# Investigation on Sensorless Estimating Method and Characteristics of Friction for Ball Screw System
###### Abstract  
In this study, a novel sensorless method is developed to estimate the friction in a ball screw system using asynchronous experimental data for a worktable position (WP) and the servo motor torque current (SMTC), which is collected by the FOCAS library functions from a FANUC digital control system. The corresponding time stamps are retrieved by a high-resolution performance counter in Windows. The fluctuations in friction over the whole travel distance of the worktable (WTDOW) are analyzed using a piecewise polynomial fitting algorithm to extract the instantaneous average friction value (IAFV) and the friction fluctuating signal (FFS). The IAFVs can describe the effect of the WP and the pitch errors of the shaft on the friction. The FFT results of the FFS show that the friction depends on the rolling tool, the pitch of the shaft and the refeeding of the balls in the ball screw and linear ball rail guides. The experimental results show that the estimated friction can capture the characteristic spectra of the FFS. The effects of the feed velocity and direction, the effects of the WP on the IAFV, and the frequencies and amplitudes of the significant FFT components are discussed. The nonuniform pitch errors of the shaft impact the repeatability of the IAFVs at a given WP. The variations in the mean value of the IAFVs with the feed velocity for tests at a fixed WP show nonconventional Stribeck behavior. These results also demonstrate that the friction force varies with the WP, which is not captured by Stribeck characteristics. This study provides an effective method to evaluate the performance of a ball screw system and to predict the friction in that system without the use of sensors. f 2020 10 3122 202  
There are two important friction behaviors in a ball screw system: (1) elastic deformation and an increase in the friction of the pre-sliding regime and (2) plastic deformation and an increase in static friction [4]. In the pre-sliding regime, frictional forces dominate the hysteretic nonlocal memory of the displacement [5]. These forces act together with the stick-slip in the contact between the drive and the balls to generate an asymmetric path for the driving force [6]. In addition, basic parameters, such as the contact angle, the ball diameter, and the preload, are nonlinearly related to the ball screw friction [7]. The LuGre model describes experimentally observed friction behaviors, which include the Stribeck effect, spring-like characteristics for stiction and a varying breakaway forces [8]. [PERSON] et al. [9] adopted various friction models, ranging from the Coulomb model to the generalized Maxwell-slip (GMS) model, to describe friction compensation. The Coulomb model and the Stribeck effect were found to be effective for describing motion with a high displacement, whereas the GMS model was effective for describing friction behavior in the pre-sliding regime. The complexity of the structures of these different friction models increases from the Coulomb model to the GMS model. A single experiment can be used to identify a model for friction behavior. However, the selection of the excitation signal is a critical component of this identification process for a single experiment [9]. [PERSON] and [PERSON] observed periodic friction for which the fast Fourier transform (FFT) results included the 1-, 2-, 3- and 4-component amplitudes of the position frequency [10]. [PERSON] and [PERSON] observed that the instantaneous average friction values (IAFVs) varied with the worktable position (WP) [11]. Manufacturing tolerances and incorrect alignment of the linear guides and the ball screw can cause preloading over the useful travel of the screw to differ from the specified value [12]. As a result, the friction varies over the useful travel of a ball screw.