Disc Bearings Research Articles

Leonardo da Vinci's studies of rolling-element, disc and sector bearings

The notebooks of Leonardo da Vinci (1452–1519) represent a unique source of information on Renaissance technology. They contain numerous references to tribological topics, including designs for bearings based either on rolling elements on axles (disc, cone, and sector bearings) or on freely rolling balls, cones or rollers. This paper provides the first comprehensive study of this material and its context, based on all of Leonardo's surviving manuscripts. While some of his bearing designs (such as the use of sector bearings to support bells) were clearly based on pre-existing technology, he showed a deep understanding of the principles behind them and remarkable ingenuity in developing them further. In some cases, however, these developments suffered from intrinsic defects or were completely impractical for other reasons. Although roller bearings pre-dated the work of Leonardo, the concept of using freely rolling balls in axial bearings appears to have originated with him.

Unbalance Bearing Fault Identification Using Highly Accurate Hilbert–Huang Transform Approach

Abstract The dynamic characteristics of rolling element bearings are strongly related to their geometric and operating parameters, most importantly the bearing unbalance. Modern condition monitoring necessitates the use of intrinsic mode functions (IMFs) to diagnose unbalance bearing failure. This paper presents a Hilbert–Huang transform (HHT) method to diagnose the unbalanced rolling bearing faults of rotating machinery. To initially reduce the noise levels with slight signal distortion, the noises of the sample in normal and unbalanced fault states are measured and denoised using the wavelet threshold approach. The complex vibration signatures are decomposed into finite IMFs with ensemble empirical mode decomposition technique. Fast Fourier techniques are employed to extract the vibration responses of bearings that are artificially damaged using electrochemical machining on a newly established test setup for rotor disc bearings. The similarities between the information-contained marginal Hilbert spectra can be used to diagnose rotating machinery bearing faults. The data marginal Hilbert spectra of Mahalanobis and cosine index are compared to determine the fault indicator index’s similarity score. The HHT model’s simplicity enhanced the precision of diagnosis correlated to the results of the experiments with weak fault characteristic signals. The effectiveness of the proposed approach is evaluated with several theoretical models from the literature. The HHT approach is experimentally proven with unbalance diagnosis and capable of classifying marginal Hilbert spectra distribution. Because of its superior time-frequency characteristics and pattern identification of marginal Hilbert spectra and fault indicator indices, the newly stated HHT can process nonlinear, non-stationary, and even transient signals. The findings demonstrate that the suggested method is superior in terms of unbalance fault identification accuracy for monitoring the dynamic stability of industrial rotating machinery.

DYNAMIC ANALYSIS OF ROTOR SYSTEM WITH ACTIVE MAGNETIC BEARINGS USING FINITE ELEMENT METHOD

The rotor is a key element of rotating machinery that can be used in different of mechanical devices such as gas turbines, industrial compressors, motors, and aero engines. The dynamic analysis of a rotor system with active magnetic bearings is presented in this paper. This system consists of a flexible shaft with a rigid disk and flexible bearings. An sys Workbench is used to study a 3D simulation of a finite element model. Correct estimation of the rotor's natural frequencies and mode shapes is required for rotating machinery safety procedures. In order to compute the natural frequencies and mode shapes of this system, in the first case it is assumed a free-free system in which no bearings are used, and the natural frequencies and mode shapes are calculated without rigid body modes. In the second case, the natural frequencies and mode shapes are determined with bearing stiffness. The natural frequencies are also evaluated using finite elements based on matlab code. A comparison between the two methods was carried out.

Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to Thermal Gradients.

