Thermal Correction Factor Research Articles

Rolling Traction in Isoviscous-Rigid, Piezoviscous-Rigid and Elasto-Hydrodynamic Lubrication Regimes at Line Contact

Abstract This paper deals with rolling traction in isoviscous-rigid (IVR), piezoviscous-rigid (PVR) and elasto-hydrodynamic lubrication (EHL) regimes at line contact. First, a measuring method of rolling traction using the two-disk machine supported by ball bearings was explained. Then, the rolling traction in the IVR, PVR, and EHL regimes at line contact was measured. The measured results showed that as load P increases, the time average rolling traction FR AVG in the IVR and PVR regimes increases, while that in the EHL regime does not significantly increase. The measured FR AVG were lower than the rolling traction FR TED/CPA under the isothermal condition calculated by using the commercial software TED/CPA. To establish the rolling traction expression, a rolling traction expression under the isothermal condition FR iso was first derived by means of curve fitting the calculated FR TED/CPA. Then, a rolling traction expression (which takes into account the thermal effects of the inlet shear heating) FR thermal was derived by multiplying the thermal correction factor Ct to the expression FR iso. Finally, it was shown that the proposed expression FR thermal is effective for estimating the rolling traction in the IVR, PVR, and EHL regimes at line contact.

Thermal boundary layer limitations on the performance of micromachined microphones

The extent to which thermal boundary layer effects limit the performance of micromachined microphones is examined. A lumped element network model for a micromachined microphone is presented which includes a ladder network in parallel with the adiabatic back volume compliance to account for the transition of the enclosure from adiabatic to isothermal conditions when the thermal boundary layer becomes large compared to the enclosure dimensions. The thermal correction to the cavity impedance contains a resistive component which contributes thermal-acoustic noise to the system. The model results are compared to measurements taken from commercially available microphone units with various back volume sizes, and the simulated relative noise power contribution of each acoustic noise source is calculated. The impedance of the back volume, including the thermal correction factor, is compared to the adiabatic compliance and the impedance derived from thermoacoustic finite element analysis. It is shown that the noise due to the thermal component of the back volume impedance becomes significant in microphones with small back volumes and effectively sets an upper bound on the signal-to-noise ratio of a microphone of given package dimensions.

Modified Differential Scanning Calorimeter for Direct Electrocaloric Measurements

Solid-state refrigeration using the electrocaloric effect (ECE) in ferroelectric materials is a promising alternative to the conventional vapor-compression technology. In spite of growing interest to the investigation of the ECE, direct measurements of the effect are still rare. In this paper, we report on a modification of a differential scanning calorimeter for direct ECE measurements. The importance of proper estimation of the thermal correction factor and use of proper values of the heat capacitance for correct ECE measurements is discussed. The ECE measurements were performed for Ba(Zr0.2Ti0.8)O3 and Ba(Zr0.12Ti0.88)O3 bulk ceramics. Large electrocaloric temperature changes of 0.54 and 0.34 K are achieved under the application of an electric field of 2 kV/mm for the Ba(Zr0.12Ti0.88)O3 and Ba(Zr0.2Ti0.8)O3 samples, respectively. The relation between the directly measured ECE values and frequently used indirect estimation based on Maxwell's relations is discussed.

Laboratory thermal calibration of contact pressure cells installed on integral bridge abutments

