# Study on Surface Roughness of Sidewall When Micro-Milling LF21 Waveguide Slits
## 1 Introduction  
LF21 has high electrical conductivity, plasticity, etch-resistant ability and solderability, which explains why it is widely used in slotted waveguide antennae [1]. However, its low strength and hardness mean that it has poor cutting properties and is prone to plastic flow under cutting forces, resulting in machinery defects such as material extrusion and build-up [2]. The surface roughness of the sidewall in waveguide slits has a significant influence on the electrical performance of the waveguide antenna. To explain, Ra is required to be less than 0.8 \(\upmu\)m [3]. Generally, micro-milling is used to manufacture high-precision parts with dimensions between 100 \(\upmu\)m and 10 mm [4]. In the previous study, we achieved 0.2 \(\upmu\)m Ra for the sidewall when micro-milling Inconel 718 [5], which strongly confirmed that micro-milling was a potential effective processing technology for the manufacturing of LF21 waveguide slits. However, the finished surface roughness is difficult to control due to rapid tool wear and the complex, dynamic characteristics of micro-milling. More importantly, elastic recovery, cutting-edge radius effects, tool runout, switching between plough and shear states with minimum cutting thickness, etc., can lead to the output of complex cutting forces and cutting heat, which ultimately have a direct impact on the surface roughness of sidewalls [6; 7; 8]. This necessitates further analysis of the potential relationship between surface roughness and cutting parameters in the micro-milling of LF21 waveguide slits, although this would be challenging in light of the complicated physics and mechanics involved in the milling process and the material response. One way to reduce the attention to physics and mechanics in machining is to take an end-to-end approach, i.e., to investigate statistical learning models on cutting parameters and surface roughness. [PERSON] et al. [9] found that the spindle speed and feed per toothsignificantly affected surface roughness when micro-end-milling brass; [PERSON] et al. [10] also found that the effects of spindle speed and feed per tooth on the surface roughness of the processed sidewall were more obvious than the axial depth of cut during the micro-end-milling of SUS 304 and Al 6061. Many scholars have developed mathematical-statistical models on micro-milling surface roughness. [PERSON] et al. [11] developed a surface roughness prediction model on the micro-milling of Inconel 718 using the response surface method in 2018 and indicated that the parameters impacting surface roughness, from high to low, were cutting depth, feed rate and spindle speed. [PERSON] [12] proposed a prediction model on surface roughness based on the dual response surface method during the micro-milling of hard aluminum alloys. [PERSON] et al. [13] established a prediction model on surface roughness based on the micro-milling of a C45W steel groove bottom, using the multiple regression method. Artificial neural networks (ANNs) lie at the frontier of complex, nonlinear science and artificial intelligence science. They establish complex and nonlinear relationships among variable parameters, which are too difficult to achieve by conventional models. [PERSON] et al. [14] presented a prediction of surface roughness using back-propagation, feed-forward neural network (BPNN), the Levenberg-Marquardt algorithm (LMA), the group method of data handling (GMDH) and multiple regression analysis (MRA) in the high-speed micro-end-milling of titanium alloy (grade 5). It has been shown that the prediction accuracy of a neural network is higher than the accuracy of the other methods. Furthermore, [PERSON] et al. [15] proposed that using the adaptive neuro-fuzzy inference system (ANFIS) methodology to establish a prediction model on surface roughness was reasonable, since it could generate prediction accuracy that reached 99.96% by using the general bell membership function. [PERSON] [16] used an ANN to establish an optimal model on surface roughness during micro-end-milling.