Thermal Contact Conductance Model Research Articles

Equivalent thin-layer temperature field model (ETTM) for bolted rotors to describe interface temperature jump

Improving the accuracy and efficiency of predicting the temperature field is a crucial requirement for iteratively calculating and online monitoring the temperature field, particularly for combined structures. The heat flow movement is impeded by incomplete interface contact, resulting in a temperature jump. To address this, the equivalent thin-layer temperature field model (ETTM) is proposed to replace the interface thermal contact conductance (TCC) model. Firstly, the fractal TCC model of a bolt connection is derived based on fractal geometry. Subsequently, the contact surface of the circumferential bolt connection is considered to be the parallel connection of multiple bolt thermal resistances. The TCC of the equivalent thin-layer is obtained. Building on this, the ETTM of the built-up rotor structure is developed. Finally, a temperature field model of the bolted rotor is derived. The validity of models is verified by comparing the model proposed in this paper with the previous research findings and ANSYS analysis results. Numerical simulation results reveal that TCC is influenced by several factors: contact pressure, the nominal contact area within the fractal domain, fractal dimension, fractal roughness, and the root mean square (RMS) height. Furthermore, the effects of the thickness of the thin layer model and the thermal conductivity of the material on heat transfer are examined. Ultimately, the findings indicate that heat transfer at the interface is significantly impeded by thermal contact resistance across various temperature boundary conditions. Notably, lower contact pressure intensifies this impedance.

Thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory

PurposeThe purpose of this study is to establish a thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory.Design/methodology/approachThe effects of contact load, inclination angle, fractal dimensional and fractal roughness on thermal contact conductance of rough surfaces were studied using numerical simulation.FindingsThe results show that the thermal contact conductance of the rough surface increases with the increase of contact load and fractal dimension and decreases with the increase of fractal roughness and inclination angle. The inclination angle of the rough surface has an important influence on the thermal contact conductance of the rough, and it is a factor that cannot be ignored in the study of the thermal contact conductance of rough surfaces.Originality/valueA thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory was established in this study. The achievements of this study provide some theoretical basis for the investigation of the thermal contact conductance of rough surfaces.

Investigation of thermal contact conductance of bare copper-copper and aluminum 1070-aluminum 1070 interfaces at low temperatures between 10 and 70 K

The prediction model of thermal contact conductance (TCC) for bare OFHC-OFHC and Al 1070-Al 1070 flat interfaces is presented. OFHC (Oxygen free high conductivity copper) and Aluminum are widely used in cryogenic systems. Since the thermal conductivity of pure copper or aluminum materials has a highly non-linear characteristic with its peak value at around 20 K, it is difficult to predict TCC of those materials at this temperature range. The TCC model in this paper proposes the dimensionless correlation through 16 experiments considering various conditions such as surface roughness, materials, pressure, and temperature. The model has been established by the modification on the previous CMY (Cooper, Mikic, Yovanovich) model with additional parameters. The first important feature of the model is to adopt the contact thermal conductivity (kc). It can be calculated by using the size effect theory at the micro-scale contact single spot. The second feature is the dimensionless temperature (T/TD). An experimental setup is constructed inside of the conduction-cooled cryostat to measure the thermal conductivity of bulk material and the TCC simultaneously for the temperature range between 10 K and 70 K. OFHC and Al 1070 specimens with various surface roughness are prepared and tested with contact pressure of 6 to 13.5 MPa in vacuum environment. The predicted TCC by the proposed model shows a reasonable agreement with the experimental results in low temperature.

Fractal analysis of the thermal contact conductance for mechanical interface

As the increasing demand for thermal performance of mechanical products, thermal contact conductance (TCC) is widely used in the thermal-mechanical analysis. This paper presents a TCC prediction model based on fractal geometry. Besides the fractal dimension and fractal roughness parameter, the fractal domain area is estimated according to the fractal characteristics of the surface topography. Based on these three fractal parameters, the TCC of the interface with or without fluidic interface material can be calculated. The experimental results show that the fractal model is superior to the TCC models based on GW geometry in accuracy and numerical stability.

