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Ball screws are subjected to complex loads during machining processes, which affects the position accuracy of the feed shaft of machine tools. The lack of a reliable model for analyzing the deformation of the ball screw, coupled with the unclear relationship between the deformation of the ball screw and the position error of the feed shaft, makes it challenging to accurately predict and compensate for the position error. The objective of the present research is to investigate the correlation between the deformation of the ball screw and the position error of the feed shaft to improve the accuracy of the machine tool. First, this paper establishes a FEM model to explore the loading and deformation of the ball screw. Secondly, a method for predicting position errors based on the deformation of the ball screw is proposed. Finally, the ball screw-loading test device is used for the position error compensation experiment to verify the reliability of the prediction method. This paper serves as a reference for understanding the generation mechanism of position errors in machine tool feed systems. [ABSTRACT FROM AUTHOR]

Ball screws are surface heat-treated/hardened to improve their fatigue strength. However, the screws inevitably deform during heating. Thus, an additional straightening process is essential. Pressurization through three-point bending is typically adopted; however, determining the appropriate stroke for certain plastic deformations is challenging, mainly due to the complex mechanical properties of surface heat-treated ball screws. In this study, ball screws composed of S55C with various geometric shapes and heat-treated depths were tested with the aim of constructing a stroke model for precise straightening. Three-point bending experiments showed that the plastic deformation of the ball screws after bending was affected by the ratio of the heat-treated area to the total cross-sectional area, as well as the absolute value of the heat-treated area. Response surfaces were constructed according to the given plastic deformation and geometric shape of the ball screws to predict the desired stroke for straightening. Based on the experimental results, a computational model was built by modeling the screws with two materials. By adjusting the mechanical properties of non-heat-treated and heat-treated areas, the computational model showed similar characteristics to the experimental results. It is expected that our approach will contribute to more precise and effective straightening of partially heat-treated ball screws with complex mechanical properties. [ABSTRACT FROM AUTHOR]

The raceway profile greatly influences the performance of a ball screw. Although the traditional circular raceway profile is simple in structure, it can be a limitation to the load carrying capacity of ball screws. In this paper, a novel type of ball screw raceway profile is proposed based on geometrical close contact theory. Firstly, the second-order approximation curve of the ball is derived using the McLaughlin formula in the normal plane of the raceway helix, which serves as the basis for constructing the close raceway profile. The mathematical expression of the contact stress distribution of the close raceway is then obtained using Chebyshev polynomials. A comparison and analysis of the contact stress distribution between the close raceway and the conventional raceway is carried out. Furthermore, simulation models of ball screws with the close raceway profile are established and the contact behavior of the ball with both types of raceways is statically simulated using ANSYS software. The dynamic performance of both ball screws is compared and analyzed using ADAMS software. The analysis results show that compared with the conventional raceway ball screw, the close raceway ball screw has lower stress, strain, and friction torque under the same load conditions. These research results have significant implications for the structural optimization of ball screws. [ABSTRACT FROM AUTHOR]

The contact properties of the screw-nut pair play a decisive role in the wear rate and service life of ball screws. The difficulty of the ball contact loads directly detected has resulted in the development of many flexible contact models to predict what happens inside the ball screw during its working process. However, few contact models account for nut flexibility when axial load is applied. This article proposes a screw-nut pair contact model with the flexible screw and nut, which are modeled as elastic beams with axial deformations. The geometric relationship of the centers of the raceways and balls is used to describe the variation of the contact loads with the positions of the balls. Effects of the axial, transverse, and torsional deformations of the screw and nut and the geometric error of balls on centers of the raceways and balls are taken into account in the model. For the dynamic model of the feed system, the screw is considered a continuum rod, while the worktable and bearings are treated as lamped masses. The effect of the contact stiffness of the screw-nut pair on the axial and torsional vibration modes of the screw is investigated using a numerical simulation. Moreover, the influences of the worktable position on vibration modes of the feed systems are discussed for the screw with fixed-free and fixed–fixed support modes, respectively. The load-deformation and dynamic experiments are conducted to verify the effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Xi'an Jiaotong University is the property of Editorial Office of Journal of Xi'an Jiaotong University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The dual-drive feed system can significantly reduce the effects of nonlinear friction. However, due to the numerous heat sources in its system, the thermal responsive mechanism is still unclear. The reason restricts the realization of high-precision micro-feed. Moreover, the existing thermal simulated model of the machine tool oversimplifies the calculation process of thermal contact resistance (TCR), resulting in a significant error in simulation. Therefore, a full-state TCR calculation model is proposed, and based on the model, a high-precision thermal behavior model of the dual-drive feed system is established. Firstly, the entire deformation process of the asperities is characterized by using fractal theory, and the TCR between the joint parts of the feed system is calculated by considering the thermal resistance of air or grease. A thermal simulated model of the dual-drive feed system is developed based on the solved heat generation and the heat transfer coefficients. Then, the temperature rise characteristics of the dual-drive feed system and the responsive mechanism of thermal deformation under different working conditions are analyzed. The influence of TCR on temperature field distribution and deformation field is discussed. Finally, the experiments on temperature rise and thermal deformation are conducted on the dual-drive feed system. The results of the simulated analysis and experiments show that the accuracy of the simulation can be significantly improved by using the full-state TCR model. The error of the thermal model based on the full-state TCR is much smaller than that of the general TCR model and the without TCR. The accurate description of the TCR has an essential impact on the accuracy of the simulated model, and the obstruction of the heat flow by air or grease cannot be neglected. [ABSTRACT FROM AUTHOR]

