Design of Flexure Pivot Tilting Pads Gas Bearings for High-speed Oil-Free Microturbomachinery

2006 ◽  
Vol 129 (1) ◽  
pp. 112-119 ◽  
Author(s):  
Kyuho Sim ◽  
Daejong Kim
Keyword(s):  
High Speed ◽  
Hydrodynamic Pressure ◽  
Design Parameters ◽  
Gas Bearings ◽  
Bearing Clearance ◽  
High Speeds ◽  
Radial Stiffness ◽  
Design Variables ◽  
Final Design ◽  
Parametric Studies

This paper introduces flexure pivot tilting pad gas bearings with pad radial compliance for high-speed oil-free microturbomachinery. The pad radial compliance was for accommodation of rotor centrifugal growth at high speeds. Analytical equation for the rotor centrifugal growth based on plane stress model agreed very well with finite element method results. Parametric studies on pivot offset, preload, and tilting stiffness were performed using nonlinear orbit simulations and coast-down simulations. Higher preload and pivot offset increased both critical speeds of the rotor-bearing system and onset speeds of instability due to the increased wedge effect. Pad radial stiffness and nominal bearing clearance were very important design parameters for high-speed applications due to the physically existing rotor centrifugal growth. From the series of parametric studies, the maximum achievable rotor speed was limited by the minimum clearance at the pad pivot calculated from the rotor growth and radial deflection of pads due to hydrodynamic pressure. Pad radial stiffness also affects the rotor instability significantly. Small radial stiffness could accommodate rotor growth more effectively but deteriorated rotor instability. From parametric studies on a bearing with 28.5mm in diameter and 33.2mm in length, optimum pad radial stiffness and bearing clearance are 1-2×107N∕m and 35μm, respectively, and the maximum achievable speed appears 180krpm. The final design with suggested optimum design variables could be also stable under relatively large destabilizing forces.

Design and Hydrodynamic Performance of Hybrid Flexural Pivot Gas Bearings for High Speed Oil-Free Micro Turbomachinery

2005 ◽  
Author(s):  
Kyuho Sim ◽  
Daejong Kim
Keyword(s):  
High Speed ◽  
Hydrodynamic Performance ◽  
Bending Vibrations ◽  
Hydrodynamic Mode ◽  
Critical Speeds ◽  
Gas Bearings ◽  
Radial Stiffness ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Final Design

This paper introduces new flexural pivot tilting pad gas bearings for high speed oil-free micro turbomachinery. The new flexural pivot tilting pad gas bearings have a special web geometry that provides a radial stiffness to accommodate rotor growths and high vibrations at critical speed, a pitching stiffness to accommodate rotor-bearing misalignments or rotor bending vibrations, and a very small tilting stiffness for rotor stability. Comprehensive numerical simulations involving orbit simulations and coast-down simulations were performed to investigate the effects of preloads and pivot offsets on the critical speeds and onset speeds of instability. Higher preload and pivot offset increased both critical speeds of the rotor-bearing system and onset speeds of instability due to the increased wedge effect. Design procedures of radial stiffness were presented considering both rotor centrifugal and thermal growths. From simple adiabatic solution of temperature distribution of gas film under pure hydrodynamic mode, enough bearing clearance at pivot was found to be a very important design aspect for high speed hydrodynamic gas bearings. Asymmetric radial stiffness was chosen as a final design to meet the target design speed of 180 krpm for bearing diameter of 28.52mm. Suggested tilting pad gas bearing with asymmetric radial stiffness was predicted to be very stable even under high external destabilizing forces.

An Approach to Represent Imprecision in Interactive Design Using Fuzzy Set Theory

1992 ◽  
Author(s):  
Numan Iqbal ◽  
Gary L. Kinzel
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Ohio State University ◽  
Design Parameters ◽  
State University ◽  
Design Variables ◽  
Final Design ◽  
The Ohio State University ◽  
Number Of Iterations

Abstract Imprecision in the values of design parameters is an inherent character of the analysis stage of engineering design when the ideas have not yet converted to precise values and some of the design parameters remain flexible. The goal of this paper is to illustrate the application of the concepts of fuzzy set theory to represent this imprecision in design after a basic analytical model of the part being evaluated is developed. The idea is to help the designer efficiently study the effect of changing the values of certain parameters so that the number of iterations required to reach a final design can be reduced. The concepts of fuzzy set theory are used to represent design variables and the vertex method is utilized to calculate the fuzzy outputs in an interactive manner through an existing constraint manager (Design Shell) developed at The Ohio State University.

