Experimental investigation of the thermal contact resistance in shrink fit assemblies with relevance to electrical machines

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1 Cite as: R. Camilleri, D.A. Howey, M.D. McCulloch, Experimental investigation of the thermal contact resistance in shrink fit assemblies with relevance to electrical machines, IET Power Electronics Machines and Drives Conference (PEMD), 2014, DOI Experimental investigation of the thermal contact resistance in shrink fit assemblies with relevance to electrical machines R. Camilleri, D.A. Howey*, M.D. McCulloch Energy and Power Group, Department of Engineering Science, University of Oxford, UK, Keywords: thermal contact resistance, shrink fit, electrical machines, thermal modelling Abbreviations CFD computational fluid dynamics LPNA lumped parameter network analysis Roman Symbols A area (m 2 ) B,C constants d average diagonal length of the Vickers indent (m) D cylinder diameter (m) F mass on Vickers Measurement (kg) hc thermal contact conductance transfer (W/m 2 K) HV Vickers Hardness (GPa) I current (A) k thermal conductivity (W/mK) L length (m) m surface asperity slope n no of samples heat flux (W/m 2 ) Q total heat (W) r radius (m) R th thermal resistance ( o C/W) T temperature ( o C) u uncertainty V voltage (V) x effective air gap (m) y vertical distance measured (µm) Greek Symbols linear thermal expansion (1/K ) D change in diameter (m) stress (MPa), RMS roughness (m) Subscripts a air H hoop i inner cylinder o outer cylinder OH oven hysteresis R radial RT reference temperature TC thermocouple ambient air Abstract Thermal design and modelling in electrical machines is important because it allows a proper choice of materials, avoids de-rating of the machine and eliminates excessive safety factors thus achieving higher current densities. In high current density electrical machines, particularly those making use of liquid cooled housing jackets for heat removal, the stator to housing thermal contact resistance is on the main heat removal path of the electrical machine. So far it has always been assumed that this parameter is dependent on the shrink fit manufacturing procedure of the machine. However this paper provides experimental evidence showing that the thermal contact resistance not only varies with shrink fit pressure but is also affected by heat flux and temperature. Hence the common notion that the thermal contact resistance is a constant value set during the machine assembly, and that during thermal design this value can be applied across the whole operating range of the machine is an over simplification. The paper presents arbitrary correlations showing the variation of thermal contact resistance with heat flux and shrink fit pressure and compares the measured values with values quoted in the literature. 1. Introduction! This paper provides an experimental investigation on the thermal contact resistance of shrink fit concentric geometries with particular relevance to electrical machines.. High power density electrical machines are becoming popular in applications in which transient modes of operation dominates, such as electric vehicles and wind turbines[1, 2]. Hence in these circumstances, a transient thermal model of the machine is important. Thermal modelling in electrical machine design is typically performed either through lumped parameter network analysis (LPNA) or computational fluid dynamics (CFD). While LPNA is quick to solve, it requires a number of unknown thermal resistances that are either obtained from experiments, CFD, or are guessed and later verified. Conversely CFD models produce a better insight and more detailed information, but may take a substantial time to simulate [3]. These are hence limited to generating parameters for particular components or locations, while the overall machine thermal simulation is performed by LPNA [4]. The difficulties in determining the thermal resistances employed in LPNA have been highlighted in [5, 6] which categorized thermal resistances into convective terms and contact terms. While there have been several efforts to provide adequate convective resistances for different machine topologies [7-9], the same cannot be said for thermal contact resistances. Thermal contact resistances such as that at the interface between the stator and the housing are critical as they are 1

