A Review of the Design and Optimization of Large-scale Hydrostatic Bearing Systems

Review A review of the design and optimization of large-scale hydrostatic bearing systems Michal Michalec a, ⇑ , Petr Svoboda a , Ivan Kr ˇupka a , Martin Hartl a a Department of Tribology, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, Brno 616 69, Czechia article info Article history: Received 15 October 2020 Revised 11 January 2021 Accepted 14 January 2021 Available online 13 February 2021 Keywords: Hydrostatic lubrication Hydraulic system Machine design Fail-safe measures Geometric errors abstract In the last decades, the demand for hydrostatic bearings application has been rising due to the possibilities and advantages they offer. The advancements in hydrostatic lubrication understanding and computer technology improvement opened new ways for hydrostatic bearing performance and precision improvement. The emergence of the trend Industry 4.0 has brought new challenges and opportunities to the heavy machinery industry. This paper reviews the overall design and optimization processes for large-scale hydrostatic bearing geometry including the hydraulic system. The latest developments in the bearing geometry optimization, pressurized fluid supply components, and flow control devices are discussed. Moreover, possible measures for avoiding costly maintenance and repairs of the hydrostatic bearing are proposed. Finally, potential future research directions in large-scale hydrostatic bearing development are suggested. This review offers a comprehensive summary of potential problems and possible solutions in the large-scale hydrostatic bearing design, and simultaneously, serves as a supporting material to overcome potential obstacles that might emerge during manufacturing, assembly, and service. Ó2021 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Contents 1. Introduction . . . ...................................................................................................... 937 2. Overview of a large hydrostatic bearing system . . . . . . . . . . . . ................................................................ 938 2.1. Hydrostatic bearing working modes . . . . . . . ......................................................................... 939 3. Calculation and optimization. . . . . . . . . ................................................................................... 940 3.1. Performance optimization . . . . . . . . . . . . . . . ......................................................................... 943 3.2. Pad geometry optimization . . . . . . . . . . . . . . ......................................................................... 944 4. Sliding surfaces. ...................................................................................................... 945 4.1. Structural deformation analysis and prevention . . . . . . . . . . . . . . . . . ...................................................... 945 4.2. Manufacturing and assembly error analysis and prevention . . . . . . . ...................................................... 947 4.3. Materials, surface treatment, and modification. . . . . . . . . . . . . . . . . . ...................................................... 949 5. Hydrostatic bearing supply system. . . . ................................................................................... 950 5.1. Flow compensation . . . . . ......................................................................................... 950 5.2. Accumulator units. . . . . . ......................................................................................... 950 5.3. Lubricants . . . . . . . . . . . . ......................................................................................... 950 6. Summary . . . . . ...................................................................................................... 953 7. Future challenges . . . . . . . . . . . . . . . . . . ................................................................................... 953 Declaration of Competing Interest . . . . ................................................................................... 954 Acknowledgments . . . . . . . . . . . . . . . . . ................................................................................... 954 References . . . . ...................................................................................................... 954 https://doi.org/10.1016/j.jestch.2021.01.010 2215-0986/Ó2021 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). ⇑ Corresponding author. E-mail address: [email protected] (M. Michalec). Peer review under responsibility of Karabuk University. Engineering Science and Technology, an International Journal 24 (2021) 936–958 Contents lists available at ScienceDirect Engineering Science and Technology, an International Journal journal homepage: www.elsevier.com/locate/jestch 1. Introduction The invention of the water-fed hydraulic bearing in 1852 by L. D. Girard opened new possibilities in the mechanical engineering industry. The development process has advanced enormously ever since. Reynold’s publication on the theory of lubrication [1] based on Tower’s discovery of the hydrodynamic lubrication in 1886 significantly contributed to the fluid flow understanding. In 1918, Lord Rayleigh [2] discussed the optimal step bearing geometry for maximum load capacity, now referred to the Rayleigh step bearing. In the next period, the development process and application of externally pressurized bearings were continuously growing, as well as numerous patents were proposed. A review paper on hydrostatic and hybrid bearings was presented by Rowe [3] in 1989 that summarized previous advances in this field. Later in 1992, Bassani and Piccigallo [4] wrote a comprehensive book describing all the important aspects of the hydrostatic bearing design and optimization based on the latest research. Research progress in the field of large hydrostatic bearings was further reviewed by Li et al. [5] in 2014. Later, an insight into hydrostatic bearing system research and applications was presented by Liu et al. [6], proving that hydrostatic lubrication was still an increasingly significant topic. Despite all the previous significant contributions in the field of hydrostatic lubrication, the latest technology developments offer new opportunities for further hydrostatic bearing improvement. Hydrostatic lubrication works on the principle of feeding pressurized fluid in between sliding surfaces to secure their separation [4] as shown in Fig. 1. The fluid is supplied from a hydraulic circuit through an inlet hole and evenly distributed by a recess. The turntable is floating and is ready for operation once the lubricating film is fully developed. The fluid pressure is gradually decreasing from the recess area to the atmospheric pressure, and the outlet fluid is collected and returned to the circulation. The key advantages of the hydrostatic bearing are very low friction only generated by the fluid shear forces and negligible wear of sliding surfaces that are completely separated by pressurized fluid film. In comparison to the hydrodynamic bearings, which require higher rotating speeds, the hydrostatic bearing is working even when standstill since the surface separation is maintained externally. Since the bearing clearance is filled with the pressurized fluid, the hydrostatic bearing shows a high damping ability and high stiffness while the noise emission and vibration transfer is very low. On account of solid contact absence, the hydrostatic bearing exhibits very high moving accuracy and stability without any undesirable stick–slip effect [7,8]. Nevertheless, there are also several disadvantages that must be considered before selecting the hydrostatic bearing for a specific application. High precision of sliding surfaces is required; thus, the initial manufacturing costs can be considerably higher. The initial cost is increased by the necessity of an external pressurized fluid supply, considering all the elements of hydraulic circuit needed for proper functioning. Considering the complexity of the hydrostatic bearing system, a larger bedding space is required for piping, hydraulic and electric energy supply. Despite the low noise emission generated in between the sliding surfaces, the hydrostatic bearing system noise emission generated by the motor of the pump should not be overlooked. However, the noise transmitted by air, fluid, and structure [9] can be reduced by insulating material or by hydrogenerator confinement in an insulated space. The fluid-transmitted vibrations [10] can be dampened by the hydraulic accumulator [11], while structural vibrations can be reduced using silentblocks or shock absorbers. Large-scale bearings are fundamental supporting elements of heavy rotary parts. The use of rolling elements is limited by the maximal diameter and load capacity. The size of rolling bearings is mostly only a few millimetres. However, large rolling bearings for wind turbines can reach 5 m [12]. The issue with large rolling bearing is not only the size and required precision of rolling elements, but also fatigue [13] and raceway/ball damage due to high contact stress [14]. In contrast to the rolling bearings, the hydrostatic bearings are beneficial for their applicability in wide constructions, large load carrying capacity, and uniform stress distribution. Hence, the hydrostatic bearings have been used for large tunnel drilling machines [15], large ship shafts and journal bearings [16], thrust bearings [17], and antenna or telescope structures carrying and operation, such as Giant Magellan telescope [18,19]. Possibly, this type of bearing can be used for large ships propellers, crushing machines, large rotating blades [15], heavy Fig. 1. Scheme of the open-type hydrostatic bearing pad and fluid pressure distribution. Fig. 2. Lift pockets on pad of a tilting pad turbine hydrodynamic journal bearing (reprinted from [27] under licence CC BY 3.0). M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 937 transportation turning, or stage and assembly line manipulation and accurate positioning. Another important applications of hydrostatic bearings are CNC turntables for dimensional workpieces [20], and dampers [21,22] thanks to the characteristics of fluid during compression, and impact loading and vibration damping, which is also a great advantage for use in grinding machines [23]. One of the most significant uses of hydrostatic bearings is hydropower units [24]; when the hydroelectric turbine [25] of the hydrogenerator [26] needs to start spinning without contacting surface damage, the hydrodynamic (HD) bearing is combined with hydrostatic bearing pockets [27], as seen in Fig. 2, when a hybrid bearing is started, stopped, or reversed without damaging the contacting surfaces of the bearing. Moreover, the high load and the possibility of pumping water is advantageous for ship sealift lock-gate hinge where the sea level difference needs to be overcome [28]. Additionally, the working principle can be used for a rotary recovery device for the desalination process and reverse osmosis [29]. As introduced above, hydrostatic bearings have a great application potential that will be increasing with the development of modern technologies and trends [30], such as Industry 4.0 [31]. Lately, detailed books and papers on hydrostatic bearing design [4,5,32-34] have been published and the recency of some publications show that the topic of hydrostatic bearings is still a relevant issue [6]. However, the publications focused mainly on hydrostatic pad and flow controlat the input into the hydrostatic pador at externally pressurized journal bearing design [35], but very little of them aimed at the most significant limitations and issues connected with large hydrostatic bearings, such as manufacturing, transportation, and assembly. Moreover, the publications mostly did not cover the whole bearing incorporating the hydraulic circuit and the significance of its characteristics and optimal parameter design. Furthermore, the operation of hydrostatic bearings in critical conditions might lead to serious damage and costly repair. However, such complications can be safely avoided during the designing process. This review paper presents a comprehensive insight into the design and optimization of large hydrostatic bearings, to make the design process of hydrostatic bearings more accessible and to enable further development of large-scale machines, help creating modern technologies and build a healthier environment. 