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A ball screw is a critical drive component capable of converting force into motion, with widespread applications in the high-precision mechanisms of various machine tools. The degradation in precision attributed to ball screw wear significantly impacts machine tool accuracy. Current ball screw wear models lack consideration for the ramifications of radial forces and ball size errors.This study introduces a pioneering approach by formulating a coupled model that integrates screw wear, ball wear, and preload degradation. Through rigorous analysis, we discern the multifaceted influences of axial force, radial force, preload adjustments, and ball size precision on the positional accuracy of ball screws.By elucidating the intricate interplay among these parameters, this study offers crucial theoretical insights into the selection and optimization of ball screws, thereby fostering advancements in machine tool design and performance.

The performance of the milling head is affected by the machining and assembly process of the parts. The key to improving machining accuracy and reliability of swing angle milling head is to establish the precision prediction model. Therefore, a precision prediction model of swing angle milling head under the influence of multiple errors’ sources is built. The transmission and accumulation of machining and assembly errors along the assembly sequence path for the transmission system are carried out. All essential components on the assembly sequence path are considered. In addition, the secondary impact of the bearing seat hole is also taken into account. The source of the gear assembly errors is explained. The predicted range of transmission error based on the coupling relationship between assembly errors and transmission error is obtained. A precision experiment is carried out, and the result is within the predicted range. This research demonstrates that the errors' coupling relationship considered in this paper does exist and has an effect on transmission error, which provides a new idea for calculating transmission error of other gear systems.

The two main failure modes of harmonic reducers are wear and contact friction between the tooth profile of the circular spline (CS) and the flexible spline (FS). The sliding speed of the meshing point is a key factor affecting friction and wear processes of the CS and FS and should therefore be accurately determined. Herein, envelope theory is used to deduce the FS trajectory and the envelope track is divided into two segments according to whether or not the meshing point is outside the top circle of the CS. The velocity of the meshing point in the second meshing stage is essentially the vector sum of the FS velocity in three directions. When the CS is fixed, the relative sliding velocity is the instantaneous velocity of the FS along the tangential direction of the enveloped tooth profile. To verify the proposed model, the finite element method (FEM) and laser sensor experiments were performed and a relationship between the angle of rotation of the wave generator (WG) and the velocity of the FS was established. The results show that the sliding speed is sensitive to the radial displacement coefficient and has a linear relationship with the rotational speed of the WG.

The internal feedback hydrostatic rotary table is a precision support device, and its performance relies heavily on the oil pad. However, uncertainties in the manufacturing process are often overlooked during the stiffness optimization, affecting the reliability of the optimized results. Accordingly, this paper aims to analyze the influence of structural parameters on the stiffness performance of the internal feedback hydrostatic rotary table and to perform reliability optimization considering the uncertainties. Initially, a theoretical computational model of internal feedback hydrostatic rotary table, accounting for the oil leakage effect, is proposed. The model's accuracy is validated through comparative simulation calculations, and based on this model, the load-bearing performance of the table is further analyzed. Subsequently, focusing on the structural characteristics of the oil pad, a reliability optimization model that considers manufacturing uncertainties is proposed. To improve the optimization efficiency, a Levenberg–Marquardt Backpropagation (LM-BP) neural network is introduced as a surrogate model for theoretical calculations. The oil pad is optimized through a particle swarm optimization algorithm. Ultimately, the optimal structural size parameters of the oil pad are obtained, achieving maximal stiffness under a high level of reliability. Both the stiffness performance and the reliability level of the rotary table are substantially enhanced. The results indicate that the proposed method can significantly improve performance and reliability in practical applications.

Ball screw mechanisms (BSMs) are used as accuracy transmission components in a wide range of industries and are characterized by their high accuracy. More specifically, the positioning accuracy of BSM has a significant effect on the accuracy of machine tool. Based on the macro-micro multiscale method, an exponential prediction model for the BSM positioning accuracy was developed considering time-varying working conditions (load and rotational speed) and feed modes. Since the accuracy degradation is mainly caused by wear, a microscopic approach was proposed to describe the positioning accuracy retention and the microscopic wear process was investigated. The sliding contact of the asperities between the ball and raceway was analyzed, and the microscopic wear behavior of the asperities was determined. Considering the time-varying working conditions, the BSM positioning accuracy characteristics were obtained under the normal feed mode by conducting suitable tests. The exponential wear model used the wear index to describe the wear status based on the positioning accuracy measurement. The accuracy loss value and the prediction index of positioning accuracy were determined based on an exponential model, and the effective lifetime of the BSM was predicted. Finally, the exponential prediction model was used in negative/positive skew feed distribution, and the effective lifetime determined.

