In the orthogonal cutting, the shear surface and the blade-scuff interface are used as boundaries to determine the temperature distribution of the chips. Because the temperature distribution on the rake face has a decisive influence on the wear of the tool, the working state of the tool, and the friction between the blades and the scrap, sufficient attention and research are needed. So far, there are mainly two different analysis methods for the temperature distribution on the shear plane. The first method focuses on the average temperature on the shear plane, and the other method is an analytical method represented by Hahn and Weiner. Hahn believes that cutting can be regarded as the process of moving a planar heat source on an infinite body. This planar heat source is at a certain angle to the direction of cutting motion, and the temperature distribution on it can directly replace the temperature distribution on the shear surface. It can be seen that the Hahn method does not consider the different directions of movement of the workpiece and the chip. Weiner largely avoided this simplification that caused the analysis model to be inconsistent with the actual situation. However, he still assumed that the vertical cutting surface of the chip flowed out, and the temperature at the intersection of the shear surface and the surface to be machined was room temperature. In order to avoid the above-mentioned unreasonable simplification and estimate the error caused by the assumption, the author proposes a new simplified boundary condition, analyzes the temperature distribution on the shear plane according to the Weiner model, and compares the temperature distribution under different shear planes. The analysis results agree with the actual cutting temperature.

Fig. 1 The temperature distribution on the shear plane of the chip model 1 with orthogonal continuous chip formation Fig. 1 shows the cutting model of orthogonal continuous chip. The workpiece moves at a speed v relative to the cutting edge and is perpendicular to it. The cutting thickness hD, the chip thickness hch, and the chip flow rate at the rake face are vch. From the continuity of the material, Vt = vchhch, and the swarf process is represented by all the swarf speeds. This determines the plastic deformation of the workpiece material at a certain flow stress value. Since the heat source for the cutting motion is a uniform planar heat source, it can be assumed that the knife-swarf interface friction heat generation is also a uniform planar heat source. According to the above cutting process model, the heat transfer in the direction of motion can be further set as the control equation of the cutting temperature on the workpiece is
(1) where: a—heat dissipation coefficient x—position coordinate y in the direction of cutting speed—positional coordinate in the direction perpendicular to the cutting speed; its initial and boundary conditions are
0<y<8 (2a)
y = tanfx (2b) where: r - material density l - thermal conductivity n - geometric constants (1-cosb) / cosb
Limq = 0 (2c) The uniform heat flux q is set on the shear plane AB, and the boundary conditions are given considering the thermal equilibrium equation (2b) on the element. Introducing a new parameter z = y - tanfx and performing mathematical processing can yield a solution to equation (1) that satisfies boundary condition equation (2). Similarly, the temperature on the shear plane is at z=0.
(3) Where: Erf x - Error function erf cx - The residual function 1-erf x of the error function is applied when solving the above problem. Laplacian Transformation and Its Inverse Transformation of Variables . Weiner's analysis only considers the state where the chips flow out in a vertical direction from the shear plane. This study considers the more general situation. Therefore, it can be said that the model built on this basis is the broadening and refinement of the Weiner model.