2. Overview of a large hydrostatic bearing system A suitable type of bearing is an essential step in machine design. Previously, several selection strategy guides were introduced for hydrostatic bearings [35] including a decision-making process and a selection guide [33] according to required characteristics for automotive industry. Hydrostatic bearings are divided into three basic groups according to load support direction – axial (thrust), radial (journal), and combined. The calculation for both axial and radial types is similar, yet in different coordinate systems. The bearings can be characterized according to construction type: open type (Fig. 3a) and closed type (Fig. 3b), where opposed recesses act on turntable or shaft, respectively. Journal bearings can be either fully closed, e.g. for spindles [36] that represent the majority, or open for the positioning of large structures [18], such as azimuth rotation. Contrastingly, open type is the most frequently used thrust hydrostatic bearing type, which is simple in construction but provides lower precision and dynamic performance [20,37]. In the enclosed type the opposed pads act on turntable, resulting in higher precision [38], stiffness [39], and dynamic performance [40]. On the contrary, closed type bearings are more expensive and demanding on hydraulic circuit components. When both radial and axial loads need to be supported, another type of hydrostatic bearings is the combination of radial and axial bearings [41], whose shape can be either flat (Fig. 3c) or conical (Fig. 3d). The combined bearing is advantageous for medium to high rotation precision [15] and a relatively small run-out [42]. Another advantage is the ability of self-compensation provided by the conical shape of bearing [43,44]. The conical bearing is especially suitable for higher combined loads as the angle can be adjusted for desired performance [45], where an optimal value was found to be 60°for best radial and 30°for best axial performance. Generally, open-type bearings are the simplest and suitable for unidirectional loading only, while closed-type bearings are desirable for bidirectional loading. The combined type is advantageous in higher precision machines. And finally, conical bearings are superior in compensation ability and suitable for similar loads in radial and axial directions. In the case of large-scale bearings, manufacturing, transportation, and assembly have become the most important criteria in Fig. 3. Types of hydrostatic bearing according to loading direction: a) thrust open type, b) thrust closed type, c) open type combined and d) conical. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 938 the design process. In terms of size, the large scale can be understood from several points of view: a) market availability – diameters greater than standardized bearings offered b) by companies (occasionally up to 2000 mm diameter), c) manufacturability – what cannot be made in one piece with satisfactory accuracy of sliding surfaces, manipulation – transport size (e.g., exceptionally large bearing diameters above 10 000 mm) or construction site build up area does not allow moving the bearing in one piece (e.g., limited bearing bedding space, hard-to-reach bearing placement – basement etc.). Considering all the above-mentioned circumstances, the hydrostatic pad can be either uniform, assembled from ring segments, or divided into separate segments supporting the turntable. Uniform hydrostatic pad (single pad bearing – Fig. 4a)is advantageous in the height positioning of turntable segments. However, the manufacturing and transportation process can be much more complicated compared to the other geometry type. Additionally, discharge grooves for hydrostatic recess separation (Fig. 4b) are recommended to avoid mutual recess flow interference [46]; however, the whole workflow will become more complicated. Therefore, a special shape can be derived to avoid flow interference and to make the manufacturing, transportation, and assembly processes simpler – separated hydrostatic pads (multi pad bearing – Fig. 4c). Moreover, the manipulation throughout the assembly process is greatly improved. Nevertheless, levelling and positioning is more difficult than in the uniform hydrostatic pad. A sealing rubber rib must be included to avoid oil leakage between pads. The distance between separated hydrostatic pads depends on the turntable rigidity and required precision. Basically, for higher precision, such as CNC turntables for machining, the number of hydrostatic pads is generally higher. In Jang and Choi [20] proposed design where the hydrostatic pads were placed in two rows: twenty outside at 1500 mm radius and eight inside at 500 mm radius. However, the circumferential distance between pads is greater for large constructions [4], high rigidity structures, or applications with lower required precision. For instance, the Giant Magellan Telescope azimuth structure is based on 24 axial hydrostatic pads. A master–slave pad variation according to load-sharing ratios [47] is beneficial in multi-pad hydrostatic bearing control. Additionally, considering a constant supply system for multi-pad bearing is very expensive [40], so flow distribution and control devices are recommended. A full scheme of a large-scale hydrostatic bearing is shown in Fig. 5. The hydrostatic bearing is composed of two main sections: the hydrostatic pad and the hydraulic circuit. The hydrostatic pad is a stationary part supporting the rotating turntable with load. The second fundamental part of hydrostatic bearing is the hydraulic circuit. A constant low supply system has a separate hydrogenerator for each recess; however, supplying many recesses would be a complication because of either space or initial costs. Therefore the multi-pad hydrostatic bearing is supplied by one pump with flow dividers and restrictors [34]. Moreover, large hydrostatic bearings are limited by manufacturing, transportation, and assembly processes, so those types of bearings are frequently composed of a large ring with numerous inlets [18] or numerous pads placed in a desired bearing diameter [20]. The pump supplies the hydrostatic pad with enough pressurized fluid at a higher pressure than required by the pad; thus, the flow volume and pressure is processed using hydraulic valves. Three types of hydraulic valves are included: way-valves to control direction of oil flow, pressure control valves to control pressure in different segments in the circuit, and flow control valves to control the flow rate in the circuit. Flow control valves are especially important components of the hydrostatic bearing because they maintain constant film thickness by compensating pressure differential during impact and nonsymmetric loading and vibrations. The hydraulic accumulator significance will be discussed later; however, it acts as a fail-safe measure in case of sudden hydraulic circuit failure. An analogy was found in hydraulic circuit modelling and electrical circuit composition [48] that might simplify the design process using the similarity of physical laws with conversion factors and corresponding dimensions. Suitable filters are necessary for the maintenance of lubricant quality. In case of insufficient passive cooling, an active cooler must be included in the hydraulic circuit to avoid hydrostatic bearing performance decrease by a significant lubricant temperature increase. 2.1. Hydrostatic bearing working modes Hydrostatic bearing working modes introduced in [4] are summarized in Table 1. The basic condition for sliding surface separation is to maintain enough lifting force generated by fluid inertia. During the design stage, working conditions must be carefully set to avoid long working periods in a critical state of hydrostatic bearing operation. The critical states of operation (Table 2) can be avoided when considered in advance, so this review paper focuses on the prevention of such states’ occurrence. States of non-symmetrical loading Fig. 4. The geometry of a) single-pad single-recess, b) single-pad multi-recess, and c) multi-pad hydrostatic bearing types. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 939 and sudden load change are a matter of proper pad-shape geometry and flow control. Lubricant behaviour and thermal characteristics can be analysed using computational software. And finally, hydraulic circuit failure can be predicted and prevented by implementing specific measures. The above-mentioned procedures will be discussed in detail in the following parts. 3. Calculation and optimization Basic requirements for flow investigation in a narrow gap are isotropic and continuous conditions in an elementary volume. Thus Navier—Stokes equation used for viscous fluid flow description is shown in Eq. (1). q D v Dt ¼ q fþ rr ð1Þ However, the complexity of Navier—Stokes equations may be reduced by applying such simplifications as averaging quantities along one direction, flow linearity and inertia terms [4]. Thus, the Reynolds equation without viscosity variations can be derived as shown in Eq. (2). Table 1 Modes of hydrostatic bearing operation. State Description Non-working state Hydraulic circuit is not supplying pressurized fluid. Sliding surfaces are in contact. No operating/turning possible. Introduction to steady state Hydraulic circuit starts supplying pressurized fluid. Sliding surfaces are being separated. No operating/turning recommended until in steady state. Steady state Hydraulic circuit is stable, and lubricating film is fully developed. Ready for operating/turning. Working state Hydraulic circuit is stable, and the bearing is operating at normal conditions. Critical state of operation / bearing failure Working at/beyond the edge of projected conditions. Possibility of lubricating film collapse or sliding surface damage. Table 2 Critical states of hydrostatic bearing operation. State Description Non-symmetrical loading Uneven load distribution. Large pressure differences in pads that can lead to tilting or eventually a contact between sliding surfaces. Sudden load change Overload can lead to sliding surface contact or hydraulic circuit damage. Operation at very high rotation speed Lubricant overheating. Pressure distribution and flow influence the carrying capacity. Lubricant overheating Loss of carrying ability of lubricant. Fluid film collapse. Sliding surfaces get into contact. Hydraulic circuit failure Sudden contact of moving sliding surfaces without developed lubricating layer. Table 3 Example of expressed equations for circular hydrostatic pad calculation [4,32,50]. Quantity Equation Required lifting pressure in the recess area p r ¼ W A min Total load-carrying capacity W¼3 lr 2 2 h 3 Q1 r 2 1 r 2 2  Flow rate Q¼ ph 3 p r 6lln r 2 =r 1 ðÞ Viscous friction s ¼ pl x 2h r 4 2 r 4 1  Fluid power loss H v ¼x s Pumping power loss H p ¼p r Q Fig. 5. Full scheme of the hydraulic circuit and cross section of two hydrostatic pads of a large multi-pad hydrostatic bearing. