Multibody dynamics of healthy and faulty rolling element bearings were modeled using vector bond graphs. A 33 degree of freedom (DOF) model was constructed for a bearing with nine balls and two rings (11 elements). The developed model can be extended to a rolling element bearing with n elements and (3×n) DOF in planar and (6×n) DOF in three dimensional motions. The model incorporates the gyroscopic and centrifugal effects, contact elastic deflections and forces, contact slip, contact separations, and localized faults. Dents and pits on inner race and outer race and balls were modeled through surface profile changes. Bearing load zones under various radial loads and clearances were simulated. The effects of type, size, and shape of faults on the vibration response in rolling element bearings and dynamics of contacts in the presence of localized faults were studied. Experiments with healthy and faulty bearings were conducted to validate the model. The proposed model clearly mimics healthy and faulty rolling element bearings.
Summary: The science base that underlies modelling and analysis of machine reliability has remained substantially unchanged for decades. Therefore, it is not surprising that a significant gap exists between available machinery technology and science to capture degradation dynamics for prediction of failure. Further, there is a lack of a systematic technique for the development of accelerated failure testing of machinery components. This article develops a thermodynamic characterization of degradation dynamics, which employs entropy, a measure of thermodynamic disorder, as the fundamental measure of degradation; this relates entropy generation to irreversible degradation and shows that components of material degradation can be related to the production of corresponding thermodynamic entropy by the irreversible dissipative processes that characterize the degradation. A theorem that relates entropy generation to irreversible degradation, via generalized thermodynamic forces and degradation forces, is constructed. This theorem provides the basis of a structured method for formulating degradation models consistent with the laws of thermodynamics. Applications of the theorem to problems involving sliding wear and fretting wear, caused by effects of friction and associated with tribological components, are presented.
A micro corona motor was fabricated using a membraneless built-on X-ray mask. Sharp stator electrodes of this motor ionize air molecules and ionized charges transfer onto the rotor surface, resulting in rotating rotor motions by Coulomb forces. For good performance, the stator’s electrodes should be wide (axial) and have sharp tips. Therefore, X-ray lithography was adopted for precise, high aspect ratio characteristics. To avoid the fabrication difficulty of a membrane X-ray mask, a built-on X-ray mask (conformal mask) technique was employed with negative toned SU-8 photoresist. SU-8 features X-ray fabrication compatibility, X-ray transparency and a large range of thickness. This technique may be suitable for fast fabrication of prototypes or very tall structures, which can be largely affected by printing gaps. For the X-ray built-on mask, 20 μm SU-8 was patterned and 8 μm gold absorber was electroplated on top of the 300 μm PMMA resist. Tests showed good quality pattern transfer from the SU-8 pattern and smooth sidewalls.
Micro bearing systems for Micro Electromechanical Systems (MEMS) have drawn attention for several decades as critical components for micro rotating machinery. Ideally, frictionless bearings are needed, and in practice, micro gas bearings approach the ideal. Typically, bearings function as a separate component, assembled onto sliding counterparts. However, in micro scale devices, assembly procedures are known to be very tedious and time consuming. This leads to the pursuit of single material monolithic structures. Critical issues arising from these approaches include: limitation of materials, friction, and reliability, among others. In this paper, new approaches have been pursued. Micro gas bearings were fabricated as a single component through X-ray lithography. A stainless steel gauge pin, machined to ultra precision, was used as a journal shaft. Simple and very easy assembly processes using self-aligning concepts were developed as an alternative method to conventional assembly. This article presents the design, fabrication, assembly, and testing of micro gas bearings.
This paper presents an updated bond graph model of a gearbox, which now includes bending of shafts. The gearbox system has an input shaft, layshaft, output shaft, spur gears, bearings, and housing. The bond graph model integrates separate sub-models into a composite model. Sub-modules include tooth-to-tooth contact, rotor dynamics of shafts, global dynamics of the gearbox housing structure, and shaft bending modeled by finite element modeling. The tooth-to-tooth model includes tooth bending; shaft torsion; gear inertia; conversion of gear torque into tooth forces; tooth contact mechanics; and multiple tooth contact. To analyze shaft dynamics more precisely, elementary finite element theory was adopted into the shaft bending module. The complete dynamics model was simulated, combining numerical methods for lumped elements and finite element techniques into a single code.
has been shown that certain patterns of surface waviness on a counter surface, in conjunction with speed and stiffness of a slider can create vibrations that reduce slider wear. This study attempts to simulate these vibrations, with the goal of understanding how the slider interacts with the surface waviness, to produce a given vibration. This paper develops a model ofa four-degree-of-freedom rigid body pressed against a sliding counter surface, and studies its vibration motions under several conditions. The four degrees of freedom include one translation normal to the sliding surface andthree rotations. The effects of waviness of the counter surface on the system responses are also studied. To model loading effects between the sliderand a wavy counter surface that has multiple points of contact, an equivalent contact point is defined that is assumed to move along a certain path on the slider's contact surface. Several possible paths of the equivalent contact point over the slider face were studied, and their effects are discussed. With appropriate choice of parameters, the simulation results were comparable to experimental results obtained in a previous study. (C) 2000 Academic Press.
