating parameters total at least ten parameters, which increases the difficulty of the performance adjustment. In addition, different performance indicators have different units and optimization directions; in order to be able to achieve high-performance machining, multiple performance indicators are often selected at the same time to carry out cutting research, resulting in difficulties in selecting a clear standard to measure each performance indicator. Therefore, when studying the cutting process based on multiple objectives, it is important to explore the degree of influence of the parameters on multiple performance indicators at the same time, select key parameters, and improve the research process.
The parameter sensitivity refers to the degree to which the parameter affects the performance indicator. Today, a number of scholars often conduct range analyses to obtain the parameter sensitivity. The main principle of a range analysis is that the greater the range value
R, the greater the degree of influence. The other researchers use modern evaluation methods to calculate the importance of each parameter. Feng et al. [
3] took a micro-texture cutter milling GH4169 as the research object; used a micro-texture size, a micro-crater diameter, and a micro-crater spacing as the research parameters; set up an L
16(3
4) orthogonal test; obtained the cutting force values corresponding to different parameter combinations using DEFORM 11.0 software; and calculated the cutting force range values of the three parameters using the range analysis method. The results show that the pit-spacing range is the largest and the pit-texture size range is the smallest, indicating that the pit-spacing sensitivity is the highest and the pit-texture size sensitivity is the smallest in terms of cutting force. Kong et al. [
4] took the laser-assisted turning titanium alloy TC6 as the research object, established the FEM model of the laser-assisted turning process with DEFORM software, established the L
9(3
3) orthogonal test to obtain tool wear values corresponding to different turning parameter groups, and analyzed the sensitivity of cutting parameters to tool wear with the range analysis method. The results show that the sensitivity of cutting speed is the highest and the sensitivity of cutting depth is the lowest. Li et al. [
5] established a FEM model of the milling nickel-based superalloy process using ABAQUS. Taking milling force and milling temperature as performance indicators, the range analysis of the cutting parameters was carried out according to milling force and milling temperature, respectively, using the range analysis method. The analysis results show that for milling force, feed per tooth > cutting depth > spindle speed; for milling temperature feed per tooth > cutting depth ≈ spindle speed. Yang et al. [
6] conducted experiments on milling titanium alloy with a micro-textured ball-end milling cutter. The diameter, depth, spacing, and distance from the cutting edge of a single pit were studied as the parameters, and the surface residual stress of titanium alloy was taken as the performance indicator to analyze the influence of the same parameters on the surface residual stress of the workpiece. The results show that pit spacing > distance from the pit to the cutting edge > pit diameter > pit depth. Li et al. [
7] studied the influence of parameters on performance indicators during the optimization of the process parameters such as tool type, feed speed, and cutting depth in Ti6Al4V dry turning. Considering the nonlinear relationship between various targets, grey correlation analysis (GRA) was used to convert each indicator into the corresponding grey correlation coefficient. Then, the kernel principal component analysis (KPCA) was used to extract the kernel principal component and determine the corresponding weights to represent the relative importance of each target.
In the process of researching the sensitivity and comprehensive importance of the parameters, it is found that the sensitivity of parameters refers to the degree of influence of parameters on a performance indicator. Commonly used methods include the range analysis method and response surface methodology (RSM). However, when two or more performance indicators need to be considered at the same time, due to the different effects of the same parameter on different performance indicators, it is easy to find that the same parameter has a strong impact on performance indicator 1 and a low impact on performance indicator 2. Therefore, the concept of parameter sensitivity cannot clearly measure the importance of the same parameter to multiple performance indicators at the same time, especially contradictory performance indicators such as tool wear and material removal rate, when the cutting parameters increase, tool wear and material removal rates will increase together; it is difficult to find the balance point between the two performance indicators. Among them, “simultaneously” considering multiple performance indicators means that the values of multiple performance indicators are input into the comprehensive evaluation method to obtain the comprehensive evaluation values of the evaluated object, and the mapping relationship is that multiple performance indicators correspond to a set of comprehensive evaluation results. Although the above scholars also studied the problem of multiple performance indicators, the parameter sensitivity analysis was carried out separately according to the number of performance indicators, and multiple performance indicators were not considered at the same time in the analysis of parameter sensitivity. Therefore, the concept of the comprehensive importance of parameters gradually emerged. The comprehensive importance of parameters is a qualitative concept, which is mainly used to describe the importance of the same parameter to two or more performance indicators “at the same time”. Each parameter itself is taken as the evaluation object and the value of the performance indicator is taken as the evaluation basis. The comprehensive importance of parameters to multiple performance indicators can be obtained using comprehensive evaluation methods, which include the grey correlation method, the fuzzy comprehensive evaluation method, and the grey–fuzzy analytic hierarchy process. Yue et al. [
8] used DEFORM finite element simulation software to establish the FEM model of the milling process of titanium alloy with a milling cutter to obtain the tool wear rate value and used analytical methods to obtain the material removal rate value. They evaluated the comprehensive importance of tool parameters and cutting parameters through the grey–fuzzy analytic hierarchy process method and selected the four parameters with the highest comprehensive importance. The result shows that the most important parameters are the clearance angle, helix angle, feed per tooth, and cutting depth. However, the grey–fuzzy analytic hierarchy process is a static comprehensive evaluation method, which evaluates the comprehensive importance of parameters according to the performance indicator value of a certain stage, but the cutting process is a dynamic change in the performance indicator value, such as tool wear gradually increasing with the increase in cutting distance. Therefore, it is of great significance to consider the variation in performance indicator values in multiple stages while conducting a comprehensive importance evaluation.