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 940 r h 3 g  r p ! ! ¼6 r U !h  þ12@h @tð2Þ Alternatively, the complexity of Navier—Stokes equations can be reduced into a 2D problem using the Dirichlet conditions [49] to obtain analytical formulations. Bassani and Piccigallo [4] derived simple-pad and single-recess geometry, such as circular, rectangular, and annular. Several other configurations for multirecess bearings were introduced by Khonosari and Booser [32]. These are based on pad coefficients, whose values are selected from a graph. In Table 3 equations for circular pad are expressed, showing the key parameters of a hydrostatic bearing. Subsequently, the key parameters of hydrostatic bearings are described in Table 4 with respect to the values of large-scale hydrostatic bearing, either obtained from references or calculated using equations in Table 3. All conditions and desired parameter specifications must be set at the beginning of the design process. There are several design criteria that are specified in Table 5. When the design criterion is selected and the key parameter is set, the equations from Table 3 are customized to match the calculation aim – the calculated parameters. At this stage, optional parameters are chosen according to budget and availability. The calculation of hydrostatic bearing base parameters is an iterative process that is performed to achieve desired performance and reasonable bearing geometry or hydraulic circuit parameters. The workflow is schematically shown in Fig. 6. To evaluate the performance of a non-derived hydrostatic bearing shape analytically, an approximation method according to Rippel [51] can be utilized to obtain roughly corresponding load capacity. Calculation generalization was introduced using performance parameters as introduced by Khonosari and Booser [32] to simplify the design process for derived geometry hydrostatic bearing shapes as shown in Eq. (3). W¼A eff p r ¼a p A tot p r ð3Þ where A eff is the effective area of a pad, A tot is the total pad area, and a p is the pressure coefficient. This form is advantageous for the application of results from the numerical simulation resultant forces [46] and for obtaining of pressure coefficients for a specific geometry. Additionally, Kang et al. [47] provided hydrostatic bearTable 4 Key parameters of hydrostatic bearings. Parameter Description Typical range Flow (Q) required steady flow distribution for all bearing pads 5–50 l/min Recess pressure (p r ) sufficient working fluid pressure for load carrying and surface separation during introduction to the working state 50–150 bar Supplied pressure (p s ) pressurized fluid output from hydrogenerator considering pressure losses 50–200 bar (according to pressure drops at hydraulic circuit elements) Dynamic viscosity (m) stable, low temperature dependency 0.05–0.15 Pas (according to oil viscosity grade for expected environment temperatures) Pad and recess geometry dependent on selected manufacturing process calculated for optimal performance and desired load capacity. Load (W) Desired or achievable load-carrying capacity wide range, up to 1000 metric tons in total [18] and more Film thickness (h) maintained a constant lubricating gap, high enough to carry load, and to overcome manufacturing and assembly errors approximately 10– 100 mm Viscous friction torque ( s ) the force acting against bearing rotation generated by viscous forces of the fluid approximately 300 Nm at 10 rpm and medium viscosity (based on calculation for 1000 t load according to eqns. in Table 3) Total power loss (H) given by required performance, lubricant viscosity, choking elements, and fluid friction during operation pumping power loss up to 3 kW (based on calculation for 1000 t hydrostatic bearing according to eqns. in Table 3), fluid film power loss is negligible. Table 5 Classification of design criteria and bearing parameters. Design criteria Key parameter Optional parameter Calculated parameter Required load capacity Predicted load range (W min –W max ) Recess pressure (p r ) Required volumetric flow (Q) Dynamic viscosity (m) Hydrostatic pad geometry (pad and recess dimensions) Film thickness (h) Required supplied pressure (p s ) Error compensation Minimal required film thickness with respect to maximum errors (h min ) Recess pressure (p r ) Required volumetric flow (Q) Predicted load range (W min - W max ) Dynamic viscosity (m) Load-carrying capacity (W) Hydrostatic pad geometry (pad and recess dimensions) Required supplied pressure (p s ) Limited bedding space Maximum pad area (A max )considering collector pan and surroundings Recess pressure (p r ) Required volumetric flow (Q) Dynamic viscosity (m) Predicted load range (W min - W max ) Film thickness (h) Required supplied pressure (p s ) Load-carrying capacity (W max ) Hydrogenerator performance Supplied volumetric flow (Q) Supplied pressure (p s ) Hydrogenerator power (H p ) Dynamic viscosity (m) Loadcarrying capacity (W) Hydrostatic pad geometry (pad and recess dimensions) Film thickness (h) Recess pressure (p r ) M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 941 ing parameters for effective area calibration based on experimental investigation. The analytical calculation process is performed using analytical expressions for the determination of basic parameters and required hydropower unit performance. The numerical approach serves as an auxiliary tool for performance optimization and deformation investigation, which is discussed in this paper in detail later. A summary of both analytical and computation approaches is listed in Table 6. Numerical methods can be implemented in the hydrostatic bearing design to achieve desired performance and eliminate possible issues in advance. The computational fluid dynamic (CFD) is a powerful tool for fluid flow simulation and investigation. An overview of the most widely used discretization methods, namely the finite volume method (FVM), the finite element method (FEM), and the finite difference method (FDM), is listed in Table 7.Ina nutshell, the FVM is most suitable for flow investigation of any geometry. A comparative investigation of the FVM and vortex visualisation for three different Reynolds number at inlet (Fig. 7) presented by Shen et al. [55] showed a good agreement in results. The FEM has more demanding computational requirements, however, it is superior for multiphysics and non-Newtonian fluid modelling. In contrast to the previously described methods, the FDM is a quick computational method that is preferred only for simple and regular domain investigation. Li et al. [62] presented a CFD analysis for a shear cavitation effect influence on the performance of journal bearings that led to a better agreement with experimental results, especially when viscosity, speed, and eccentricity increased. For specific simulations considering also solid interfaces, the fluid–structure interaction (FSI) problems are widely used for multiphysics problems [63], sliding surface deformation and error investigation [64], and thermal analyses. In comparison to CFD, FSI is more demanding on computational requirements [65] and therefore preferred only in predicting solid interface stress and deformation. Additionally, simulation accuracy improvement can be achieved by considering FSI and temperature influence [66], which resulted in significant static stiffness decrease. In comparison to analytical representation, the proposed exact FEM Reynolds equation formulation by Chasalevris and Sfyris [79] results in a significant design process improvement. Thermal-elastohydrodynamic (TEHD) simulation of hydrodynamic Fig. 6. Bearing parameter calculation process. Table 6 Comparison of analytical and numerical approaches in hydrostatic bearing calculation. Analytical Numerical Simple and quick calculation of key parameters. Can be used for [4]: static and dynamic performance analysis, thermal and flow properties prediction, optimization of basic shape pads using, nomographs. Required advanced knowledge of fluid modelling. Can be used for: static and dynamic performance analysis [52,53], flow investigation [54,55], thermal properties evaluation [56,57], deformation evaluation [24,36], error modelling [58-60]. Preferred for basic derived pad geometry shapes. Powerful tool for obtaining resultant force for various pad and recess geometry from simulation [29], including unusual shapes. Limited to simple geometry configurations. Suitable for unusual configurations of recess and pad shapes design that is very difficult or impossible to express analytically [61]. Table 7 Overview of CFD discretization methods used in hydrostatic bearing modelling. FVM FEM FDM Suitability pressure distribution [67], heat transfer [68,69], and turbulent flows mixed formulations and multiphysics problems pressure distribution [70,71], heat transfer [37] Computation speed moderate slower [38] quicker [72] Geometry regular geometry any geometry (including curved) simple and regular domains (required cartesian meshes) [72] Problems related to hydrostatic bearings relationships among rotation speed, recess pressure and dynamic viscosity [69], high speed and high viscosity conditions [62], flow investigation [55], oil film temperature field in variable viscosity condition and rotation [68,69,73], recess pressure field and investigation of heavy bearing [67] high rotation speed effects [41], static and dynamic performance of conical bearings and bearings with restrictors [44,45,74,75], non-Newtonian and smart fluid modelling [7678], static, dynamic and thermal characteristics [37], carrying capacity according to pressure distribution considering surface waviness effect [30] M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 942 (HD) bearing aimed at film thickness evaluation compared to induced fluorescence measurements [80] showed a relatively good agreement at lower speeds; however, the deviation was higher at higher speeds. Generally, it is necessary to identify the flow regime according to Reynolds number [81] because turbulent flow provides higher load carrying capacity, however, also increases the fluid friction. The resulting accuracy of hydrostatic bearing simulations can be improved using inertia effects [82] and dynamic grid technology [83], where dynamic changes of boundary conditions are implemented. The workflow of numerical investigation provided by Zhang et al. [83] considered symmetric conditions of periodic oil pads to cut down the calculation time and increase result accuracy. Numerical approach based on the CFD simulation was experimentally investigated by Cui [84] for large hydrostatic bearing, where a maximal 9.52% error in results of recess pressure was observed, while measurements of oil film thickness resulted in a 13.8% error, so the simulation results errors should be always considered. However, the results are heavily influenced by mesh quality. A meshless method with radial basis functions was introduced by Nicoletti [72]. It significantly improves the computing time with only a 5% error even with a coarse grid. Another important demand on simulation is the computational time that significantly affects price and result accuracy. Therefore, a fast thermo-hydrodynamic CFD model was proposed by Novotny ´ et al. [85] that greatly improves computational speed. The proposed computation model accuracy is lower compared to the CFD simulation (Fig. 8), which is caused by the location of the boundary condition of the simplified model. Another dynamic model for rapid static and dynamic characteristics analysis of a closed type bearing that is roughly 10 times faster than the FEM was introduced and experimentally verified by Wang et al. [86]. Another significant computational time improvement in simplified model for static and dynamic performance calculation of hydrostatic bearing with errors lower than 6.5% while taking only 1/603 of the FDM’s runtime was proposed by Liang et al. [87]. 