Thermal Loading Parameters Research Articles

A NUMERICAL STUDY ON THERMAL FRACTURE OF PRECRACKED CERAMIC COATINGSIN HIGH-HEAT-FLUX ENVIRONMENT

The thermomechanical fracture and interface delamination of thermal barrier coatings (TBCs) in a high-heat-flux environment is the result of large surface temperature and thermal gradient across the coating thickness and the resulting viscoplastic deformations induced in the ceramic material. The maximum coating surface temperature has been used as the key loading parameter in previous studies. The current study explores the effects of several other thermal loading parameters on thermomechanical response and fracture behavior of TBCs with or without preexisting surface cracks. Results show that for a constant maximum surface temperature, the thermal fracture of the coating is increased by (i) an increased temperature difference across the coating, (ii) longer heating duration, and (iii) more aggressive coating surface cooling after heating. These results provide insights into TBC thermal fracture mechanisms and can potentially improve the design of the morphology of preexisting cracks in the coating to reduce fatal interface fracture.

Compensation of Thermo-elastic Machine Tool Deformation Based on Control internal Data

The thermo-elastic behaviour of machine tool structures leads to unwanted displacements at the tool centre point (TCP) and has a significant influence on the machining accuracy. In the past, therefore, numerous direct and indirect compensation methods were developed to reduce and/or compensate the thermo-elastic displacements. The paper describes a new indirect compensation approach which allows the abandonment of all additional sensors with the exception of one environmental temperature sensor. As input control internal data of the feed drives and the main spindle are used exclusively. The rotational speed and motor current values - the latter correlate to the drive torque - represent the thermal load parameters of the machine. A combination of first and second order time delay elements describes the displacement behaviour of the machine resulting from these load parameters. The parameters of the time delay elements are determined by a systematic calibration procedure. The resulting displacements are calculated online and superposed as offset-values for the correction of the respective axis positions. Practical experiments show that with this elementary method a reduction of the thermo-elastic displacements of more than 80 % of the initial value is possible.

THERMAL BEHAVIOUR OF COMPOSITE BOX-GIRDER BRIDGES.

This paper investigates the behaviour of composite box-girder bridges subject to environmental thermal effects such as solar radiation, air temperature and wind speed. It is based on the statistical analysis of measured temperature data which were recorded hourly in a newly constructed composite box-girder bridge for about 20 months continuously. Major thermal loading parameters that characterize the temperature profile are defined, and the seasonal behaviour of the parameters is described in detail. The experimental results are compared to the specifications suggested in the design codes for thermal loads. In addition, a series of heat transfer analyses using the two-dimensional finite element method is conducted in order to generalize the results to bridges with different cross-sections. The findings of this study show that the design temperature distribution with uniform differential between the concrete slab and the steel girder is unsuitable for representing the thermal effects in design purpose.

Thermal behaviour of composite box-girder bridges

This paper investigates the behaviour of composite box-girder bridges subject to environmental thermal effects such as solar radiation, air temperature and wind speed. It is based on the statistical analysis of measured temperature data which were recorded hourly in a newly constructed composite box-girder bridge for about 20 months continuously. Major thermal loading parameters that characterize the temperature profile are defined, and the seasonal behaviour of the parameters is described in detail. The experimental results are compared to the specifications suggested in the design codes for thermal loads. In addition, a series of heat transfer analyses using the two-dimensional finite element method is conducted in order to generalize the results to bridges with different cross-sections. The findings of this study show that the design temperature distribution with uniform differential between the concrete slab and the steel girder is unsuitable for representing the thermal effects in design purpose.

