Tilt Stiffness Research Articles

Operational range of a ferrofluid pocket bearing

Ferrofluid pocket bearings are interesting for fast and precise positioning systems thank to the absence of stick-slip, the low viscous friction and their cost-effective nature. However, the characteristics of the bearing change due to over(de)compression since air escapes out of the enclosed pocket. This article presents an experimentally validated model that includes the air mass inside the pocket in the calculation of the equilibrium position of the ferrofluid bearing. Moreover, a simple and efficient way to obtain the operational range of the bearing is presented and a sensitivity analysis was performed. The sensitivity analysis showed that ferrofluid pocket bearings are always self-aligning and that the tilt stiffness increases when the fly height decreases or the tilt angle increases.

Updating Bearing Stiffness and Damping Coefficients of a Rotor System

Finite element (FE) models of structures have been quite useful in both static and dynamic analyses of structures. However, quite often, these models are not reliable enough since predictions based on them may not be found to have acceptable correlation with experimentally obtained data. This paper attempts updating of bearing radial and tilt stiffness as well as damping parameters of a rotor system by using inverse eigen sensitivity method (IESM). Non-proportional viscous damping model has been used in modelling damping coefficients of bearings. The state space form of equations of motion of the system is used in applying the IESM for model updating. The results show that both stiffness and damping coefficients of bearings can be effectively found out by using the IESM. The method is found to update the eigenvalues quite well even under the presence of measurement noise.

Design analysis and experimental study of aerostatic linear guideways used in a high acceleration and high precision xy stage

Profiting from its low friction, non-hysteresis, ease of manufacture and high motion accuracy, air bearings have been widely used in various precision or ultra-precision low acceleration stages. In this paper, a high acceleration and high precision xy stage using aerostatic linear guideways is designed and manufactured to meet the requirements of chip manufacturing equipment. During the design of these guideways, the parameters, such as orifice diameter, distribution of orifices and film thickness are determined by calculating load carrying capacity, tilt stiffness, and mass flowrate of the guideways using the finite-element method. The experimental results show that the performance of these guideways coincides very well with that of the numerical calculations and satisfies the requirements of the stage.

Coupled Torsional and Transverse Vibration of a Back-to-Back Gearbox Rig

The coupled torsional and transverse vibration of a back-to-back gearbox system has been investigated experimentally and analytically. Receptance methods were used to model the system, and were shown to be effective. A detailed experimental modal analysis was performed using the swept-sine technique with an a.c. servomotor torsional exciter. Torsional excitation allowed for the dynamic response to be measured up to 1600 Hz. The model included a combination of lumped mass elements and continuous shafts with distributed inertia and damping. The bearings were modelled as having both radial and tilt stiffness and damping elements. The model simulated the experimental results well and predicted each of the first 11 natural frequencies to within 8 per cent. Of the 11 natural frequencies, 9 simulated deflected shapes matched very well, validating the modelling approach taken for the project together with the assumptions made in the derivation of the model. This paper presents the detailed results of a full torsional/transverse model analysis of the gearbox system.

Design of flexural pivot for use in hard disc drive actuator

A cross leaf flexural pivot is proposed and designed for use in disc drive actuator to replace the currently used ball bearing system. The static and dynamic performances of the proposed design are investigated using finite element analysis. It is shown that flexural pivot can achieve a translatory stiffness comparable to currently used ball bearing. The tilt stiffness is lower than that of ball bearing. The design is prototyped and the life cycling test shows that the prototype can work for more than 3 million life cycles without any failure. Our experimental results show that the single-stage servo loop using the flexural pivot can achieve the performances of open-loop bandwidth of 630 Hz and closed loop bandwidth of 1100 Hz, with phase margin of 60° and gain margin of 6.6 dB. When attaching an actuated suspension to from a dual stage servo loop, we show that the performances as open-loop bandwidth of 1700 Hz with the phase margin of 45° and gain margin of 7 dB.

