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This paper is the third part of a serial studies for constant and variable compensations of the closed-type hydrostatic thrust bearings which has face-to-face recesses couple. The static stiffness of closed-type hydrostatic thrust bearings can then be obtained from the differentiation of recess pressure with respect to worktable displacement. The paper aims to discuss these issues.

In this paper, the double-action restrictors of cylindrical-spool-type and tapered-spool-type are taken into consideration for variable compensation of hydrostatic bearings.

The static stiffness in thrust direction of hydrostatic bearing is determined by the flow continuity equations that are formulated by film flow and compensation flow for each recess, respectively. The type selection and parameter determination of the double-action spool-type restrictors can be obtained from finding results of this study for maximum stiffness in design of hydrostatic bearings.

This study reveals that the appropriate range of recess pressure ratio and design parameters of restrictors for the maximum stiffness can be obtained, the avoidance of negative stiffness is also provided.

THE primary duties of an aircraft design team are to design an aircraft capable of meeting a certain specification of performance and manoeuvrability with suitable flying qualities, and to ensure that it will be strong enough to withstand any aerodynamic loads it may suffer in flight. It will be found that the aircraft when built is not a rigid structure, but this in itself is not important. We are all familiar with the flexing of an aircraft's wings when struck by a sharp gust of wind in flight, but as long as the wings are strong enough no harm is done. On the contrary, in a passenger aircraft the flexibility of the wings in bending will have a favourable effect, as it will cushion the passengers to some extent from the suddenness of the gust. Flexibility of the structure, however, is not always beneficial and it often introduces new difficulties in the designer's problems. These difficulties arise when the deformation of the aircraft structure introduces additional aerodynamic forces of appreciable magnitude. The additional forces will themselves cause deformation of the structure which may introduce still further aerodynamic forces, and so on. It is interactions of this type between elastic and aerodynamic forces which lead to the oscillatory phenomenon of flutter, and to the non‐oscillatory phenomena of divergence and reversal of control. The study of these three aero‐elastic problems becomes more important as aircraft speeds increase, because increase of design speeds leads to more slender aircraft with thinner wings, and therefore to relatively greater flexibility of the structure. The dangers, in fact, are such that the designers of a modern high‐performance aircraft have to spend considerable effort on the prediction of aero‐elastic effects in order that suitable safeguards can be included in the design. By far the greatest part of this effort is spent on flutter, which will be discussed in Parts II, III and IV of this series, but any of the three problems may force the designers to increase the structural stiffness of parts of the aircraft. The wing skin thickness on a modern aircraft, for example, is nearly always designed by consideration either of aileron reversal or wing flutter. Divergence is usually less important but as it is the simplest of the three phenomena to treat analytically, we shall study it first.

This study aims to utilize the equations of flow equilibrium to determine the variations of film thickness or worktable displacement with respect to the recess pressure for both open‐ and closed‐type hydrostatic flat bearings. The static stiffness can be not only presented directly by these variations but also determined by the differentiation of flow equilibrium equations.

The single‐action variable compensations of three types including cylindrical‐spool, conical‐spool and membrane restrictors are taken into consideration in this study. Specifically, this study presents that membrane restrictor and both spool restrictors with or without preload whilst considering initial opening.

Consequently, the usage range of recess pressure and optimal parameters of appropriate compensation type can be obtained from maximum stiffness and also according to smallest gradient in variations of worktable displacement or film thickness.

This article studies the influences of single‐action variable compensations for its design varieties. The determination of stiffness comes from the differentiating recess pressure with respect to worktable displacement. The large and small positive stiffness correspond to a negative slope in steep and plain gradient, respectively; the negative stiffness and infinite stiffness are obtained by positive gradient and zero gradient, respectively, in the variations of film thickness. The finding results can be expressed further in the relationship between the static stiffness and the static load.

This article is the fourth part of a serial studies about constant and variable compensations of the closed-type hydrostatic plane-pad bearing, which is presented for the double-action membrane-type restrictor and self-type compensation. The paper aims to discuss these issues.

The load capacity and static stiffness in thrust direction of the planar bearing is determined by the flow continuity equation which belongs to the same approaches as shown in previous parts of this serial studies.

The results reveal that the appropriate range of recess pressure ratio and design parameters of bearing and restrictor for the infinite or maximum stiffness can be obtained. Also, the influence of design parameters on negative stiffness that should be avoided in bearing design is revealed in detail.

The determination of design parameters of a double-action membrane-type restrictor can be yielded from finding results of this study for maximum stiffness in design of hydrostatic bearings.

Permanent magnet passive magnetic bearings (PMBs) are used for suspension of rotating shafts in one direction. PMBs with alternating radially magnetized rings having back iron is one of the most optimum configurations among all configurations of PMBs. This paper aims to investigate the effect of the conductivity and permeability of these back irons on the stiffness and damping of the configuration.

The stiffness and damping of the configuration will be calculated through a 2D dynamic analytical method and validated by FEM simulations.

The results of the paper show how the permeability and conductivity of the back irons can affect stiffness and damping of PMB. Furthermore, the size of the magnets and the air intervals between them are optimized for maximum stiffness and damping.

The results show that these bearings can have some intrinsic damping without any loss of stiffness, which can be useful for many applications.

The Bernoulli gripper fixedly installed on the manipulator is subject to limitations such as a small-working region and poor anti-interference capacity. This paper aims to propose a novel Bernoulli gripper design that involves the connection of a positive stiffness component such as a spring in series, based on the force characteristic curve synthesis method, to optimize the mechanical performance.