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Lubricating grease plays an important role in the rolling screw transmission of the actuation system and is particularly concerned with the performance stability of long-term storage in aerospace applications. In this article, a batch of ball screws that were lying flat in the warehouse for about eight years were selected to extract lubricating grease from the screw raceway after being stored in situ. The oxidation performance, friction performance and rheological properties of lubricating grease were tested and compared to those of fresh grease to analyze and summarize the performance changes in lubricating grease. The transmission efficiency, friction torque, and temperature rise of ball screws without removing the original grease and those filled with fresh grease after cleaning were tested and compared. The impact of grease degradation on the transmission performance of ball screws was analyzed to provide a reference for ball screw lubrication schemes and further accelerated storage experimental design. [ABSTRACT FROM AUTHOR]

The machining accuracy of CNC machine tools is significantly affected by the thermal deformation of the feed system. The ball screw feed system is extensively used as a transmission component in precise CNC machine tools, responsible for converting rotational motion into linear motion or converting torque into repetitive axial force. This study presents a multi-physical coupling analysis model for the ball screw feed system, considering internal thermal generation, intending to reduce the influence of screw-induced thermal deformation on machining accuracy. This model utilizes the Fourier thermal conduction law and the principle of energy conservation. By performing calculations, the thermal source and thermal transfer coefficient of the ball screw feed system are determined. Moreover, the thermal characteristics of the ball screw feed system are effectively analyzed through the utilization of finite element analysis. To validate the proposed analysis model for the ball screw feed system, a dedicated test platform is designed and constructed specifically to investigate the thermal characteristics of the ball screw feed system in CNC machine tools. By selecting specific CNC machine tools as the subjects of investigation, a comprehensive study is conducted on the thermal characteristics of the ball screw feed system. The analysis entails evaluating parameters like temperature field distribution, thermal deformation, thermal stress, and thermal equilibrium state of the ball screw feed system. By comparing the simulation results from the analysis model with the experimental test results, the study yields the following findings: The maximum absolute error between the simulated and experimental temperatures at each measuring point of the feed system components is 2.4°C, with a maximum relative error of 8.7%. The maximum absolute error between the simulated and experimental temperatures at the measuring point on the lead screw is 2.0°C, with a maximum relative error of 6.8%. The thermal characteristics obtained from the steady-state thermal analysis model of the feed system exhibit a prominent level of agreement with the experimental results. The research outcomes presented in this paper provide valuable insights for the development of ball screw feed systems and offer guidance for the thermal design of machine tools. [ABSTRACT FROM AUTHOR]

When subjected to extreme loads and ultra-low cycling conditions, the primary mode of failure in a ball screw is that excessive plastic contact deformation of the raceway surface exceeds acceptable limits. Consequently, traditional fatigue life theories based on pitting fatigue are not applicable in this context. This study evaluated the load distribution within the ball screw, considering factors such as the nut position and screw length. The plastic deformation of the raceway surfaces is analyzed using Thornton's elastoplastic theory. Furthermore, this paper integrates the concepts of plastic deformation and fatigue elastic life to investigate the fatigue elastic life of ball screws under extreme conditions. To validate the proposed approach, the calculated results are compared with those from previous experimental studies, confirming its effectiveness. When the ratio of the nut position to the screw length approaches 0.7, the fatigue elastic life of the ball screw achieves its maximum. An increase in screw length, load, or raceway conformity ratio leads to a decrease in fatigue elastic life. Conversely, an increase in contact angle and ball diameter enhances the fatigue elastic life. [ABSTRACT FROM AUTHOR]

In recent years, the demand for lighter and more compact equipment has been increasing due to reduce product manufacturing time and the viewpoint of environmental load. Therefore, further lightweighting is demanded with the ball screw. The ball screw has step shape on both ends of shaft. Therefore, the lightweighting method of drilling to center of ball screw shaft makes it difficult to significantly reduce weight due to the thicker wall thickness to secure the strength of the shaft end. The lightweighting method devised is to form the step shape of the shaft end by swaging process to have a structure with a large space inside, which enables a significant weight reduction. The appearance and surface roughness of the lightweight ball screw shaft does not differ from that of conventional shaft. The weight of 0.70 kg is 0.55 times that of the conventional shaft, which enables a significant weight reduction. In the rotary bending fatigue test, the fatigue limit decreases with the ratio of wall-thickness, but the allowable torsional stress of the conventional shaft is satisfied. The axial rigidity is approximately 0.76 times that of the conventional shaft, which is smaller due to the reduction of the area moment of inertia in the hollow structure. The maximum torque is 0.02 Nm, satisfying the specified value of ±0.41 Nm. The torque fluctuation ratio is ±5 %, satisfying the best accuracy grade of ±15 %. The quietness is equivalent to number of revolutions above 2100 and improve at number of revolutions below 1000. Vibration characteristic is on the high-frequency side of resonance frequency in bending vibration, which increases the allowable rotational speed by approximately 1.2 times.