3.1. Performance optimization Performance optimization is an important process that includes both optimal control establishment and the whole system energy consumption minimization. The hydrostatic bearing performance is provided according to a selected design criterion as listed in Table 5. Simple cases deal only with the optimization of one parameter, which is, however, not enough for obtaining high performance, good thermal properties, and economical energy management. Hence, a multicriteria optimization was introduced by Solmaz et al. [88] as an iterative process considering the most important parameters, specifically minimum power and temperature rise. The better required overall performance, the more criteria should be considered. A remarkable 30–60% accuracy [89] can be achieved by considering the influence of design parameters, geometric errors, deformation, temperature, and random parameters. Fedorynenko et al. [90] proposed an innovative design of hybrid bearing achieved a significant efficiency increase, i.e. 1.5 times decreased total energy loss in hydrostatic mode and 4 times in HD mode. Additional details on the performance characteristics optimization are listed in Table 8. The hydrostatic bearing has a significant advantage in comparison to rolling bearings owing to the fluid film presence when it comes to managing vibrations. It should be stated that damping capacity of a flat pad is higher than a pad with recess of same size and operating parameters. The lubricating film stiffness is proportional to its height (Eq. (4)); however, it differs with the type of flow compensation [32]. Damping coefficient is given by ratio of Fig. 7. Comparison of simulation and experiment results of flow patterns in the recess area for Re in a) 140, b) 350, and c) 701 (reprinted from [55] with permission of Taylor & Francis Ltd, http://www.tandfonline.com). M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 943 damping load and squeeze velocity [95], which is proportional to lubricant dynamic viscosity, pad geometry and compensation type, and film thickness (Eq. (5)). The required parameters should be reflected in the bearing optimization to achieve desired and optimal performance. Comparative stiffness and damping values can be found in references [86,96]; however, only for small-scale applications. k¼dW dh ð4Þ c¼W _ hð5Þ 3.2. Pad geometry optimization The bearing pad recess area provides enough lifting force to the bearing turntable and load. Additionally, the recessed pad has significantly better performance compared to a non-recessed pad [97,98], allowing the bearing to withstand higher rotating speeds and load variations. However, different recess shapes exhibit slightly different characteristics. Generally, mostly preferred are ones conventional shapes [99], such as circular, rectangular and annular, because of derived equations and manufacturability. Nonetheless, unusual and specific hydrostatic bearing recess geometry can be developed using sand casting, as introduced by Kotilainen and Slocum [100]. With the advancement of computational software and manufacturing technologies, triangular and elliptic [101], or even unconventional geometry shapes [102] can be developed. A comparison provided by Sharma et al. [99] summarized the recess shapes as follows: the circular shape is advantageous for the highest pocket pressure and the lowest required flow, annular exhibited highest stiffness and load capacity, and finally rectangular shape showed the highest damping ability. Sing et al. [101] confirmed the previous findings and investigated also a triangular shape, which happened to provide the highest film thickness from all compared shapes. Investigated unconventional shapes using numerical simulations, such as sector or cross shapes [103], can be adjusted to optimal performance and temperature control. Aside from the recess outline, the straightness of the recess cross section provides slightly different performance in aerostatic bearing investigation, as noticed Gao et al. [53]. The conical shape (Fig. 9a) exhibits higher load capacity at higher rotational speeds, while the straight shape (Fig. 9b) maintains higher load capacity Table 8 Optimization considerations of selected performance characteristics. Bearing characteristic Description Stiffness Oil supply rate redistribution among pads according to actual conditions can improve static performance by 17% while maintaining the same dynamic performance without further energy consumption [91]. Damping Impact resistance is improved by lowering film thickness [70,92]. Friction The higher the flow rates, the greater the friction torque. The effect is more significant while considering laminar and turbulent conditions [93]. Thermal effects Considering thermal effects in simulation decreases the load carrying capacity by about 3% and stiffness and damping by up to 10% [94]. Moreover, static stiffness drops significantly when considering temperature influence [66] according to FSI analysis results. Fig. 8. Results of CFD and proposed fast computation model calculation for load capacity, friction torque, and mass flow in 0.02 mm and 0.08 mm film thicknesses (reprinted from [85] with permission from Elsevier Ò ). M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 944 stage. Moreover, viscosity-shear dependence should also be taken into account, especially at rotational speeds above 60 r/min and heavy loads, because the hot oil carrying phenomenon occurs [189]. Basically, a higher viscosity fluid carries more load; however, it requires a higher pumping power, and generates more fluid friction. A low viscosity fluid might not reach desired load carrying capacity of the hydrostatic bearing [54]. Therefore, the lubricant should be selected for the optimal supply power and loadcarrying ability. Mostly used lubricants are oils because of certified classification of viscosity index (VI) according to ISO VG. In order to modify the performance or lubricant characteristics, VI improvers are used [190]. However, the NMR (Nuclear magnetic resonance) spectroscopy for the viscosity-temperature relation prediction offers more accurate results than standard measurements, which makes it beneficial mainly for high-precision bearings [191]. Basically, mineral oils are of satisfactory performance and relatively reasonable price. ISO VG 10/15/22/32/46/68/100/150 are chosen according to expected working and surrounding temperatures, and the hydrogenerator performance. Oils of these grades are advantageous due to low friction performance and a neutral effect Fig. 17. Final shapes of generated textures based on genetic algorithm and their performance compared to basic circular shape (reprinted from [61] with permission from Elsevier Ò ). Fig. 18. Flowchart of a hydraulic circuit design process and considerations. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 951 on sealing elements. Standard hydraulic oils are providing protection of the hydraulic circulation system components and are suitable for use at high pressures, up to 350 bar. Hydraulic oils performance is usually enhanced using lubricant additives [192], such as viscosity/temperature stabilizers, anti-wear and oxidation inhibitors and extreme pressure additives, which are often used for increased protection of extremely stressed contact surfaces. However, they might act aggressively when used in lubricating copper-based metals [193], especially at higher temperatures. Therefore, the lubricant should be selected regarding the material selection of hydrostatic bearing components. Obviously, the lubricant properties should be also controlled throughout the service life of the hydrostatic bearing since its working principle and performance relies on the lubricant properties. An important approach to bearing diagnostics is an oil monitoring technique, which is, however, difficult for ball bearings [194]. On the other hand, hydrostatic bearings have hydraulic circulation that can be easily modified for oil diagnostics and special filter addition. For specific environments other fluids could be used, based on their applicability and suitability. An example is water [36,175,195,196] and saltwater [28,29] that are beneficial for use in mechanism manipulation with a difficulty of oil sealing. However, in such aggressive conditions materials must be carefully selected and treated [152]. In case of extreme operating conditions, such as high vacuum, ionic liquid can be a suitable choice [197].In terms of performance improvement, non-Newtonian fluids have been recently investigated in numerous applications. As reported, a micropolar lubricant can improve the hydrostatic bearing performance [78] in terms of film thickness and stiffness. Yet, the restrictor performance is decreased, which influences the overall performance of the micropolar fluid-lubricated hydrostatic bearing. To find the optimal performance, fluid modelling is induced for the simplification of the design and development processes of hydrostatic bearing [198], such a model is, for example, the Rabinowitch fluid model that can be used for pseudoplastic, Newtonian, and dilatant fluids by changing a single parameter. The application of fluid modelling showed that a pseudoplastic lubricant has lower load-carrying capacity and higher frictional torque than Newtonian fluids, while dilatant fluids were reported [157] to exhibit a lower frictional power loss. In contrast, investigations on additive percentage included an improvement of the VI [199], which can be beneficial in environments with a large temperature difference. Compared to pseudoplastic fluids, fluid modelling of non-Newtonian fluids for the Bingham type showed higher load capacity [200] compared to conventional hydrostatic bearings. This type of fluid can describe the behaviour of smart fluids whose rheology can be modified [158] by electric and magnetic fields. Surface modification, such as magnetic texturing [201] (Fig. 20), can help to increase the load capacity of an magnetorheological fluid and improve the sealing ability [202] of the land, but it also increases the fluid friction. However, the required amount of hydrostatic bearing lubricant exceeds hundreds of litres. While the smart fluid price is very high [203], they have only been investigated in small applications. Other limitations are high required voltage for inducing a noticeable difference in electrorheological fluid performance [204] and an abrasive effect of magnetorheological particles [205,206] caused by high-pressure flow on sliding surfaces and hydraulic circuit components. Besides the abrasive effect, another limitation introduced by Urreta et al. [207] suggested the active compensation of unbalanced machine tool spindle shaft cannot be used due to slow response of hybrid bearing lubricated with magnetorheological fluid. Table 9 Comparison of compensating devices types for hydrostatic bearings flow control. Geometry type Restriction type Restrictor device Flow maintenance Stiffness Variable load range Film thickness compensation Power losses Cost Suitability Fixed geometry Constant flow [40] None High Medium Medium Medium Low High High accuracy systems Small hydrostatic bearing systems Pump needed for each pad (for multi-pad bearings) Capillary [101] Capillary tube Low Low Low Low High Low Low accuracy systems Any size Orifice [40,54,171,172] Orifice plate Low Low Low Low Medium/ high Low Low accuracy systems Any size Self-regulating [15] Flow divider High High High High Medium/ High High High viscous damping No restrictor needed Only for closed-type bearings Variable geometry Elastic member Elastic tube [4] Low Low Low Low Medium/ high Low Rubber capillary Limited pressure range Elastic surface plate [144] Low High High Low Medium/ high Low/medium (dependent on size) Inaccurate design for optimal compensation Inherent Membrane [101,173176] Medium High High High Medium Medium/high High accuracy systems Feedback system Servo valve [177,178] High High High High Medium (depended on load) High Variable loads – quick response (0.1 s) Long-term operation machines (variable viscosity condition) Feedback system (PID) – variable viscosity compensation M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 952 6. Summary This review has summarized the design and optimization process of large-scale hydrostatic bearings. This paper has also highlighted the latest improvements and challenges including hydraulic circuit components and modern advancements in digital technology. The hydrostatic bearing types are selected according to the expected loading direction and designed for the required static and dynamic performance. Analytical calculation provides the pad geometry and approximate static performance, while numerical simulations are utilized for geometry optimization, dynamic performance evaluation, and investigation of thermal properties. Analytical calculation provides a quick estimation of the bearing geometry and supply performance. In contrast, numerical analyses provide a critical insight into the possible future problem minimization, such as structural deformations and thermal influence effects on the performance and lubricating film stability. The bearing land texturing can improve the dynamic properties at higher speeds. As it turned out, the manufacturing process does influence the final bearing performance. It is required to achieve high bearing straightness, which is, however, difficult for large-scale structures. Therefore, a suitable compensation method must be applied – either flow compensation using restrictors, or surface compensation using compliant materials. Latest advancements in control technology offer a wide range of possibilities for bearing performance monitoring, management, and diagnostics. Hydraulic accumulators offer both fail-safe and vibration damping effects. Special lubricant additives can improve the bearing performance. As found out, smart fluids are not yet suitable for large-scale hydrostatic bearings, especially due to high price. The stated remarks can be applied both to radial and axial hydrostatic bearings of all sizes. 