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The development of air bearing demands further research and certain guidance. The previous technical reviews focused on specific aspects, while bibliometric analysis employed in this paper gave a general overview on air bearing field and provided clearer research interest and development trend. The publications in the field of air bearing from 1990 to 2017 based on the Science Citation Index Expanded (SCIE) database were analyzed from the aspects of countries, institutions, research areas, journals, authors, keywords, reviews, and high cited papers, implemented by some representative and convincing indicators. The result showed that the USA held the dominant position in this field, followed by Japan and China. The University of California System held the top position in terms of total papers and h-indexes. It had shown a multi-disciplinary development trend of air bearings from the aspect of research area. Tribology related journal took high ranking of the list, in which “Journal of Tribology-Transactions of the ASME” ranked first. Bogy, D. B., made most contributions to the air bearing field, with the highest total citations and h-index. Thermal effects, foil bearing, dynamic analysis, and active compensation were hotspots. Reynolds equation, stability, optimization, load-carrying capacity, foil bearings, and aerostatic bearings were potential directions that might have greater opportunities for improvement. The improvement of air bearing requires common progress in multiple aspects.

This paper studies the stability and control problem of linear systems with non-symmetrical input saturation. A system with non-symmetrical input saturation is transformed into a system with switching symmetrical input saturation. A switching controller is designed based on a parametric algebra Riccati equation, dwell time and the equivalent switched system. Exponential stability is guaranteed with the proposed switching controller. The main advantages of the proposed method lie in reducing the conservatism caused by directly using symmetrical input saturation control and increasing the state convergent speed. The designed controller can be computed easily by solving the Riccati equation. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

In order to study the machining mechanism and process of abrasive flow machining for the titanium alloy artificial joint surface, the abrasive flow machining experimental platform and the curved surface profiling flow channel were established for the machining. The influence of various process parameters (abrasive particle size, abrasive particle concentration, and processing time) and interaction factors on surface roughness and surface micro-topography of the workpiece was quantitatively evaluated through response surface analysis, and a surface roughness prediction model was established. The experimental results show that coverage constraint abrasive flow machining can significantly improve the surface quality of the titanium alloy artificial joint surface, thereby improving the wear resistance and service life of the artificial joint. Using abrasive flow machining with a smaller abrasive particle size and a larger concentration can obtain smaller surface roughness. Under the experimental conditions, the influence of process parameters on the surface roughness is in descending order of processing time, abrasive particle concentration, and abrasive particle size. And the interaction of processing time and abrasive particle size is more effective during processing. The research results can provide the basis for optimizing the flow channel structure for the abrasive flow machining of the titanium alloy artificial joint surface and have a certain guiding significance on the process optimization.

Dynamic vibrations of air bearing motor spindles have significant influence on the surface quality in ultra-precision machining. In this article, the influence of the vibration caused by the unbalanced magnetic force on the diamond turning is investigated on the basis of the theoretical and experimental method. A permanent magnet motor model (10 poles and 12 slots) is built and then simulated to gain a periodic unbalanced magnetic force. The effects of unbalanced magnetic force on the inclination of the spindle shaft is analyzed, which would affect the surface quality of the workpiece, and the surface topography of the workpiece is predicted during an unbalanced magnetic force acting on air bearing motor spindle. The theoretical analysis and experimental turning results validate that the angle between the direction of unbalanced magnetic force and the feed direction has a certain relationship with the profile of the machined surface. Also, under different turning speeds and directions, the surface topography of the machined workpiece shows a 10-cycle-per-revolution pattern, which has good agreement with the simulations of periodic unbalanced magnetic force. This research work provides a theoretical foundation for the fault diagnosis of air bearing motor spindle caused by motor rotor eccentricity and its effect on surface generation in turning.