Experimental determination of fractional thermal loading in an operating diode-pumped Nd:YVO_4 minilaser at 1064 nm

A practical in situ method is described and used for determination of the fractional thermal-loading parameter eta(h) in an operating diode-pumped Nd:YVO(4) minilaser at 1064 nm. Readily applicable to the thermal characterization of other solid-state media, the method is based on the fact that thermally induced lensing will cause the laser oscillation to be quenched at a critical pump power whose magnitude depends on the cavity configuration, thermo-optical properties of the gain medium, and, in particular, on the value of eta(h). In the experiments described here, a 0.5-mm-long coated Nd:YVO(4) crystal with 3-at. % Nd concentration was used to construct the diode-pumped laser with a flat highly reflecting end mirror and an intracavity lens. For the method to be effective, the resonator was set up close to the edge of the stability range. Above the oscillation threshold, the pump power at which lasing was quenched because of the onset of the thermally induced resonator instability was measured as a function of the intracavity lens position. A numerical model that accounted for absorption saturation and pump-induced thermal lensing was then used to analyze the experimentally measured data with eta(h) as an adjustable parameter. The average best-fit value of eta(h) was determined to be 0.40 with an estimated statistical variation of 8%.

Temperature rise due to sliding in rolling/sliding elastohydrodynamic lubrication line contacts: an efficient numerical analysis for contact zone temperatures

An efficient numerical method based on Lobatto quadrature analysis is adopted for a rigorous analysis of temperature in elastohydrodynamic lubrication (EHL) line contacts. Temperature distributions are calculated for maximum Hertzian pressures and rolling speeds varying between 0.5 to 2.0 GPa and 1 to 30 m/s, respectively. Significant mid-film temperature and surface temperature increases have been observed at higher rolling speeds with an increase in loads and slip ratios. Results have been compared with the results of Manton, S. M., O'Donoghue, J. P. and Cameron, A., Temperatures at lubricated rolling/sliding contacts. Proceedings of the Institution of Mechanical Engineers, 1967–68, 182(417), 813–824. An empirical equation is presented for the prediction of non-dimensional maximum mid-film temperature in the contact zone in terms of the dimensionless thermal loading parameter Q, dimensionless load W and slip S, as: T ̄ md=11.08W 0.249S 0.0265e 0.201Q

Thermomechanical buckling of delaminated composite laminates

A thermomechanical buckling analysis of multilayered laminates with (across-the-width) strip delaminations is conducted on the basis of anisotropic thermoelasticity of the constituent layers and the Kirchhoff Love hypothesis of the classical laminate theory. With the assumption of generalized plane deformation, the present analysis yields exact, closed-form solutions of the delamination model under in-plane compression and shear loads and a temperature load that may vary arbitrarily in the thickness direction. A characteristic equation is obtained for the thermal and mechanical load parameters associated with the states of bifurcation. This equation reveals explicitly the effects of various geometrical, material and load parameters on the buckling of the delaminated plate. The solutions of the characteristic equation indicate that a moderate temperature gradient in the thickness direction may drastically reduce the axial bifurcation load.

A thermal analysis of traction in elastohydrodynamic rolling/sliding line contacts

An accurate thermal analysis of traction in elastohydrodynamically lubricated (EHL) line contacts has been done using an efficient numerical method based on Lobatto quadrature developed by Elrod and Brewe [H.G. Elrod, D.E. Brewe, Thermohydrodynamic analysis for laminar lubricating films, NASA Tech. Memorandum No. 88845, 1986.]. Roelands' viscosity model for P-150 and Santotrac-50 oils has been used in the present analysis. The variation of traction coefficient with slip for maximum contact pressures and rolling speeds varying between 0.4 to 1.52 GPa and 5 to 35 m s −1, respectively, are presented. Significant reduction in traction coefficient at high rolling speeds due to thermal effects have been found. Large increments in traction coefficient have been determined at high contact pressures, e.g., at 1.52 GPa as compared to 0.4 GPa at a particular rolling speed. The results of the present work have been compared with the results of Crook [A.W. Crook. The lubrication of rollers: IV. Measurements of friction and effective viscosity. Philos. Trans. R. Soc. London, Ser. A, 255 (Jan. 1963) 281–312.]. Cheng [H.S. Cheng, A refined solution to the thermal elastohydrodynamic lubrication of rolling and sliding cylinders, Trans, ASLE, 8 (4) (1965) 397–411.] and Walowit and Smith [J.A. Walowit, R.L. Smith. Traction characteristics of a MIL-L-7808 oil, Trans. ASME, J. Lubric. Technol., Oct. 1976, pp. 607–612.]. It was found that the results obtained by the present method are consistent with more elaborate theories and with the available traction data. Significant reduction in traction coefficient has been noticed at high rolling speeds (above 15 m s −1) and high slips (above 10%). The thermal effect on the sliding traction coefficient, μ, is expressed in terms of the dimensionless thermal loading parameter, Q, dimensionless load W and slip S as: μ = 2.31 W 0.80 Q −0.66 S −0.72.