7. Future challenges Some of the greatest challenges will be the design of new largescale structures based on the hydrostatic lubrication principle, and the replacement of existing old rail turntables with silent hydrostatic bearings. A substantial part of future development will be aimed at numerical simulations improvement and combination, such as FSI etc. The future research might be oriented towards tolerable error specification to simplify the manufacturing and assembly processes of large-scale hydrostatic bearings. Error compensation can be improved using durable and stable compliant materials. Further improvement can be made in optical scanning of sliding surfaces during manufacturing and assembly to speed Fig. 19. Pressure-volume relationship for compressed gas in a hydraulic accumulator (reprinted from [182] with permission from Elsevier Ò ). Fig. 20. Pressure distribution of a magnetic texture in hybrid bearing system (reprinted from [201] under licence CC BY 3.0). M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 953 up the whole construction process. To avoid costly repairs, a failsafe surface texturing that act like lubricant reservoirs in case of sliding surface collision can be developed. A significant advancement can be achieved in real-time hydraulic circuit monitoring and adaptive regulation to provide optimal maintenance and condition prediction and adaptation based on big data analysis [208]. The emerging trend of utilizing modern progressive technologies of the Industry 4.0. era, such as Digital Twin (DT) and Internet of Things (IoT), open new ways in machine design, manufacturing [209] and control in the mechanical engineering industry. Possibly, the next industrial epoch might bring fully automated design, optimization and eventually also manufacturing using artificial intelligence (AI) that could exceptionally improve future technologies and satisfy increasing societal demands. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was carried out under the project FSI-S-17-4415 with financial support from the Ministry of Education, Youth and Sports of the Czech Republic. References [1] O. Reynolds, On the theory of lubrication and its application to Mr. Lowe’s experiments, Philos. Trans. R. Soc. London. 177 (1886) 157–234. [2] O.M.F.R.S. Lord Rayleigh, Notes on the theory of lubrication, London, Edinburgh, Dublin Philos, Mag. J. Sci. 35 (1918) 1–12, https://doi.org/ 10.1080/14786440108635730. [3] W.B. Rowe, Advances in hydrostatic and hybrid bearing technology, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 203 (1989) 225–242. https://doi.org/ 10.1243/PIME_PROC_1989_203_110_02. [4] R. Bassani, B. Piccigallo, Hydrostatic Lubrication, 22nd ed.,., Elsevier B.V, 1992. [5] X.B. Li, X. Wang, M. Li, Y.S. Ma, Y. Huang, The Research Status and Progress of Heavy/Large Hydrostatic Thrust Bearing, Adv. Mech. Eng. (2014), https://doi. org/10.1155/2014/982584. [6] Z.F. Liu, Y.M. Wang, L.G. Cai, Y.S. Zhao, Q. Cheng, X.M. Dong, A review of hydrostatic bearing system: Researches and applications, Adv. Mech. Eng. 9 (2017), https://doi.org/10.1177/1687814017730536. [7] R. Mahdi, K. Stephan, B. Friedrich, Experimental investigations on stick-slip phenomenon and friction characteristics of linear guides, Procedia Eng. 100 (2015) 1023–1031, https://doi.org/10.1016/j.proeng.2015.01.462. [8] J. Awrejcewicz, P. Olejnik, The Occurrence of Stick-Slip Phenomenon, (2017). [9] A. Bonanno, F. Pedrielli, a Study on the structureborne noise of hydraulic gear pumps, Proc. JFPS Int. Symp. Fluid Power. 2008 (2008) 641–646, https://doi. org/10.5739/isfp.2008.641. [10] V. Induced, I.F. Flow, Vibrations induced by internal fluid flow, Flow-Induced Vib. (2014) 157–195, https://doi.org/10.1016/b978-0-08-098347-9.00004-7. [11] H. Ortwig, Experimental and analytical vibration analysis in fluid power systems, Int. J. Solids Struct. 42 (2005) 5821–5830, https://doi.org/10.1016/j. ijsolstr.2005.03.028. [12] G. Chen, J. Wen, Load performance of large-scale rolling bearings with supporting structure in wind turbines, J. Tribol. 134 (2012), https://doi.org/ 10.1115/1.4007349. [13] G. Chen, J. Wen, Effects of size and raceway hardness on the fatigue life of large rolling bearing, J. Mech. Sci. Technol. 29 (2015) 3873–3883, https://doi. org/10.1007/s12206-015-0833-3. [14] L. Chen, X.T. Xia, H. tian Zheng, M. Qiu, Rework solution method on large size radial roller bearings, J. Brazilian Soc. Mech. Sci. Eng. 38 (2016) 1249–1260. https://doi.org/10.1007/s40430-015-0364-y. [15] R. Bassani, Hydrostatic self-regulating multipad journal and integral bearings, Tribol. Trans. 56 (2013) 187–195, https://doi.org/10.1080/ 10402004.2012.737501. [16] J.Y. Jang, M.M. Khonsari, On the characteristics of misaligned journal bearings, Lubricants. 3 (2015) 27–53, https://doi.org/10.3390/lubricants3010027. [17] E.A. Novikov, I.A. Shitikov, V.A. Maksimov, Calculation of the characteristics of a hydrostatic ring thrust bearing for refrigeration compressors, Chem. Pet. Eng. 40 (2004) 222–228, https://doi.org/10.1023/B:CAPE.0000033680.91322.0f. [18] M. Sheehan, S. Gunnels, C. Hull, J. Kern, C. Smith, M. Johns, S. Shectman, Progress on the structural and mechanical design of the Giant Magellan Telescope, Ground-Based Airborne Telesc. IV. 8444 (2012) 84440N, https:// doi.org/10.1117/12.926469. [19] M. Johns, C. Hull, G. Muller, B. Irarrazaval, A. Bouchez, T. Chylek, C. Smith, A. Wadhavkar, B. Bigelow, S. Gunnels, B. McLeod, C. Buleri, Design of the giant magellan telescope, Ground-Based Airborne Telesc. 9145 (2014) 91451F, https://doi.org/10.1117/12.2057286. [20] S.-H. Jang, Y.-H. Choi, S.-T. Kim, H.-S. An, H.-B. Choi, J.-S. Hong, Development of core technologies of multi-tasking machine tools for machining highly precision large parts, J. Korean Soc. Precis. Eng. 29 (2012) 129–138, https:// doi.org/10.7736/kspe.2012.29.2.129. [21] Z. Guo, T. Hirano, R.G. Kirk, Application of CFD analysis for rotating machinery - Part I: Hydrodynamic, hydrostatic bearings and squeeze film damper, J. Eng. Gas Turbines Power. 127 (2005) 445–451, https://doi.org/10.1115/ 1.1807415. [22] A. Bouzidane, M. Thomas, Nonlinear dynamic analysis of a rigid rotor supported by a three-pad hydrostatic squeeze film dampers, Tribol. Trans. 56 (2013) 717–727, https://doi.org/10.1080/10402004.2013.788238. [23] W.B. Rowe, Grinding Machine Developments, in: Princ. Mod. Grind. Technol., Elsevier, 2009: pp. 163–210. https://doi.org/10.1016/b978-0-8155-20184.50016-1. [24] Z. Liming, L. Yongyao, W. Zhengwei, L. Xin, X. Yexiang, A review on the large tilting pad thrust bearings in the hydropower units, Renew. Sustain. Energy Rev. 69 (2017) 1182–1198, https://doi.org/10.1016/j.rser.2016.09.140. [25] D.V. De Pellegrin, D.J. Hargreaves, An isoviscous, isothermal model investigating the influence of hydrostatic recesses on a spring-supported tilting pad thrust bearing, Tribol. Int. 51 (2012) 25–35, https://doi.org/ 10.1016/j.triboint.2012.02.008. [26] M. Wasilczuk, Friction and lubrication of large tilting-pad thrust bearings, Lubricants. 3 (2015) 164–180, https://doi.org/10.3390/lubricants3020164. [27] X. Raud, M. Fillon, M. Helene, Numerical modelling of hydrostatic lift pockets in hydrodynamic journal bearings – Application to low speed working conditions of highly loaded tilting pad journal bearings, Mech. Ind. 14 (2013) 327–334, https://doi.org/10.1051/meca/2013073. [28] R.A.J. Van Ostayen, A. Van Beek, M. Ros, A mathematical model of the hydro-support: An elasto-hydrostatic thrust bearing with mixed lubrication, Tribol. Int. 37 (2004) 607–616, https://doi.org/10.1016/j. triboint.2004.01.008. [29] E. Xu, Y. Wang, J. Wu, S. Xu, Y. Wang, S. Wang, Investigations on the applicability of hydrostatic bearing technology in a rotary energy recovery device through CFD simulation and validating experiment, Desalination. 383 (2016) 60–67, https://doi.org/10.1016/j.desal.2016.01.018. [30] Z. Liu, Y. Wang, L. Cai, Q. Cheng, H. Zhang, Design and manufacturing model of customized hydrostatic bearing system based on cloud and big data technology, Int. J. Adv. Manuf. Technol. 84 (2016) 261–273, https://doi.org/ 10.1007/s00170-015-8066-2. [31] I.F. Santos, Controllable sliding bearings and controllable lubrication principles-an overview, Lubricants. 6 (2018), https://doi.org/10.3390/ lubricants6010016. [32] M.M. Khonsari, E.R. Booser, Applied Tribology: Bearing Design and Lubrication, John Wiley & Sons Ltd, Chichester, UK (2017), https://doi.org/ 10.1002/9781118700280. [33] T. Seperamaniam, N.A.A. Jalil, Z.A. Zulkefli, Hydrostatic Bearing Design Selection for Automotive Application Using Pugh Controlled Convergence Method, Procedia Eng. 170 (2017) 422–429, https://doi.org/10.1016/j. proeng.2017.03.068. [34] A. Harnoy, Bearing design in machinery, Eng. Tribol. Lubrication (2003), https://doi.org/10.1201/9780203909072.ch6. [35] K. Cheng, W.B. Rowe, A selection strategy for the design of externally pressurized journal bearings, Tribol. Int. 28 (1995) 465–474, https://doi.org/ 10.1016/0301-679X(95)00011-R. [36] D. Fedorynenko, R. Kirigaya, Y. Nakao, Dynamic characteristics of spindle with water-lubricated hydrostatic bearings for ultra-precision machine tools, Precis. Eng. 63 (2020) 187–196, https://doi.org/10.1016/ j.precisioneng.2020.02.003. [37] Y. Wang, Z. Liu, Y. Zhao, X. Dong, L. Hun, L. Cai, Design of an intelligent monitoring system for hydrostatic turntable service performance evaluation, J. Ambient Intell. Humaniz. Comput. (2018), https://doi.org/10.1007/s12652018-1027-5. [38] C. Liu, J. Hu, Q. Hu, Preview Control of Hydrostatic Guideway for Ultraprecision CNC Machine Tools, Iran. J. Sci. Technol. - Trans, Mech. Eng. 43 (2019) 749–759, https://doi.org/10.1007/s40997-018-0192-7. [39] X. Zuo, S. Li, Z. Yin, J. Wang, Design and Parameter Study of a SelfCompensating Hydrostatic Rotary Bearing, Int. J. Rotating Mach. 2013 (2013) 1–10, https://doi.org/10.1155/2013/638193. [40] Y. Kang, J.L. Lee, H.C. Huang, C.Y. Lin, H.H. Lee, D.X. Peng, C.C. Huang, Design for static stiffness of hydrostatic plain bearings: Constant compensations, Ind. Lubr. Tribol. 63 (2011) 178–191, https://doi.org/10.1108/ 00368791111126608. [41] G. Hong, L. Xinmin, W. Xiaoling, C. Shaoqi, Performance of flat capillary compensated deep/shallow pockets hydrostatic/hydrodynamic journalthrust floating ring bearing, Tribol. Trans. 52 (2009) 204–212, https://doi. org/10.1080/10402000802354061. [42] X.O. Zuo, J.M. Wang, Z.Q. Yin, S.Y. Li, Self-compensated precision hydrostatic rotary bearing, Adv. Mater. Res. 662 (2013) 674–677, https://doi.org/10.4028/ www.scientific.net/AMR.662.674. [43] N.R. Kane, J. Sihler, A.H. Slocum, A hydrostatic rotary bearing with angled surface self-compensation, Precis. Eng. 27 (2003) 125–139, https://doi.org/ 10.1016/S0141-6359(02)00194-0. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 954 [44] S.C. Sharma, V.M. Phalle, S.C. Jain, Performance analysis of a multirecess capillary compensated conical hydrostatic journal bearing, Tribol. Int. 44 (2011) 617–626, https://doi.org/10.1016/j.triboint.2010.12.012. [45] X. Zuo, J. Wang, Z. Yin, S. Li, Comparative performance analysis of conical hydrostatic bearings compensated by variable slot and fixed slot, Tribol. Int. 66 (2013) 83–92, https://doi.org/10.1016/j.triboint.2013.04.013. [46] M. Kozdera, S. Drbáková, Numerical modelling of the flow in the annular multi-recess hydrostatic thrust bearing using CFD methods, EPJ Web Conf. 45 (2013), https://doi.org/10.1051/epjconf/20134501051. [47] Y. Kang, S.Y. Hu, Y.P. Chang, T.P. Wang, Identification of Characteristic Parameters for Hydrostatic Bearings, J. Mech. 31 (2015) 227–240, https://doi. org/10.1017/jmech.2014.91. [48] N.G. Chikurov, Modeling of hydrostatic bearings by electrical analogy, Russ. Eng. Res. 37 (2017) 517–522, https://doi.org/10.3103/S1068798X17060107. [49] B.M.A. Maher, Performance characteristics of an elliptic hydrostatic bearing and comparative analysis based on Stokes’ conditions, Acta Mech. 223 (2012) 1187–1198, https://doi.org/10.1007/s00707-012-0647-7. [50] B.J. Hamrock, S.R. Schmid, B.O. Jacobson, Fundamentals of Fluid Film Lubrication, 2nd ed., Marcel Dekker, New York, 2004. [51] H.C. Rippel, Cast bronze bearing design manual, Cast Bronze Bearing Institute (1960). [52] D. Chen, S. Zhou, L. Dong, J. Fan, Performance evaluation and comparative analysis of hydrostatic spindle affect by the oil film slip, J. Manuf. Process. 20 (2015) 128–136, https://doi.org/10.1016/j.jmapro.2015.09.002. [53] S. Gao, K. Cheng, S. Chen, H. Ding, H. Fu, CFD based investigation on influence of orifice chamber shapes for the design of aerostatic thrust bearings at ultrahigh speed spindles, Tribol. Int. 92 (2015) 211–221, https://doi.org/10.1016/j. triboint.2015.06.020. [54] F. Ghezali, A. Bouzidane, M. Thomas, 3D Numerical investigation of pressure field of an orifice compensated hydrostatic bearing, Mech. Ind. 18 (2017), https://doi.org/10.1051/meca/2016008. [55] F. Shen, C.L. Chen, Z.M. Liu, Effect of pocket geometry on the performance of a circular thrust pad hydrostatic bearing in machine tools, Tribol. Trans. 57 (2014) 700–714, https://doi.org/10.1080/10402004.2014.906694. [56] S. Yang, C. Li, M. Jiang, S. Pei, A study of inlet temperature models of a large size tilting thrust bearing comparison between theory and experiment, Tribol. Int. 140 (2019), https://doi.org/10.1016/j.triboint.2019.105881 105881. [57] X. Li, X. Wang, M. Li, Y. Ma, Y. Huang, The research status and progress of heavy/large hydrostatic thrust bearing, Adv. Mech. Eng. 2014 (2014), https:// doi.org/10.1155/2014/982584. [58] Y.T. Zhang, C.H. Lu, H.X. Zhao, W.J. Shi, P. Liang, Error Averaging Effect of Hydrostatic Journal Bearings Considering the Influences of Shaft Rotating Speed and External Load, IEEE Access. 7 (2019) 106346–106358, https://doi. org/10.1109/ACCESS.2019.2931948. [59] J. Zha, F. Xue, Y. Chen, Straightness error modeling and compensation for gantry type open hydrostatic guideways in grinding machine, Int. J. Mach. Tools Manuf. 112 (2017) 1–6, https://doi.org/10.1016/j. ijmachtools.2016.10.002. [60] F. Xue, W. Zhao, Y. Chen, Z. Wang, Research on error averaging effect of hydrostatic guideways, Precis. Eng. 36 (2012) 84–90, https://doi.org/10.1016/ j.precisioneng.2011.07.007. [61] H. Zhang, M. Hua, G. zhong Dong, D. ya Zhang, W. jian Chen, G. neng Dong, Optimization of texture shape based on Genetic Algorithm under unidirectional sliding, Tribol. Int. 115 (2017) 222–232. https://doi.org/ 10.1016/j.triboint.2017.05.017. [62] Q. Li, S. Zhang, Y. Wang, W.W. Xu, Z. Wang, Z. Wang, Principal normal stress cavitation criterion for CFD analysis of loading capacity in journal bearings, Ind. Lubr. Tribol. 71 (2019) 1047–1054, https://doi.org/10.1108/ILT-01-20190013. [63] X.D. Yu, X. Zuo, C. Liu, X.H. Zheng, H. Qu, T.F. Yuan, Oil film shape prediction of hydrostatic thrust bearing under the condition of high speed and heavy load, Ind. Lubr. Tribol. 70 (2018) 1243–1250, https://doi.org/10.1108/ILT-07-20170220. [64] M. Wodtke, A. Schubert, M. Fillon, M. Wasilczuk, P. Pajaczkowski, Large hydrodynamic thrust bearing: Comparison of the calculations and measurements, Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 228 (2014) 974– 983. https://doi.org/10.1177/1350650114528317. [65] M. Badshah, S. Badshah, S. Jan, Comparison of computational fluid dynamics and fluid structure interaction models for the performance prediction of tidal current turbines, J. Ocean Eng. Sci. 5 (2020) 164–172, https://doi.org/10.1016/ j.joes.2019.10.001. [66] L. Lu, H. Su, Y. Liang, Q. Zhang, Research on static stiffness of hydrostatic bearing using fluid-structure interaction analysis, Procedia Eng. 29 (2012) 1304–1308, https://doi.org/10.1016/j.proeng.2012.01.131. [67] Y.Q. Zhang, L.G. Fan, R. Li, C.X. Dai, X.D. Yu, Simulation and experimental analysis of supporting characteristics of multiple oil pad hydrostatic bearing disk, J. Hydrodyn. 25 (2013) 236–241, https://doi.org/10.1016/S1001-6058 (13)60358-3. [68] Y.Q. Zhang, X.Q. Xu, X.D. Yang, H.M. Li, H. Jiang, X.Y. Yu, Z.M. Shi, Analysis on influence of oil film thickness on temperature field of heavy hydrostatic bearing in variable viscosity condition, Adv. Mater. Res. 239–242 (2011) 1418–1421, https://doi.org/10.4028/www.scientific.net/AMR.239-242.1418. [69] J.P. Shao, C.X. Dai, Y.Q. Zhang, X.D. Yu, X.Q. Xu, Y.F. Wang, The effect of oil cavity depth on temperature field in heavy hydrostatic thrust bearing, J. Hydrodyn. 23 (2011) 676–680, https://doi.org/10.1016/S1001-6058(10) 60164-3. [70] L.G. Cai, Y.M. Wang, Z.F. Liu, Q. Cheng, Carrying capacity analysis and optimizing of hydrostatic slider bearings under inertial force and vibration impact using finite difference method (FDM), J. Vibroengineering. 17 (2015) 2781–2794. [71] X. Wang, Q. Xu, B. Wang, L. Zhang, H. Yang, Z. Peng, Effect of surface waviness on the static performance of aerostatic journal bearings, Tribol. Int. 103 (2016) 394–405, https://doi.org/10.1016/j.triboint.2016.07.026. [72] R. Nicoletti, Comparison between a meshless method and the finite difference method for solving the reynolds equation in finite bearings, J. Tribol. 135 (2013) 1–9, https://doi.org/10.1115/1.4024752. [73] Y. Zhang, X. Yang, H. Li, H. Jiang, X. Yu, Z. Shi, Research on influence of cavity depth on load capacity of heavy hydrostatic bearing in variable viscosity condition, Adv. Mater. Res. 129–131 (2010) 1181–1185, https://doi.org/ 10.4028/www.scientific.net/AMR.129-131.1181. [74] P.G. Khakse, V.M. Phalle, S.S. Mantha, Comparative performance of a non-recessed hole-entry hybrid/hydrostatic conical journal bearing compensated with capillary and orifice restrictors, Tribol. Ind. 38 (2016) 133– 148. [75] P.G. Khakse, V.M. Phalle, S.S. Mantha, Performance Analysis of a Nonrecessed Hybrid Conical Journal Bearing Compensated With Capillary Restrictors, J. Tribol. 138 (2016) 1–9, https://doi.org/10.1115/1.4030808. [76] V. Kumar, S.C. Sharma, Magneto-hydrostatic lubrication of thrust bearings considering different configurations of recess, Ind. Lubr. Tribol. 71 (2019) 915–923, https://doi.org/10.1108/ILT-10-2018-0370. [77] C.B. Khatri, S.C. Sharma, Influence of textured surface on the performance of non-recessed hybrid journal bearing operating with non-Newtonian lubricant, Tribol. Int. 95 (2016) 221–235, https://doi.org/10.1016/j. triboint.2015.11.017. [78] E. Rajasekhar Nicodemus, S.C. Sharma, Orifice compensated multirecess hydrostatic/hybrid journal bearing system of various geometric shapes of recess operating with micropolar lubricant, Tribol. Int. 44 (2011) 284–296, https://doi.org/10.1016/j.triboint.2010.10.026. [79] A. Chasalevris, D. Sfyris, Evaluation of the finite journal bearing characteristics, using the exact analytical solution of the Reynolds equation, Tribol. Int. 57 (2013) 216–234, https://doi.org/10.1016/j.triboint.2012.08.011. [80] X. Liang, X. Yan, W. Ouyang, R.J.K. Wood, F. Kuang, Z. Liu, X. Zhou, Comparison of measured and calculated water film thickness of a water-lubricated elastically supported tilting pad thrust bearing, Surf. Topogr. Metrol. Prop. 7 (2019), https://doi.org/10.1088/2051-672X/ab47a6. [81] B.S. Shenoy, R. Pai, Effect of turbulence on the static performance of a misaligned externally adjustable fluid film bearing lubricated with couple stress fluids, Tribol. Int. 44 (2011) 1774–1781, https://doi.org/10.1016/j. triboint.2011.06.025. [82] D. Dowson, Inertia effects in hydrostatic thrust bearings, J. Fluids Eng. Trans. ASME. 83 (1961) 227–234. https://doi.org/https://dx.doi.org/10.1115/ 1.3658931. [83] Y.Q. Zhang, Z.Q. Zhang, X.B. Kong, R. Li, H. Jiang, Application of dynamic mesh technology in the oil film flow simulation for hydrostatic bearing, Ind. Lubr. Tribol. 71 (2019) 74–82, https://doi.org/10.1108/ILT-08-2017-0222. [84] C. Cui, T. Guo, Y. Wang, Q. Dai, Research on carrying capacity of hydrostatic slideway on heavy-duty gantry CNC machine, AIP Conf. Proc. 1839 (2017), https://doi.org/10.1063/1.4982524. [85] P. Novotny ´, J. Hrabovsky ´, J. Jurac ˇka, J. Klíma, V. Hort, Effective thrust bearing model for simulations of transient rotor dynamics, Int. J. Mech. Sci. 157–158 (2019) 374–383, https://doi.org/10.1016/j.ijmecsci.2019.04.057. [86] Z. Wang, Y. Liu, F. Wang, Rapid calculation method for estimating static and dynamic performances of closed hydrostatic guideways, Ind. Lubr. Tribol. 69 (2017) 1040–1048, https://doi.org/10.1108/ILT-01-2017-0003. [87] P. Liang, C.H. Lu, W. Pan, S.Y. Li, A new method for calculating the static performance of hydrostatic journal bearing, Tribol. Int. 77 (2014) 72–77, https://doi.org/10.1016/j.triboint.2014.04.019. [88] E. Solmaz, F.C. Babalik, F. Öztürk, Multicriteria optimization approach for hydrostatic bearing design, Ind. Lubr. Tribol. 54 (2002) 20–25, https://doi.org/ 10.1108/00368790210415338. [89] D. Fedorynenko, S. Sapon, S. Boyko, Accuracy of spindle units with hydrostatic bearings, Acta Mech. Autom. 10 (2016) 117–124, https://doi.org/10.1515/ ama-2016-0019. [90] D. Fedorynenko, S. Sapon, S. Boyko, A. Urlina, Increasing of energy efficiency of spindles with fluid bearings, Acta Mech. Autom. 11 (2017) 204–209, https://doi.org/10.1515/ama-2017-0031. [91] Y. Wang, Z. Liu, Q. Cheng, Y. Zhao, Y. Wang, L. Cai, Analysis and optimization of nonlinear carrying performance of hydrostatic ram based on finite difference method and Runge-Kutta method, Adv. Mech. Eng. 11 (2019) 1– 12, https://doi.org/10.1177/1687814019856128. [92] X.C. Zhu, W.G. Gao, T. Liu, S.H. Zhao, G.W. Zhang, D.W. Zhang, Analysis on dynamic characteristics of closed hydrostatic guideway throttled by capillary, Appl. Mech. Mater. 607 (2014) 594–599, https://doi.org/10.4028/ www.scientific.net/AMM.607.594. [93] L.J. Nypan, B.J. Hamrock, H.W. Scibbe, W.J. Anderson, Optimization of Conical Hydrostatic Bearing for Minimum Friction, J. Lubr. Technol. 94 (1972) 136– 142, https://doi.org/10.1115/1.3451656. [94] Z.F. Liu, C.P. Zhan, Q. Cheng, Y.S. Zhao, X.Y. Li, Y.D. Wang, Thermal and tilt effects on bearing characteristics of hydrostatic oil pad in rotary table, J. Hydrodyn. 28 (2016) 585–595, https://doi.org/10.1016/S1001-6058(16) 60662-5. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 955 [95] M.L. Adams, W. Shapiro, Squeeze film characteristics in flat hydrostatic bearings with incompressible flow, ASLE Trans. 12 (1969) 183–189, https:// doi.org/10.1080/05698196908972260. [96] A. Bouzidane, M. Thomas, Equivalent stiffness and damping investigation of a hydrostatic journal bearing, Tribol. Trans. 50 (2007) 257–267, https://doi.org/ 10.1080/10402000701309745. [97] A.W. Yacout, A.S. Ismaeel, S.Z. Kassab, The surface roughness effect on the hydrostatic thrust spherical bearing performance (part 2 of 5, clearance type of bearings), Am. Soc. Mech. Eng. Tribol. Div. TRIB. (2006), https://doi.org/ 10.1115/imece2006-13004. [98] A.W. Yacout, The surfacse roughness effect on the hydrostatic thrust spherical bearings performance (part 3 of 5, recessed clearance type of bearings), ASME Int, Mech. Eng. Congr. Expo. Proc. 9 (2007) 431–447, https://doi.org/10.1115/ IMECE2007-41013. [99] S.C. Sharma, S.C. Jain, D.K. Bharuka, Influence of recess shape on the performance of a capillary compensated circular thrust pad hydrostatic bearing, Tribol. Int. 35 (2002) 347–356, https://doi.org/10.1016/S0301-679X (02)00013-0. [100] M.S. Kotilainen, A.H. Slocum, Manufacturing of cast monolithic hydrostatic journal bearings, Precis. Eng. 25 (2001) 235–244, https://doi.org/10.1016/ S0141-6359(01)00075-7. [101] N. Singh, S.C. Sharma, S.C. Jain, S.S. Reddy, Performance of membrane compensated multirecess hydrostatic/hybrid flexible journal bearing system considering various recess shapes, Tribol. Int. 37 (2004) 11–24, https://doi. org/10.1016/S0301-679X(03)00110-5. [102] S.C. Sharma, R. Sinhasan, S.C. Jain, N. Singh, S.K. Singh, Performance of hydrostatic/hybrid journal bearings with unconventional recess geometries, Tribol. Trans. 