The dynamic stiffness matrix (DSM) method, an analytical method that provides exact solutions, has been used for the first time for the free vibration analysis of a functionally graded (FG) rotor bearing system subjected to temperature gradients and to investigate its application to FG rotors. The material gradation occurs based on the power law between the inner metal core and the outer ceramic rich layer of the FG rotor. The temperature gradation follows the Fourier law of heat conduction which leads to non-linear temperature distribution (NLTD) in the radial direction of the FG rotor. The development of the DSM formulations for Timoshenko FG rotor elements using the governing equations derived from translational and rotational equilibrium conditions is the novelty of the present work. The DSM of the FG rotor elements, rigid disk and linear isotropic bearings are assembled to obtain the global dynamic stiffness matrix of the FG rotor bearing system. The natural whirl frequencies are computed from the global DSM using the Wittrick–William algorithm as a root searching technique. The natural and whirl frequencies are validated with the results available in the literature and the exactness of the DSM method has been exemplified.

Numerical and Experimental Investigation on Axial Rub Impact Dynamic Characteristics of Flexible Rotor Supported by Hybrid Gas Bearings

Gas bearings are widely used in micro- and small turbomachinery. Because of the pursuit of high efficiency, turbomachinery adopts small clearance of rotor and stator. The gas bearing rotor system easily suffers from rub impact due to the inherently low damping and load capacity of gas film. Axial rub impact may lead to catastrophic failure of gas bearing rotor system. Previous work put emphasis on radial rub, and only a few papers researched on the axial rub impact by simulation method. In this paper, dynamic responses of full annular axial rub are investigated numerically and experimentally. A single span flexible rotor test rig is established to support this research. Dynamic characteristics of full annular axial rub of this gas bearing rotor system are obtained with finite element language-APDL. Dynamic characteristics within full speed range are experimentally researched based on the test rig. The dynamic behaviors are analyzed by means of waterfall diagrams, frequency spectrums, orbit trails, and vibration amplitude waveforms. During speed up, half speed whirl and gas film oscillation occur in radial direction. During speed down, the full annular axial rub between rotor thrust disk and gas bearing occurs. When lightly axial rub impact happens, the vibration patterns in the radial direction change barely, and 0 Hz component appears in the axial direction. When serious full annular axial rub impact happens, 0 Hz component occurs in both radial and axial directions and rotor orbit shows transverse motion in radial direction. These forms of dynamic characteristics can be effectively used to diagnose the full annular axial rub impact.

Dynamic stability and bifurcation phenomena of an axially loaded flexible shaft-disk system supported by flexible bearing

The present research studies the vibration and bifurcation analysis of a spinning rotor-disk-bearing system to carefully scrutinize the dynamic stability under extrinsic mass unbalance and pulsating axial load. The shaft is flexible and taken into account the geometrical nonlinearities due to large elastic deformation in bending. The rotor is supported by flexible bearings, which are modeled as an equivalent spring-damper system having linear and nonlinear stiffness elements. Equation of motion of the rotating system, which includes flexible shaft, rigid disk, and flexible bearing, is derived using extended Hamilton principle with the assumption of the Euler's beam theory. We studied initially the modal analysis to determine the modal parameters, i.e. natural frequency and mode shapes prior to the investigation of the dynamics of the system. Further, we developed the bifurcation diagram for steady-state solutions and to study the subsequent dynamic stability and verify with the findings solved numerically. The interactive behavior among the nonlinear shaft-bearing, axial load and an unbalance has been analyzed. Numerical simulation tools, i.e. frequency–response characteristics, time history, phase trajectories, and Poincaré map have been used to highlight the presence of nonlinear phenomena and its important role towards evaluating the system dynamics and subsequent stability. This current research showed that flexible bearings stabilize the system as a result of increasing the restoring force. Analyzing the bifurcation diagrams of pulsating axial load, we found that the system exhibits complex phenomena as multiple but stable periodic orbits leading to period doubling. The present system is highly vulnerable to catastrophic failure due to the S–N and Pitchfork bifurcation. The present research enables the notability of axial load and mechanical unbalance on the overall system behavior and stability in real working conditions.