2 on the main thermal path of an electrical machine. Thus they strongly affect the accuracy of model predicted temperatures. This is particularly important in high current density machines which make use of shrink fit liquid cooled housing jackets as their main source of heat removal. Whereas research in improving the effectiveness of the cooling jacket itself has been very active [10-13], work that provides an understanding of the thermal contact resistances in electrical machines is still lacking. While some modellers have applied fixed thermal contact resistances, which are calibrated with experiments others have attempted to use theoretical or semi-empirical correlations from flat joints in contact. However in flat contacts, the interface pressure can be controlled by the torque setting and is independent of the heat flux through the interface. Conversely, in coaxial cylindrical surfaces the interface pressure is dependent on the initial degree of fit and the differential expansion of the two cylinders. This is in turn a function of the temperature, which is effected by the heat flux through the interface [14]. Following a brief literature review about research in thermal contact resistances on cylindrical joints, thermal contact resistances within the context of electrical machines are also examined. The paper describes the experimental procedure and discusses the developed correlations of thermal contact resistance with contact pressure and heat flux. 2. Literature review 2.1 Thermal contact resistances in cylindrical joints While the works on thermal contact resistances in flat joints is substantial (in the order of 200 publications [15]), studies on cylindrical joints is much more limited (about an order of magnitude less). Four main thermal contact resistance models for flat joints have been developed and are known as the Shlykov model [16], the Ross and Stoute model [17], Veziroglu model [18] and the Cooper-Mikic- Yovanovich model [19]. A comparison of these models has been presented in [20-22] and is now generally accepted that the Cooper-Mikic-Yovanovich model offers better predictions. [23] shows that the Cooper-Mikic-Yovanovich model can be adapted for curved surfaces if the heat transfer is coupled to classical thermo-elastic stress analysis. His model was found to achieve accuracy within 5% of experimental data by [24]. The authors also compared alternative models and showed that they grossly overestimate the contact resistance with errors in the range of 25%-100% for the Ross and Stoute model and the Shlykov Model, while 100%-200% by the Veziroglu model. [14] proposes an extension to this work in which he shows that the thermal contact conductance in coaxial cylindrical joints not only depend on the contact pressures and the surface and material properties of the cylinders, but is affected also by the heat flux and the resulting maximum temperatures. The analysis takes into account the differential expansion of concentric cylinders due to the temperature gradients caused by the heat flow. This consequently changes the contact pressure at the interface. An iterative solution to solve the contact pressure during a heat load was proposed. The paper uses the model to investigate the effects of surface parameters. However the need for more experimental work with clear information on the material properties, surface properties and temperatures reached is highlighted in [14, 23]. 2.2 Thermal Contact Resistances in Electrical Machines [25] measured the thermal contact resistance of three totally enclosed fan cooled electrical machines and compared the results to the Shlykov flat joint model. The model was extrapolated to predict the component temperatures in a LPNA model. Conversely [26] designed a series of experiments to obtain values of the thermal contact resistances between a silicon steel stator and a shrink fit mild steel housing used in a liquid cooled generator applied in a wind turbines. A number of assemblies were developed with shrink fit pressures varying up to 39 MPa. The authors offer a series of guidelines in which the thermal contact resistances is found to decrease with increasing contact pressure, improved surface finish and with the application of thermal interface material. However the paper does not provide any values of heat loads, motor dimensions and surface finish. Hence results cannot be replicated or compared to. The paper fails to provide a correlation that can be used for thermal modelling and assumes that the thermal contact resistances are independent of heat flux and only dependent on the initial shrink fit pressure. Conversely, [4, 6] investigates unknown thermal contact resistance values in LPNA models by introducing a small effective interface air gap between the stator and the machine housing. While suggested values of the effective air gap are also quoted in [27, 28] the authors found that real machines often require effective gaps that are an order of magnitude larger than those suggested. With this method, the modeller will be required to perform an initial calibration with experimental results in order to determine the correct size of the effective gap. Despite its effectiveness during steady state machine operation, this technique also assumes that the thermal contact resistances is fixed and hence may lead to inaccuracies in the temperature prediction when applied during transient operation. 3. Experimental Work An experimental approach was taken with the aim to provide a better insight on thermal contact resistance and providing the thermal designer with better correlations that can then be applied to thermal models. In order to allow the thermal designer to replicate results, material and surface properties that are also key players in thermal contact resistances, such as the hardness and the surface roughness were also measured and the results are presented. 2