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Transmission efficiency is a pivotal indicator, providing a comprehensive view of the overall performance of a ball screw. While extensive research has predominantly focused on computing transmission efficiency across various operating conditions, the factors influencing the variability have often been overlooked. This study introduces an innovative method for computing transmission efficiency, which considers lead error, drawing on deformation coordination theory and load distribution. Multiple ball screws of varying precision grades underwent rigorous testing to quantify lead errors. Subsequently, each screw was matched with an identical set of nuts to measure the respective transmission efficiencies. Experimental results reveal a linear correlation between lead error and transmission efficiency when both lead error and uneven ball load distribution in ball screws are considered. The relative error between the calculated transmission efficiency results and experimental values for ball screws of different precision grades falls within the range of 0 % to 7.42 %, confirming the validity of the proposed model in this paper. [ABSTRACT FROM AUTHOR]

The internal contact state of the ball screw nut pair will affect its heat source strength, and the heat source will further affect the contact state until a certain equilibrium is reached. At present, the research on the time-varying characteristics of the heat source in the ball screw nut pair has not obtained the interaction law between the structure and thermal effects. To solve this problem, this paper proposes a thermoelastic coupling analysis method for the time-varying characteristics of the heat source. A thermoelastic coupling model for the heat source is established, and a contact deformation analysis method based on the plane strain model is proposed. The variation law of the contact deformation between the ball and raceway under thermal influence is studied. An experimental verification method for the thermoelastic variation law of the heat source is designed to demonstrate the compensation principle of thermal deformation on elastic deformation. The results indicate that when considering thermal effects, the contact relationship between the ball and raceway undergoes four stages from the initial unloaded state to the final stable state, namely the unloaded stage, the working load stage, the thermal load stage, and the stable stage. The strength of the ball screw nut pair heat source shows an oscillating decrease. Under specific conditions, thermal deformation has a compensating effect on contact deformation. And the thermoelastic coupling effect of the ball screw nut pair will have an impact on the preheating time of the ball screw feed system. [ABSTRACT FROM AUTHOR]

In this article, a method is proposed to effectively extract weak fault features and accurately diagnose faults in ball screws, even in the presence of strong background noise. This method combines singular value decomposition (SVD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and the 1.5-dimensional spectrum (1.5D) to process and analyze fault vibration signals. The first step involves decomposing the fault signal using the SVD algorithm. The singular values are then screened, and the part of the screen containing more noise information is extracted to complete the first denoising step. The second step involves decomposing the signal after the initial denoising process using CEEMDAN and removing some of the false components from the intrinsic mode function (IMF) components, based on the kurtosis correlation function index. The signal is then reconstructed to complete the second denoising step. Finally, the denoised signal is analyzed using Teager energy operator demodulation and 1.5D spectral analysis to extract the fault frequency and determine the location of the fault in the ball screw. This method has been compared with other denoising methods, such as wavelet packet decomposition combined with CEEMDAN or SVD combined with variational mode decomposition (VMD), and the results show that under the condition of strong background noise, the proposed method can better extract the fault frequency of ball screw. [ABSTRACT FROM AUTHOR]

Ball screws need to be applied with different preloads in most applications, however, very few studies had paid attention to preload detection, which is one of the most common failure modes of ball screws. To detect the preload of a ball screw, we propose a novel approach using vibration signals and ensemble empirical mode decomposition (EEMD) combined with linear discriminant analysis (LDA) and a support vector machine (SVM). The vibration signals under different preloads are obtained for the same ball screw through degradation experiments, and decomposed and reconstructed by EEMD. Statistical features are extracted from the reconstructed signals in the time and frequency domains. Linear discriminant analysis is used to reduce the dimensionality of the original feature space. Finally, the preload can be identified by the SVM, in which the identification accuracy can be higher than 90%. Further analysis showed that the high-frequency signal has a stronger correlation with preload degradation than the low-frequency signal, and the proposed method can be more effective than other existing methods, especially when the degradation of preload is more than 300N. [ABSTRACT FROM AUTHOR]

Metallic dampers with plastic energy dissipation are often used in the seismic protection of civil structures. However, conventional metallic dampers cannot provide adequate energy dissipation capacity due to the small displacement vibrations. This paper proposed a torsional metallic damper to improve energy dissipation performance. The proposed damper utilized ball screw devices to amplify plastic deformation, which can excessively enhance its damping capacity. First, the axial tension and pure torsion experiments were conducted to evaluate the energy dissipation capacity of solid aluminum round rods under different loads. The torsional tests of three different sections of aluminum rods were carried out to explore the optimal section of torsional energy consumption. The results showed that aluminum 1060 exhibits good plastic properties under pure torsion and the solid aluminum rod had the best energy dissipation capacity among the three test specimens. Second, the dynamic theoretical model of the proposed damper was established and verified by experiment results. The influence of the diameter and length of the aluminum rod and the lead of the ball screw on the energy dissipation performance of the damper was also analyzed. Finally, a cable-stayed bridge was numerically modeled to verify the damping performance of the proposed damper for longitudinal seismic control, which indicates that the displacement of the bridge at the girder end and tower top is significantly reduced with the proposed damper compared to that without the damper. In general, the displacement amplification mechanism of the proposed damper can increase the damping capacity, and the optimal parameters of the damper designed from one certain earthquake wave are also effective for response reduction under other waves. [ABSTRACT FROM AUTHOR]

The ball screw feed system has been an important part of precision machinery and machine tools. Its preload degradation affects machining accuracy and the issue should be first coped with per manufacturers’ suggestion. The study aims to apply the adaptive order tracking technique and other spectrum analysis schemes as well to differentiate the preload conditions of ball screws. Here varied preload conditions (4 %, 1 % preload and 12um backlash) were considered for monitoring during normal operation. The sideband energy of higher harmonics of ball pass frequency (BPF) are featured to highlight the preload degradation. The control charts together with sideband ratios were established to differentiate preload conditions and single out backlash ball screws.