Hydraulic contact pressure cells were installed on the abutments of an integral abutment bridge to monitor changes in earth pressure over an extended period of time. The accuracy of field data from such instruments is affected by a number of factors. In particular, temperature changes are one of the key factors that can influence earth pressure measurements. Thermal calibration factors supplied by manufacturers of such cells tend to only account for the effect of temperature on the pressure transducer, rather than on the instrument as a whole. Therefore, in an effort to quantify the effect of temperature on data collected from the contact pressure cells installed on the integral abutment bridge, laboratory thermal calibration of these sensors was undertaken. Construction-related time constraints precluded extensive testing of the instruments installed in the field; however, extensive tests were conducted on an identical contact and earth pressure cell. Laboratory thermal calibration tests were conducted on the sensors for an unloaded, unconfined condition and with sensors confined in soil and loaded with uniform pressure. All tests were conducted in a cold room where temperatures could be controlled over a wide range. Results indicate that both temperature and applied pressure affect the performance of hydraulic pressure cells. Thermal correction factors were developed from linear-regression analysis of the unloaded, unconfined test data; however, application of these factors to the loaded, confined test data was found to account for only a portion of the pressure variation, with the remaining variation still being significant. Similar correction factors by linear regression analysis could not be developed from the loaded, confined pressure test data. However, when considering the range of temperatures experienced by the pressure cells installed on the integral abutment bridge, it was concluded in a 2013 study by the authors that the thermal pressure variations present in the field data should not exceed ±10 kPa. The results of this research demonstrate the need for extensive laboratory calibration of these types of pressure cells for proper interpretation of field data.

Hydrodynamic Load Calculation in Rolling Element Bearings

ABSTRACTHydrodynamic effects are responsible for a dimensionless load increase ΔW (relative to the load WHertz calculated in a dry contact) calculated primarily as a function of the dimensionless rolling element–race geometrical interference Δ/Rx, dimensionless speed, and radii ratio. The final load (W = WHertz + ΔW) is therefore never nil, even in cases when the geometrical interference is negative or nil, which corresponds to a Hertzian load nil.The final load is calculated by solving the following dimensionless algebraic relationship: , where δ is the elastic deformation (function of the load and radii ratio) calculated using a Hertzian relationship and H is the dimensionless film thickness, again a function of the load and radii ratio but also dimensionless speed and material parameters, the latter being included in piezoviscous-rigid (PVR) and piezoviscous-elastic (PVE, also called elastohydrodynamic or EHD) film thickness relationships. Advanced new curve-fitted relationships are also suggested in this article for calculating miscellaneous Hertzian parameters, such as contact dimensions, maximum pressure, and deformation.A detailed survey of several film thickness relationships was conducted covering different lubrication regimes: isoviscous-rigid (IVR, found at low dimensionless load and speed), PVR, and EHD (high dimensionless load and low dimensionless speed). It has been shown that the IVR regime prevails when Δ/Rx is negative or nil and the radii ratio is large (as found in roller bearings); hence, an IVR approach can be suggested for numerically calculating ΔW.A powerful set of curve-fitted relationships is then suggested for easily calculating ΔW.A simplified approach based on a previously published analytical solution of ΔW applicable to line contact (LC) but used here in a sliced point contact (PC) was also tested after having demonstrated that LC results (for H and δ) can be used in slices for retrieving (within 10%) PC results on H and δ. This result is surprising given that the exponents used for calculating H and δ differ substantially in LC versus PC.In addition, a new IVR thermal correction factor was developed for better calculating the film thickness.Although very small, ΔW can be responsible for a moderate bearing preload and torque increase, calculated using previously published IVR hydrodynamic rolling forces when the dimensionless speed is high and the bearing clearance is small or nil.Hydrodynamic effects, both normal and tangential to the contact, also contribute to the roller speed decreases in the unloaded zone of a bearing, so there is no need to consider large drag force to explain this drop. Previously published roller drag force relationships may therefore overestimate these forces when calibrated versus tests by not considering the rolling element–race hydrodynamic effect described herein.

A computational evaluation of the steric and electronic contributions to the stability of the structures of α− and β−D‐glucopyanose Part 1: conformational analysis of monosubstituted cyclohexanes and pyrans (593.2)