Field and computational investigation of elastomeric bearings in high-demand steel girder application

Steel-reinforced elastomeric bearings are commonly used on short- to moderate- span prestressed concrete girder systems. This type of bearing has also been used on a limited number of steel girder applications where the girders have long spans, large reactions, and complex movements, referred to herein as “high demand” bearing applications. Whereas such systems would typically use pot or disc bearings, elastomeric bearings may offer both cost and performance advantages. However, isolated cases were encountered in which some of the elastomeric bearings in such applications had performed poorly. This paper documents the results of a research study including three-dimensional finite-element thermal-structural analysis and field instrumentation measurements of damaged elastomeric bearings on a horizontally curved trapezoidal steel box girder bridge in Austin, Texas to investigate the use of large-sized elastomeric bearings in high demand steel girder applications. The study shows that the bearing damage was not caused by thermal or truck-induced girder movements, but the excessive transverse rotational deformation due to inadequate control of the top the pier seat geometry during construction. The results of this study support the use of large-sized steel-reinforced elastomeric bearings in high-demand steel girder applications such as trapezoidal steel box girder systems. Recommendations on large-sized bearing design and construction are made based on the results of this study.

A thermohydrodynamic approach for single-film and double-film floating disk fixed thrust bearings verified with experiment

Abstract A comprehensive thermohydrodynamic model of single-film and double-film floating disk thrust bearings is presented. Reynolds and energy equations are solved and a modified groove mixing model is used to predict the oil leading edge temperature. A multi-step search algorithm is used to find floating disk rotational speed, and the two film thicknesses. Results are validated with experimental data. It is shown that the floating disk rotates with 30%–50% of the runner rotational speed. The turbine side in general hotter with a thinner film thickness. The main advantage of a double-film floating disk bearings is in their up to 40% lower power loss compared to a single-film. The introduced model provides a practical design tool for the fixed pad thrust bearings.

Investigation of Stress, Deformation, and Cracks in the Brakes of Car Using Finite Element Method

Twisting forces in disc brakes and friction forces between disc brakes and bearings produce heat on the disc brakes. The compression force produced by the brake piston pushes the brake pads to produce heat and deformation in the disc brakes. For the development of vehicle braking systems, wrought iron is used to make disks. However, a failure still occurs during a crack testing. The results of the analysis using the finite element method showed that the highest total deformation was 4,411 x 105 mm. The highest maximum equivalent stress (represented by the red area) is 715.48 MPa. The maximum value of SIFS (K1) around the disc brake hole is -0.9030 MPa.mm0.5, while at the edge of the disc is 5.385 MPa.mm0.5.

The method for calculating the traction resistance of a flat disk

Scuffler with flat discs are widely used in areas, which are subject to wind erosion of soils, to cover moisture on the stubble fields. Flat discs do not wrap the layers they remove, but only loosen them, shifting them aside. It is preferable to use such scrapers during presowing tillage and on steam, since in this case there is less sputtering of the soil, and its lower (moist) layers are not carried to the surface. Therefore, many industrially manufactured scufflers are equipped with flat discs, and the task of constructing a mathematical model for the interaction of such discs with soil is topical. Many mathematical models of the disc-soil interaction, taking into account the distribution of soil reaction forces on the disk, have been proposed, but all these models were constructed assuming that the disk is moving in its plane. Therefore, they are not applicable to the disk of a lakeshield moving with a non-zero angle of attack in the soil. The purpose of this work is to construct a mathematical model that allows calculating the traction resistance of a disk moving with a given angle of attack. The basic assumptions made in the construction of this model: the speed of the translational movement of the disk and its depth are constant; friction in the disk bearing can be neglected; the soil pressure on the lateral surface of the disc and the force of the soil reactions per unit length of its blade can be replaced by their mean values. An explicit expression is obtained for the traction resistance of a disk of a scuffler moving with an angle of attack, depending on its relative depth, the angle of attack, and the empirical coefficients. The adequacy of the constructed mathematical model is confirmed by comparison with known experimental data. It makes it possible to significantly reduce the number of full-scale experiments on the study of the interaction of flat discs of a scuffler with the soil, replacing them with computational ones, and reasonably carry out power and strength calculations of such discs. In addition, it can be used to optimize the parameters of the flat discs of the scuffler.

