Experimental Study on Coupling Characteristics of Cutting Heat and Cutting Vibration Under Different Tool Wear States


 The thermo-mechanical-vibration coupling characteristics of turning system has always been an important research topic in the field of machining, and the material, states and performance of cutting tools will directly affect this coupling characteristics. In this paper, a synchronous testing system for cutting temperature and cutting vibration is built to collect the cutting temperature and cutting vibration near the tip of three worn tools D1 (new blade), D2 (moderately worn blade) and D3 (severely worn blade). Based on the test data and the grey correlation theory, the coupling characteristics of cutting temperature rise and cutting vibration of tools in different wear states are analyzed. Based on the experimental data and least square method, (1) the regression model of cutting temperature rise about cutting vibration and cutting parameters (2) the regression model of cutting vibration about cutting temperature rise and cutting parameters have been established respectively. The undetermined parameters and correlation coefficients are obtained by MATLAB software programming. The research show that the coupling of cutting heat and cutting vibration of tools D1 and D2 is one-way coupling, that is, cutting vibration significantly affects cutting heat, but cutting heat has little effect on cutting vibration, while the coupling of cutting heat and cutting vibration of tool D3 is a bidirectional coupling.


Nomenclature n
The spindle speed

Introduction
In the turning process, there is relative friction between the tool and the workpiece, which not only causes the continuous rise of temperature in the tool and in the work-piece, but also produces serious cutting vibration, which speeds up the tool wear. The tool wear will accelerate the rising speed of cutting temperature, shorten the tool life, and reduce the strength of the work-piece and the surface quality. In flexible production system, if the tool wear states is not known or the worn tool cannot be replaced in time, the production efficiency will be reduced [1].
There are a lot of literatures on the influence of cutting tool material, geometric parameters, processing conditions and cutting parameters on cutting temperature. Zhang et al. [2] studied the influence of geometric parameters of cutting tools on cutting temperature, and found that the cutting temperature will also rise when the rake angle and edge angle increase.
Majumdar et al. [3] studied the influence of turning conditions, tool geometry and temperature distribution of tool material on tool life, established a finite element model, and obtained the range of turning conditions for machining high-speed steel. Karaguzel, Cui and Chinchanikar [4][5][6] studied the correlation between cutting parameters and cutting temperature. Liu and Li [7][8] studied the tool temperature in the turning process of titanium alloy, and found the interaction between the degree of tool wear and the cutting temperature.
Zhang et al. [9] studied the change of cutting temperature with different cutting parameters for titanium matrix composite tool, and found that the lower the cutting speed, the higher the cutting temperature. analyzed the wear mechanism of titanium alloy cutting tools, and determined the interaction between cutting temperature and tool wear. Shi [10] and Qu [11] established a mathematical model of cutting temperature and cutting force to prove the correlation between cutting temperature and cutting parameters. Shah et al. [12] studied the influence of cutting parameters on the cutting temperature of Ti-6Al-4V cutting process through particle swarm optimization algorithm. Turkes et al. [13] used the finite element analysis to calculate the cutting parameters, and found that the temperature distribution of cutting tools and processing materials through the parameters. Luo and Maroju [14][15] studied the cutting temperature by vibration assisted turning.
Taking cutting vibration as the research object, some scholars study the influence of cutting parameters, cutting force, machine structure and processing conditions on the vibration through experiments and regression models. Li, Chanda, Deshpande and Chen [16][17][18][19] analyzed the influence of cutting and cutting parameters on cutting vibration through experiments. Hu et al. [20] studied the influence of lathe internal structure on cutting vibration, established the dynamic model of turning system based on ER damper, and found that the cutting vibration reduction effect was different under different cutting parameters. Cui et al. [21] proved that the cutting parameters has a direct impact on the cutting force and cutting vibration, and the cutting vibration can be controlled by changing the cutting parameters.
Chuan et al. [22] tried to monitor the wear of cutting tool by cutting vibration. Ozbekp et al. [23] used three different cutting speeds to evaluate the tool vibration amplitude under dry cutting conditions. The results showed that the faster the cutting speed, the more the vibration amplitude of the tool decreased. Prasad et al. [24] studied the relationship between tool vibration and tool wear, and found that the change of the two will accelerate the speed of tool wear. Thomas  Some scholars have also studied the influence of different machining conditions on tool wear through experiments. Liu et al. [28] found that the tool wear of ultrasonic assisted milling is less than that of conventional milling. Mou et al. [29] compared the effects of liquid nitrogen machining and dry machining on tool wear, and found that liquid nitrogen machining reduced tool side wear. Das et al. [30] studied tool wear through variance analysis, and obtained that tool wear increased with the increase of cutting parameters. Fang et al. [31] found that increasing coolant pressure can reduce tool wear. UPase and Dou [32][33]

