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spindle. However, in practice, these axes deviate slightly in position. This deviation causes a cyclical variation in transmission energy between these two optical fibers, causing a measurement error. Temperature is obtained using a two-color pyrometer by taking the output ratio of the signals from two photocells. Since the variations in incident energy to each photocell due to the deviation are equivalent, their effects are canceled in the process of taking the output ratio of the pyrometers. Thus, the two-color pyrometer can compensate for the variation in transmission energy caused by the deviation between the two fibers in the fiber coupler. 3 Temperature Analysis 3.1 Analysis Model. In end milling, the cutting tool is subjected to cyclical heating and cooling. Stephenson et al. [3] investigated the general nature of the tool temperature distribution in interrupted cutting. A cutting tool was modeled as a semi-infinite rectangular corner, x > =0, y >= 0, and z > =0, heated by a heat flux, as shown in Fig. 4. According to Stephenson et al., if the thermal properties of the tool are independent of the temperature and heat radiation is neglected, the governing equation and boundary condition for this problem are where T is the temperature, k is the thermal conductivity, cv is the thermal diffusivity, Lx and /y are the dimensions of the heat source, and Q(x, y,t) is the source heat flux. All other surfaces can be treated as insulated, and the initial temperature throughout the body at infinity can be assumed to be zero. This problem was solved using Green's function. The Green's function Oc for the temperature in a semi-infinite corner due to an instantaneous pomt source at time t at the surface point x=xi,, y = yi,, a e mutually perpendicular instantaneous plane sources in semi-infinite half-spaces [3]. The result is (4) is a parameter with units of length. The solution for the temperature field T(x,y,z,t) in the corner is [3](5) Stephenson et al. calculated the average temperature over the heat source for several simpler heat source distributions in interrupted Cutting of constant depth of cut and obtained many valuable results. In end milling, new surface is generated as each tooth cuts away an arc-shaped segment. Thus, the undeformed chip thickness is not constant but varies with tool rotation, and the tool-chip contact length on the rake face varies with time. Therefore, the heat source dimension in the x-axis direction is a function of cutting time. In this study, this effect is taken into account. In up milling, at the beginning of the cutting, the depth of cut is 0; it increases with the progress of the cutting. In contrast, in down milling, the depth of cut is greatest at the beginning of the cutting, and it becomes o at the end. Figure 5 is a schematic illustration of the variation of heat source area in up milling and down milling. In up milling, the instantaneous undeformed chip thickness he at rotational angle 庐 in Fig. 5 is approximately given by where f is the feed per tooth, and 函 is the angle at the circumference from the cutting start point to the cutting point. Thus, the variation in tool-chip contact length /x(with the progress of cutting is approximately given by where is the angle at the circumference from the cutting start point to the cutting end point, 'r is the time elapsed in one cutting, it is the cutting time, and c is the ratio of tool-chip contact length Fig. 5 Variation of heat source area: (a) up milling and (b) down milling and undeformed chip thickness. Similarly, in down milling, the variation of the tool-chip contact length as cutting
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progresses is given by Figure 6 shows the variation in tool-chip contact length /x(r) given by Eqs. (7) and (8) in up milling and down milling, respectively. In the governing equation and boundary condition, constant thermal_properties were assumed in order to obtain solutions. Jen et al. [5] performed numerical analysis to study the transient cutting tool temperatures with temperature-dependent thermal properties. They showed that for a high-speed steel tool, the effect of nonlinearities due to temperature-dependent thermal properties on the tool temperature is very strong, but for tungsten carbide, the effect is not so significant due to much less sensitivity of the thermal properties to the temperature under typical cutting conditions. Thus, the assumption of constant thermal properties may yield satisfactory results in the case of a tungsten carbide tool. 3.2 Calculation Example. Figure 7 shows the calculated temperature history in up and down milling. The temperature is that at x=0.6 mm, y=1.3 mm, and z=0.1 mm, which is the point of temperature measurement, and at elapsed time t=740 ms after cutting starts. The heat conductivity k and thermal diffusivity a of the cutting tool composed of sintered carbide type K are 67 W/mK and 2.2 X l0-5 m2/s, respectively. The ratio c of the tool-chip contact length and the undeformed chip thickness is given as 4. The spindle speed is 1300 rpm, the cutting speed is 214 m/min, the cutting length is 35.9 mm, the cutting time is 10.1 ms, and the noncutting time is 36.1 ms. The heat flux qc per unit area on the rake face, which is determined by the measured cutting force, is 2.6 X l09 W/m2 and is uniformly distributed in the tool-chip contact area. The partition ratio of the non-cutting Fig. 7 Calculated temperature history (z=0.1 mm): (a) up milling and (b) down milling heat flux flowing into the tool along the chip-tool contact region on the rake face is determined experimentally by equating the calculated peak temperature to the measured peak temperature at a depth z=0.1 mm. The ratios are given as 12.2% and 12.1% in up and down milling, respectively. In up milling, the temperature begins to increase a few milliseconds after cutting begins, as shown in the figure. It increases as the cutting progresses, reaching a maximum just after the cutting. During the noncutting period, the temperature decreases gradually; the next cutting starts before it reaches room temperature. In down milling, the temperature increases immediately after cutting begins, and the rate of increase is higher than that in up milling. The temperature reaches a maximum during cutting and begins to decrease before the cutting ends. Since the temperature begins to decrease during the cutting period, the thermal impact of cooling on the cutting tool can be estimated to be smaller in down milling than in up milling. 4 Experimental Results 4.1 Calibration of Pyrometer. The pyrometer is calibrated by sighting on a radiating target, which is heated and kept at a constant temperature. The target is made of the same material as the cutting tool in the experiment. The target temperature is monitored by a thermocouple embedded in it. Figure 8 shows the results of the calibration. Figure 8(a) shows the relationship between the output voltage of the InAs/lnSb pyrometers and the target temperature, and Fig. 8(b) shows the relationship between the output ratio of the pyrometers
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