Interface evaluation of a Bi–Zn eutectic solder alloy: Effects of different substrate materials on thermal contact conductance

Industry is searching for ways of improving the process control required for the manufacture of electronic circuitry. In this respect, a numerical mathematical model for thermal contact conductance of solder/substrate couples is developed based on an inverse heat conduction problem. The intention of this research is combining the model results and wetting experiments in order to determine if there is a compromise between them in the matter of the Bi–Zn eutectic alloy. Substrate materials considered as priority for the electronics industry were tested. It was found that the heat transfer coefficients (h) and the contact angles (θ) might be related to each other. The Bi–Zn/copper, Bi–Zn/nickel, Bi–Zn/Invar and Bi–Zn/steel couples, in this order, generated θ varying from the smallest to the largest as well as h from the largest to the smallest. Microstructural coarsening effect has been realized with higher spacing between Zn fibers (λZn) referring to a condition of worse heat extraction imposed by an alloy/substrate couple during solidification.

Thermal contact conductance between balls and bearing rings

The thermal contact conductance (TCC) between balls and bearing rings is predicted by proposing the TCC model between the curved and spherical surfaces. The Weierstrass-Mandelbrot function is applied to characterize the microscopic topography of surfaces. The fractal contact model is constructed by considering the elastic, elastic-plastic, and plastic deformations of microprotrusions, and then an effective contact coefficient is built to modify the fractal contact parameters. Finally, the TCC modeling method is proposed by considering the elastic and plastic TCCs of different contacting microprotrusions with different sizes. The experiments of TCCs were conducted under different conditions to verify the validity of the proposed model. The results show that the predicted TCCs fit well with measured values and that the predictive accuracy can be improved greatly by considering the effective contact coefficient. Then the effect of critical factors on TCCs is discussed, and the TCC increases with the external load, and increases with the fractal dimension D and decreases with the scaling constant G. The TCC of the dynamic lubricated ball bearing is much greater than that of the static lubricated ball bearing and the TCC of the static lubricated ball bearing is much greater than that of the static non-lubricated ball bearing.

A multiscale model for thermal contact conductance of rough surfaces under low applied pressure

The scope of this work is to investigate how the interfacial pressure and the scale of the asperities as well as the temperature, influence the thermal contact conductance TCC in rough surfaces under low pressure. For that, a two- dimensional numerical model is developed, in which the macroscopic TCC coefficient is obtained from the solution of the heat conduction problem at the scale of asperities. The morphology of the rough surface, which is characterized by a fractal interpolation function, is applied to mechanical and thermal modeling. The contact model calculates the different contact scales at the asperities by considering elastic, elastic–plastic and fully plastic deformations as well as the changes in material parameters due to the temperature. Finally, several contacting asperities are combined to get the macroscopic TCC coefficient. The obtained results showed that at small values of normal pressure, TCC becomes smaller at higher resolutions of the interface where waviness is more intense. On the contrary, the rate of increase of TCC with the increase of the normal pressure is larger at these interfaces at larger values of normal pressure, where the smaller scales of asperities deform more easily. This phenomenon appears to be more intense with the time as the temperature of the interface rises and consequently more plastifications of the asperities occur.

Thermal contact conductance modeling of baring outer ring/bearing housing interface

