## 1 Introduction
The vibration induced in a machining process can be modeled as a function of cutting parameters via ANN analysis. As presented in the study by [PERSON] et al. [34], individual vibration components (ax, ay, and az) were well predicted based on the ANN model for a specified cutting depth, feed rate, and cutting speed in the milling process for the AZ91D alloy. Further, the prediction accuracy based on a multilayered perception model was better than that of the radial basis function. The accurate modeling of vibration components allows optimizing the cutting conditions to enhance machining stability. [PERSON] et al. [35] considered the influence of machining vibration on surface quality when establishing the surface prediction model, wherein the input variables include cutting parameters, tooling condition, and tool vibration were assessed in the turning process. Such models have higher prediction accuracies compared to those of models determined by only cutting parameters. To include the effects of cutting forces and tool vibrations in a surface roughness prediction model, [PERSON] et al. [36] proposed a nested ANN composed of two networks: An enclosed network that uses the cutting parameters to predict the cutting force and tool vibration, and an output network that takes all outputs of the first network and the cutting parameters as inputs to predict surface roughness. According to the analysis results, the nested-ANN model using three cutting parameters as inputs shows superior prediction accuracy than any other regression and ANN models that use the cutting parameter and tool vibration as inputs. These investigations clearly illustrate the significant influences of the machining state such as the cutting forces and tool vibrations on the machined surface roughness; these effects can be adequately introduced in the roughness prediction models by acquiring sensory data from machining or through an estimation algorithm with cutting parameters as inputs. From previous studies, it is clear that factors affecting machined surface quality are multifaceted, including cutting parameters, tooling conditions, workpiece material, and machining state. The effect of each factor and the interactions between them on surface quality and machining vibration are found to be inconsistent because of the scope of machining conditions defined in different researches [20; 21; 22; 23]. Further, various factors used as input variables in the modeling of surface roughness enable the model demonstrating different prediction accuracies; this limits the application in practical machining. The results obtained may work well in the design space of experiments; however, there are constraints in the ranges of the cutting parameters, which limit the application of the specific models in the machining process with different cutting conditions for the desired precision or productivity [37]. This study was aimed to model the surface roughness of the machined part based on cutting parameters with the effect of machining vibration. As the occurrence of chatter is a common factor affecting productivity and surface quality, selecting an optimum chatter-free cutting parameter is prerequisite to ensure machining performance [38]. Considering the effect of chatter on the machining process, the cutting parameters from rough to finish machining were selected within the stable regions defined by the machining stability lobes of the milling tool. Then, machining vibration and surface roughness of the machined parts were collected from milling experiments conducted on the aluminum alloy under various cutting conditions. Multivariable linear regression analysis was employed to establish the mathematical models for predicting the surface roughness and machining vibration. In addition, the surface roughness was modeled as a function of cutting parameters and machining vibration using a multilayer perception neural network with a back-propagation algorithm.