Ball screws are frequently used as drive elements in the feed axes of machine tools. The failure of ball screw drives is associated with high downtimes and costs for manufacturing companies, which harm competitiveness. Data-based monitoring approaches derive the ball screw condition based on sensor data in cases where no knowledge is available to derive a physical model-based approach. An essential criterion for selecting the condition assessment method is the availability of fault data. In the literature, fault patterns are often artificially created in an experimental test bench scenario. This paper presents ball screw drive monitoring approaches for machine tool fleets based on machine learning. First, the potentials of automated machine learning for supervised anomaly detection are investigated. It is shown that the AutoML tool Auto-Sklearn achieves a higher monitoring quality compared to literature approaches. However, fault data are often not available. Therefore, unified outlier scores are applied in a semi-supervised anomaly detection mode. The unified outlier score approach outperforms threshold-based approaches commonly used in industry. The considered data set originates from a machine tool fleet used in series production in the automotive industry collected over 8 months. Within the observation period, multiple ball screw failures are observed so that sensor data about the transient phases between normal and fault conditions is available. [ABSTRACT FROM AUTHOR]

The temperature rise of a ball screw is the main factor affecting machining accuracy. The traditional methods of calculation and analysis carry out coefficient fitting of known experimental data or using the formula for a friction heat source in bearing theory. However, the screw raceway parameters are ignored in the model. The variation in friction torque with temperature is not considered in the model, so it cannot be effectively applied to engineering. In this paper, the friction heat equation of the ball screw is established theoretically with the screw raceway parameter, and the friction torque is considered with the effect of temperature. A mathematical model of steady temperature and stable time is established for the effective heat source stroke section of the screw, and the temperature rise curve of the screw is fitted. The friction is divided into Coulomb friction torque and viscous friction torque. The viscosity affects viscous friction torque at low temperatures, so the variation in friction torque should be considered when calculating the temperature rise. When a specific temperature is reached, the viscous friction torque has little effect on the overall friction torque; then the ratio of temperature rises at different rotational speeds has an exponential relationship with the ratio of those speeds. The screw stability time decreases with increasing rotational speed. Twelve groups of tests are conducted to verify the theoretical analysis using two samples, two lubricating media, and three speeds. The experimental results agree well with the theory. This proves that the approach can be applied to engineering practice. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Ball screw preload is an important factor in maintaining repeatably, rigidity, and in reducing or eliminating backlash in feed drive systems. Ball screw feeds drives are used in computer numerical control (CNC) machine tools to manufacture high-quality, precision parts. Many fault detection and condition monitoring (CM) methods have been proposed for measuring and detecting loss of preload, however, most of these methods require external sensors. Ideally, sensors, measurements, and methods integral to a CNC machine tool could be used to eliminate the extra cost and complexity of external sensors. A sensor-less method of estimating levels of preload using the mode probability of interacting multiple models (IMMs) is proposed. This method calculates a weighted sum which utilizes the mode probability of models representing different levels of preload, along with an activation function and weighing factor, to estimate the current level of preload. Unlike many other methods used for detecting levels of preload, this method requires only a system model and data collected by the CNC systems, while requiring no external sensors. The proposed method was shown to be robust and able to accurately and quickly predict preload levels under many different testing conditions. This method demonstrated a high degree of prediction accuracy (95%) which is comparable to, or better than other methods in the literature. In addition to being a novel method for preload detection, this work is also a novel implementation of IMM for fault detection, as it has not yet been applied to fault detection in feed drives.

As a linear actuator, accurate dimension measurement is crucial to the transmission reliability and interchangeability of ball screws. However, most of the current approaches are ineligible for rapid ball screw in-situ inspections due to the installation condition requirement of the production line. In this research, a machine vision method is presented to achieve highly accurate measurements of crucial parameters (the center distance and raceway arcs) in ball screws using a curvature edge detection algorithm. To capture images of the immediate area surrounding the area of interest, a telecentric lens is used. Thereafter, the curvature-based edge detection algorithm is employed to extract the contours. The measurement location on the object is automatically chosen by using a shape-matching algorithm. Additionally, random noise is suppressed by using the multiple-measurement averaging technique. Based on the results of the experiments, it is concluded that the center distance and the two raceway arcs computed absolute errors are 0.0019 mm, 0.0055 mm, and 0.0059 mm, respectively.

Lubricating grease plays an important role in the rolling screw transmission of the actuation system and is particularly concerned with the performance stability of long-term storage in aerospace applications. In this article, a batch of ball screws that were lying flat in the warehouse for about eight years were selected to extract lubricating grease from the screw raceway after being stored in situ. The oxidation performance, friction performance and rheological properties of lubricating grease were tested and compared to those of fresh grease to analyze and summarize the performance changes in lubricating grease. The transmission efficiency, friction torque, and temperature rise of ball screws without removing the original grease and those filled with fresh grease after cleaning were tested and compared. The impact of grease degradation on the transmission performance of ball screws was analyzed to provide a reference for ball screw lubrication schemes and further accelerated storage experimental design.

When subjected to extreme loads and ultra-low cycling conditions, the primary mode of failure in a ball screw is that excessive plastic contact deformation of the raceway surface exceeds acceptable limits. Consequently, traditional fatigue life theories based on pitting fatigue are not applicable in this context. This study evaluated the load distribution within the ball screw, considering factors such as the nut position and screw length. The plastic deformation of the raceway surfaces is analyzed using Thornton’s elastoplastic theory. Furthermore, this paper integrates the concepts of plastic deformation and fatigue elastic life to investigate the fatigue elastic life of ball screws under extreme conditions. To validate the proposed approach, the calculated results are compared with those from previous experimental studies, confirming its effectiveness. When the ratio of the nut position to the screw length approaches 0.7, the fatigue elastic life of the ball screw achieves its maximum. An increase in screw length, load, or raceway conformity ratio leads to a decrease in fatigue elastic life. Conversely, an increase in contact angle and ball diameter enhances the fatigue elastic life.