41 (1998) 375–381, https://doi.org/10.1080/ 10402009808983761. [103] M.B. Yu, X.D. Yu, X.H. Zheng, H. Qu, T.F. Yuan, D.G. Li, Influence of recess shape on comprehensive lubrication performance of high speed and heavy load hydrostatic thrust bearing, Ind. Lubr. Tribol. 71 (2019) 301–308, https:// doi.org/10.1108/ILT-05-2018-0204. [104] M. Dzodzo, M.J. Braun, R.C. Hendricks, Pressure and flow characteristics in a shallow hydrostatic pocket with rounded pocket/land joints, Tribol. Int. 29 (1996) 69–76, https://doi.org/10.1016/0301-679X(95)00036-4. [105] M. Fillon, M. Wodtke, M. Wasilczuk, Effect of presence of lifting pocket on the THD performance of a large tilting-pad thrust bearing, Friction. 3 (2015) 266– 274, https://doi.org/10.1007/s40544-015-0092-4. [106] M. Wasilczuk, M. Wodtke, L. Dabrowski, Field tests on hydrodynamic and hybrid operation of a bidirectional thrust bearing of a pump-turbine, Lubricants. 5 (2017), https://doi.org/10.3390/lubricants5040048. [107] F. Canbulut, C. Sinanog ˘lu, E. Koç, Experimental analysis of frictional power loss of hydrostatic slipper bearings, Ind. Lubr. Tribol. 61 (2009) 123–131, https://doi.org/10.1108/00368790910953631. [108] O.J. Bakker, R.A.J. van Ostayen, Recess depth optimization for rotating, annular, and circular recess hydrostatic thrust bearings, J. Tribol. 132 (2010) 1–7, https://doi.org/10.1115/1.4000545. [109] F.E. Horvat, M.J. Braun, Comparative experimental and numerical analysis of flow and pressure fields inside deep and shallow pockets for a hydrostatic bearing, Tribol. Trans. 54 (2011) 548–567. https://doi.org/10.1080/ 10402004.2011.575535. [111] Z. Tian, M. Zhao, Y. Huang, Static properties of hydrostatic thrust bearing considering couple stress, DEStech Trans. Eng. Technol. Res. (2017) 29–33. [112] X. Yu, D. Liu, X. Meng, X. Fu, Z. Wang, Q. Zhou, B. Wu, Y. Zhang, B. Qin, X. Dong, Numerical Simulation of the Effects of Recess Depth on Dynamic Effect of Hydrostatic Thrust Bearing, 31 (2013) 1–5. https://doi.org/10.14257/ astl.2013.31.01. [113] J.P. Shao, G.D. Liu, X.D. Yu, Y.Q. Zhang, X.L. Meng, H. Jiang, Effect of recess depth on lubrication performance of annular recess hydrostatic thrust bearing by constant rate flow, Ind. Lubr. Tribol. 70 (2018) 68–75, https:// doi.org/10.1108/ILT-03-2017-0066. [114] M. Helene, M. Arghir, J. Frene, Numerical study of the pressure pattern in a two-dimensional hybrid journal bearing recess, laminar, and turbulent flow results, J. Tribol. 125 (2003) 283–290, https://doi.org/10.1115/1.1537233. [115] X. Xu, J. Shao, X. Yang, Y. Zang, X. Yu, B. Gao, Simulation on multi-oil-cavity and multi-oil-pad hydrostatic bearings, Appl. Mech. Mater. 274 (2013) 274– 277, https://doi.org/10.4028/www.scientific.net/AMM.274.274. [116] J. Peng Shao, G. dong Liu, X. Yu, Simulation and experiment on pressure field characteristics of hydrostatic hydrodynamic hybrid thrust bearings, Ind. Lubr. Tribol. 71 (2019) 102–108. https://doi.org/10.1108/ILT-02-2018-0063. [117] S. Wang, X. Du, D. Li, Q. Hu, Characteristic study on temperature field of hydrostatic bearing of hydroforming machine, Adv. Mater. Res. 605–607 (2013) 630–635, https://doi.org/10.4028/www.scientific.net/AMR.605607.630. [118] M. Weck, Werkzeugmaschinen 2 - Konstruktion und Berechnung, Springer, Berlin Heidelberg, Berlin, Heidelberg (2006), https://doi.org/10.1007/978-3540-30438-8. [119] J.P. Shao, Y.Q. Zhang, Y.H. Li, X.D. Yu, H. Jiang, Influence of load capcaity on hydrostatic journal support deformation in finite element calculation, J. Cent. South Univ. Technol. 15 (2008) 245–249, https://doi.org/10.1007/ s1177100804651. [120] T. Liu, W. Gao, Y. Tian, K. Mao, G. Pan, D. Zhang, Thermal simulation modeling of a hydrostatic machine feed platform, Int. J. Adv. Manuf. Technol. 79 (2015) 1581–1595, https://doi.org/10.1007/s00170-015-6881-0. [121] Y.Q. Zhang, L.G. Fan, Y. Chen, R. Li, T.Z. Wu, X.D. Yu, Deformation analysis of hydrostatic thrust bearing under different load, Appl. Mech. Mater. 494–495 (2014) 583–586, https://doi.org/10.4028/www.scientific.net/AMM.494495.583. [122] P. Pajaczkowski, A. Schubert, M. Wasilczuk, M. Wodtke, Simulation of large thrust-bearing performance at transient states, warm and cold start-up, Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 228 (2014) 96–103. https://doi.org/ 10.1177/1350650113500483. [123] X.D. Yu, Y. Wang, D.F. Zhou, G.P. Wu, W.K. Zhou, H.W. Bi, Heat Transfer Characteristics of High Speed and Heavy Load Hydrostatic Bearing, Ieee Access. 7 (2019) 110770–110780, https://doi.org/10.1109/ ACCESS.2019.2933471. [124] M.B. Yu, X.D. Yu, X.H. Zheng, H. Jiang, Thermal-fluid-solid coupling deformation of hydrostatic thrust bearing friction pairs, Ind. Lubr. Tribol. 71 (2019) 467–473, https://doi.org/10.1108/ILT-07-2018-0262. [125] Y.Q. Zhang, Z. Quan, M. Shi, H.D. Feng, Y.L. Liu, Improvement of hydrostatic bearing workbench structure based on the thermal deformation, 10th Int, Conf. Comput. Sci. Educ. ICCSE 2015 (2015) 528–531, https://doi.org/ 10.1109/ICCSE.2015.7250303. [126] X.B. Li, W.X. Li, X.Y. Chen, M. Li, H.Y. Chen, X. Yue, Design and performance analysis on heat pipe hydrostatic thrust bearings based on rectangular oil pad, Ind. Lubr. Tribol. 70 (2018) 1251–1257, https://doi.org/10.1108/ILT-102017-0303. [127] H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, F. Delbressine, Geometric error measurement and compensation of machinesAn update, CIRP Ann. - Manuf. Technol. 57 (2008) 660–675, https://doi.org/ 10.1016/j.cirp.2008.09.008. [128] W. Huang, Z. Kong, Simulation and integration of geometric and rigid body kinematics errors for assembly variation analysis, J. Manuf. Syst. 27 (2008) 36–44, https://doi.org/10.1016/j.jmsy.2008.06.004. [129] Z. Wang, W. Zhao, Y. Chen, B. Lu, Prediction of the effect of speed on motion errors in hydrostatic guideways, Int. J. Mach. Tools Manuf. 64 (2013) 78–84, https://doi.org/10.1016/j.ijmachtools.2012.07.011. [130] P. Zhang, Y. Chen, C. Zhang, J. Zha, T. Wang, Influence of geometric errors of guide rails and table on motion errors of hydrostatic guideways under quasistatic condition, Int. J. Mach. Tools Manuf. 125 (2018) 55–67, https://doi.org/ 10.1016/j.ijmachtools.2017.10.006. [131] E. Qi, Z. Fang, T. Sun, J. Chen, C. Liu, J. Wang, A method for predicting hydrostatic guide error averaging effects based on three-dimensional profile error, Tribol. Int. 95 (2016) 279–289, https://doi.org/10.1016/j. triboint.2015.11.032. [132] J. Zha, Y. Chen, Z. Wang, A tolerance design method for hydrostatic guideways motion accuracy based on error averaging effect, Procedia CIRP. 75 (2018) 196–201, https://doi.org/10.1016/j.procir.2018.04.054. [133] P.H. Zhang, Y.L. Chen, X.T. Liu, Relationship between roundness errors of shaft and radial error motions of hydrostatic journal bearings under quasi-static condition, Precis. Eng. Int. Soc. Precis. Eng. Nanotechnol. 51 (2018) 564–576, https://doi.org/10.1016/j.precisioneng.2017.10.012. [134] A.K. Rajput, S.C. Sharma, Combined influence of geometric imperfections and misalignment of journal on the performance of four pocket hybrid journal bearing, Tribol. Int. 97 (2016) 59–70, https://doi.org/10.1016/j. triboint.2015.12.049. [135] P.H. Zhang, Y.L. Chen, J. Zha, Relationship between geometric errors of thrust plates and error motions of hydrostatic thrust bearings under quasi-static condition, Precis. Eng. Int. Soc. Precis. Eng. Nanotechnol. 50 (2017) 119–131, https://doi.org/10.1016/j.precisioneng.2017.04.020. [136] H. Cui, Y. Wang, X. Yue, M. Huang, W. Wang, Effects of manufacturing errors on the static characteristics of aerostatic journal bearings with porous restrictor, Tribol. Int. 115 (2017) 246–260, https://doi.org/10.1016/j. triboint.2017.05.008. [137] N.D. Manring, R.E. Johnson, H.P. Cherukuri, The Impact of Linear Deformations on Stationary Hydrostatic Thrust Bearings, J. Tribol. 124 (2002) 874–877, https://doi.org/10.1115/1.1482118. [138] L. Zoupas, M. Wodtke, C.I. Papadopoulos, M. Wasilczuk, Effect of manufacturing errors of the pad sliding surface on the performance of the hydrodynamic thrust bearing, Tribol. Int. 134 (2019) 211–220, https://doi. org/10.1016/j.triboint.2019.01.046. [139] J.R. Lin, Surface roughness effect on the dynamic stiffness and damping characteristics of compensated hydrostatic thrust bearings, Int. J. Mach. Tools Manuf. 40 (2000) 1671–1689, https://doi.org/10.1016/S0890-6955(00) 00012-2. [140] S. Zhu, J. Sun, B. Li, G. Zhu, Thermal turbulent lubrication analysis of rough surface journal bearing with journal misalignment, Tribol. Int. 144 (2020), https://doi.org/10.1016/j.triboint.2019.106109 106109. [141] Y. Wang, Y. Zhao, L. Cai, Z. Liu, Q. Cheng, Effects of thermal and hydrodynamic characteristics of heavy-duty rotary table on the hydrostatic circular pads, J. Vibroengineering. 18 (2016) 4193–4206. https://doi.org/10.21595/jve.2016. 17079. [142] P. Sapirstein, Accurate measurement with photogrammetry at large sites, J. Archaeol. Sci. 66 (2016) 137–145, https://doi.org/10.1016/j.jas.2016.01.002. [143] A. Van Beek, A. Segal, Rubber supported hydrostatic thrust bearings with rigid bearing surfaces, Tribol. Int. 30 (1997) 47–52, https://doi.org/10.1016/ 0301-679X(96)00021-7. [144] A. Van Beck, L. Lepic, Rubber supported hydrostatic thrust bearings with elastic bearing surfaces of infinite length, 201 (1996) 45–50. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 956 [145] Y.C. Shiau, M.T. Wang, C.M. Huang, J.Y. Zeng, Discussion of pot bearing for concrete bridge, ISARC 2008 - Proc. from 25th Int. Symp. Autom. Robot. Constr. (2008) 213–223. https://doi.org/10.3846/isarc.20080626.213. [146] A. Niemierko, Modern Bridge Bearings and Expansion Joints for Road Bridges, Transp. Res. Procedia. 14 (2016) 4040–4049, https://doi.org/10.1016/j. trpro.2016.05.501. [147] K. Ahmed, S.S. Nizami, N.Z. Raza, K. Mahmood, Mechanical, swelling, and thermal aging properties of marble sludge-natural rubber composites, Int. J. Ind. Chem. 3 (2012) 1–12, https://doi.org/10.1186/2228-5547-3-21. [148] T. Susanto, R. Affandy, G. Katon, Rahmaniar, Thermal aging properties of natural rubber-styrene butadiene rubber composites filled with modified starch from Dioscorea Hispida Denst extract prepared by latex compounding method, AIP Conf. Proc. 2049 (2018), https://doi.org/10.1063/1.5082421. [149] B. Moon, J. Lee, S. Park, C.S. Seok, Study on the aging behavior of natural rubber/butadiene rubber (NR/BR) blends using a parallel spring model, Polymers (Basel). 10 (2018), https://doi.org/10.3390/polym10060658. [150] M. Ben Hassine, M. Naït-Abdelaziz, F. Zaïri, X. Colin, C. Tourcher, G. Marque, Time to failure prediction in rubber components subjected to thermal ageing: A combined approach based upon the intrinsic defect concept and the fracture mechanics, Mech. Mater. 79 (2014) 15–24, https://doi.org/10.1016/j. mechmat.2014.07.015. [151] N.D.S.A. Santos, V.R. Roso, M.T.C. Faria, Review of engine journal bearing tribology in start-stop applications, Eng. Fail. Anal. 108 (2020), https://doi. org/10.1016/j.engfailanal.2019.104344 104344. [152] J. Alcántara, D. de la Fuente, B. Chico, J. Simancas, I. Díaz, M. Morcillo, Marine atmospheric corrosion of carbon steel: A review, Materials (Basel). 10 (2017), https://doi.org/10.3390/ma10040406. [153] F. Summer, F. Grün, E.R. Ravenhill, Friction and wear performance of various polymer coatings for journal bearings under stop start sliding, Lubricants. 