Geometry optimizations at a variety of computational levels were carried out on a series of substituted cyclohexanes (‐CH3 ‐OH and ‐CH2OH) and similarly 2‐substituted tetrahydro‐2H‐pyrans. By comparing the relationship between structure and energy of the cyclohexane series to the tetrahydro‐2H‐pyran series, it is possible to isolate the steric factors that are the principle contributor to the energy in the cyclohexanes from the combined steric and electronic factors that are present in pyrans.The optimized geometries and minimum energies for each compound were determined using HF, DFT and MP2 methods with increasingly complex basis sets. Thermal correction factors were applied to the conformational energies and the conformational free energy from the B3LYP/6‐311G++(d,p) optimizations closely reflected the available experimental values. Relaxed scans (also at the B3LYP/6‐311G++(d,p) level) of rotations of the exocyclic substituents helped to identifiy the steric contributions for different orientations of the rotamers. Analysis of the optimized geometries non‐bonded distances bond lengths, and bond angles contributed to an understanding of the steric contributions. Additionally, analysis of bond lengths and bond angles showed changes that reflected possible hyper‐conjugation (electronic) contributions to the stability of some configurations. The series of compounds selected in this study provide a series of model compounds that lead to modeling the steric and electronic contributions to the free energies energies of D‐glucopyranose.

VARIOMETRIC TESTS FOR ACCELEROMETER SENSORS

Abstract. We present a comprehensive review of several variometric tests recently carried out on a home-made measurement system composed of a tern of low-cost accelerometer sensors of MEMS (Micro-Electro-Mechanical Systems) type equipped with autonomous electric supply and wireless transmission. The most important parameters characterizing the systematic errors, i.e. bias, scale factor and thermal correction factor, have been evaluated by calibration tests based upon the so-called "six -positions" static test proposed by the IEEE 517 Standard. In this way the system optimal configuration has been defined in terms of data acquisition frequency and of scale factor. In addition to such tests, partly documented elsewhere, the results of some sensitivity tests on the influence of external environmental factors are also presented. With the aim of employing the proposed MEMS-based system as a device for monitoring the onset of slope landslides, some further tests have been carried out in order to measure the inclination of rigid objects which the sensors have been fixed to. The most significant results of the tests are illustrated and discussed.

Experimental Investigation of Elastohydrodynamic (EHD) Film Thickness Behavior at High Speeds

At very high speeds, elastohydrodynamic (EHD) films may be considerably thinner than is predicted by classical isothermal regression equations such as that due to Dowson and Hamrock. This may arise because of viscous dissipation, shear thinning, frictional heating or starvation. In this article, the contact between a steel ball and a glass disc over an entrainment speed ranging from 0.05 m s−1 to 20 m s−1 was studied. Two sets of tests were performed. In the preliminary testing, the disc was driven at speeds of up to 20 m s−1 and the ball was driven by tractive rolling against the disc, its speed being determined using a magnetic method. After all possible explanations for the reduction in film thickness at high speeds were considered, it was shown that the results, which fall well below classical predictions, are consistent with inlet shear heating at the observed sliding speeds. Another set of tests was then performed, with both disc and ball driven separately, so that the accuracy of the shear heating theory for different types of oils and at different sliding conditions could be assessed. It was found that the thermal correction factor predicts the trend of film thickness behavior well for the oils tested and is particularly accurate at certain slide–roll ratios (depending on the type of oil). Experimental data were also used to obtain improved coefficients for the correction factor for different types of oil to achieve better prediction of film thickness at high speed throughout the whole range of slide–roll ratios.

Enhanced Polarization of the Cosmic Microwave Background Radiation from Thermal Gravitational Waves

If inflation was preceded by a radiation era, then at the time of inflation there will exist a decoupled thermal distribution of gravitons. Gravitational waves generated during inflation will be amplified by the process of stimulated emission into the existing thermal distribution of gravitons. Consequently, the usual zero temperature scale invariant tensor spectrum is modified by a temperature dependent factor. This thermal correction factor amplifies the B-mode polarization of the cosmic microwave background radiation by an order of magnitude at large angles, which may now be in the range of observability of the Wilkinson Microwave Anisotropy Probe.