Thermal Elastohydrodynamic Lubrication of Heavily Loaded Line Contacts—An Efficient Inlet Zone Analysis

An inlet zone analysis of TEHD lubrication of heavily loaded line contacts has been done using a computationally efficient and accurate numerical method based on Lobatto quadrature developed by Elrod and Brewe (1986). The results under extremely heavy conditions of dimensionless load W = 5.2*10−4 (pH = 2.0 GPa) and dimensionless rolling velocity U = 2.0*10−10(50 m/s) are presented. Significant reduction in thermal reduction factor (film thickness) at high rolling speeds relative to isothermal conditions have been observed. The results of the present work have been compared with the results of Wilson and Sheu (1983) and Hsu and Lee (1994). A correction formula of the thermal reduction factor for the minimum film thickness has been derived for a range of thermal loading parameters, loads, and slip ratios.

Thermal effects on film thickness and traction in rolling/sliding EHL line contacts—an accurate inlet zone analysis

Thermal analysis in an EHL line contact has been obtained using a computational method developed by Elrod and Brewe ( NASA Tech. Mem. 88845). Piezoviscous effects have been incorporated using Barus and Roelands' viscosity models for the P-150 oil used in the present analysis. A significant reduction in film thickness and traction at high rolling speeds relative to isothermal conditions has been obtained. Results are presented through figures and tables in the text. The results of the present analysis have been compared with the results of Murch and Wilson ( ASMEJ. Lubr. Technol., 97 (1975) 212), Goksem and Hargreaves ( Trans. ASME, 100 (1978) 346) and Ghosh and Hamrock ( NASA Tech. Mem. 83424). The thermal effect on film thickness reduction factor C, is expressed in terms of the dimensionless thermal loading parameter Q and slip S as: C = 1.0 [ 1.0 + 0.133 Q 0.71 ( 1.0 + 5.65 S 0.96 ) ]

An Efficient Algorithm for Thermal Elastohydrodynamic Lubrication Under Rolling/Sliding Line Contacts

One of the most time-consuming routines in thermal EHL problem is the calculation of the surface temperature integral. Combining the multigrid technique and the Newton-Raphson method, a modified multilevel, multi-integration algorithm for this integral is developed that can reduce the computational complexity from O (n2) to O (n ln n) for the thermal EHL problem of rolling/sliding line contacts. The employed standard central difference approximation to the coupled Reynolds and energy equations can yield the maximum difference of mass flow flux within one percent. Effects of dimensionless load, dimensionless materials parameter, slip ratio, and thermal loading parameter on the minimum film thickness are investigated. Correlation formula of thermal reduction factor for the minimum film thickness is derived for a wide range of slip ratios, loads, thermal loading parameters, and materials parameters.