Air bearing spindles (ABS) can meet high accuracy demands for the precise rotation motion, which adopt air bearings to support spindle shaft, and the spindle shaft directly connects the motor rotor. The unbalanced electromagnetic force caused by motor rotor eccentricity (MRE) and air pressure fluctuation (APF) are two important influential factors to the dynamic performance of the spindle system and machining surface quality. This paper addresses the problems of measuring the MRE and APF in an ABS through testing machining surface topography. A permanent magnet synchronous motor (PMSM) was modelled by finite element simulation (FES). Through FES it found that the MRE between the motor rotor and stator hole produced a radial magnetic force (RMF), which could cause ABS to periodically vibrate in the axial direction. Besides, the change of the air supply caused the stiffness variation of ABS and result in the tilt error motions of the spindle shaft. A theoretical model of machining surface topography considering MRE and APF was then proposed for the first time, which revealed that the MRE and APF resulted in the periodic fluctuations of the machining surface topography. The overall surface topography then became grooved surfaces. The above findings were finally validated by measurement results of ultraprecision diamond turning experiments.

The air bearing motorized spindle (ABMS) is the key component of the ultra-precision machine tool, which plays an important role in the ultra-precision machining process and directly influences machining accuracy. The influence of unbalanced magnetic force (UMF) on the nonlinear dynamic behavior of the ABMS is not understood clearly. To reveal the potential influence of the UMF, a mathematical model of the ABMS considering multiphysics fields is established. The variation trend of the UMF is simulated, and the nonlinear dynamic behavior of the ABMS is analyzed which emphasizes on the stability of the rotating shaft. It is shown that the UMF varies linearly at large rotor eccentricity which meets well with previous research, but it is noteworthy the UMF varies nearly to a quadratic function at small rotor eccentricity. The result of rotor dynamics shows that the UMF can change the converge position of the rotor center and the converge speed. Moreover, when at certain rotor mass and external load, the UMF can enlarge the stability boundary of the rotor. This research provides an example of analyzing the nonlinear dynamic behavior of the ABMS considering multiphysics fields which may help to the further investigation.

Ribbed holes can serve to increase the efficiency of the heat exchangers and improve the performance of industrial equipment. Increasing demand for small ribbed holes is a key driver in manufacturing technology research. Electrochemical machining has been shown to be a promising method for this. In this paper, an intermittent low-frequency vibration tool is used to demonstrate significant improvement to the geometry of internal ribbed holes. The process stability, material removal rates, and uniformity of features along the flow direction are improved. Firstly, a 3D model of the flow field within the interelectrode gap was developed to calculate and governing flow regime in the interelectrode gap. The simulation demonstrated that the fluid velocity fluctuates periodically and this enhances electrolyte flushing in the interelectrode gap during the machining process. Then, experimental tests for the manufacture of spiral ribs on small holes (Ø1.5 mm and 20–40 mm depth) are also demonstrated with accompanying variation of the tool vibration amplitude and frequency, respectively. Results show that groove depth was most greatly influenced by the vibration amplitude and that better uniformity could be obtained at higher vibration frequencies. The groove depth increased by 15% over nonvibrating control tests with enhanced uniformity.

The performances of aerostatic spindle are highly affected by the fluid-structure interaction (FSI) between air film and solid structure. This paper proposes a novel modeling method to investigate the FSI of aerostatic spindle system, by which the structure deformation included by air film force can be acquired. Furthermore, a virtual weight loading method is proposed to estimate the stiffness of spindle with consideration of structure deformation and gravitational eccentricity. The reliability of the proposed method is verified by experiments. Based on the proposed FSI model, the influences of air film geometrical parameters and structure dimension on the performance of aerostatic spindle are further investigated and discussed to guide the design of air spindle.

Subsurface microstructure alteration has been a major concern to implement micromachining of titanium alloy in the high-tech industry. To quantitatively promulgate the underlying mechanisms of this alteration, a discrete dislocation dynamics-based model is proposed and used to simulate the subsurface defects and their evolution under different cutting conditions. The model considers the subsurface dislocation configuration and inner stress distribution during the orthogonal cutting of titanium alloy. The results show that subsurface defect structure consists of plenty of dislocation dipoles, twining dislocation bands, and refined grains after cutting. In the primary shear zone, two different characteristics of subsurface damage layers can be found, the near-surface damage layer and deep-surface damage layer, which have different structural natures and distribution features. Moreover, it is found that high cutting speed and small depth of the cut can suppress the formation and propagation of subsurface defects. A powerful inner stress state would promote the distortion of the lattice and result in a microcrack within the subsurface matrix. The simulation results have been compared with experimental findings on the machined surface and subsurface of similar materials, and strong similarities were revealed and discussed.