Recent studies have shown that micro-vibrations (10-100 μm amplitude. 10 to 100 Hz) can reduce sliding wear 50%, especially rigid body rockings of the slider. In this article. clearances between a carbon brush ( called a carbon sample in this article) and its holder were reduced while sliding over a slightly wavy (8 to 20 μm) steel surface. Undulations of the counter surface induced rigid body vibrations of the slider. including rocking. Tighter fits restricted rocking. looser fits permitted it. Plotted were wear (μg s -1 rate vs. speed (rpm) with clearance between brush and holder a parameter. Normal and nicking motions were measured. we found: (a) Micro-vibrations reduced brush wear on steel: (b) No rocking gave higher levels of wear: (c) An optimal fit (150 to 200 μm clearance), which kinematically permitted optimum rocking, 10 1 to 10 1 degrees, gave maximum wear reduction: (d) Fits too loose increased wear beyond smooth rotor levels: (e) Rocking with rotation vectors parallel or perpendicular to the sliding direction gave similar wear reduction, 50% or more; (f) Rocking with a rotation vector perpendicular to the sliding direction generated 'chatter', audible acoustic noise: (g) Rocking with a rotation vector parallel to sliding was quiet: (h) Wear reduction can occur at low waviness amplitudes (8 μm). Also in this article, wear particles were inspected under Scanning Electron Microscope. At low to moderate speeds particles shed from wavy and smooth copper counter surfaces were similar. At higher speeds, smooth surface particles were larger than wavy surface particles: often snowball like compactions of sub-particles similar to those shed from the wavy surface. This is consistent with a hypothesis wherein small wear particles shed from a slider running over a wavy surface escape the sliding interface through gaps opened by vibrations without gaps, particles become entrapped and compacted, In addition, clearances optimal for wear reduction correlated to the size of the gaps required for particles to escape.
Wear rates (pgm/s) versus rotor speed for carbon samples sliding against smooth
and wavy copper rotors (250 fj,m thick copper sheets were attached to smooth and
wavy steel and polycarbonate backings) were identical at some speeds, but at other
speeds wear rates for the wavy rotors were almost half those of the smooth rotors.
Slider vibrations (periodic, with period set by rotation) perpendicular to the sliding
surface were measured and Fourier analyzed. Comparison of vibration spectral
amplitudes to spectral amplitudes derived from surface profiles identified vibration
modes dynamically enhanced by surface waviness on the wavy rotor. At speeds where
wear rates on the wavy rotor were most reduced, amplitudes of certain modes in the
vibration spectrum were most enhanced. For all these cases, the product of mode
number times speed was nearly constant, suggesting resonance. Contact forces and
contact voltage drop (due to a mA current flowing from slider to rotor) were measured
and plotted versus time during all experiments. Friction coefficients rapidly varied
between 0.1 and 0.4, but averaged 0.2. Traces of friction coefficient versus time for
both wavy and smooth rotors were similar, even when wear rates plunged on the
wavy rotor. There were no large jumps in the contact voltage drop data, suggesting
that the slider never disconnected from any of the rotors. Photoelastic visualizations
(Bryant and Lin, 1993) of slider-rotor interfaces revealed concentrated contact on
the smooth rotors, but none on the wavy rotors. The absence (induced by vibration)
of concentrated contact may have caused differences in wear rates. Appreciable
reductions (up to 50 percent) in wear rate are possible by adding small surface waves
to a rotor that induce micro-vibrations of the slider-spring-rotor contact system. The
effect appears most pronounced at resonance.
Wear tests are presented in which a carbon brush, loaded by a constant force spring, conducts current and slides against smooth and wavy copper rotors. The wavy rotors possessed surface waves of tens to hundreds of microns. With brush current varying from 0 to 40 A, carbon brushes slid over the smooth and wavy rotors and wear rates (μg/s) were plotted versus rotor speed. Wear rates on the wavy rotor were generally less than wear rates on the smooth rotor, with and without current. Wear rates on the wavy rotor were considerably less than corresponding wear rates on the smooth rotor at certain rotor speeds. Evidence suggests that wear rates were most reduced at those rotor speeds where surface waves on the wavy rotor passing beneath the brush caused the brush-stiffness-rotor system to resonate. Studies of contact voltage drop suggest that under these resonant conditions, the brush and rotor stayed connected. Also, no evidence of arcing or micro-arcing was found on the copper track. This study shows appreciable reductions (up to 50%) in wear rate possible on brush rotor systems by prescribing tiny surface waves on the rotor and running the rotor at speeds such that the surface waves induce microvibrations and resonance