## 2 Transient Temperature Field Model of Wear Band on the Flank of End Mills
### Temperature Rise Model of the Wear Band Affected by Heat Source in the RCZ  
During the peripheral milling process, the heat source in the RCZ contacts with the rake face of end mills, then the heat generated by the heat source in the RCZ is transmitted to wear land on the flank of end mills through the inside of the end mills, so the transient temperature field of wear land on the flank of end mills will inevitably be affected by the heat source in the RCZ. According to [PERSON]'s dynamic heat source theory [31], the temperature field model of the heat source in the RCZ is established. The contact surface between the chip and the rake face formed by the peripheral milling process is a parallelogram; a rectangular heat source in the RCZ is considered to simplify the problem. [PERSON] et al. [32] considered that the rake angle effect on rake face temperature could be ignored. However, [PERSON] et al. [33] found out by finite element simulation that the chip plastic deformation decreased with the increase of rake angle, which ultimately reduced the temperature rise of rake face (Figure 4). Therefore, the rake angle should be considered for establishing the heat source model in the RCZ. The heat source in the RCZ is composed of both native and mirror heat sources, and the heat intensity of the two heat sources are relatively similar (Figure 5). The temperature rise \(\Delta T\)_fank-II_ (\(x^{\prime}\), 0, \(z^{\prime}\)) at any point \(P_{II}\) (\(x^{\prime}\), 0, \(z^{\prime}\)) in the plane \(X^{\prime}\), 0, \(Z^{\prime}\) can be calculated by Equations (12), (13) and (14). \[\Delta T_{II}(x^{\prime},0,z^{\prime})=\frac{q_{II}(\theta,x^{\prime})B_{II- rake}(\theta)}{2\pi\lambda_{t}}\int_{0}^{l_{c}(\theta)}dx^{\prime}_{i-2}\int_{- \frac{\pi^{\prime}}{2}}^{\frac{\pi^{\prime}}{2}}\frac{1}{R_{i-2}}dy^{\prime}_ {i-2} \tag{12}\]  
\[\Delta T_{II}(x^{\prime},0,z^{\prime})=\frac{q_{II}(\theta,x^{\prime})B_{II- rake}(\theta)}{2\pi\lambda_{t}}\int_{l_{c}}^{l_{c}(\theta)[1+\cos(2\gamma_{n})]} \frac{1}{\cos(2\gamma_{n})}dx^{\prime}_{i-2^{\prime}}\int_{-\frac{\pi^{\prime }}{2}}^{\frac{\pi^{\prime}}{2}}\frac{n_{r}}{R_{i-2^{\prime}}}dy^{\prime}_{i-2} \tag{13}\]  
\[\Delta T_{fank-II}(x^{\prime},0,z^{\prime})=\Delta T_{II}(x^{\prime},0,z^{ \prime})+\Delta T_{II^{\prime}}(x^{\prime},0,z^{\prime}) \tag{14}\]  
From Equation (12) to (14), \(\Delta T_{II}\) (\(x^{\prime}\), 0, \(z^{\prime}\)) and \(\Delta T_{II^{\prime}}\) (\(x^{\prime}\), 0, \(z^{\prime}\)) are the temperature rise caused by native heat source and mirror heat source in the RCZ, respectively. The distance from any point \(P_{II}\)  
Figure 4: Effect of rake angle on tool temperature field [33]. (\(x^{\prime}\), 0, \(z^{\prime}\)) along \(X^{\prime}\) direction to the points of both native and mirror heat sources in the RCZ can be measured by Equation (15). \[\left\{ \begin{array}{l}R_{i-2}=\sqrt{\left(x^{\prime}-x^{\prime}_{i-2}\right)^ {2}+\left(y^{\prime}_{i-2}\right)^{2}+\left(z^{\prime}\right)^{2}}\\ R_{i-2^{\prime}}=\sqrt{\left(x^{\prime}-x^{\prime}_{i-2}\right)^{2}+\left(y^{ \prime}_{i-2}\right)^{2}+\left(z^{\prime}-\frac{x^{\prime}_{i-2}-l_{c}(\theta )}{\cos(2)_{n}}\right)^{2}}\end{array} \right. \tag{15}\]  
Under dry cutting conditions and with a new tool for machining, the flank is generally considered as adiabatic. Therefore, \(n_{r}=1\), when wear land on the flank of end mills contacts with the machined surface, it is calculated as \(0<\)\(n_{r}<1\). The value obtained in this study was 0.5, for which the simulation result of the transient temperature field model of wear land on the flank of end mills is closest to the experimental results. In the process of peripheral milling, the tool chip contact area of cuttings may exhibit time-varying characteristics, leading to the time-varying characteristics of heat source strength in the second deformation zone. In addition, the non-uniform friction distribution between tool and chip may contribute to the non-uniformity of heat intensity in the RCZ.