In ultra-precision diamond turning (UPDT), the spindle axial drift directly affects the machining accuracy. Due to the difficulty of measuring the spindle drift during the machining process, the spindle axial drift was rarely studied. In this paper, an experimental method is used to prove and measure the existence of the spindle axial drift at the machining process, and the influence of spindle drift error on the machined surface is further studied. A mechanical model of the spindle system is considering the mass eccentricity, and the dynamic behavior of the spindle in working conditions are simulated with the mathematical model. Periodicity whirl of the spindle is found in the simulation, which is verified by the end face turning experiments. Then, the influence of the spindle vibration on surface topography is discussed, considering the spindle rotation speed and its dynamic balance. Meanwhile, the vibration frequencies induced by the spindle rotation are detected by the signal analyzer, and the detected frequency has been found to agree well with the experimental wave period of the workpiece surface (WS). This study is quite meaningful for deeply understanding the influence rule of spindle unbalanced error from the viewpoint of machined surface and vibration frequency. The research results are useful for the spindle error control and machined surface error prediction.

In ultra-precision machining field, the air motorized spindle which is composed of a motor and an air bearing, plays a major role. In air motorized spindle, the motor eccentricity between the stator and the rotor is inevitably introduced during the manufacturing process, which directly affects the machining results of workpiece surface, and this phenomenon is particularly unwanted in machining. However, little attention has been paid to the motor eccentricity of air motorized spindle. In this paper, a new integrated electromechanical coupling method for estimating unbalanced force in air motorized spindle is presented, and the effects of motor rotor eccentricity on surface topography in ultra-precision processes are analyzed. An electromagnetic-mechanical method is used to study the coupling effects between the motor rotor and the aerostatic spindle. Meanwhile, the motor rotor and the aerostatic spindle are analyzed as a whole. In order to clearly describe the electromagnetic–mechanical method, the ultra-precision spindle for potassium dihydrogen phosphate crystal machining tool is selected as the research object, and the model of air motorized spindle and motor rotor eccentricity are presented. Besides, in order to assess the impact of the radial magnetic force caused by motor rotor eccentricity on the spindle performance, a range of rotor eccentricities is calculated. Additionally, the influence of the motor rotor eccentricity on the dynamic response of spindle is further analyzed. It is found that motor rotor eccentricity has a significant influence on the spindle vibration, which dramatically reduces the processing quality. Finally, the machining experiments are carried out, and the flatness errors of the workpiece caused by the motor rotor eccentricity are obtained by the wavelet method. The experimental results are consistent with the analysis results, which verifies the reliability of this method. This study is quite meaningful for deeply understanding the influence of motor rotor eccentricity on the machined surface.

The aerostatic spindle in the ultra-precision machine tool shows the complex multi-field coupling dynamics behavior under working condition. The numerical investigation helps to better understand the dynamic characteristics of the aerostatic spindle and improve its structure and performance with low cost. A multi-field coupling 5-DOF dynamics model for the aerostatic spindle is proposed in this paper, which considers the interaction between the air film, spindle shaft and the motor. The restoring force method is employed to deal with the times varying air film force, the transient Reynolds equation of the aerostatic journal bearing and the aerostatic thrust bearing is solved using ADI method and Thomas method. The transient air film pressure of aerostatic bearings is obtained which clearly presents the influence induced by the tilt motion of the spindle shaft. The motion trajectory of the spindle shaft is obtained which shows different stability of the shaft under different external forces. The dynamics model shows good performance on simulating the multi-field coupling behavior of the aerostatic spindle under external force. which is quite meaningful and useful for the further research on the dynamic characteristics of the aerostatic spindle.