Experiments plan
In this experimental design, D1, D2 and D3 tools are used to carry out the dry turning tests on aluminum rods with a diameter of 45mm.
In the cutting experiment, the spindle speed n is designed as four levels: 800 r / min, 1200r / min, 1600r / min and 2000r / min, and the feed speed vf is designed as three levels: 40mm / min, 80mm / min, 160mm / min, and the cutting depth has three levels :0.3mm, 0.5mm and 0.8mm. In order to prevent tests failure, the cutting experiments corresponding to each group of cutting parameters were conducted twice, and the time of each cutting test is designed as 1 minute. The specific parameters are shown in Table 1.

Test procedure
During the cutting test, the cutting temperature and three-way acceleration are collected at the same time, the test procedures are as follows: (1) Prepare the work-piece: select the aluminum bar with the diameter of 45mm after rough machining as the test work-piece; (2) Connect and check temperature measurement equipment: connect the infrared thermometer to the personal computer with a special data line, and turn on the switch of the infrared thermometer, and then keep the infrared thermometer in acquisition locked state.
Emissivity of infrared thermometer is 0.95. The temperature near the tool tip is collected and recorded by the infrared thermometer and the temperature measurement software in the computer; (3) Connect and check three-way vibration measuring equipment: Fix the three-way acceleration sensor on the lower surface of the tool handle near the tool tip through the magnetic base. The three outputs of the three-way sensor are respectively connected to the 9, (4) Carry out the cutting experiments: According to the cutting parameters set in Table 1, the cutting tests were completed one by one and at the same time the signals of the cutting temperature and three-way vibration acceleration are collected and recorded synchronously.
After all the tests were finished, switch off the power.

Time curve of cutting vibration and cutting temperature of three tools
By the time domain analysis, the average value of cutting temperature rise in each cutting test can be obtained. As a representative, Fig.3 gives the curves of cutting temperature with time for tools D1, D2 and D3 at n = 1200r / min, vf = 80 mm / min, ap = 0.3mm. By vibration signal acquisition and analysis system, the time-domain curves of three-way vibration acceleration signals can be obtained. And for the three-way vibration acceleration, its maximum value, root-mean-square and so on can be obtained through time-domain analysis. Table 2 represents the time-history curves of three-way vibration acceleration for tools D1, D2 and D3 at n = 800r / min, vf = 80 mm / min, ap = 0.3mm. During the test, we found that the cutting temperature of severely worn tool increases sharply, and the spark sputtering phenomenon occurs for many times, and the sensor transmission line is burned out, which leads to the test interruption. Therefore, this paper mainly gives the experimental data of tools D1 and D2, and only a part of the test data of severely worn tool D3 are shown in Table 3.
In each test, the diameter of the work-piece is different and the cutting speed is also different. The cutting speed v can be obtained by the following formula. Since the cutting test is continuous, the temperature of the tool is higher than the indoor environment temperature after each cutting test, so the initial temperature of the tool in each cutting test is different. Therefore, in the later temperature signal analysis ΔT ，namely the average value of the difference between the actual measured temperature at each time and the initial temperature of each test is extracted as the characteristic value of, , and RMS-a