The internal feedback hydrostatic bearing features a distinctive structural design, playing a pivotal role in high-precision machine tools. Its performance significantly influences the improvement of machining accuracy and stiffness. In this study, the working principle of the internal feedback closed hydrostatic bearing is described, the equivalent liquid resistance model of oil circuit considering internal flow effect is established, an analysis method for evaluating the support performance of the internal feedback hydrostatic bearing is proposed, flow rate correction methods are proposed, and the influence of load-carrying capacity and flow rate due to inlet pressure, oil film thickness, and the size of the restrictor is discussed. The accuracy of the method is verified by simulation, and insights for the future development of hydrostatic bearings are provided.

Contact stiffness and backlash in the harmonic drive significantly impact a robot's positioning accuracy and vibration characteristics. The height of the harmonic drive tooth pair is typically less than 1 mm, making the measurement and modeling of backlash and contact stiffness inherently complex. This paper proposes a contact stiffness and backlash model by establishing a correlation between fractal parameters and tooth contact load. To obtain the fractal roughness parameters of the real machined tooth surface, a combination of a noncontact optical profiler and the RMS method is employed. Subsequently, the study explores the influence of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash. The results demonstrate the substantial impact of surface topography parameters and contact force on contact stiffness and backlash. Specifically, an increase in the fractal dimension correlates with a reduction in gear backlash and contact stiffness. Conversely, the fractal roughness parameter exhibits the opposite effect. Notably, an increase in contact force enhances contact stiffness.

Geometric errors in gantry milling machines with long-span beams and large travel can seriously degrade workpiece accuracy. Sensitivity analysis and compensation of geometric errors with coupling and fluctuation can significantly improve the machining performance of machine tools. An accuracy enhancement approach for gantry milling machines is proposed in this paper. Firstly, the geometry error analytic fluctuation eigenfunctions are established by using the high-order Fourier series fitting. Secondly, a non-linear generalized correlation analysis model is proposed to identify the crucial errors that significantly affect the machining accuracy. Thirdly, the motion commands compensated for geometric errors are calculated. Specifically, compared to traditional inverse kinematics, the proposed error compensation process is simple and suitable for most machine tools with orthogonal linear axes. Finally, comparative cutting experiments are performed. The accuracy of the test piece is improved by approximately 34.7 % with error compensation. The effectiveness of the proposed method is validated.

The motion accuracy of hydrostatic turntable is the key in improving the machining accuracy of heavy-duty machine tool. However, the motion accuracy of hydrostatic turntable depends not only on the offset load but also on the rotating speed of the turntable as well as the profile errors of the guide rails. In this paper, a simulation model is developed to analyze the effect of guide rail profile errors on the motion accuracy of hydrostatic turntable. The reaction forces of preload thrust bearing and hydrostatic circular oil pads are obtained based on the Reynolds equation of the lubricant film. The motion equations of hydrostatic turntable are derived in which the profile errors of two guide rails are considered. The results show that the motion accuracy of hydrostatic turntable can be affected by wavelength, amplitude of profile errors and speed, and offset load of turntable. Finally, the motion accuracy of heavy-duty hydrostatic turntable used in XCKA28105 type turning and milling composite machine tool is obtained by using the presented method. Comparing with the experimental results, the proposed model can be used to predict the machining accuracy caused by the profile errors of guide rails for any heavy-duty hydrostatic turntable.

The stability of the tribological properties of polymer coatings is vital to ensure their long term use. The superlubricity of the poly(vinylphosphonic acid) (PVPA)-modified Ti6Al4V/polytetrafluoroethylene (PTFE) interface can be obtained when lubricated by phosphate-buffered saline (PBS, pH = 7.2), but not when lubricated by deionized water and ethanol. Therefore, the mechanisms for the superlubricity of PVPA coatings affected by lubricant were investigated in detail. The stability of the PVPA coatings and their compatibility with the lubricant are critical factors in realizing ideal tribological properties of PVPA coatings. Robust PVPA coatings are stable under a wide range of pH values (6–10) using PBS as the basic solution, and are also characterized by superlubricity. The hydrolysis kinetics of phosphate anhydride is the main reason for the pH responses. In addition, along with stability, PVPA coatings exhibit different friction coefficients in salt solutions which are composed of various ions, which indicates that the compatibility between PVPA coatings and the lubricant can be used to regulate the superlubricity properties. Based on a fundamental understanding of the mechanism of surperlubricity by considering the effects of the lubricant, PVPA coatings with stability and perfect tribological performance are expected to be applied in more aspects.

Flange connections are widely used in various mechanical components. The most important purpose of tightening for flanged bolts is to achieve designed clamping force for the maintenance of overall performance. In this work, a multi-bolt tightening algorithm is proposed based on elastic interaction coefficient and gasket creep relaxation. Firstly, dispersion of the individual bolt clamping forces for torque control method is considered in the algorithm. Relationship between the nut factors of the flange bolts in multi-pass tightening is established through experiment. Subsequently, the elastic interaction coefficient matrix was updated during the multi-pass tightening process to reduce the error. Two cases, without gasket and silicone gasket, are considered in the multi-bolt tightening experiment. Without gasket, the elastoplastic deformation at the initial stage after tightening will also cause a loss of clamping force. When using gasket, the clamping force loss due to gasket creep relaxation is more pronounced. Through experimental verification, the proposed multi-bolt tightening algorithm are able to achieve the target range of designed clamping forces and reduce its dispersion. Finally, the main influencing factors of the multi-bolt tightening are analyzed to provide a reference for the design of flange connections.