The ultra-precision spindle is the key component of ultra-precision machine tool, which largely influences the machining accuracy. Its frequency characteristics mainly affect the frequency domain error of the machined surface. In this article, the error measurement setup for the ultra-precision aerostatic spindle in a flycutting machine tool is established. The dynamic and multi-direction errors of the spindle are real-time measured under different rotation speeds. Then, frequency domain analysis is carried out to obtain its regularity characteristics based on the measurement result. Through the analysis, the main synchronous and asynchronous errors with relatively large amplitude of the spindle errors are found, and the amplitude change law of these main spindle errors is obtained. Besides, the cause of the main synchronous and asynchronous errors is also analyzed and indicated. This study deepens the understanding of ultra-precision spindle dynamic characteristics and plays the important role in the spindle frequency domain errors’ control, machining process planning, frequency characteristics analysis and oriented control of the machined surface errors.

The frequency domain error of the machined surface in the ultra-precision machining attracts more attention for its strong relationship with the functional requirements of the workpieces. As the key component of ultra-precision machine tool, the spindle error largely influences the machined surface errors. However, little attention has been paid to the influence of spindle error on the surface error formation mechanism in the frequency domain for ultra-precision flycutting. This paper deeply studies the influence of spindle error on the frequency domain error formation of machined surface in ultra-precision flycutting. The influence analysis of the spindle error is theoretically and experimentally carried out according to two different evaluation directions of the machined surface by flycutting, i.e., cutting direction and feed direction. The KDP crystal flycutting experiment is designed and conducted for the theoretical verification. The theoretical analysis has been found to agree well with the experimental results. This study is quite meaningful for deeply understanding the influence law of spindle error from the viewpoint of frequency domain. The research results are quite useful for the spindle error control, machined surface error prediction, machining process planning, and also show the potential use for the spindle (machine tool) design.

This article presents the dynamic design and thermal analysis of an ultra-precision flycutting machine tool. The hydrostatic bearings are used both in the spindle and slide to ensure the stiffness of the machine tool. The fluid–structure interaction method is used to obtain the actual clearance changes of the hydrostatic bearing. The dynamic and thermal performances of the machine tool are analyzed considering the effect of hydrostatic bearings. The influence of the thermal effect on the static and dynamic performance of the machine tool is further studied. The prototype machine tool is built. Preliminary machining trials have been carried out and provided evidence of fluid–structure interaction method being helpful to design the ultra-precision machine tool based on the hydrostatic technology.

Ultra-precision machine tool is the most important physical tool to machining the workpiece with the frequency domain error requirement, in the design process of which the dynamic accuracy design (DAD) is indispensable and the related research is rarely available. In light of above reasons, a DAD method of ultra-precision machine tool is proposed in this paper, which is based on the frequency domain error allocation. The basic procedure and enabling knowledge of the DAD method is introduced. The application case of DAD method in the ultra-precision flycutting machine tool for KDP crystal machining is described to show the procedure detailedly. In this case, the KDP workpiece surface has the requirements in four different spatial frequency bands, and the emphasis for this study is put on the middle-frequency band with the PSD specifications. The results of the application case basically show the feasibility of the proposed DAD method. The DAD method of ultra-precision machine tool can effectively minimize the technical risk and improve the machining reliability of the designed machine tool. This paper will play an important role in the design and manufacture of new ultra-precision machine tool.

A multi-objective optimal model of a K-H-V cycloid pin gear planetary reducer is presented in this article. The optimal model is established by taking the objective functions of the reducer volume, the force of the turning arm bearing, and the maximum bending stress of the pin. The optimization aims to decrease these objectives and obtains a set of Pareto optimal solutions. In order to improve the spread of the Pareto front, the density estimation metric (crowding distance) of non-dominated sorting genetic algorithm II is replaced by the k nearest neighbor distance. Then, the improved algorithm is used to solve this optimal model. The results indicate that the modified algorithm can obtain the better Pareto optimal solutions than the solution by the routine design.

This paper has designed a robust discrete gain scheduling controller for the linear systems by considering the parameter uncertainties and input saturation based on the invariant sets and linear matrix inequalities(LMIs). The proposed method can improve the dynamic performance by introducing a parameter. By the Lyapunov approach and the scheduling technology, the existence conditions for admissible controller are formulated in the form of LMIs. The numerical simulations illustrate the effectiveness of the proposed method.