Influence of cutting parameters on cutting temperature rise under different tool wear states
According to Table 3, first by single variable analysis method we can compare and analyze the change rules of ΔT for three kinds of tools D1, D2 and D3 under different levels of cutting parameters. Fig. 4 shows the ΔT comparison between tools D1, D2 and D3 with the changing of spindle speed, feed rate and cutting depth.  According to Fig.4 (a), with the increase of spindle speed, ΔT of tool D3 rises sharply, which is far greater than that of tools D1 and D2. While for tools D1 and D2, their temperature rise difference is not significant.
According to Fig.4 (b), with the increase of feed rate, the ΔT curve of tools D1 and D2 shows a slow upward trend, and the ΔT of tool D3 is much higher than that of tools D1 and D2. It is worth mentioning that when the feed speed of tool D3 reaches 160mm/min, the cutting temperature is too high and the sensor transmission line is burned off, resulting in the missing data of tool D3.
According to Fig.4 (c), the ΔT of the three tools increases sharply with the increase of cutting depth, and the more serious the tool wear is, the faster ΔT rises and the maximum ΔT reaches 153 ℃.
In conclusion, the temperature rise ΔT of tool D3 increases more than that of tools D1 and D2, and when the cutting depth is large, the temperature rise ΔT of tool D3 with severe wear is more obvious. and work-piece is small, which accelerates tool wear and leads to relatively severe vibration.

Influence of tool wear states on cutting vibration
While for tool D3 its cutting vibration is serious due to serious wear.

Grey correlation analysis of cutting temperature rise, cutting vibration and cutting parameters
According to the relationship between the series change rate relative to the starting point, the grey relational analysis can judge whether the relationship between series is close. The closer the change rate is, the greater the relative correlation is. Combined with the test data, the grey relational analysis can be used to find the factors which have the greatest influence on the cutting temperature rise and the cutting vibration, and analyze the correlation between the cutting temperature rise and the cutting vibration. The grey relational analysis value [34] needs to be calculated by the relative grey relational analysis theory, and the grey relational analysis related to the three tools is represented by RD1, RD2 and RD3 respectively. Firstly, the grey correlation between cutting temperature rise, cutting vibration and cutting parameters is analyzed, and then the grey correlation between cutting temperature rise and cutting vibration is analyzed.

Grey relational analysis of cutting temperature rise and cutting parameters
According to the cutting parameters v, vf, ap and the average value of temperature rise ΔT of three kinds of cutting tools in each test, the grey relational analysis between the cutting temperature rise of three kinds of cutting tools and cutting parameters is calculated, and which cutting parameters have the most significant influence on the tool temperature rise is analyzed.
The calculation results are shown in Table 4. and the lowest correlation with the cutting speed v. Therefore, the cutting depth has the greatest effect on the cutting temperature of tool D3, while the feed rate has the least effect.

Grey relational analysis of cutting vibration and cutting parameters
According to the cutting parameters and  Table 5. According to Table 5, we can see that cutting parameters have the most significant influence on the acceleration root-mean-square value.

Grey relational analysis between cutting temperature rise and cutting vibration
Based on the grey relational analysis, the correlation between the average cutting temperature rise T and RMS-a a , RMS-r a , RMS-t a of the three tools under given cutting parameters is analyzed. The corresponding calculation results are shown in Table 6. According to Table 6, (1) compare the correlation between average cutting temperature rise T and root-mean-square value of acceleration RMS a for three tools under the same cutting parameters, we can obtain RD3> RD1> RD2。The average cutting temperature rise T of severely worn tools has the highest correlation with the root-mean-square value of acceleration RMS a , so the change of cutting vibration will significantly affect the cutting temperature of severely worn tools, but the effect on moderately worn tools is small. (2) For the same tool, which direction vibration acceleration has the highest correlation with cutting temperature rise can be compared. It can be seen that for tools D2 and D3, the correlation between cutting temperature rise T and radial vibration RMS By the measured cutting temperature T, Ta and temperature measurement area, according to Eq.(1), we can calculate the cutting heat I radiated per unit time near the contact between the cutting tool and the workpiece. Therefore, the correlation between cutting heat and cutting vibration can be obtained by analyzing the correlation between cutting temperature rise and cutting vibration. The following specifically studies the coupling characteristics of cutting temperature rise and cutting vibration.