The proposed gripper is designed and manufactured. In the suction procedure, the force characteristic curve of the proposed gripper is theoretically and experimentally investigated. In the hovering detection procedure, a dynamic model of the manipulator-gripper-workpiece system is established, and an apparatus is set up to compare the displacements of the workpiece and the manipulator. The proposed gripper is finally applied in the lifting procedure, showing good impact resistance.

The optimization of mechanical performance of the proposed gripper is realized. The proposed gripper has the effect of increasing the stiffness of the negative stiffness part of the force characteristic curve and reducing the stiffness of the positive stiffness part, increasing the working region. The stability and the anti-interference ability of the workpiece under high-frequency vibration are improved. Meanwhile, the impact resistance in the lifting procedure is enhanced, compared with the original one.

This research proposes a novel design for the Bernoulli grippers to optimize the mechanical performance. The proposed gripper has advantages of a larger working region, better anti-interference ability and better impact resistance. These findings serve as important theoretical and experimental references for the design of the Bernoulli gripper.

The purpose of this paper is to investigate the static stiffness of hydrostatic bearings with three constant compensations in types of constant‐flow pump, capillary and orifice, and both single‐action and double‐action variable restrictors with cylindrical‐spool, tapered‐spool, and membrane types by film gradient and recess pressure.

This paper utilizes the equations of flow equilibrium to determine the variations of film thickness or displacement of loading table with respect to the varying of recess pressure. For a hydrostatic bearing whose recess pressures are controlled by compensations, the stiffness characteristics can be presented directly by these variations.

The usage range of recess pressure and compensation parameters should be selected to correspond to a variation with smallest gradient.

This paper proposes an extensive database as a critical requirement for the selection of types and parameters of the compensation as to yield the acceptable or optimized characteristics in design of hydrostatic bearings.

The main purpose of this paper is to investigate the vibration isolation performance of a quasi-zero stiffness (QZS) metastructure by employing the band gap (BG) mechanism.

The metastructure QZS characteristic was investigated through static analysis by numerical simulation. Based on that, the BG mechanism is primarily used in this article to investigate the wave propagation characteristics of this structure. The model's dispersion relation is then examined using theoretical (perturbation method) and finite element techniques. The dynamic response of the finite-size systems and experimental analysis is used to confirm the vibration mitigation property under investigation. Finally, the model's ability to absorb energy was examined and contrasted with a traditional model.

The analytical analysis reveals the dispersion curve and the effect of the nonlinear parameter on the curve shifting. The dispersion curve in the finite element method (FEM) result depicts five complete BGs within the range of 0–1,000 Hz, and the BG width accounted for 67.4% of the frequency concerned (0–1,000 Hz). Eigenmodes of the dispersion curves were analyzed to investigate the BG formation mechanisms. The dependence of BG opening and closure on structure parameters was also studied. Finally, the energy absorption property of the QZS metastructure was evaluated by comparing it with a classical model. The QZS structure absorbs 4.08 J/Kg compared to the 3.69 J/Kg absorbed by the classical model, which reveals that the QZS demonstrates better energy absorption performance. Based on the BG mechanism, it is clear that this model is an excellent vibration isolator, and the study reveals the frequencies at which complete vibration mitigation is achieved. As a result, this model could be a promising candidate for vibration mitigation engineering structures and energy absorption.

The tough vibration issue, which is primarily experienced in mechanical equipment, will be resolved in this study. This study provides a precise understanding of the QZS metastructure's isolation of vibration, including the frequencies at which this isolation occurs.

IN Part I wc saw how structural flexibility could introduce aerodynamic forces which might eventually lead to instability, or to the complete nullification of a desired aerodynamic effect. The phenomenon of flutter presents another problem in stability, but in this case an oscillatory instability is threatened. It must be realized at the outset that flutter is no mere resonance phenomenon such as the bad vibrations a motor‐car may exhibit at a particular engine speed. Flutter is a vibration in which energy is extracted from the airstrcam to help build up the amplitude, and a catastrophic failure can easily occur within a second of the start of the flutter.

This paper aims to study the static characteristics of the hydrostatic conical journal bearings by utilizing single-action membrane restrictors to compensate the working pressures of recesses.

The flow resistance network method is used to analyze the influences of load capacity and static stiffness of bearing with the design parameters, including the number of recesses, radial eccentricity ratio, axial displacement ratio, restriction constant, membrane compliance, length-diameter ratio, circumferential land width ratio, axial land width ratio and half of cone angle.

This study shows the infinite stiffness of the oil produced in the first and second recesses while single-action membrane restriction constant of 2 and 3, respectively, as well as in the fourth recess while single-action membrane restriction constant of 0.01 and 0.1, respectively.

This article provides the hydrostatic conical bearings in static and unbiased states for analyses of design parameters. The analyses ignore dynamic pressure effect and do not use the Reynolds equation, and assuming that each oil recesses pressure is constant.

The influences of the design parameters including the number of recesses, membrane restriction, membrane compliance, length-diameter ratio, half of con-angle, circumferential land width ratio, and axial land width ratio are discussed to the load capacity and static stiffness of conical bearing.

Based on the characteristics of the conical bearing through analysis, this article suggests the front bearing with hard membrane restrictor (capillary) and the back bearing with soft membrane restrictor are the most appropriate for axial stiffness.