8 (2020), https://doi.org/10.3390/lubricants8010001. [154] A. Matthews, S. Franklin, K. Holmberg, Tribological coatings: Contact mechanisms and selection, J. Phys. D. Appl. Phys. 40 (2007) 5463–5475, https://doi.org/10.1088/0022-3727/40/18/S07. [155] A. Vencl, L. Ivanovic ´, B. Stojanovic ´, E. Zadorozhnaya, S. Miladinovic ´,P. Svoboda, Surface texturing for tribological applications: a review, Proc. Eng. Sci. 1 (2019) 227–239. https://doi.org/10.24874/PES01.01.029. [156] S.C. Sharma, S.K. Yadav, Performance analysis of a fully textured hybrid circular thrust pad bearing system operating with non-Newtonian lubricant, Tribol. Int. 77 (2014) 50–64, https://doi.org/10.1016/j.triboint.2014.04.013. [157] S.K. Yadav, S.C. Sharma, Performance of Hydrostatic Textured Thrust Bearing with Supply Holes Operating with Non-Newtonian Lubricant, Tribol. Trans. 59 (2016) 408–420, https://doi.org/10.1080/10402004.2015.1083065. [158] M. Michalec, P. Svoboda, I. Krupka, M. Hartl, Tribological Behaviour of Smart Fluids Influenced by Magnetic and Electric Field – A Review, Tribol. Ind. 40 (2018) 515–528. https://doi.org/10.24874/ti.2018.40.04.01. [159] J. Ji, Y. Fu, Q. Bi, Influence of geometric shapes on the hydrodynamic lubrication of a partially textured slider with micro-grooves, J. Tribol. 136 (2014), https://doi.org/10.1115/1.4027633. [160] D. Gropper, T.J. Harvey, L. Wang, Numerical analysis and optimization of surface textures for a tilting pad thrust bearing, Tribol. Int. 124 (2018) 134– 144, https://doi.org/10.1016/j.triboint.2018.03.034. [161] I. Etsion, G. Halperin, A laser surface textured hydrostatic mechanical seal, Tribol. Trans. 45 (2002) 430–434, https://doi.org/10.1080/ 10402000208982570. [162] V. Brizmer, Y. Kligerman, I. Etsion, A laser surface textured parallel thrust bearing, Tribol. Trans. 46 (2003) 397–403, https://doi.org/10.1080/ 10402000308982643. [163] F.M. Meng, On influence of cavitation in lubricant upon tribological performances of textured surfaces, Opt. Laser Technol. 48 (2013) 422–431, https://doi.org/10.1016/j.optlastec.2012.10.020. [164] F. Avellan, Introduction to cavitation in hydraulic machinery, 6th Int, Conf. Hydraul. Mach. Hydrodyn. (2004) 11–22. [165] D. Gropper, L. Wang, T.J. Harvey, Hydrodynamic lubrication of textured surfaces: A review of modeling techniques and key findings, Tribol. Int. 94 (2016) 509–529, https://doi.org/10.1016/j.triboint.2015.10.009. [166] Q. Li, Y. Wang, S. Zhang, W.W. Xu, Z. Wang, Z. Wang, Optimal design of parallel sliders with square-shaped textures considering fluid-structure interaction, Ind. Lubr. Tribol. 71 (2019) 620–627, https://doi.org/10.1108/ ILT-09-2018-0366. [167] Y. Zhang, G. Chen, L. Wang, Effects of thermal and elastic deformations on lubricating properties of the textured journal bearing, Adv. Mech. Eng. 11 (2019) 1–12, https://doi.org/10.1177/1687814019883790. [168] C. Xu, S. Jiang, Analysis of the Static Characteristics of a Self-Compensation Hydrostatic Spherical Hinge, J. Tribol. 137 (2015) 1–5, https://doi.org/ 10.1115/1.4030712. [169] W.U.R. Rehman, Y.X. Luo, Y.Q. Wang, G.Y. Jiang, N. Iqbal, S.U.R. Rehman, S. Bibi, Fuzzy logic-based intelligent control for hydrostatic journal bearing, Meas. Control. 52 (2019) 229–243, https://doi.org/10.1177/ 0020294019830110. [170] W.J. Moore, A.G. Starr, An intelligent maintenance system for continuous cost-based prioritisation of maintenance activities, Comput. Ind. 57 (2006) 595–606, https://doi.org/10.1016/j.compind.2006.02.008. [171] D.W. Childs, P. Esser, Measurements Versus Predictions for a Hybrid (Hydrostatic Plus Hydrodynamic) Thrust Bearing for a Range of Orifice Diameters, J. Eng. Gas Turbines Power-Transactions Asme. 141 (2019), https://doi.org/10.1115/1.4042721. [172] M.S. Shah, J.B. Joshi, A.S. Kalsi, C.S.R. Prasad, D.S. Shukla, Analysis of flow through an orifice meter: CFD simulation, Chem. Eng. Sci. 71 (2012) 300–309, https://doi.org/10.1016/j.ces.2011.11.022. [173] D.C. Chen, M.F. Chen, C.H. Pan, J.Y. Pan, Study of membrane restrictors in hydrostatic bearing, Adv. Mech. Eng. 10 (2018) 1–8, https://doi.org/10.1177/ 1687814018799604. [174] T.H. Lai, T.Y. Chang, Y.L. Yang, S.C. Lin, Parameters design of a membrane-type restrictor with single-pad hydrostatic bearing to achieve high static stiffness, Tribol. Int. 107 (2017) 206–212, https://doi.org/10.1016/j. triboint.2016.11.037. [175] M. Gohara, K. Somaya, M. Miyatake, S. Yoshimoto, Static characteristics of a water-lubricated hydrostatic thrust bearing using a membrane restrictor, Tribol. Int. 75 (2014) 111–116, https://doi.org/10.1016/j. triboint.2014.03.016. [176] H. Sawano, Y. Nakamura, H. Yoshioka, H. Shinno, High performance hydrostatic bearing using a variable inherent restrictor with a thin metal plate, Precis. Eng. Int. Soc. Precis. Eng. Nanotechnol. 41 (2015) 78–85, https:// doi.org/10.1016/j.precisioneng.2015.02.001. [177] W.U. Rehman, G. Jiang, Y. Luo, Y. Wang, W. Khan, S.U. Rehman, N. Iqbal, Control of active lubrication for hydrostatic journal bearing by monitoring bearing clearance, Adv. Mech. Eng. 10 (2018) 1–17, https://doi.org/10.1177/ 1687814018768142. [178] W.U. Rehman, L. Yuanxin, J. Guiyun, W. Yongqin, X. Yun, M.N. Iqbal, M.A. Zaheer, I. Azhar, H. Elahi, Y. Xiaogao, Control of an oil film thickness in a hydrostatic journal bearing under different dynamic conditions, Proc. 29th Chinese Control Decis. Conf. CCDC 2017 (2017) 5072–5076, https://doi.org/ 10.1109/CCDC.2017.7979395. [179] K.E. Rydberg, Hydraulic accumulators as key components in energy efficient mobile systems, Proc. 6th Int, Conf. Fluid Power Transm. Control. ICFP 2005 (2005,) 124–129. [180] M. Xian-ting, Review of the present status of hydraulic accumulator, Appl. Mech. Mater. 246–247 (2013) 629–634, https://doi.org/10.4028/ www.scientific.net/AMM.246-247.629. [181] W. Latas, J. Stojek, A new type of hydrokinetic accumulator and its simulation in hydraulic lift with energy recovery system, Energy. 153 (2018) 836–848, https://doi.org/10.1016/j.energy.2018.04.040. [182] D. Buhagiar, T. Sant, Modelling of a novel hydro-pneumatic accumulator for large-scale offshore energy storage applications, J. Energy Storage. 14 (2017) 283–294, https://doi.org/10.1016/j.est.2017.05.005. [183] D. Zhao, W. Ge, X. Mo, B. Liu, D. Dong, Design of a new hydraulic accumulator for transient large flow compensation, Energies. 12 (2019), https://doi.org/ 10.3390/en12163104. [184] M. Dai, S. Zhao, X. Yuan, The application study of accumulator used in hydraulic system of 20MN fast forging machine, Appl. Mech. Mater. 80–81 (2011) 870–874, https://doi.org/10.4028/www.scientific.net/AMM.8081.870. [185] S. Mamc ˇic, M. Bogdevic ˇius, Simulation of dynamic processes in hydraulic accumulators, Transport. 25 (2010), https://doi.org/ 10.3846/transport.2010.26. [186] K. Kuze, H. Sawano, H. Yoshioka, H. Shinno, Hydrostatic bearing with high bulk modulus fluid, Key Eng. Mater. 523–524 (2012) 532–537, https://doi. org/10.4028/www.scientific.net/KEM.523-524.532. [187] Y. Zhang, X. Yu, X. Yang, G. Sun, X. Yu, Z. Shi, Viscosity influence research on load capacity of heavy hydrostatic bearing, Key Eng. Mater. 450 (2011) 63– 66, https://doi.org/10.4028/www.scientific.net/KEM.450.63. [188] Y.W. Liu, S.C. Lin, C.H. Chang, P.S. Lan, Design and test of hydrostatic built-in spindle compensated by orifice restrictors, Proc. 2018 IEEE Int. Conf. Adv. Manuf. ICAM 2018. (2019) 302–305. https://doi.org/10.1109/ AMCON.2018.8614907. [189] Y.Q. Zhang, P.R. Kong, Y.A. Feng, L.L. Guo, Hot oil carrying characteristic about hydrostatic bearing oil film of heavy vertical lathe in high speed, Ind. Lubr. Tribol. 71 (2019) 126–132, https://doi.org/10.1108/ILT-03-2018-0091. [190] E.F. Jordan, S. Smith, R.E. Koos, W.E. Parker, B. Artymyshyn, A.N. Wrigley, Viscosity index. I. Evaluation of selected copolymers incorporating noctadecyl acrylate as viscosity index improvers, J. Appl. Polym. Sci. 22 (1978) 1509–1528, https://doi.org/10.1002/app.1978.070220606. [191] S. Verdier, J.A.P. Coutinho, A.M.S. Silva, O.F. Alkilde, J.A. Hansen, A critical approach to viscosity index, Fuel. 88 (2009) 2199–2206, https://doi.org/ 10.1016/j.fuel.2009.05.016. [192] P.D. Srivyas, M.S. Charoo, Effect of lubricants additive: Use and benefit, Mater. Today Proc. 18 (2019) 4773–4781, https://doi.org/10.1016/ j.matpr.2019.07.465. [193] R.W. Wilson, S.B. Lyon, Corrosion in lubricants/fuels, in, Shreir’s Corros., Elsevier (2010) 1299–1307, https://doi.org/10.1016/B978-0444527875.00059-7. [194] X. Bai, H. Xiao, L. Zhang, The condition monitoring of large slewing bearing based on oil analysis method, Key Eng. Mater. 474–476 (2011) 716–719, https://doi.org/10.4028/www.scientific.net/KEM.474-476.716. [195] A. Yui, G. Okahata, S. Okuyama, H. Kobayashi, A.H. Slocum, Development of a linear-motor-driven table supported by hydrostatic water bearings: Effect of air volume contained in water-supply tube on pitching motion of table slider, Key Eng. Mater., Trans Tech Publications Ltd (2010) 508–512, https://doi.org/ 10.4028/www.scientific.net/KEM.447-448.508. [196] A.H. Slocum, P.A. Scagnetti, N.R. Kane, C. Brunner, Design of selfcompensated, water-hydrostatic bearings, Precis. Eng. 17 (1995) 173–185, https://doi.org/10.1016/0141-6359(94)00015-R. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 957 [197] T. Okabe, S. Sasaki, Y. Kondo, M. Miyatake, S. Yoshimoto, Hydrostatic ionic liquid-lubricated fluid film bearing for a rotational electron-beam lithography system, Precis. Eng. 61 (2020) 194–203. https://doi.org/ 10.1016/j.precisioneng.2019.10.008. [198] Y. Huang, Z. Tian, A new derivation to study the steady performance of hydrostatic thrust bearing: Rabinowitch fluid model, J. Nonnewton. Fluid Mech. 246 (2017) 31–35, https://doi.org/10.1016/j.jnnfm.2017.04.012. [199] U.P. Singh, R.S. Gupta, V.K. Kapur, On the steady performance of hydrostatic thrust bearing: Rabinowitsch fluid model, Tribol. Trans. 54 (2011) 723–729, https://doi.org/10.1080/10402004.2011.597541. [200] S.G.E. Lampaert, R.A.J. van Ostayen, Load and stiffness of a hydrostatic bearing lubricated with a Bingham plastic fluid, J. Intell. Mater. Syst. Struct. (2019), https://doi.org/10.1177/1045389X19873426. [201] S.G.E. Lampaert, F. Quinci, R.A.J. van Ostayen, Rheological texture in a journal bearing with magnetorheological fluids, J. Magn. Magn. Mater. 499 (2020), https://doi.org/10.1016/j.jmmm.2019.166218 166218. [202] H. Urreta, G. Aguirre, P. Kuzhir, L.N. Lopez De Lacalle, Seals Based on Magnetic Fluids for High Precision Spindles of Machine Tools, Int. J. Precis. Eng. Manuf. 19 (2018) 495, https://doi.org/10.1007/s12541-018-0060-9. [203] J. Hesselbach, C. Abel-Keilhack, Active hydrostatic bearing with magnetorheological fluid, J. Appl. Phys. 93 (2003) 8441–8443, https://doi. org/10.1063/1.1555850. [204] C.B. Khatri, S.C. Sharma, Analysis of textured multi-lobe non-recessed hybrid journal bearings with various restrictors, Int. J. Mech. Sci. 145 (2018) 258– 286, https://doi.org/10.1016/j.ijmecsci.2018.07.014. [205] W.L. Song, C.H. Lee, S.B. Choi, Sliding wear behavior of magnetorheological fluid for brass with and without magnetic field, Trans. Nonferrous Met. Soc. China (English Ed. 23 (2013) 400–405, https://doi.org/10.1016/S1003-6326 (13)62476-0. [206] H.W. Sun, S.C. Yang, Revolved Surface Finishing with Smart Fluid Abrasives, Key Eng. Mater. 304–305 (2006) 579–583, https://doi.org/10.4028/ www.scientific.net/KEM.304-305.579. [207] H. Urreta, G. Aguirre, P. Kuzhir, L.N. Lopez de Lacalle, Actively lubricated hybrid journal bearings based on magnetic fluids for high-precision spindles of machine tools, J. Intell. Mater. Syst. Struct. 30 (2019) 2257–2271, https:// doi.org/10.1177/1045389X19862358. [208] Q. Qi, F. Tao, Y. Zuo, D. Zhao, Digital Twin Service towards Smart Manufacturing, Procedia CIRP. 72 (2018) 237–242, https://doi.org/10.1016/ j.procir.2018.03.103. [209] V. Alcácer, V. Cruz-Machado, Scanning the Industry 4.0: A Literature Review on Technologies for Manufacturing Systems, Eng. Sci. Technol. an Int. J. 22 (2019) 899–919, https://doi.org/10.1016/j.jestch.2019.01.006. M. Michalec, P. Svoboda, I. Kr ˇupka et al. Engineering Science and Technology, an International Journal 24 (2021) 936–958 958