Bolted joints are widely used in mechanical construction due to their ease of disassembly. When the bolting member is subjected to the alternating load, the pretightening force is gradually reduced, which may cause the interface contact performance to decrease, and the surface may be microslipped. Preload relaxation of threaded fasteners is the main factor that influences the joint failure under normal cyclic loading, but it is difficult to monitor the energy dissipation between the interface of the bolted joint. This paper presents an energy dissipation model for the bolted joint based on two-degree-of-freedom vibration differential mathematical model. The parameters of the model is calculated by using the fractal theory and differential operator method. The efficiency of the proposed model is verified by experiments. The results show that the experimental modal shape agrees well with the theoretical modal shape. According to the change of cyclic load and vibration frequency, the vibration response and the law of energy dissipation under different factors can be obtained. The results show that the vibration frequency and cyclic load are the main factors affecting the energy dissipation between interfaces. The energy dissipation of the contact surface of the bolted joints account for the main part of the energy dissipation of the bolted structure. The results provide a theoretical basis for reducing the looseness of the bolt connection and ensuring the reliability of the equipment.

In order to improve the modeling accuracy of the motorized spindle, a comprehensive thermal contact resistance (TCR) modeling method was proposed. The fractal theory was introduced to calculate the joint thermal contact resistance. The W-M function and the M-B fractal model were established to characterize the microscopic contour of the rough surface. The bulk thermal resistance, constrained thermal resistance, micro-gap thermal resistance and overall thermal contact resistance of the rough surface of different materials were discussed. The finite element method(FEM)was used to establish the multi-physics coupling analysis model of the motorized spindle, adding the theoretical calculation of thermal contact resistance in the joint surface of the motorized spindle. The temperature rise and deformation variation of the motorized spindle were simulated under the condition of thermal contact resistance. The simulation results demonstrate the influence of thermal contact resistance on the temperature and thermal deformation of the motorized spindle. The results show that when the thermal resistance of the high-speed motorized spindle is considered, the temperature rises and the deformation increases, and the accuracy of the model is more accurate, which is closer to the actual processing.

Because of the friction and damping effect between the interfaces, when the bolted structure bears the axial load, there will be no interface dislocation and only axial reciprocating tension and pressure, so it is difficult to have fretting fatigue and wear. Only under the tangential load, the interface will be staggered and the peaks and valleys between the micro-convex bodies will be alternately rubbed. After repeated cycles, the interface will generate sliding and adhesion areas of micro-fatigue and wear. Therefore, this paper conducts an in-depth study on the influence of bolt relaxation on surface fretting fatigue and wear. The relationship between tightening torque and clamping force, design and implementation of tangential relaxation experiment and acquisition and analysis of 3d surface topography are studied.

Fractal parameters (FP) significantly influence contact mechanics characteristics, such as contact stiffness, friction and wear. The existing methods liking the power spectral density (PSD), structure function (SF), autocorrelation function (ACF), box-counting (Box) and roughness length (RMS) methods are limited by the identification accuracy of FP (fractal dimension D and fractal roughness G). These methods are not suitable for global D interval (Kulesza et al., 2014; Feng et al., 2018), thereby resulting in large estimation errors (error (D) exceeds 40 %, and the value of G is incorrect). Thus, in this paper, a neural network FP estimation method based on the exact spectral moment is proposed. The main contribution of this paper is to establish the mapping relationship between the exact spectral moment and FP through the neural network. Firstly, the exact spectral moments, m 0 , m 2 and m 4 , are derived via the differentiability of the series Weierstrass-Mandelbrot (WM) function in the finite interval. Secondly, a series of spectral moment parameter correspondence tables are generated according to the provided ideal fractal parameters. Then, the spectral moment is taken as the input layer and fractal parameters as the output layer, after which the BP neural network is optimized using the NSGA-II algorithm. Moreover, the mapping relationship between the FP and the spectral moment is established, thus obtaining the Fractal parameters estimation neural network (FPENN). The FP estimation model is trained by a relatively large amount of data and packaged to form a brand-new FP estimation method. Finally, the effectiveness of the proposed method is demonstrated by comparison with the existing methods. The results show that the relative error of D is <0.1 %, and the relative error of G is <25 %. • Proposing a neural network FP estimation method based on the exact spectral moment. • The calculated FP by FPENN method is obviously superior to other methods. • Studying the FP of Gaussian and machining surfaces [ABSTRACT FROM AUTHOR]