The coupling characteristics of cutting temperature rise and cutting vibration of tools with different wear states
In order to comprehensively analyze the coupling characteristics of cutting temperature rise, cutting vibration and cutting parameters, the nonlinear regression analysis based on the least square method is adopted because the grey correlation analysis method is only suitable for studying the correlation degree of two groups of data. The regression models of (1) cutting vibration on cutting temperature rise and cutting parameters and (2) the regression models of cutting temperature rise on cutting vibration and cutting parameters were established respectively to analyze the mutual effects of cutting temperature rise, cutting vibration and cutting parameters.

The fitting model of cutting temperature rise by cutting vibration and cutting parameters
In order to analyze the effect of cutting vibration and cutting parameters on cutting temperature rise, the following uses the root-mean-square value of acceleration in a certain direction of the three-way vibration RMS a and three cutting parameters as independent variables to establish a fitting model for predicting the mean value of cutting temperature rise Where T -the fitted average value of cutting temperature rise, C, x, y, z, wundetermined coefficients in fitting formula.
Take the logarithm operation respectively on both sides of Eq. (2), we have RMS ln =ln ln ln ln ln The average value of the measured cutting temperature is T , and the Logarithmic Where  According to Table 7, the correlation coefficient of D1 is higher than that of D3 and D2, and the probability P value of tool D1 correlation of 0 is less than that of tools D2 and D3, which means that the cutting vibration of tool D1 has a very good correlation with the cutting temperature rise, which can be used to predict the measured cutting temperature of the tool very well. The fitting correlation of the radial vibration of the three tools is relatively high, indicating that the cutting temperature changes of the tools will have a certain influence on the radial vibration of cutting.

The fitting model of cutting vibration by cutting temperature rise and cutting parameters
In order to analyze the effect of cutting temperature rise and cutting parameters on cutting vibration, here we use the average cutting temperature rise T and three cutting parameters as variables to establish a fitting model for predicting the root-mean-square value of cutting vibration acceleration RMS a , namely RMS f p x y z w a C v v a T Then for the three directional vibration, let where RMS-a a , RMS-r a , RMS-t a is the fitted value of the root-mean-square value of unidirectional acceleration corresponding to axial vibration, radial vibration and tangential vibration respectively.
By the same method as in Section 3.5.1, we can solve the undetermined coefficients , , , , ( =1,2,3) And the correlation coefficient between the predicted value RMS a and the measured value RMS a can be calculated as shown in Table 8.  According to Table 8, the correlation coefficients of tools D1 and D2 are relatively low, indicating that the change of cutting temperature has no significant effect on cutting vibration; for tool D3, the correlation coefficients are all greater than 0.6, and the correlation with axial vibration fitting is relatively high, indicating that the cutting temperature changes of severely worn tools will have a certain effect on the cutting axial vibration.

Conclusions
The cutting experiments of the tools with the same cutting parameters and the same workpiece size were completed for three kinds of tools with different wear states. The cutting temperature and cutting vibration near the tool tip were collected synchronously, and the mutual coupling characteristics of tool cutting heat and cutting vibration under different wear states were studied. research shows: (1) The cutting temperature of the severely worn tool has the highest correlation with the cutting parameters, and the new tool has the lowest correlation, indicating that the more severely worn tools are affected by the cutting temperature more significantly.
(2) Cutting parameters have the most significant impact on cutting vibration of severely worn tools, while moderately worn tools are the least affected.
(3) Based on the cutting vibration and cutting parameters, a fitting model of the average cutting temperature rise is established. This model can better predict the average cutting temperature rise of the tool under the given cutting parameters. Based on the cutting temperature changes and cutting parameters, a prediction model of cutting vibration is established, and the correlation calculation shows that the cutting heat of tools D1 and D2 has a weak effect on the cutting vibration.
(4) In the experimental data, there is a sharp rise and a sharp drop in the cutting temperature, and especially when the severely worn tool adopts larger cutting parameters, the cutting temperature is too high, smoke appears, and the test is forced to stop. The possible reason is that the chips did not fall off in time when the tool was cutting the workpiece, which resulted in the accumulation of chips, which caused a large change in the cutting temperature.
(5) The wear state of the three cutting tools is obtained through observation, and the division of the tool wear state is further studied in the follow-up.