Ball screws and ball bearings are important mechanical elements in automobiles and machine tools due to their high mechanical transmission efficiency. However, with the spread of electric vehicles, the designs that ensure low noise and high durability are required. Currently, numerical analysis is mainly used to clarify the inner balls motion, but it is necessary to tune simulation models based on knowledge obtained from experiments in order to reproduce the behavior of experimental systems. Moreover, while there are the quantification methods of contact states and rolling motion of steel balls inside the ball screw using mathematical methods, the contact state and the ball motion are only considered in limited circumstances. Therefore, this study aims to extend mathematical methods to clarify the contact state and rolling motion of steel balls and guide grooves inside ball screws in order to contribute to noise reduction and longevity of ball screws. Four arc shapes of a Gothic arc, considering the helix orbit of steel balls and the position and dimensional errors of the steel balls in the contact plane under non-driven and non-loaded conditions of the ball screw, are given as geometric shapes, and the balance and rolling motion of steel balls during ball screw drive are calculated. Next, numerical examples are presented to examine the effects of changes in the arc shape on the revolution and rotation of steel balls and the impact on noise, wear, and lost motion inside the ball screw. Finally, the validity of the mathematical model is demonstrated by comparing the measured values with the theoretical values using a device composed of intersecting straight grooves with a crossing angle.

This study used innovative testing methods to investigate the effect of physical temperature rise on low-speed friction torque of double nut ball screws. 72 experiments were conducted using two samples and three protocols. Found the inflection point temperature and inflection point velocity. Below the inflection point temperature, the frictional torque increases with the increase of speed; Above this temperature, the frictional torque first decreases and then increases. Below this inflection point speed, the frictional torque first decreases and then increases; Above the inflection point velocity, the friction torque decreases with increasing temperature. Based on the Strebeck theory, the variation of friction coefficient with temperature was studied; When it is below the inflection point speed, it fluctuates greatly with the increase of temperature, but when it is above the inflection point speed, the fluctuation is small and steadily decreases with the increase of temperature. In addition, based on the theoretical models of Coulomb friction torque and viscous friction torque, the results of this model are in good agreement with the measurement results above the inflection point speed, indicating the correctness of the theory and providing good theoretical guidance for engineering designers.

Ball screw has the advantages of high precision, high efficiency, high stiffness and smooth operation, so it has been widely used in automotive industry, semiconductor, aerospace, medical and other fields. It is significant to research the lubrication theory of ball screw and its influence on friction torque to improve its life. In the complex working conditions of ball screw, the elastohydrodynamic lubrication performance is greatly influenced by the thermal effect, and the lubricating oil will no longer be Newtonian fluid under the coupling action of temperature and pressure. Therefore, a Non-Newtonian thermal elastohydrodynamic lubrication model for ball screw is established and a novel modeling method of friction torque for ball screw is proposed, and the correction of the novel method is verified by experiments. [ABSTRACT FROM AUTHOR]

Regarding the problem of reduced remaining useful life (RUL) due to wear of the ball screw in the feed system of CNC (computer numerical control) machine tools, a prediction method based on constructing the degradation feature vector of the signal data and the improved gray-wolf optimization with bidirectional long short-term memory (IGWO-BiLSTM) neural network regression model is proposed. Firstly, a time-domain analysis and the complete ensemble empirical mode decomposition with adaptive noise analysis (CEEMDAN) were carried out based on the collected life cycle signal data of a ball screw. The time-domain feature vector and the energy feature vector of each IMF (intrinsic mode function) component after CEEMDAN decomposition were constructed. The Pearson correlation coefficient was used to filter feature vectors and construct the multivariate feature vector. Secondly, this paper improves the traditional gray wolf optimization algorithm, adds a search strategy based on dimension learning, and combines the improved algorithm with the BiLSTM model, based on the IGWO-BiLSTM theory. A regression model between feature vectors and the remaining life of a ball-screw system was established. Finally, the prediction model was established according to the proposed method and compared with the other five neural network models: LSTM, BiLSTM, BO-LSTM (Bayesian optimization of LSTM), BO-BiLSTM, and IGWO-LSTM. The results indicate that this method has high accuracy and good generalization ability for predicting the remaining life of a ball-screw system. [ABSTRACT FROM AUTHOR]

A ball screw (BS) is a key functional component for precision machining equipment, medical instruments, and intelligent manufacturing production lines. The accuracy reliability of a ball screw plays a key role in the functioning of all such equipment. Since the operating conditions have time-dependent characteristics, the non-constant operating conditions affect the BS accuracy decay. In this paper, the numerical modeling and analysis of the BS accuracy decay are considered under non-constant operating conditions. The BS accuracy reliability under single and multiple non-constant operating conditions is investigated. The experimental findings on accuracy decay under non-constant operating conditions validate the proposed analysis. The average relative error of accuracy decay between the theoretical and the experimental findings is estimated at 10% (in the range of 10.15%–12.66%). The error is evaluated under the three different amplitudes operating conditions, including AL (non-constant axial load), FR (non-constant feed rate), and AL plus FR. The results show that the accuracy decay prediction model successfully predicts the BS accuracy reliability under non-constant operating conditions. [ABSTRACT FROM AUTHOR]