Currently, no model could be used to readily predict the TCR of baring outer ring/bearing housing interface, then a thermal contact conductance (TCC) model between cylindrical surfaces with transition fits is constructed. The topography is described by the fractal geometry to characterize the multiscale and self-affinity behaviors and two stochastic variables are introduced into the fractal function to guarantee the random and disordered features. Then the contact states of contact points are analyzed, and a new fractal inner contact model is established. An effective contact factor is introduced to modify the contact parameters. Eventually, the predictive model of TCCs is constructed by summing up the TCCs of all the contacting protrusions with different scales. To demonstrate the validity of the TCC model, the measuring setup of TCCs was developed, and then the tests were conducted. The results show that the average deviations between the measured data and predicted TCCs are 10.25% and 8.73% for SS304 and carbon steel, respectively. When the effective contact factor is not considered, the average deviations between the predicted TCCs and measured data are 25.47% and 20.61% for SS304 and carbon steel, respectively. Then the necessity to introduce the effective contact factor is verified. For SS304, the prediction accuracy of the present model is 15.22%, 56.36%, and 31.55% higher than that of the present model without effective contact factor, M-T model, and Zou model, respectively. For carbon steel, the prediction accuracy of the present model is 11.88%, 63.76%, and 34.87% higher than that of the present model without effective contact factor, M-T model, and Zou model, respectively. Finally, the effects of the surface roughness, the protrusion top radius, the effective contact factor, and the transition fit on TCC are discussed. The results show that TCC decreases with surface roughness. The TCC with different protrusion top radii is greater than that with identical top radius. The TCC increases with the effective contact factor slowly and then the growth rate increases rapidly. Besides, the TCC increases with transition fit sharply at the early stage, and then increases slowly for both SS304 and carbon steel.

Thermal contact conductance between rollers and bearing rings

To predict the TCC between rollers and bearing rings, an integrated thermal contact conductance (TCC) model between cylindrical surfaces was proposed. The surface topography was characterized by the Cantor set theory, and the structure function of the surface topography was used to identify the equivalent fractal dimension. Then the fractal contact model was established, and an effective contact factor was constructed to modify the contact parameters by considering the contact between two cylindrical surfaces. Finally, the discrete and continuous models were established to predict the TCC between rollers and bearing rings. To verify the validity of the TCC model, the experiments of TCCs were conducted and then the comparison between the measured and predicted TCCs was performed. The results show that the maximum and average errors between the predicted TCC and the measured data are 10.21% and 8.14%, respectively. Besides, the effects of the key factors on the TCC between rollers and rings were discussed. The TCC increases with the contact pressure because the critical generation nc increases with the contact load. Moreover, the smaller the fractal dimension, the rougher is the surfaces, and then the smaller is the TCC. The TCC between rollers and bearing rings increases with the dimensionless contact area. Besides, the TCC increases with the rotational speed for the fully run-in roller bearing, and the TCC of the dynamic lubricated roller bearing is much higher than that of the static lubricated roller bearing and that of the static non-lubricated roller bearing.

A three-dimensional fractal theory based on thermal contact conductance model of rough surfaces

The thermal contact conductance is an important problem in the field of heat transfer. In this research, a three-dimensional fractal theory based on the thermal contact conductance model is presented. The topography of the contact surfaces was fractal featured and determined by fractal parameters. The asperities in the microscale were considered as elastic, elastic-plastic, or plastic deformations. The real contact area of the asperities could be obtained based on the Hertz contact theory. It was assumed that the rough contact surface was composed of numerous discrete and parallel microcontact cylinders. Consequently, the thermal contact conductance of the surface roughness was composed of the thermal constriction conductance of microcontacts and the air medium thermal conductance of microgaps. The thermal contact conductance of rough surfaces could be calculated by the microasperities integration. An experimental set-up with annular interface was designed to verify the presented thermal contact conductance model. Three materials were used for the thermal contact conductance analysis with different fractal dimensions D and fractal roughness parameters G. The numerical results demonstrated that the thermal contact conductance could be affected by the elastic-plastic deformation of the asperities and the gap thermal conductance should not be ignored under the lower contact load. The presented model would provide a theoretical basis for thermal transfer engineering application.

Dynamic Thermal-Structure Coupling Analysis and Experimental Study on Ball Screw Feed Drive System of Precision Machine Tools

To improve the simulation accuracy of the thermal characteristic of ball screw feed drive systems, a dynamic thermal-structure coupling model, which considered the effect of the thermal contact conductance (TCC) of the solid joint on the accuracy of simulation results, was proposed to conduct thermal characteristic analysis of ball screw feed drive systems. The predictive model for TCC was proposed based on the micro morphology description of rough surfaces and the contact load distribution of solid joints. Then, the dynamic thermal-structure model of the ball screw feed drive system was established. To validate the effectiveness of the dynamic thermal-structure coupling model, thermal characteristic experiments of the ball screw feed drive system were conducted under different feed rates. The results showed that the simulation accuracy of temperature field and axial thermal elongation can be improved from 65% to 87% and from 70% to 85%, respectively.