Figure 2 Two-dimensional heat transfer shear plane temperature distribution
Figure 3 Effect of geometric settings Figure 2 shows the effect of temperature distribution and cutting speed on the shear plane. The graph in Fig. 2 shows the situation of a quasi-stable or saturated state where the temperature increases rapidly along the shear plane. It can also be seen that as the cutting speed increases, the time taken to reach saturation decreases. Therefore, when the cutting speed reaches a certain value, it is reasonable to assume that the shear plane temperature is a constant value in the Rapier model. From Figure 2 it can also be seen that higher cutting speeds result in lower stable temperatures; as the cutting speed increases, the steady temperature decreases. This is due to the fact that the heat conduction is dominant during cutting, and the higher the cutting speed, the greater the proportion of the shear surface heat loss to the chip. Figure 3 shows the results of the slope heat source calculated according to Equation (3) and the approximate solution to the case where the chip flow direction is reduced to be perpendicular to the shear plane (b=fg=0 in Figure 1, n== in Equation (3). 0). By comparing the two, it can be seen that the two temperature profiles are relatively close. When using the above assumptions, the maximum deviation between the two is not greater than 3.5%. It should be noted that the assumption that the chips flow out perpendicularly to the shear plane is that the shear angle is equal to the rake angle of the tool, ie f = g. This means that the shear angle is constant and does not have to take into account changes in cutting. Although this is not practical, the above numerical analysis shows that this assumption is reasonable in terms of shear plane temperature. Here, a highly sensitive infrared thermometer was used to measure the change in chip temperature when turning 45 steel. In this measurement system, the sensor receives infrared light and converts it into an electrical signal, which is then linearized to obtain the corresponding temperature value. Three components of the cutting force were measured in each test and monitored to ensure that the measured temperature was measured under steady state cutting. Of course, tests are performed under orthogonal cutting conditions. Point A is the intersection of the chip-workpiece-shear surface. In Fig. 2, the temperature near point A under various cutting speeds is greater than 170°C. Compared with the room temperature of 25°C, the test curve is inconsistent with the boundary conditions determined by equation (2). We use this test as the basis for the opponent program ( 2a) Amend it.
Where: qamh - room temperature qA - measurement temperature of point A p - the cutting temperature to calculate the cutting temperature so that the average shear plane temperature is equal to or equal to the test value of the adjustment of the same steps suitable for equation (3) The shear surface temperature distribution analysis, using the boundary conditional formula (2a') instead of formula (2a), gives a more complex expression about the people.
(3') Where: The correction of the boundary conditions will have an effect on the shear plane temperature analysis. It can be seen that the results from equation (3') increase faster along the shear plane than the modified Weiner model. Although the formula (2a') is more acceptable and a suitable shear plane temperature can be obtained, the measurement temperature at the point A is still a problem. Numerical analysis shows that when qA changes within 60°C; the temperature change at point B is not more than 10°C. The reasonable boundary condition given by formula (2a') can obviously improve the original model. 2 The chip temperature is distributed in the cutting process. The metal in the cutting zone is transformed into chips in the first deformation zone at the free surface of the workpiece from the tip to the chip. The workpiece speed v is replaced by the chip speed vch. The characteristics of metal heat transfer in the cutting zone are similar in the first deformation zone. The control equation given in the above section is suitable for analysis of chip temperature distribution. With the new h-x Cartesian coordinate system and cutting process parameters, the control equation for the cutting temperature change has the following form:
(4) where the thermal parameter R=rcvchhch/l, and the corresponding boundary condition is
(5a) (5b) (5c) where: Dqe - the temperature increase applied to the chip, assumes that the heat on the chip is uniform and BC is a planar heat source. The shear plane temperature qB obtained in the upper section is used here as a boundary condition. Notice that we have taken two different coordinate systems and we should establish a connection between them. Consider point P, which can be expressed in (x,y) or (h,x) respectively; here are
(6) Then x=(hch-x)cosf/cosb for qB explicit in the (h,x) coordinate system, substituting equation (6) into equation (3) to obtain a refined Weiner model, substituting equation (3) The revised model proposed by the author. In order to solve equations (4) and (5), substitutions and variations are obtained.
(7) Change the score to get
(8) It satisfies the heat equations, boundary conditions, and equations (5b) and (5c). If formula (5a) is satisfied, then formula (5a) and formula (8) must be completely equal, ie,
Qe(r,x)=qd (9) From the viewpoint of positive cutting, the solution of the coefficient Am in equation (9) does not exist. We can resort to numerical methods. Note that the increase in m exp(-m2p2tanb/Rhch) decreases rapidly, and partial and alternative qe(h,a) are feasible. If the m + 1 term is used as the partial sum, the coefficients A0, A1, ..., Am can be substituted into the equation (9) by the known qB values ​​of m+1 points. In this way, the chip temperature distribution is
(10) After the coefficient Am is obtained, the chip temperature can be regarded as an extension of the Weiner model. This is done so that qB is applied to equation (3') and the results are differentiated to obtain the corrected shear plane temperature analysis model proposed by the author. Figure 4 shows the chip temperature distribution corresponding to the shear plane temperature at the lowest cutting speed in Figure 2. It can be seen that the maximum temperature is somewhere away from the high point on the knife-chip interface, and the temperature gradient near the knife-chip interface is large; this is an overall trend, mainly due to the strong friction between the knife and the chip.

(a) Model
(b) Chip temperature analysis Fig. 4 Chip temperature distribution model and chip temperature distribution Under special conditions (b = 0), qs can be assumed to be constant. Equation (9) can be simplified to
(11) At this time, Fu's cosine series, the corresponding coefficient is
(12) (13) Substituting equation (13) into equation (12), and using the new parameter g = lc/hch, due to the action of the cutting edge, the temperature of the chip edge is lower than the temperature of the other parts. The temperature of the middle of the chip is directly measured by infrared temperature measurement, and the predicted temperature at x=hch can be obtained. These results are shown in FIG. 5 . The experimental values ​​and predicted values ​​at the cutting speeds of 84 m/min and 120 m/min are shown in Fig. 5 with the elbow.

Fig. 5 Distribution of cutting temperature
Fig. 6 The temperature of the cutter-chip interface temperature distribution is predicted to be larger than the test value with the constant temperature of the cut surface; the improved Weiner result has a larger deviation at the free surface A of the workpiece's chip interface. The more accurate estimation of the temperature distribution by the author is based on equation (2a') and the result is slightly larger than the actual value. The reason for the error is to assume that the free surface of the chip bottom is insulated. For the cutting situation shown in Fig. 5, the trends of both are consistent. All of these are not suitable for prompting the use of equation (2a) as a boundary condition to obtain a shear plane temperature distribution. The precision of the chip temperature distribution model proposed in this paper is sufficient. The above test results show that the model proposed in this study is more appropriate than the other theoretical analysis methods for the chip temperature distribution. From this model, an accurate temperature distribution of the tool-chip interface can be obtained. The temperature predictions at the three cutting speeds shown in FIG. 5 are given in FIG. 6 . From point B, the cutting temperature rises monotonically until the chips leave the rake face, and the cutting temperature increases as the cutting speed increases. However, at higher cutting speeds, the temperature near point B is lower. This phenomenon is explained and explained in the section discussing the influence of the change of cutting speed on heat transfer. 3 Conclusions The following conclusions have been drawn from the above analysis. In the previous model, it was assumed that the free surface of all workpieces was room temperature, and the test data had a large gap. The given model was more practical. In order to simplify the calculation, the flow of the chip is approximately perpendicular to the shear plane. In actual cutting, it is feasible to analyze the temperature distribution of the shear plane. At a higher cutting speed, the cutting temperature along the shear-facing edge quickly reaches a stable or saturated state. In this case, Rapier proposes that the simplified model with a constant shear plane temperature is reasonable. The directly measured experimental results show that using the calculation model proposed by the author, the metal cutting temperature distribution can be relatively satisfactory.

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