The Effect of Centrifugal Stretching in High-Speed, Self-Acting Gas Bearings Operating under Steady-State Conditions

1974 ◽  
Vol 16 (3) ◽  
pp. 139-146
Author(s):  
K. S. H. Sadek ◽  
B. N. Cole ◽  
D. Dowson
Keyword(s):  
Radial Growth ◽  
High Speed ◽  
Load Carrying Capacity ◽  
Gas Bearings ◽  
Rotary Machine ◽  
Lubricating Film ◽  
Pressure Distributions ◽  
High Speeds ◽  
Load Carrying ◽  
Very High

The study reported in this paper arose from an investigation of methods of achieving oil-free compression of refrigerant vapours. One part of the investigation included a feasibility study of a high-speed rotary machine running in self-acting gas bearings lubricated by the refrigerant. In certain designs of very high-speed rotor-bearing arrangements, centrifugal or radial growth of the journal might disturb the shape and magnitude of the nominal clearance space and thus affect the performance characteristics of the bearing. The nature and magnitude of these changes in bearing performance for uniform and for two forms of non-uniform centrifugal growth have been examined theoretically. Typical gas-film pressure distributions are presented together with design charts showing how attitude angle and load carrying capacity vary with speed. Comparisons are made with the performance of bearings having the same eccentricity ratio on the mid-plane, and guidance is given on the calculation of uniform radial growth at high speeds. It is concluded that changes in lubricating film geometry resulting from centrigual stretching might have a significant effect upon the performance of certain high-speed, self-acting gas-lubricated bearings.

Parametric Studies on Dynamic Performance of Hydrostatic Flexure Pivot Tilting Pad Gas Bearing With Radial Compliance

2007 ◽  
Author(s):  
Robert N. Petro ◽  
Daejong Kim
Keyword(s):  
High Speed ◽  
Heat Dissipation ◽  
Optimal Choice ◽  
Hollow Shaft ◽  
Bearing Clearance ◽  
Radial Stiffness ◽  
Hybrid Operation ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Gas Bearing

Flexure pivot tilting pad gas bearings are recognized as an alternative to foil gas bearing [1, 2] for high speed turbomachinery, due to their capability to provide high rotor-bearing stability and simple structure. The flexure pivot design eliminates wear problem of axial pins or sockets at the pivots which are common in traditional tilting pad bearings. Added features such as a pivot offset and pad preloads can also be optimized to further improve the stability. Hybrid flexure pivot tilting pad gas bearing have also been reported [3]. The hybrid bearing has a direct air supply to the bearing clearance through a tiny orifice. It has shown that the hybrid operation of the tilting pad gas bearing can also increase the rotor-bearing stability [3]. In many microturbomachinery applications, hollow shafts are adopted to reduce the rotor weight and increase the bending critical speeds. However, the hollow shaft has a large centrifugal growth at high speeds requiring the gas bearing to have radial compliances. However, the radial compliance within the tilting pads can compromise the rotor-bearing stability because large displacement of the pads along the radial direction can cause hydrodynamic rotor-bearing instability associated with the increased bearing clearance (i.e. decreased effective preload) if the radial stiffness is not designed properly. Analytical studies show that optimal choice of pad radial stiffness could extend operating envelope of flexure pivot tilting pad gas bearing without deteriorating rotor-bearing stability [4]. High speed operation can generate significant amount of heat and adequate heat dissipation mechanism should also be developed. Hybrid operation is considered to have added benefit of effective cooling capability. This paper presents design studies on hybrid flexure tilting pad gas bearing with radial compliance which can accommodate large rotor centrifugal growth and also provide effective cooling mechanism.

An Integrated Approach Toward the Dynamic Analysis of High-Speed Spindles: Part I — System Model

1993 ◽  
Author(s):  
C. H. Chen ◽  
K. W. Wang ◽  
Y. C. Shin
Keyword(s):  
High Speed ◽  
Integrated Approach ◽  
Ball Bearings ◽  
Basic Principles ◽  
Gyroscopic Moment ◽  
High Speeds ◽  
Modeling Process ◽  
Radial Stiffness ◽  
Bearing Stiffness ◽  
Made In

