# Cutting Force Estimation Using Milling Spindle Vibration-Based Machine Learning
## 1 Introduction  
Replacing tools at the optimal time during machining processes is critical for maintaining productivity and ensuring consistent product quality. In most industrial settings, tool replacement timing is traditionally determined through visual inspections conducted by experienced operators. However, as the availability of skilled operators declines and production automation becomes increasingly widespread, the demand for systems capable of accurately estimating tool replacement timing has grown significantly. Consequently, tool condition monitoring (TCM) systems have become indispensable, as real-time monitoring of tool wear and damage is essential to establish appropriate replacement intervals [1, 2, 3]. Current TCM systems utilize various sensors to assess tool conditions based on physical signals, including cutting force, motor current, acoustic emission (AE), and vibration. Among these, cutting force is a key indicator directly reflecting tool wear and damage, making it central to TCM. Dynamometers are commonly employed to measure cutting force, offering highly accurate data [4, 5, 6, 7]. However, their structural limitation of typicallybeing installed beneath the workpiece complicates practical usage, while their high cost further restricts applicability in industrial settings. Current sensors monitor tool conditions by detecting increases in motor load current, which are correlated with rising cutting forces as tool wear progresses [8; 9; 10; 11]. The sensor is relatively inexpensive and supports real-time monitoring. However, if the motor-spindle connection involves multiple stages, such as through a reducer, or if a relatively small tool is used compared to the motor's specifications, the motor current changes may become less sensitive. Consequently, accurately estimating the cutting force using this method can become challenging or even infeasible. Acoustic emission (AE) sensors detect high-frequency sound signals generated during material cutting, which are closely associated with cutting forces and are effective for identifying tool wear and damage. However, AE monitoring typically relies on processed signals, such as root mean square (RMS) values, rather than raw data, due to the high sampling rates required. This reliance can obscure subtle or rapid changes in tool condition. As a result, the sensitivity of the monitoring system may be reduced [12; 13; 14; 15]. Vibration sensors provide a cost-effective alternative by measuring the interaction between the tool and workpiece through vibration signals, which are then used to indirectly estimate tool conditions. These sensors are easy to install and affordable, but their performance is affected by external factors such as machine structure, tool geometry, workpiece material, and environmental noise. Advanced signal processing techniques are often required to isolate relevant signals from background noise [16; 17; 18]. As previously mentioned, many studies have been conducted to develop deep learning-based monitoring approaches to overcome the limitations of sensor-based TCM. Since tool condition monitoring exhibits time-dependent characteristics, research has increasingly focused on utilizing recurrent neural networks (RNNs) and long short-term memory (LSTM) networks [19; 20; 21; 22]. Various studies have employed current and vibration data to predict surface roughness and classify tool conditions, demonstrating the effectiveness of deep learning models in machining process monitoring [23]. However, existing tool condition classification and surface roughness prediction models face challenges in real-time implementation, highlighting the need for more efficient learning models capable of real-time monitoring. In sensor-based TCM systems, key requirements include a cost-effective approach and the ability to accurately estimate cutting forces in real time. To address these challenges, this study proposes a method to estimate cutting forces in real time using a cost-efficient vibration sensor, which is based on the machine learning using an LSTM.