A geometrical–mechanical–thermal predictive model for thermal contact conductance in vacuum environment

In this article, a comprehensive geometrical–mechanical–thermal predictive model is developed for thermal contact conductance between two flat metallic rough surfaces. The rough surface was characterized by Weierstrass–Mandelbrot fractal function. The micro-morphology was measured by laser microscope to identify the fractal parameters that were then applied to mechanical and thermal modeling. A new contact mechanics model was then proposed to calculate the contact parameters, and different contact scales between asperities and three modes of deformation, elastic, elastic–plastic and fully plastic, were taken into account. The normal contact pressure, which should be equal to the exterior load, was formulated as a function of the fractal parameters, the maximum contact area and the material physical properties of the given surface. Based on the contact mechanics model, first a single pair of contacting asperities was proposed and then multi-contacting asperities were combined to get total thermal contact conductance. The influences of contact load, surface roughness, asperity top radius and contact area as well as the temperature on the thermal contact conductance were investigated by using the proposed model. The investigation results showed that thermal contact conductance increases with the contact load and contact area. The larger the surface roughness, the smaller is the thermal contact conductance. Finally, the experiments were conducted to validate the effectiveness of the thermal contact conductance modeling. This geometrical–mechanical–thermal predictive model was compared with the two existing predictive models and a series of experimental data. The results showed good agreement, demonstrating the validity of the model and providing certainty for further study on the heat transfer between contact surfaces.

Numerical Modeling of Electrical Contact Conductance of Rough Bodies

Since the beginning of the 20th century to the present time, efforts have been made to develop a model of the electrical contact conductance. The development of micro- and nanotechnologies make contact conductance problem more essential. To conduct borrowing from a welldeveloped thermal contact conductance models on the basis of thermal and electrical conductivity analogy is often not possible due to a number of fundamental differences. While some 3Dmodels of rough bodies deformation have been developed in one way or another, a 3D-model of the electrical conductance through rough bodies contact is still not. A spatial model of electrical contact of rough bodies is proposed, allows one to calculate the electrical contact conductance as a function of the contact pressure. Representative elements of the bodies are parallelepipeds with deterministic roughness on the contacting surfaces. First the non-linear elastic-plastic deformation of rough surface under external pressure is solved using the finite element software ANSYS. Then the solution of electrostatic problem goes on the same finite element mesh. Aluminum AD1 is used as the material of the contacting bodies with properties that account for cold work hardening of the surface. The numerical model is built within the continuum mechanics and nanoscale effects are not taken into account. The electrical contact conductance was calculated on the basis of the concept of electrical resistance of the model as the sum of the electrical resistances of the contacting bodies and the contact itself. It was assumed that there is no air in the gap between the bodies. The dependence of the electrical contact conductance on the contact pressure is calculated as well as voltage and current density distributions in the contact bodies. It is determined that the multi-asperity contact mode, adequate to real roughness, is achieved at pressures higher than 3MPa, while results within the single contact spot are suitable for modelling a structured artificial roughness only.

The Physical-Mechanism Based High-Temperature Thermal Contact Conductance Model with Experimental Verification

The physical-mechanism based high-temperature thermal contact conductance model is proposed, in which the temperature effect on the material properties and interface radiation effect are considered. A testing platform of high temperature thermal contact conductance is also established, and the thermal contact conductance between three-dimensional braid C/C composite material and superalloy GH600 is tested under different interface roughness and temperatures. Experimental results verify the rationality of the present model. Results also show that it is necessary to take the effect of temperature into account especially at high temperatures, and the interface radiation effect is negligible compared to spot conduction under 850 K.

An Experimental Study to Show the Effect of Thermal Stress on Thermal Contact Conductance at Sub-megapascal Contact Pressures

Experimental studies are presented to show the effect of thermal stresses on thermal contact conductance (TCC) at low contact pressures. It is observed that in a closed contact assembly, contact pressure acting on the interface changes with the changing temperature of contact members. This change in contact pressure consequently causes variations in the TCC of the junction. A relationship between temperature change and the corresponding magnitude of developed thermal stress in a contact assembly is determined experimentally. Inclusion of a term called temperature dependent load correction factor is suggested in the theoretical model for TCC to make it capable of predicting TCC values more accurately in contact assemblies that experience large temperature fluctuations.