Structural and Conceptual Design Analysis of an Axial Compressor for a 100 MW Industrial Gas Turbine (IND100)

The structural design of the IND100 axial compressor requires a multistage interrelationship between the thermodynamic, aerodynamic, mechanical design and structural integrity analysis of the component. These design criteria, sometimes act in opposition, hence engineering balance is employed within the specified design performance limits. This paper presents the structural and conceptual design of a sixteen stage single shaft high pressure compressor of IND100 with an overall pressure ratio of 12 and mass flow of 310 kg/s at ISOSLS conditions. Furthermore, in order to evaluate the conceptual design analysis, basic parameters like compressor sizing, load and blade mass, disc stress analysis, bearings and material selections, conceptual disc design and rotor dynamics are considered using existing tools and analytical technique. These techniques employed the basic thermodynamic and aerodynamic theory of axial flow compressors to determine the temperature and pressure for all stages, geometrical parameters, velocity triangle, and weight and stress calculations of the compressor disc using Sagerser Empirical Weight Estimation. The result analysis shows a constant hub diameter annulus configuration with compressor overall axial length of 3.75 m, tip blade speed of 301 m/s, maximum blade centrifugal force stress of 170 MPa, with major emphasis on industrial application for the structural component design selections.

Evaluation of Steering Disks in Mi-17 and Mi-24 Helicopters by Means of the Fam-C Method

Abstract The paper deals with selected issues related to operation of steering disks designed for helicopters that are currently in operation of the Air Force of the Republic of Poland. The attempt is made to present a prediction of hazards to the transmission gear of that helicopter where the forecast is based on a theoretical analysis of mechanical phenomena as well as the statistical and diagnostic analyses. The major attention is paid to the opportunity to diagnose hazardous locations of the helicopter steering disk with use of a non-destructive FAM-C method originally developed by ITWL. The method is based on tracking of frequency modulation parameters generated by the on-board AC generator. The examination does not require the installation of any additional sensor since the transmission is subjected to neither additional load nor distortions of the rotation speed occur. The authors of this study disclosed the initial results from diagnostic measurements as well as snapshots taken during the disassembling of steering disks from Mi-24 and Mi-17 helicopters that were operated under heavy duty conditions of military missions in Iraq and Afghanistan. They also suggested an easy and cheap method for field checking of the steering disk bearing by photogrammetric measurements. It is also demonstrated that the method of diagnostic investigations can be also spread onto other helicopter makes and types.

Behavior of Bridge Bearings for Railway Bridges under Running Vehicle

Open steel plate girder (OPSG) bridges are the most prevalent railroad bridge type in Korea, constituting about 40% of all railroad bridges. Solid steel bearings, known as line type bearings, are placed in most OSPG railway bridges. However, the line type rigid bearings generate several problems with the bridge's dynamic behavior and maintenance in service. To compare and investigate the dynamic behaviors of line type, spherical and disk bearings, the vertical displacements of each bearing, including fixed and expansion type, under running vehicles are measured and analyzed. The displacements of disk and spherical bearings are measured after replacing the line type bearings with spherical and disk bearings. This study also analyzed dynamic behaviors of bridges. Furthermore, the deformation of the PTFE (Polytetrafluoroethylene) plate that is placed inside of expansion type spherical and disk bearings is measured and its effect on the dynamic behavior of the bridges is discussed. The up-lift phenomenon at the bearings installed for the steel bridges is estimated. The vertical displacements at mid-span of the bridges are compared according to the bearing types. Finally, the 1st mode natural frequencies are estimated, and the relationship to the vertical displacement is discussed.