An analysis model of the contact characteristics of the double-nut preloaded ball screw which can consider the combined action of the axial load and the overturning moment is established, the model can consider non-uniform load distribution, and the validity of the model is verified by experiments. Based on this model, the influence of the combined action of axial load and overturning moment on the average value and distribution fluctuation value of the contact angle of the ball screw, the number of unloaded balls, the distribution fluctuation value of the contact load, and the static contact stiffness and other contact parameters are systematically analyzed, and get the following conclusions: The contact parameters of the ball screw are mainly affected by the axial load and the contact state between the ball and the raceway. The gradually increasing axial load basically reduces the influence of the overturning moment on the contact parameters of the ball screw. There is a critical value of the load in the axial direction within the range of the action value of the preload load. Only when the critical value is above the critical value, the contact parameters will change regularly with the changes in the axial stiffness and overturning moment. However, different critical values for the regular variation of contact parameters with axial load and overturning moment vary. [ABSTRACT FROM AUTHOR]

Due to the processing mechanism difference, the raceway topography of the screw processed by whirling milling and by the traditional method is very different, which has a great impact on the load distribution. Based on the homogeneous coordinate transformation, a novel model is established to calculate the raceway surface topography of the whirling milling ball screw. The validity of the raceway model is proved by comparing the result with Liu's theoretical and experimental results. Then, the influence of the machining parameters on the raceway profile is studied. On this basis, the load distribution of the whirling milling ball screw under different axial forces and processing parameters is studied by considering the raceway topography as raceway error. The findings indicate that the tool ring's rotational speed, the workpiece's rotational speed, the number of tools, and eccentricity all affect the raceway form. The load distribution of whirling milling ball screws is highly dependent on the raceway's surface topography. [ABSTRACT FROM AUTHOR]

Due to extreme operating conditions such as high-speed and heavy loads, ball screws are prone to damages, that affect the accuracy and operational safety of the mechanical equipment. As strong background noise and weak fault characteristics, it is difficult to capture the inherent fault state only depending on the time-domain or frequency-domain information from the vibration signal. In this paper, a fault diagnosis method for the ball screw based on continuous wavelet transform (CWT) and two-dimensional convolutional neural network (2DCNN) is proposed. The noise-reducing vibration signal is obtained via CWT. The time-frequency graph of the noise reduction signal can more comprehensively reflect the fault information of the ball screw. The time-frequency graph is used as the input to train and test the 2DCNN. Finally, diagnosis results of different types of faults reveal that the proposed CWT-2DCNN fault diagnosis method can achieve an average recognition rate of 99.67%. Compared with one-dimensional convolutional neural network (1DCNN) and traditional BP neural network, the proposed method has fast network convergence and high recognition accuracy. Time-frequency graphs of the noise-reduced signal used as fault features for classification can effectively avoid the problem of uncertainty due to the manual extraction of features. The proposed method has high application potential in the field of ball screw pair fault diagnosis. [ABSTRACT FROM AUTHOR]

In the field of precision machining, temperature fluctuation tends to cause the most significant machining errors. In particular, heat, which is generated in the nut of the ball screw feed system during movement, can deform the screw shaft significantly. In order to calculate and evaluate the thermal deformation of the ball screw shaft, the rate of the heat transfer from the nut to the screw shaft must be known. This rate can be calculated by subtracting the heat transfer rate to the nut raceway from the heat generation rate of the nut. Hence, it is necessary to calculate the heat flux from the nut to the nut raceway. This paper introduces a novel method to calculate the heat flux from the nut to the nut raceway. The new approach also enables calculations for different operating conditions. Furthermore, an experimental setup is established to measure the temperature increase, from 0 to 180 s after the nut starts moving, for various operating conditions. It is then theoretically shown that the 0–180 s temperature increase/heat flux curves for the nut are "universal", i.e., the curve remains unchanged for the different operating conditions. Subsequently, a thermal model using the finite element method (FEM) is developed to simulate the nut temperature increase over time, which is then compared with the experimental data. As a result, it becomes possible to determine the heat flux from the nut to the nut raceway and calculate the 0–180 s temperature increase/heat flux curve ( Δ T ˜ 0 ~ 180 s , Training   Data ) for the training group. Finally, the heat flux from the nut to the nut raceway is calculated for ten different operating conditions in the test group using the 0–180 s temperature increase/heat flux curve of the training group ( Δ T ˜ 0 ~ 180 s , Training   Data ). The corresponding temperature curves are then calculated by inputting the values of the heat fluxes into the FEM model. The highest root mean square error (RMSE) between the calculated and experimentally measured temperature increase was 0.16 °C for Test 7 (the error was 10.7%). This result indicates that the new method is valid and feasible for calculating the heat flux from a ball screw nut to the nut raceway. [ABSTRACT FROM AUTHOR]

Modern electromechanical actuators for the rotary control diaphragms of cogeneration steam turbines are reviewed. A kinematic diagram of an electromechanical actuator with an unpowered spring return (failsafe) is proposed. The results of studying the following main components of an actuator are reported: spiral spring, screw gear, electric motor. Adynamic model was developed and used to examine the emergency (failsafe) operation mode of the actuator. The necessity of using a damper to prevent plastic strains is justified. [ABSTRACT FROM AUTHOR]

In order to study the influence of internal heat source of ball screw feed transmission system on the thermal error of ball screw, the theoretical modeling and experimental research are carried out on the temperature field and temperature rise characteristics of ball screw in this paper. Firstly, on the basis of analyzing heat generation mechanism and heat transfer of ball screw, the positive temperature field of ideal heat transfer of heat source and the negative temperature field caused by heat transfer are derived. In addition, the mathematical model of dynamic temperature field of ball screw feed system about time and position is established according to the superposition principle of temperature field, and the temperature field and thermal error of x-axis ball screw in horizontal machining center are measured. Secondly based on the experimental temperature field data, a complete finite element model of the temperature field of the ball screw feeding system is constructed, and temperature at any point of the system and the undetermined coefficient of the numerical model of temperature field under this working condition are determined by the finite element model. Finally, the thermal error distribution of the ball screw is calculated by the numerical model, the theoretical and experimental error distributions are compared, and the correctness of the theoretical model of the temperature field under this working condition is verified. [ABSTRACT FROM AUTHOR]