When milling difficult materials such as titanium alloys, the high strength and hardness of those materials at high temperatures accelerate the rate of tool wear, resulting in rapid tool failure and reduced machining efficiency [
9,
10,
11]. In this paper, the key problems of large tool wear and low machining efficiency in the milling process of titanium alloy are investigated. Taking the side milling of titanium alloy with an end mill as the research object, the phenomenon existing in the cutting process is studied and the causes are analyzed. Considering the dynamic change in performance indicators, the tool wear and material removal rate are selected as the evaluation basis, and the comprehensive evaluation model is composed of the grey–fuzzy analytic hierarchy process and the dynamic comprehensive evaluation method based on the double incentives model. The model is used to evaluate milling parameters comprehensively, and the dynamic comprehensive evaluation values of each milling parameter are obtained. Finally, the radar map of the comprehensive importance of cutting parameters is plotted to visually show the comprehensive importance of each cutting parameter.
4. Conclusions
In the cutting process, the performance indicators are different, the optimization direction is different, and the parameters have different effects on the performance indicator; there is no clear standard to measure each performance indicator, and the data of the performance indicators in the cutting process will change with the increase in the cutting distance. In this paper, titanium alloy milling with an end milling cutter is studied, and the characteristics and causes of the tool wear value change at different stages of each parameter combination in the test process are analyzed. The dynamic comprehensive evaluation method based on the double incentives model is used to assess the comprehensive importance of each cutting parameter. As a result of the evaluation, the cutting parameter with the highest comprehensive importance is selected. And, the reliability of the comprehensive evaluation results is verified using the comparison between the range analysis method and the comprehensive evaluation results. The following conclusions can be made as a result of the conducted research:
In the process of milling titanium alloy with an end mill, it is found that it has a serious built-up edge phenomenon. The tool wear of two adjacent stages has decreased and slightly changed. The reason for these problems is that the built-up edge bond on the cutting edge affects the measurement of the tool wear;
There is a phenomenon of the sharp increase in the tool wear of two adjacent stages, which is caused by the built-up edge instead of the edge cutting and falling off at a certain time, caused by the cutting edge continuing to cut;
According to the dynamic comprehensive evaluation results, cutting speed > cutting width > feed per tooth > cutting depth. The comprehensive importance of cutting speed is the highest, cutting width ranks second, the difference between the evaluation values of the two parameters is small, the feed per tooth ranks third, and the comprehensive importance of cutting depth is the lowest;
Through the range analysis, it is found that the range analysis results are similar to the comprehensive evaluation results. Therefore, the result of a comprehensive evaluation is reliable.
The dynamic, evaluation method based on the double incentives model is an evaluation method with high universality and applicability. The method can be applied in other fields, such as mechanical manufacturing, mechanical design, urban management, economics, etc. However, certain prerequisites are required for the method to be used to evaluate the evaluated object:
The research object is a dynamic research object;
The number of performance indicators based on the comprehensive evaluation should be at least two, and the performance indicator itself is a quantifiable indicator;
Among the performance indicators involved in the evaluation, at least one performance indicator must be sufficient to change over time.