Abstract Experimental evidence [Shin, 1992] has shown that the natural frequencies of high speed spindles with angular contact ball bearings decrease with increasing rotational speed. A recent study [Wang, et al., 1991] illustrated that this phenomenon is caused by stiffness change of the bearings. A simplified approximation was used in the analysis to examine the bearing radial stiffness at high speeds. While the investigation explained the experimental observations in a qualitative sense, the analytical results so far are not sufficient to quantitatively describe the spindle behavior under high speed operations due to the approximations made in the modeling process. This paper presents an integrated approach toward the modelling of flexible spindles with angular contact ball bearings from basic principles. The local dynamics of the bearings are coupled with the global shaft motion. The model derived includes both the longitudinal and transverse vibrations of the shaft interacting with the nonlinear bearings. The influences of shaft speed on the bearing stiffness matrix and the system frequencies have been studied. It is shown that the spindle dynamic behavior can vary substantially as speed increases due to the bearing gyroscopic moment and centrifugal force. These effects have been ignored in most of the previous spindle models. Lab tests were conducted to validate the model. The analytical predictions are quantitatively verified by the experimental results.

Design Considerations and Validation of Trailing Edge Pressure Side Bleed Cooling

2009 ◽  
Author(s):  
Joerg Krueckels ◽  
Michael Gritsch ◽  
Martin Schnieder
Keyword(s):  
Gas Turbines ◽  
High Speed ◽  
Thickness Effect ◽  
Design Parameters ◽  
Pressure Side ◽  
Trailing Edge ◽  
Low Speed ◽  
Final Design ◽  
Overhang Length ◽  
Important Design

One important design measure, which allows achieving a higher efficiency in heavy-duty gas turbines, is reducing the trailing edge thickness of the turbine vanes and blades. A common approach to achieve an efficient cooling of thin trailing edges is pressure side coolant ejection. As the trailing edge is one of the areas of the vanes and blades with the highest heat load, a careful design and validation approach is required. First, the most important design parameters were identified for the design of pressure side bleed. In the present investigation, focus is given to the blockage of the internal features, slot width, overhang length, pressure side lip thickness, effect of rotation and blowing rate. Flat plate test results from a low speed rig are used to choose suitable parameters, which fulfill requirements of a specific design. Previous investigations have shown that contrary to CFD using steady RaNS, unsteady detached eddy simulations can predict film effectiveness of pressure side bleed with good accuracy. Therefore, this approach is used to complete experimental data. The effect of going from low speed rig conditions to engine conditions is modeled with this approach. The final design is investigated in a high-speed cascade rig. Film effectiveness is measured using thermocromic liquid crystals. The cascade results confirm results from the low speed rig. High levels of film effectiveness allow effective cooling of the trailing edge overhang.

scholarly journals Design Optimisation of Lower-Bound Buckling Capacities for FRP-Laminated Cylindrical Shells

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Hongtao Wang ◽  
James G. A. Croll
Keyword(s):  
Lower Bound ◽  
Cylindrical Shells ◽  
Design Parameters ◽  
Design Decision ◽  
Buckling Loads ◽  
Frp Composite ◽  
Elastic Load ◽  
Design Variables ◽  
Mathematical Algorithms ◽  
Parametric Studies

The imperfection sensitive buckling loads of fibre reinforced polymeric (FRP) composite cylindrical shells under axial compression can be optimised with respect to many material and geometric parameters. Current approaches, using mathematical algorithms to optimise the linearised classical critical loads with respect to many design variables, generally ignore the potential reductions in elastic load carrying capacities that result from the severe sensitivities of buckling loads to the effects of initial imperfections. This paper applies a lower-bound design philosophy called the reduced stiffness method (RSM) to the optimisation design of FRP shell buckling. A physical optimisation in terms of parametric studies is carried out for simply supported, 6-ply symmetric, glass-epoxy circular cylindrical shells under uniform axial load. It is shown that under the guidance of RSM, safe lower-bound buckling loads can be enhanced greatly by choosing appropriate combinations of design parameters. It is demonstrated how this approach encourages the delineation of those components of the shell’s membrane and bending stiffness that are important and those that are unimportant within each of the prospective buckling modes. On this basis, it is argued that the RSM provides not only a safe but also a more rational strategy for better design decision making.

scholarly journals Speed Effects on Inherent Rotating Frequency of Motorized Spindle System

2011 ◽  
Vol 2-3 ◽  
pp. 900-905 ◽  
Author(s):  
Bo Wang ◽  
Wei Sun ◽  
Kun Peng Xu ◽  
Bang Сhuan Wen
Keyword(s):  
Centrifugal Force ◽  
High Speed ◽  
Impact Factors ◽  
Motorized Spindle ◽  
Spindle System ◽  
High Speeds ◽  
Radial Stiffness ◽  
Bearing Stiffness ◽  
Coupling Factors ◽  
The Impact

