## 1 Introduction  
Mechanical vibrations are present in many machine tools, affecting the cutting tool and the surface finish of the machined part. For this reason, the study of vibration behavior in machine tools has been a topic of interest. Pioneers in this topic, [PERSON] and [PERSON], [PERSON] and [PERSON] [1, 2], analyzed the vibrations in a machining process in the frequency domain. [PERSON] and [PERSON] [1] proposed a method to predict chattering in a machining process by modeling the system as a system of finite differences equations and analyzing stability via Fourier analysis. [PERSON] and [PERSON] [2] presented a method to predict stability by modeling the system as a transfer function. Subsequently, many authors proposed different perspectives to analyze machining processes. More recently, [PERSON] and [PERSON] [3] studied the influence of vibrations in micromachining using microchemical processes. [PERSON] and [PERSON] [4] presented a review of the state of the art about chattering. The dynamics of the cutting process and the effect in vibrations have also been investigated [5, 6, 7]. The reduction of vibrations has also received attention. Different methods have been used for this purpose. The classic passive method adds masses and damping. The semi-actives used dynamic adapting dampers and the ones used active control through the use of fast actuators to compensate for vibrations. [PERSON] et al. [8] proposed a control system for peripheral machining operations. The relative vibration between the tool and the machined part is controlled with piezoelectric actuators that adjust the part with two degrees of freedom. Similarly, [PERSON] et al. [9] proposed a mechatronic platform to actively control the vibrations of a micromachined tool of high precision using piezoelectric actuators. The frequency of the vibrations is a relevant parameter to understand the behavior of the tool. [PERSON] et al. [10] analyzed the frequency of the vibrations during a cutting process modeling the tool as an elastic component. The vibrations at the tip of the cutting tool had an influence on the surface finish of the part; therefore, they reported that the excitation of the second vibrational flexional mode dissipated energy reducing vibrations in the system. A piezoelectric was used to excite the mode. [PERSON] and [PERSON] [11] used filters to compensate for the commands of the axes to avoid vibrations. They tested experimentally their algorithm in a table of two axes. Finally, in this effort to control the vibrations of the tool, [PERSON] et al. [12], proposed a method to improve the performance of a machine tool controlling adaptive structural vibrations of the machine. The control system was implemented in a vertical milling machine. Deep learning techniques have also been investigated for application in monitoring and maintaining machinery that produces vibrations [13; 14]. It has been of interest in the community to develop techniques that are computationally inexpensive to be implemented in equipment health monitoring by collecting data and applying algorithms in real-time [15]. The use of deep learning has great potential due to the access to data handling and acquisition, as well as the ability to process complex algorithms with reasonable computational cost in equipment maintenance. However, these methods require training and data input, limiting their use and application to situations where large data are available. In design and concept testing validation stages, methods that do not require training may be more suitable. A particular machine sensible to mechanical vibrations is the so-called CNC _router_. The equipment RoutakitHD [16], Pro60120 CNC [17], X-Carve [18], Zenbot CNC [19] are commercially available and present similar geometries. These equipment are widely used for different tasks such as cutting and engraving. Understanding the mechanical vibrations in this equipment may result in enhancing the quality of the operation and increasing the lifetime of the machine. [PERSON] et al.