Mechanical Coupling via the Membrane Fusion SNARE Protein Syntaxin 1A: A Molecular Dynamics Study

SNARE trans complexes between membranes likely promote membrane fusion. For the t-SNARE syntaxin 1A involved in synaptic transmission, the secondary structure and bending stiffness of the five-residue juxtamembrane linker is assumed to determine the required mechanical energy transfer from the cytosolic core complex to the membrane. These properties have here been studied by molecular dynamics and annealing simulations for the wild-type and a C-terminal-prolongated mutant within a neutral and an acidic bilayer, suggesting linker stiffnesses above 1.7 but below 50 × 10 −3 kcal mol −1 deg −2. The transmembrane helix was found to be tilted by 15° and tightly anchored within the membrane with a stiffness of 4–5 kcal mol −1 Å −2. The linker turned out to be marginally helical and strongly influenced by its lipid environment. Charged lipids increased the helicity and H3 helix tilt stiffness. For the wild type, the linker was seen embedded deeply within the polar region of the bilayer, whereas the prolongation shifted the linker outward. This reduced its helicity and increased its average tilt, thereby presumably reducing fusion efficiency. Our results suggest that partially unstructured linkers provide considerable mechanical coupling; the energy transduced cooperatively by the linkers in a native fusion event is thus estimated to be 3–8 kcal/mol, implying a two-to-five orders of magnitude fusion rate increase.

Tilt characteristics of circular centrally fed aerostatic bearings

The general titl characteristics of circular aerostatic bearings are investigated. A theoretical model is developed on the basis of two idealizing assumptions; the resulting problem is then satisfactorily solved by the method of small perturbations. An experimental investigation is also carried out to verify the theory, comprising a broad range of carefully performed tests. A fair agreement is obtained between the theoretical and experimental results. In general, the tilt stiffness and damping coefficient are found to be small in magnitude; they decrease with increasing gap convergence; the first increases and the second decreases with increasing tilt frequency.

Calculation of tilt stiffness of an externally pressurized hole-admission gas journal bearing

A numerical method is given to evaluate static tilt stiffness of an externally pressurized gas journal bearing. The analysis is based on a first-order perturbation with respect to small angular displacement. The method makes an account of discrete feeder rather than a line source, which is commonly used.

Dynamic characteristics of gas-lubricated externally pressurized porous bearings with journal rotation II

The dynamic tilt stiffness and damping coefficients of an externally pressurized porous gas bearing with journal rotation have been calculated theoretically. A periodic disturbance (angular displacement) about the transverse axis is imposed on the bearing and the dynamic pressure distribution is determined by small perturbations of the Reynolds equation. Non-dimensional tilt stiffness and damping coefficients for various design conditions are calculated numerically using a digital computer and presented in the form of figures and tables.

Analysis of Dynamic Tilt Stiffness and Damping Coefficients of Externally Pressurized Porous Gas Journal Bearings

A theoretical estimate of dynamic characteristics in terms of stiffness and damping of an externally pressurized gas-lubricated porous journal under tilting mode of vibration is made. The governing nonlinear partial differential equations in the porous medium and in the bearing clearance are linearized using a first-order perturbation analysis. The tilt stiffness and damping are then determined from the solution of the resulting linear partial differential equations numerically. The effect of feeding parameter, supply pressure, porosity parameter, L/D ratio and eccentricity ratio on these two above characteristics is shown.

Tilt stiffness and damping of externally pressurized porous gas journal bearings

The dynamic behaviour of an externally pressurized porous gas journal bearing is analysed by assuming one-dimensional flow through the porous bushing. A periodic disturbance (angular displacement) about the transverse axis is imposed on the bearing and the resulting dynamic pressure distribution is determined by small perturbations of the Reynolds equation. A finite difference method is used to determine the dynamic pressure. Design data for tilt stiffness and damping as a function of squeeze number, feeding parameter, supply pressure and porosity parameter are calculated numerically using a digital computer and are presented in tables and figures.

Tilt stiffness and damping coefficients for finite journal bearings

An analytical solution of Reynolds' equation for a finite bearing with an inclined journal has been attempted. The tilt stiffness and a bearing coefficient were obtained by analysing the components of couples exerted by the fluid on the journal for small tilt and tilt rates. A transformation of the coordinate systems was adopted to separate the effects produced by tilt — change in attitude angle and change in eccentricity with length. Expressions for pressure distribution were obtained by solving Reynolds' equation using a perturbation technique together with Fedor-type assumptions. Justification for Fedor-type assumptions is given for length-to-diameter ratios greater than 0.8.