The ball screw (BS) has become an indispensable key functional component in many fields, such as CNC machine tools, precision transmission system, and special service requirements. Its accuracy reliability is a key performance in many application fields. There is a phenomenon of mixed slip-roll motion during the BS operation; however, both non-constant working conditions and mixed sliding-rolling motion mode affect its accuracy decay. In this paper, the modeling method of accuracy decay for mixed sliding-rolling motion behavior is established under non-constant operating conditions. The accuracy reliability of the BS is analyzed under single non-constant operation condition or multiple non-constant operating conditions, and the accuracy decay is predicted though modeling method proposed. In addition, the experimental analysis of the BS accuracy degradation is carried out under three different amplitudes of AL (non-constant axial load), FR (non-constant feed rate), and AL + FR combination conditions. The average value of the accuracy loss relative error (5.90 ~ 8.50%) between theoretical model and experimental test results is smaller than that (11.18 ~ 12.66%) under pure sliding motion. It shows that the accuracy decay analysis model established is beneficial to predict the BS accuracy reliability. [ABSTRACT FROM AUTHOR]

As an important precision transmission functional component in industrial fields such as large mechanical equipment, high-speed CNC machining center, and aerospace, the service life of the ball screw are directly related to the life of high-end equipment. Fatigue failure is the main failure mode of the ball screw in the transmission application where the transmission accuracy is not high. Therefore, the fatigue life of the ball screw is studied from the perspective of fatigue. The load distribution form of the double-nut ball screw under axial load is analyzed. Based on the ball load distribution, a mixed lubrication model of the ball screw considering non-Newtonian effect of lubricant is established, and a fatigue life prediction method of the ball screw based on maximum secondary surface stress is proposed. The lubrication performance of the ball screw under maximum contact load is compared with that under equal load distribution, and the effects of ball load distribution, curvature ratio, and temperature rise on fatigue life are analyzed. Two kinds of ball screw including BT GD8020 and NSK DFD8020 are used for running test of fatigue life, and the fatigue life calculation method based on the maximum secondary surface stress is verified. The hardness distribution of the transition zone between ball and raceway is analyzed, and the fatigue failure modes of two ball screws are explored. [ABSTRACT FROM AUTHOR]

Ball screw feed systems serve as the feed components of machine tools, and its dynamic characteristics directly affect the machining quality of workpieces and reliability of ball screws. In this paper, the lateral equivalent dynamic model of ball screw feed systems is established considering the bending vibration of the ball screw, nut location, and joints based on the Euler–Bernoulli beam theory. Subsequently, the dynamic parameters of joints are identified according to the measured dynamic stiffness using the particle swarm optimization (PSO) algorithm with the determined initial range of stiffness and damping. The robustness of the dynamic model is verified by experiments conducted at different nut locations. In addition, the nonlinear dynamic model is established and the effects of cutting force, bearing clearance, and nut motion on dynamic characteristics are investigated. The numerical results indicate that bearing clearance mainly affects the equilibrium position of worktable vibration, while the cutting force at different rotational and moving speeds of the nut mainly affects the vibration mode of the worktable, but the vibration mode is always a quasi-periodic motion. The established dynamic model and numerical analysis results provide a useful understanding of the dynamic characteristics of ball screw feed systems. [ABSTRACT FROM AUTHOR]

Ball screw has become a key functional component commonly used in actuators of high-end machine tools because of its high transmission efficiency, low environmental impact, and strong universality of working conditions. For the high-precision ball screw, the proper and constant preload is the premise to maintain the transmission accuracy and reliable dynamic characteristics of the ball screw. The direct measurement of the preload is difficult to be achieved. Usually, the preload of the ball screw is indirectly determined by the friction torque of the ball screw under no-load condition. In previous studies, the influence of lubrication on friction torque of the ball screw was not considered, and the influence of operating conditions on performance of lubricant was ignored, and the influence of contact elastic hysteresis effect and the sliding friction effect was not considered, which seriously affected the modeling accuracy of friction torque for the ball screw. Therefore, on the basis of considering the contact elastic hysteresis friction and the sliding friction of the ball screw in the paper, a calculation model of friction torque for the ball screw based on the coupling of the ball load distribution and the thermal elastohydrodynamic lubrication is proposed. The mechanism of different friction terms on the friction torque of the ball screw is analyzed, and the coupling relationship among preload, rotational speed, and friction torque is established. The experimental results show that the proposed method, which the ball load distribution, the thermal elastohydrodynamic lubrication, the elastic hysteresis, and the sliding friction are comprehensively considered, has a good reference significance for improving the internal preload and predicting the precision degradation of the ball screw. [ABSTRACT FROM AUTHOR]

The thermal behaviors of the ball screw feed system significantly affect the machining accuracy of the machine tool, which is widely valued by users and manufacturers. In the current ball screws thermal error models, the moving heat source at nuts is simplified to a fixed heat source to simplify the calculation, which can decrease the model's prediction accuracy. A novel thermal error modeling method for the ball screw feed system is proposed by this paper based on the FEM. In the proposed method, the moving heat source at the nut is loaded into the model by changing the grid distribution at different time steps. Meanwhile, a series of thermal experiments are carried out to collect the thermodynamic data with the machine tool's feed drive system operating at a different speed. And then the multi-objective optimization method is introduced to obtain the heat generated by the nuts and the convection coefficient between the air and the screw. The experimental results show that the thermal error of the ball screw feed system is different when the feed system runs in different intervals, even if the temperature rise at measuring points is the same. In the final, experiments under different conditions are carried out, and the proposed model is accurate enough to predict the thermal error of the ball screw feed system. [ABSTRACT FROM AUTHOR]

