# Diagnosis of the Hollow Ball Screw Preload Classification Using Machine Learning
## 3 Experiment Set-Up and Results  
### Experiment Set-Up  
An experimental platform was designed and assembled, as displayed in Figures 1 and 2. The apparatus was fabricated according to the industrial standard for a tapping machine. It had a 2-kW and 3000-rpm servo motor (Delta Electronics, Taiwan); an oil-cooling system of 3 \(\psi\) and 220 V, with an accuracy of \(\pm\)2 \({}^{\circ}\)C; a mechanical structure accuracy of 5 \(\upmu\)m, with a repeated accuracy of 2 \(\upmu\)m; a maximum positioning speed of 48 m/min, with an acceleration of 1\(\times\)\(g\) when the motor speed was 3000 rpm; and a sampling frequency of 5.12 kHz for data acquisition from the acceleration sensor.  
The table was set for a traveling distance of 270 mm with reciprocating movement by varying the motor speed from 300 rpm to 900 rpm, with or without oil-cooling circulation and 20-kg payload conditions. The table was driven by a servomotor, followed by a coupler and a single-nut hollow ball screw (Hiwin R-36-16(K3)-FSC-C1-527-855-0.006-H) with various ball-nut preload and pretension levels. The standard ball-screw preload force was determined to be 4% of its maximum dynamic force of 3750 kgf. The maximum static force of the ball-screw preload was 9542 kgf. In this study, the preload percentage of the maximum dynamic force was divided into three categories: 2%, 4%, and 6%. Oversized balls were used in the single-nut ball screw to provide various preload statuses. The speed, acceleration, and S curve were controlled with a CNC controller (LNC-M310i-V) with feedback from a Heidenha(r) encoder strip.  
A preload adjustable ball-screw mechanism was constructed by the authors of [17] to examine the formula of drag torque and preload of ball screws. Parameters such as the helix angle, contact angle, friction coefficient, ball diameter, sliding direction, and normal contact force of the ball-nut contact were taken into consideration. A new correlation between the preload and no-load drag torque was obtained. The literature includes limited discussions regarding a direct preload sensing mechanism or prognostic diagnosis for a ball screw nut. In general, for a CNC feeding table, the specification of the ball screw preload is selected when the positioning accuracy is determined a priori. The growing  
Figure 1: (**a**) Picture of the in-house single-axis platform with a servo motor and linear scale positioning sensor, and (**b**) picture of the acceleration sensor attached to the ball nut (right).  
Figure 2: Oil-cooling circulating system around the hollow ball screw in Figure 1.  
demand for machining learning in preload loss diagnosis increased the reliability of ball screws used in CNC machining equipment. In this study, the 4% preload was treated as the standard preload for typical precision motion in industrial applications. Therefore, a 2% preload indicates a preload loss situation, increased mechanical backlash, increased pitted ball trace, low stiffness, and oscillatory position errors. Moreover, the pretension and oil-cooling system on the hollow ball screw were used to achieve thermal rigidity compensation for improving the positioning accuracy. Changes in the aforementioned conditions can be considered as various feature classifications.