The effective thermodynamic temperature of the emitting surface at 6.6 GHz and consequences for soil moisture monitoring from space

An analysis of nine years of Nimbus/SMMR 6.6 GHz brightness temperatures over central Spain revealed a systematic discrepancy between daytime and nighttime H-polarization emissivities, calculated using independently derived surface temperatures. It was found that daytime emissivities were systematically lower than nighttime emissivities which is explained from the difference between the actual surface temperature (T/sub s/) and the effective temperature of the microwave emitting surface layer (T/sub eff/). In order to estimate the long-term mean difference between T/sub s/ and T/sub eff/, average daytime and nighttime thermal correction factors were calculated. The criterion used for judging the magnitude of these thermal correction factors is the hypothesis that daytime emissivity, when averaged over a longer period, should not be lower than nighttime emissivity. From a combined analysis of all daytime and nighttime Nimbus/SMMR signatures over the nine-year period, and short-term field evidence of daytime and nighttime soil temperature profiles, the magnitude of the thermal correction factors could be estimated. Averaged over the nine-year period with 320 nighttime and 498 daytime observations the thermal correction factors amount to -12.5 K for the daytime and +5.0 K for the nighttime, with 90% of the cases satisfying the defined criterion.

Heat transfer between a fluid-saturated porous medium and a permeable wall with fluid injection or withdrawal

The present paper addresses heat and mass transfer between a permeable wall and a fluid-saturated porous medium. To assess the effect of wall suction or injection on sensible heat transfer, a stagnant film model is developed. The model yields a thermal correction factor accounting for the effect of wall transpiration on heat transfer. In order to apply this correction factor, neutral (or zero mass transfer) heat transfer rates must be specified. In the past, for a large number of practical situations heat transfer correlations have been obtained with the boundary layer model, which are summarized here. Subsequently, the derived correction factor is applied to free, mixed and forced convection flows along vertical and horizontal permeable walls embedded in a porous medium. The predictions of the film model are compared and found to be in good agreement with corresponding results obtained with the boundary layer model (also provided by the literature). Hence, the film model approach appears to be a compact and adequate description of the processes considered.

A film model for free convection over a vertical porous plate with blowing or suction

A film model is described for free convective heat transfer and friction in the presence of wall suction or injection. The analysis yields a thermal correction factor, which appears to be the classical (Ackermann) expression, and a novel friction correction factor, derived here for the first time. Both correction factors are applied to free convection along a vertical flat porous plate for values of the Prandtl number of 0.73, 1 and 7. Subsequently, the film theory predictions are compared with the numerical and asymptotic results of a boundary layer analysis, performed by previous investigators. On the basis of this comparison, a modified correction factor is proposed which correlates excellently with the results of the boundary layer analyses.

Fast Numerical Calculations of EHD Sliding Traction Forces; Application to Rolling Bearings

Based on analytical calculations assuming isothermal elastohydrodynamic (EHD) lubrication conditions, and on curve-fitting of a thermal correction factor, a new formula is proposed to calculate the sliding traction force developed in a concentrated contact, assuming a nonlinear, viscoelastic lubricant and undirectional sliding. When sliding occurs in the rolling and transverse directions (bidimensional sliding), a simplified numerical method is outlined by which the components of the local shear stress are quickly calculated. The latter method is applied to the calculation of the shear stress and temperature distribution in the ball-raceway contacts of an angular-contact ball bearing. Because of the viscoelastic behavior of the lubricant, a nonzero lateral traction force is obtained.

A Simple Method for Determining Thermal EHL Correction Factors for Rolling Element Bearings and Gears

The Murch and Wilson thermal EHL analysis is used together with data on commercial mineral and synthetic lubricants to develop simple charts from which thermal correction factors can be determined for rolling element bearings and gears. It was found that for bearings operating at or below their maximum catalogued speed, with a lubricant viscosity giving an operating specific film thickness, λ, of 1.5, the thermal effects are not very significant. For high-speed bearings and gears, or with high-viscosity lubricants, the charts give simple, yet accurate, information on thermal effects. Presented as an American Society of Lubrication Engineers paper at the ASLE/ASME Lubrication Conference in Dayton, Ohio, October 16–18, 1979