교량받침 형식에 따른 판형교 동적 분석

철도 판형교의 선받침, 스페리칼받침 및 디스크받침의 차량주행에 의한 동적 거동을 측정 분석 하고, 각 받침에 따른 판형교의 동적 거동을 분석하였다. 이를 위해 각 받침은 고정단과 가동단의 형태에 따라 차량주행에 의한 수직변위가 측정되었고, 비교 분석하였다. 또한, 가동단의 스페리칼받침과 디스크받침의 내부에 설치된 PTFE판의 변형 및 이 변형이 교량의 거동에 미치는 영향을 분석하였다. 판형교에 설치된 교량받침에서 들림 현상이 관측되는데, 받침 형태에 따른 들림량을 분석하였다. 중앙 거더의 수직변위를 교량받침 별로 비교하여 교량받침 교체에 의한 교량 수직변위 변화를 분석하였으며, 각 받침에 따른 중앙 거더의 수직변위와 고유진동수의 변화를 상관적으로 분석하여 설명하였다. Dynamic behaviors of line type bearings, spherical bearings and disk bearings which are being used for railway steel bridges are investigated, and that of the bridges is also analyzed. For the purpose, the vertical displacements of the three bearings including fixed and expansion type are measured and analyzed. Also, the deformation of the PTFE plate placed inside of spherical and disk bearings of expansion type is measured and its effect on the dynamic behavior of the bridges is discussed. The up-lift phenomenon at the bearings installed for the steel bridges is estimated. The vertical displacements at mid-span of the bridges are compared according to the bearing types. Finally, the 1st mode natural frequencies are estimated and the relationship to the vertical displacement is discussed.

장기 공용 후, 디스크받침이 설치된 판형교의 동적 거동 평가

철도판형교에 설치된 디스크받침의 장기간 공용 후의 판형교 및 디스크받침의 거동을 평가하기 위해서 디스크받침 설치 직후와 5.5년의 공용 후에 차량 주행에 의한 동적 응답을 측정하고 분석하였다. 본 연구에서 12 m 판형교를 대상으로 연구를 수행하였으며, 교량의 수직 변위 및 가속도, 교량받침의 수직 변형량 및 고유진동수의 변화를 비교 분석하였다. 또한, 디스크받침의 수직 강성을 추정하였으며, 이를 이용하여 계산된 디스크받침의 변형과 측정된 응답을 비교하였다. 교량의 중앙 수직변위, 디스크받침의 고정단의 변형 및 1차 모드 고유진동수는 5.5년의 공용에 의해서 크게 변하지 않았으나, 가동단의 변형이 상대적으로 크게 증가하는 현상이 발생하였다. This study conducts two field tests of a steel railway bridge supported disk bearings to assess the long-term dynamic behavior of the steel railway bridge and a disk bearing in the service for 5.5 years; the length of the bridge is 12 m. Displacement and acceleration in vertical direction, deformation of disk bearings and natural frequency of the first mode are measured and analyzed. In addition, the vertical stiffness of the disk bearing is estimated, and the deformation of the disk bearing due to static loading is calculated using the estimated stiffness and compared to the measured dynamic response. Vertical displacement at mid-span, deformation of a fixed disk bearing, and the first natural frequency do not vary due to the 5.5 year service. However, deformation of an expansion disk bearing increases sharply comparing to other components.

Static and dynamic behavior of disk bearings for OSPG railway bridges under railway vehicle loading

The aim of the present study is to investigate the static and dynamic behavior of disk bearings under railway vehicle loadings. A disk bearing is operated as an elastic bearing in the vertical direction and is composed of a Polyether Urethane (Polyurethane) disk for elastic support and Polytetrafluoroethylene (PTFE) to accommodate lateral movements. Static tests are conducted in a laboratory to determine the static behavior of a Polyurethane disk. Finite Element (FE) analysis is also performed to assess the friction and the role of the pin inside a disk bearing. For dynamic behavior, four disk bearings having the identical Polyurethane disk, which are used in the static tests, are installed in a real railway bridge and tested under a running locomotive. From the test results, the static and dynamic stiffness of disk bearings are estimated and compared with each other. The estimated static stiffness of the disk bearing is almost half of that under dynamic loading. In addition, under relatively light loads the dynamic stiffness of a fixed disk bearing is approximately 80% greater than that of an expansion disk bearing since the PTFE deflects and the gap is closed in the expansion bearing. Deformation of the disk bearings in the real bridge is measured with varying locomotive speeds. The deformation of the disk bearings does not vary significantly with changes in the locomotive’s speed.