Advanced multilevel solution for thermal elastohydrodynamic lubrication of simple sliding line contacts

A new computational algorithm is developed for the problem of thermal elastohydrodynamic lubrication of line contacts under simple sliding conditions. Because of the applications of multilevel multi-integration to the calculations of elastic deformation and moving surface temperature and the use of a new relaxation process in the stationary surface temperature, the computational complexity has been reduced from O( n 2) to O( n ln n). The standard central difference approximation to the coupled Reynolds and energy equation employed can yield the maximum mass flux defect within 1%. The correlation formula of film thickness reduction factor, c t, is obtained for a wide range of operating parameters. Results show that the thermal effect on c t, is more pronounced for simple sliding conditions than for rolling/sliding conditions. The contour maps for the maximum film temperature rise and maximum surface temperature rise are also presented for a wide range of loads and thermal loading parameters.

Thermal Postbuckling of Uniform Columns on Elastic Foundation

The effect of elastic foundation on the thermal postbuckling behavior of columns is evaluated because it was shown that the foundation stiffness plays an important role in determining the mode shape of linear buckling. Closed-form expressions for critical linear thermal load and thermal load in the postbuckling range are obtained using the Rayleigh-Ritz method. Results in the form of λ\N\I\dL\N, the linear ctitical load, and λ\N\I\dN\dL\N, the thermal load parameters are presented for different values of foundation stiffness and modes. A discussion on the effect of elastic foundation with stiffness around the transition value (where the change of mode shape occurs), on the thermal buckling and postbuckling is included.

Extreme values of thermal loading parameters in concrete bridges

The present paper addresses the question of developing design criteria for thermal effects in concrete bridges. The objective is to determine extreme temperature effects having specified return periods. The parameters of the local meteorological regime which critically affect the extreme thermal effects are identified. Their variation in time is analyzed and related to the thermal loading parameters in a concrete bridge. These include average temperature, temperature difference between sections, linear temperature differential, and residual temperature fields. The analysis of the extreme values of these parameters is described in detail.The reduction of data, the model development, and the statistical analysis are clarified by the application to the Bow River light rail transit bridge in Calgary, Alberta. Temperature profiles in several sections of this structure are being measured on an hourly basis. The findings of this study show certain shortcomings of the temperature effects design criteria currently included in the Canadian bridge design codes. Key words: extreme values, design temperature, thermal loading, thermal gradients, temperature measurements, concrete box girder bridges.

Thermal buckling of cross-ply composite laminates

Thermal buckling of antisymmetric cross-ply composite laminates is investigated in this paper. A one-dimensional finite element having two nodes and six degrees of freedom, namely axial displacement, transverse displacement, rotation of the normal to the beam axis and their derivatives with respect to the beam coordinate axis at each node, is developed based on the first-order shear deformation theory. The element elastic stiffness matrix and the geometric stiffness matrix (based on thermal stresses) each of order 12 x 12 are derived to compute the bifurcation thermal load (critical temperature). Correspondence of thermal critical load parameter and mechanical critical load parameter in the case of isotropic and composite laminates is discussed. Results are presented for various boundary conditions, lay-up sequences and slenderness ratios.

Thermal Elastohydrodynamic Lubrication of Line Contacts

A numerical solution to the problem of thermal elastotydrodynamic lubrication of line contacts was obtained by using a finite-difference formulation. The solution procedure consists of simultaneous solution of the thermal Reynolds equation, the elasticity equation, and the energy equation subject to appropriate boundary conditions. Pressure distribution, film shape, and temperature distribution were obtained for fully flooded conjunctions, a paraffinic lubricant, and various dimensionless speed parameters while the dimensionless load and materials parameters were held constant. Reduction in the minimum film thickness due to thermal effects (as a ratio of thermal to isothermal minimum film thickness) is given by a simple formula as a function of the thermal loading parameter, Q: Plots of pressure distribution, films shape, temperature distribution, and flow are shown for some representative cases.

Determination of external thermal load parameters by solving the two-dimensional inverse heat-conduction problem

A method is proposed for recovering the space-time behavior of an external unsteady heat load to a cylindrical body by solving the two-dimensional inverse heat-conduction boundary problem.