The paper determines the impact factors of high-speed spindle system including the centrifugal force, gyroscopic moments and the bearing stiffness softening, etc, then builds the general spindle-bearing FEM considering high speeds. Taking a motorized spindle as example, the effect of centrifugal force, gyroscopic effect, the radial stiffness and the coupling factors are analyzed qualitatively and quantitatively. Finally the research shows the variations of bearing radial stiffness, centrifugal force and gyroscopic moments have a significant effect on dynamics of spindle system in high speeds, while modeling the high speed spindle system, above factors must be considered.

Optimization of orthotropic girders in cable supported bridges by parametric studies

2019 ◽  
Author(s):  
Mads Baandrup ◽  
Peter Noe Poulsen ◽  
John Forbes Olesen ◽  
Henrik Polk
Keyword(s):  
Boundary Conditions ◽  
Suspension Bridge ◽  
Design Parameters ◽  
Fe Model ◽  
Design Variables ◽  
Gradient Based ◽  
Parametric Studies ◽  
Bridge Girder ◽  
Support Conditions ◽  
Material Utilization

<p>For the last six decades closed-box orthotropic steel girders have been widely used in cable supported bridges due to their simple but useful structural concepts. Several numerical parametric studies were previously carried out in order to investigate inherent fatigue stress problems and in general, to improve the bridge girder designs. However, often such studies have been carried out with over-simplified finite element models, especially where boundary conditions have been challenging. In the present work, an advanced multi-scale FE model of a suspension bridge is established with sophisticated boundary conditions applied to a local parametric sub-model of a bridge girder. Thus, the model accommodates realistic support conditions. With this sub-model, a parametric study of the usual design parameters is carried out with focus on fatigue and a Eurocode stiffness requirement. The study reveals trends and correlations for the varying design parameters. Finally, the parametric sub-model is utilized in an automatic gradient-based optimization of multiple design variables simultaneously with the goal of minimizing weight. The methods allow bridge engineers to push material utilization to its limits by giving new insight into the effect of changing design parameters.</p>

scholarly journals Use of Orthogonal Arrays for Efficient Evaluation of Geometric Designs for Reducing Vibration of a Non-Pneumatic Wheel during High-Speed Rolling

2010 ◽  
Vol 38 (4) ◽  
pp. 246-275 ◽  
Author(s):  
William Rutherford ◽  
Shashank Bezgam ◽  
Amarnath Proddaturi ◽  
Lonny Thompson ◽  
John C. Ziegert ◽  
...  
Keyword(s):  
Orthogonal Array ◽  
High Speed ◽  
Contact Region ◽  
Orthogonal Arrays ◽  
Nonlinear Effects ◽  
Element Model ◽  
Geometric Design ◽  
Design Parameters ◽  
Design Variables ◽  
Wheel Vibration

Abstract During high speed rolling of a nonpneumatic wheel, vibration may be produced by the interaction of collapsible spokes with a shear deformable ring as they enter the contact region, buckle, and then snap back into a state of tension. In the present work, a systematic study of the effects of six key geometric design parameters is presented using Orthogonal Arrays. Orthogonal Arrays are part of a design process method developed by Taguchi which provides an efficient way to determine optimal combinations of design variables. In the present work, a two-dimensional planar finite element model with geometric nonlinearity and explicit time-stepping is used to simulate rolling of the nonpneumatic wheel. Vibration characteristics are measured from the FFT frequency spectrum of the time signals of perpendicular distance of marker nodes from the virtual plane of the spoke, and ground reaction forces. Both maximum peak amplitudes and RMS measures are considered. Two complementary Orthogonal Arrays are evaluated. The first is the L8 orthogonal array which considers the six geometric design variables evaluated at lower and higher limiting values for a total of eight experiments defined by statistically efficient variable combinations. Based on the results from the L8 orthogonal array, a second L9 orthogonal array experiment evaluates the nonlinear effects in the four parameters of greatest interest, (a) spoke length, (b) spoke curvature, (c) spoke thickness, and (d) shear beam thickness. The L9 array consists of nine experiments with efficient combinations of low, intermediate, and high value levels. Results from use of the Orthogonal Array experiments were used to find combinations of parameters which significantly reduce peak and RMS amplitudes, and suggest that spoke length has the greatest effect on vibration amplitudes.

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