Thermo-mechanical analysis of pebble beds in HELICA mock-up experiments

In this investigation, a thermo-mechanical model for pebble beds and a method for the identification of the material parameters, recently developed in Forschungszentrum Karlsruhe, are adopted for the analysis of HE-FUS3 Lithium Cassette (HELICA) mock-up. A pressure-dependent thermal contact conductance model to represent the pebble–wall interactions has been implemented in the FE code ABAQUS. First, the current material model has been verified by uniaxial compression and creep experiments under a wide range of temperature fields, and good agreement between experiments and theory has been achieved. The HELICA mock-up has been modelled by 2D generalized plane strain elements, and analyzed in ABAQUS. The results show that the temperature and mechanical fields obtained in FE analysis agree well with the measurements by thermo-couples and LVDTs located at different positions.

Thermal Contact Conductance at Low Contact Pressures

New correlations are presented for the truncated Gaussian (TG) thermal contact conductance model during first loading. The TG model is also incorporated into existing models for the hysteresis effect of thermal contact conductance and for the plastic contact pressure. The TG models, as well as the existing fully Gaussian models, are compared against new experimental data collected at very low contact pressures. Comparison between the models and the data shows that the fully Gaussian model underpredicts data at low contact pressures, as already extensively reported in the literature. The first-loading TG model predicts the experiments very well over the entire range of the contact pressures tested. The hysteresis effect model proved to be accurate only for contact pressure above 400 kPa, in general. The TG model requires a surface roughness parameter, the level of truncation of the probability density function of surface heights, which cannot be obtained accurately from ordinary surface profilometry. The most accurate and straightforward way to estimate this surface geometry parameter is from thermal tests. The levels of truncation of bead-blasted stainless steel 304 and Ni 200 are obtained and presented.

Effect of surface asperity truncation on thermal contact conductance

This paper presents studies on thermal contact conductance at light contact loads. Surface profilometry measurements are presented which show that actual surface asperity height distributions are not perfectly Gaussian. The highest asperities are truncated, causing existing thermal contact conductance models to underpredict experimental data. These observations have been incorporated into modifications of existing contact conductance models. The truncation leads to an enhancement of thermal contact conductance at light contact pressures. The preliminary model has been compared against thermal contact conductance data presented in the open literature, and good agreement is observed. The results show that the truncation is a function of the roughness level: the rougher the surface, the more truncated the surface height distribution.

Theoretical and experimental study of a thermal contact conductance model for elastic, elastoplastic and plastic deformation of rough surfaces

This study developed a thermal contact conductance model that takes into account surface asperities with elastic, elastoplastic and plastic deformation. The surface asperity model considers the continuity and smoothness of variables across different modes of deformation. Experiments were also conducted to measure thermal contact conductance for samples with different surface roughness when the contact pressure was increased or decreased. The trend of the test data supports the theoretical results.

Thermal Contact Conductance of Metal/Polymer Joints: An Analytical and Experimental Investigation

The heat e ow across a metal/polymer interface is a very important problem in many modern engineering applications. A thermal joint conductance model that employs the surface mechanics of a contact interface in conjunction with an existing elastic thermal contact conductance model was developed. In developing the model, an elastic contact hardness term was derived to predict the actual contact area of a metal/polymer interface under loading. The model predicts a microscopic resistance region where the interface resistance is dominant and a bulk resistance region where the thermal conductivity of the polymer is dominant. An experimental apparatus was fabricated, and a successful experimental program was conducted. New experimental data were gathered on different polymeric specimens over a pressure range of 138 ‐2758 kPa (20‐400 psi). The experimental data were compared to the proposed thermal joint conductance model. It was found that the proposed model predicted the data quite well. The data followed the predicted trends for both the microscopic and bulk resistance regions.