The correct evaluation of the curvatures of ball screw grooves allows the accurate design of the constructive parameters of this mechanism and enhancing its performance. The formulation commonly used in the literature, however, refers to ball bearing geometry, ignoring the shape of the section's profile and the helix angle. In this paper, the exact formulae for calculating the principal curvature radii of the screw shaft and the nut grooves are analytically derived and presented. These equations, obtained through a rigorous differential geometry approach, consider the helix angle and a gothic arch profile. An approximated formulation is proposed simplifying the exact solution under the assumption of a circular groove profile. These new simple formulae accurately reproduce the exact curvature radii values with a mean relative error of approximatively 0.51% and 0.40%, respectively, for the screw shaft and nut grooves, against the value of more than 50% obtained by using the literature formulae for common off-the-shelf ball screws, especially those with high helix angles. Furthermore, they allow a computational time saving of 98%, making them suitable for being incorporated in high-fidelity dynamic models of ball. Finally, two MATLAB functions are provided to easily evaluate the complex curvature exact solution. [ABSTRACT FROM AUTHOR]

The development of accurate dynamic stiffness models is a key aspect in the design process of ball screws. However, variations in the nut center of mass position can affect the dynamic stiffness, which makes it difficult to develop a stiffness model. To address this issue, this paper considers the variation of the nut center of mass position and the approach between the ball screw beam unit stiffness matrix and the nut interface element stiffness matrix. Then, based on Timoshenko beam theory and a concentrated mass parameter method, a dynamic stiffness model for a high-speed ball screw pair considering the variation of the nut center of mass position is developed. Finally, the feasibility of the dynamic stiffness matrix of the high-speed ball screw pairs is verified through the inherent frequencies obtained from experiments and simulations of the ball screw pair in the free state and compared with the classical finite element method to verify the importance of this method and to provide a theoretical basis for its dynamic design and structural optimisation. [ABSTRACT FROM AUTHOR]

To increase the dynamics of ball screw drives, a nonlinear position controller based on sliding-mode control is presented along with its parameterization to ensure robust stability. The controller is validated experimentally on a ball screw axis and shown to increase the controller bandwidth from 8 Hz to 15.9 Hz in comparison to proportional (P) position control with feedforward. The mean absolute tracking error under high performance cutting forces is reduced by 24%. Under variation of the model parameters by 20%, the controller shows excellent robust performance with only 2.7% degradation of the tracking error. [ABSTRACT FROM AUTHOR]

In this article, a method is proposed to effectively extract weak fault features and accurately diagnose faults in ball screws, even in the presence of strong background noise. This method combines singular value decomposition (SVD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and the 1.5-dimensional spectrum (1.5D) to process and analyze fault vibration signals. The first step involves decomposing the fault signal using the SVD algorithm. The singular values are then screened, and the part of the screen containing more noise information is extracted to complete the first denoising step. The second step involves decomposing the signal after the initial denoising process using CEEMDAN and removing some of the false components from the intrinsic mode function (IMF) components, based on the kurtosis correlation function index. The signal is then reconstructed to complete the second denoising step. Finally, the denoised signal is analyzed using Teager energy operator demodulation and 1.5D spectral analysis to extract the fault frequency and determine the location of the fault in the ball screw. This method has been compared with other denoising methods, such as wavelet packet decomposition combined with CEEMDAN or SVD combined with variational mode decomposition (VMD), and the results show that under the condition of strong background noise, the proposed method can better extract the fault frequency of ball screw.

Thermal error always exists in a machine tool and accounts for a large part of the total error in the machine. Thermal displacement in X-axis on a CNC lathe is controlled based on a rapid heating system. Positive Temperature Coefficient (PTC) heating plates are installed on the X-axis of the machine. A control temperature system is constructed for rapid heating which further helps the thermal displacement to quickly reach stability. The system then continuously maintains stable compensation of the thermal error. The presented rapid heating technique is simpler than the compensation of machine thermal errors by interference in the numerical control system. Results show that the steady state of the thermal displacement in the X-axis can be acquired in a shorter time. In addition, almost all thermal errors in constant and varying working conditions could be significantly reduced, by above 80% and 60%, respectively, compared to those without using the rapid heating. Therefore, the proposed method has a high potential for application on the CNC lathe machine for improving its precision.

The transmission efficiency is an aggregative indicator that directly reflects the overall performance of the ball screw. While most researches focus on calculating transmission efficiency under different working conditions, few of them investigate the influencing factors that lead to the transmission efficiency change. To this end, this paper proposed a new analysis method to acquire the changing transmission efficiency with running revolution based on wear volume calculation considering lubrication. The fractal theory is introduced to describe the surface roughness, through which the modified expression of the wear volume between the balls and raceway is proposed. By submitting the wear volume into the transmission efficiency analysis model, the change of the transmission efficiency is obtained. From the experimental results, two obvious stages are shown: the rising stage with the increase of the wear volume and a steady stage as the initial preload vanishes. For higher transmission efficiency for the preloaded ball screw of the same type, the ratio of 0.75, which compares the initial preload to the external load, has some certain reference for the practical application. [ABSTRACT FROM AUTHOR]