A novel transient infrared-thermography based experimental method for the inverse estimation of heat transfer coefficients in rotating bearings

Abstract

Heat Transfer at moving bearing interfaces is a key parameter for the thermal characterization and design of high precision machine tools and electrical engine systems for e-mobility application. Yet, the majority of experimental approaches use tactile sensors to obtain the required temperature information for the calculation of heat transfer coefficients. However, only a limited amount of sensors can be placed in the investigated system, also including significant measurement uncertainties, long investigation times, and providing only access to local temperature information. To overcome these shortcomings, a novel method is presented, using infrared thermography to obtain transient and spatially resolved temperature information of bearing front surfaces. The recorded temperature data is used in an inverse evaluation algorithm, to determine the heat transfer coefficient, considering for modeling heat conduction as well as convective fluxes due to rotating components. Finally, experimental temperature data and calculated heat transfer coefficients are presented, discussing further the effect of low angular velocities on the heat transfer. It is shown, that this method is capable to detect changes in heat transfer coefficient due to variations in rotational speed which was not possible with existing methods. Concluding, this approach can be used in future work to focus in detail on the influence of different rolling elements, geometry and interstitial media.

Introduction

During the last decades, there has been an increasing demand in high precision manufacturing processes operating at an accuracy of a few micro- or even hundreds of nanometers [1]. To ensure this desired accuracy, thermal defects in material and surface due to heat generation, dissipation and inhomogeneous temperature fields need to be avoided or compensated [[2], [3], [4]]. A common approach to solve this problem is the modeling, simulation and prediction of thermal behavior, connecting the temperature fields of the system with the heat transfer at the interface to adjacent components. In this context, an often occurring type of boundary condition is the contact heat transfer at contacting interfaces, which arises due to surface roughness, leading to a restriction of heat flow and finally to a temperature drop across the interface. This phenomena has been first analyzed analytically by Cooper et al. [5] and continuously extended by the group of Bahrami, Mikic and Yovanovich to consider various contact pressures, interstitial media and macroscopic surface structures [[6], [7], [8], [9], [10]], giving later on also a comprehensive review of existing approaches [11]. However, besides theoretical and analytical considerations, also experimental methods to quantify the thermal contact conductance have been developed and presented in literature during the last years. Regarding static as well as moving interfaces, a common experimental method involves the measurement of stationary temperature fields, induced by the application of a known heat flux [[12], [13], [14], [15]]. Using this method, the group by Takeuchi et al. [[16], [17], [18], [19]] published comprehensive data regarding the impact of varying loads and lubrication conditions in context of bearings. The majority of published studies focus in particular on heat transfer at high angular velocities [[17], [18], [19]]. However, there has been an growing interest in thermo-mechanical modeling of systems at low angular velocities [20,21]. Recently, Lui et al. [22] have presented a numerical approach to estimate contact conductance of bearing elements which has shown good agreement with performed experiments, however requiring on the one hand significant effort to place the sensors and second long investigation times until the system reaches the thermal equilibrium.

Recapitulating, the majority of experimental approaches involve temperature measurements by thermocouples or thermistors along the specimens providing the necessary data to calculate the temperature drop across the surface and the corresponding heat transfer coefficient including certain limitations and simplifications. First, this method requires a steady-state temperature field and long observation times up to several hours. For accurate measurements, the specimen needs to be located in a housing to reduce thermal influences of the environment. Further, the temperature data need to be extrapolated to the specimen surface, to calculate the resulting temperature drop, which makes this method prone to errors in sensor location and measured temperature. However, an alternative non-invasive method is the use of highspeed infrared-thermography which can capture rapid temporal variations in the temperature field and allows for a precise observation of local temperature changes. This method has been successfully applied to quantify contact heat transfer at static interfaces under varying loads and material combinations including also interstitial media [[23], [24], [25], [26], [27], [28]]. Hence, knowledge and experiences of this mentioned work will be transferred to quantify heat transfer coefficients at moving interfaces.

The proposed method reduces the investigation time significantly and catches transient effects on the heat transfer such as the passing rollers or variation in the angular velocity. Further, low angular velocities are evaluated due to two reasons: First, it is investigated whether there is an immediate thermal impact of passing rollers on the contacting surfaces. Second, heat source terms due to friction have only a minor impact on the resulting temperature field at these operating conditions and are neglected. Nevertheless, a precise differentiation between heat flow caused by friction and heat transfer at elevated angular velocities will be part of future research. It is stressed that the investigated overall heat transfer coefficient summarizes three major phenomena: Contact Heat Transfer at the shaft-roller interfaces, heat conduction in the roller and contact heat transfer at the roller-housing interface. Due to comparable small volume of the roller elements, the impact of heat storage and thermal damping on the heat transfer coefficient is neglected.

Concluding, the main aim of this work is to establish a novel high precision and transient experimental method for the quantification of heat transfer coefficients at bearing interfaces and to provide fundamentals for future research.