Inverse theory of elasticity problem of mounting a disk on a rotating shaft

A theoretical analysis of the determination of the tightness of mounting an elastic disk on a rotating shaft ensuring the absence of stress concentration on the inner rim of the disk, i.e., constant normal circular (optimal) stress, is performed on the basis of the equal-strength principle. The value of optimal constant stress is determined upon solution of the optimization problem. A closed system of algebraic equations providing the possibility of solving the optimal design problem is constructed. The found mounting tightness ensures an increase in disk bearing capacity.

Elastomeric Bearings for Steel Trapezoidal Box Girder Bridges

Traditionally, bridge bearings supporting steel trapezoidal box girders (tub girders) consist of fabricator-designed mechanical devices, such as pot or disc bearings, that may be guided or unguided and are expensive to fabricate and place. Performance of these bearings has been mixed: some are maintenance-free and others require significant maintenance, repair, or replacement. In Texas, bridge bearings supporting concrete and steel superstructure types are typically steel-laminated elastomeric bearings that are tapered or have a constant thickness. Recently, the Texas Department of Transportation has used these structurally engineered elastomeric bearings for tub girders in place of mechanically engineered pot or disc bearings. This paper describes the rationale for the application of elastomeric bearings to tub girders and outlines design recommendations that are based on the use of elastomeric bearings for the tub girder direct connectors of the interchange of US-290 and I-35 built in Austin in the late...

Elastomeric Bearings for Steel Trapezoidal Box Girder Bridges

Traditionally, bridge bearings supporting steel trapezoidal box girders (tub girders) consist of fabricator-designed mechanical devices, such as pot or disc bearings, that may be guided or unguided and are expensive to fabricate and place. Performance of these bearings has been mixed: some are maintenance-free and others require significant maintenance, repair, or replacement. In Texas, bridge bearings supporting concrete and steel superstructure types are typically steel-laminated elastomeric bearings that are tapered or have a constant thickness. Recently, the Texas Department of Transportation has used these structurally engineered elastomeric bearings for tub girders in place of mechanically engineered pot or disc bearings. This paper describes the rationale for the application of elastomeric bearings to tub girders and outlines design recommendations that are based on the use of elastomeric bearings for the tub girder direct connectors of the interchange of US-290 and I-35 built in Austin in the late 1990s and placed in service in 2001.

Nonlinear Dynamics of a Magnetically Supported Rotor on Safety Auxiliary Bearings

This study concerns the dynamic response of a rotor landed on auxiliary (catcher) bearings in an Active Magnetic Bearing (AMB) supported rotor, following postulated loss of power or overload of the AMB. An analytical model involving a disk, a shaft and auxiliary bearings on damped flexible supports is constructed and appropriate equations of the nonlinear dynamic system are developed. The equations include a switch function to indicate contact/non-contact events and determine the existence of contact normal forces and tangential friction forces between the shaft and the bearings. Steady state solutions are obtained. An analytical method was formulated and used to yield solutions for cases with well balanced rotors, in absence of any side forces. The Fixed Point Algorithm (FPA) is used to obtain steady state periodic solutions of the unbalanced rotor for various parameters. The FPA is used to determine the stability of the periodic solutions and the type of bifurcation involved. Multiple periodic solutions, quasi-periodic and chaotic responses are detected and discussed. A set of preliminary guidelines for selection of the parameters of the catcher bearings is given.