# Diagnosis of the Hollow Ball Screw Preload Classification Using Machine Learning
## 1 Introduction  
Precision computer numerical control (CNC) machines are widely used in modern industries for mass production. Recently, many strategies were proposed for the diagnosis of machine status, providing operators with information critical for the extension of the machine's useful lifespan. The authors of [1] established a system to acquire and analyze vibration signals corresponding to various machine-tool states. The calculated results were saved in a database, and a training model was established using Bayesian classification. The ball screws of CNC machines are widely used in linear actuators, which are used in various types of machinery and equipment. Preloading is an effective method of eliminating backlash and increasing the stiffness of the ball screw for precision motion, which maximizes the productive efficiency [2]. Preload loss leads to a low natural frequency, low stiffness, oscillatory positioning, and a possibility of rapid downtime in the manufacturing process. For a double-nut ball-screw preload, tuning the preload values is time-consuming and requires increased downtime. Thus, the ball-screw-nut preload must be protected during machine operation. The fault diagnosis of acquired signals requires performing a conventional Fourier transform or discrete wavelet transform in the frequency and time domains. The authors of [3] developed a new approach to signal analysis that avoids generating nonphysical results from complex trace formalism [4], defining the concepts of instantaneous amplitude, phase, and frequency such that the original signal could beexpressed in terms of a Fourier-like expansion. This process and the definition of the instantaneous frequency were effective for monocomponent signals. However, in many real applications, signals have multiple components and are often corrupted by noise. Recently, the Hilbert-Huang transform (HHT) was applied to diagnose faults and damage in electrical machines, rolling bearings, and tools in mechanical engineering [5; 6]. The loss of the ball-screw preload decreases the bandwidth of the frequency response spectrum, and reduces the positioning accuracy. Accordingly, industrial mass-production applications benefit from a lifetime prediction of the ball-screw preload. However, few studies focus on this topic. The HHT involves the time and frequency analysis of engineering applications. However, the complexity of a ball screw with a preload in operation is highly nonlinear and nonstationary. Traditional entropy measurements quantify only the regularity (predictability) of a time series on a single scale. However, no straightforward correlation exists between the regularity and complexity. In our previous study [7], multiscale entropy (MSE) analysis [8] was used to measure the complexity of a ball-nut preload based on the finite length of motor current signals. However, the selective feature of the motor current for the MSE calculation was based on the intrinsic mode function of the empirical mode decomposition technique. Feature extraction for on-line diagnosis is difficult. The MSE computational tool [8] was successfully applied to sound and laser Doppler vibrometer datasets for air-turbine dental handpieces [9]. However, the sound acquired through a microphone is corrupted in a CNC shop-floor environment. Moreover, the cost of the vibration data acquired using the laser Doppler vibrometer is expensive. In this study, the support vector machine (SVM) [10; 11; 12; 13; 14; 15] algorithm was used to classify the complexity of the finite-length time series of the vibration signals, servo-motor speed, servo-motor current signals, and linear scale counts. The vibration signal was acquired by attaching an accelerometer to the ball nut. SVM analysis with a low classification rate could be used to determine the preload status of the ball screws.