3 3.1 Manufacturing Four pairs of concentric cylinders were manufactured. The materials were chosen so as to replicate the interaction between the shrink-fit aluminium housing onto the stator. Hence for each of the manufactured pairs, the inner cylinder was made of mild steel while the outer cylinder was made of aluminium. Despite some minor differences in the thermal properties between silicon steel and mild steel as shown in Table 1, mild steel was was still used due to its ease of manufacturing. Material *Thermal conductivity [W/mK] *Specific heat capacity [J/kgK] Silicon steel HF Silicon Steel Arnon Silicon Steel Arnon Silicon Steel M1924GA Silicon Steel M1926GA Silicon Steel M1929GA % Carbon Mild Steel Aluminium Alloy Table 1: Comparison of thermal properties of different types of silicon steel with carbon steel as from [29]. *properties at 25 o C. Each pair was machined so that it contains an interference fit, thus enabling to test a range of shrink fit pressures. Each cylinder height was kept at 50 mm thus keeping a cylinder height/thickness ratio to approx. 10. The geometrical dimensions are listed in Table 2. The locations for thermocouple temperature sensors were also machined. This allows end effects caused by thermo-mechanical stresses to be kept to a minimum. 3.2 Hardness Measurement Six samples of each material were placed under a Vickers Armstrong indenter and with the machine loaded an indent was applied. In order to ensure that the effect of work hardening during machining was accounted for, the hardness tests were performed on the curved surfaces of both the inner and outer cylinders. Loads were varied between 20 kg and 40 kg. The diagonal lengths of the indent were measured and the hardness was determined using [30]: eqn. 1! Indents whose diagonal lengths varied by more than 10% from each other were discarded so as to avoid skewed deformations. The mean and standard deviation of the measured hardness values for the two materials is shown in Table 3. Material Hardness [GPa] Mild Steel Inner Cylinder Aluminium Outer Cylinder Table 3: Hardness values for the inner and outer cylinders. 3.3 Surface Roughness Measurement The outer aluminium cylinders were machined using a 19 mm precision reaming tool while the interface surface of the inner mild steel cylinders was machined on the lathe using a carbide-tip tool. The surface finish of a material is dependent on the material itself and the process used for machining the component. While machine surface finish charts [31] are available, several verification tests were done using an Alicona Infinite Focus Digital Profilometer. The measured RMS roughness values were determined using: eqn. 2! where n is the number of equally spaced samples taken along a trace and y is the vertical distance from the mean line to the data point. Table 4 compares the measured RMS roughness with suggested values found in the literature. Pair No Cylinder position Material Inner diameter [mm] Outer diameter [mm] Interference [mm] Shrink fit contact pressure [MPa] 1 Inner Mild steel Outer Aluminium 2 Inner Mild steel Outer Aluminium 3 Inner Mild steel Outer Aluminium 4 Inner Mild steel Outer Aluminium Table 2: Dimensions of test geometry. 3

4 Description Mild Steel surface machined with a Carbide-tip lathe tool Measured RMS roughness [µm] Suggested RMS roughness [µm] [31] Aluminium surface machined with a Reaming tool [31] Table 4: Comparison of the measured and suggested surface roughness 3.4 Shrink fit Assembly Following machining, the interface diameters of all inner outer cylinders were surveyed at 45 o intervals, at various cylinder heights. This ensured that the cylinders are paired with the correct interference fit and that the desired range of shrink fit pressure is achieved. The cylinders were assembled by a shrink fit procedure in which the inner steel cylinder was subjected to a thermal contraction at a temperature of -5 o C while the aluminium outer cylinder was placed in a Carbolite oven and subjected to a thermal expansion at a temperature of 300 o C. The change in diameter for each cylinder due to temperature difference was calculated using: eqn. 3! The resulting contact pressure at the interface of each assembly was determined by solving Lame s equations [32]: eqn. 4! eqn. 5! The resulting contact pressures at the interface are also shown in Table 1. An example of a final shrink fit assembly is shown in Figure 1. Figure 1: Example of a shrink fit assembly investigated 3.5 Temperature and Thermal Contact Resistance Measurement A 230 V, 150 W cartridge heater was mounted inside the inner cylinder. Silicon based thermal interface material was applied to improve the heat transfer between the heater and the inner cylinder. T-type thermocouples were mounted on each of the two cylinders and were also used to measure a controlled ambient temperature. Temperature sensor location holes were also filled with thermal interface material to ensure a good contact between the sensor and the component. Temperature sensors were recorded using TC-08 Pico data loggers. The heater was connected to a transformer so that the heat input could be regulated. A current meter and a differential probe were connected to PicoScope 3000 series and were recorded at 1s intervals. The heat input was calculated as: eqn. 6! The test setup is shown in Figure 2. The assembly was placed between thick polystyrene blocks to reduce thermal losses from the end surfaces. Figure 2: test setup with 1) temperature sensors (locations marked with a red dot), 2) concentric assembly with 3) internal cartridge heater, 4) variable transformer, 5) ac power supply The variable transformer was used to regulate the voltage to the heating element and the test was repeated for a number of heat fluxes. For each heat flux, the experiment was left to run for approximately 6 hours until a steady state condition was reached, and a further 2 hours during steady state. The temperatures and power for the steady state period were averaged and the overall thermal resistance was calculated using: eqn. 7! In order to eliminate the effect of the thermal conductivity across each cylinder, and account only for the joint contact conductance, the thermal resistance was defined as follows: Hence the joint conductance could be calculated. 3.6 Calibration and Uncertainty Analysis eqn. 8! A calibration procedure was performed in which the test setup was mounted with thermocouples and inserted into a Carbolite oven. The thermocouples and data acquisition 4

5 system were calibrated against a reference PT100 temperature sensor with an accuracy of o C. The calibration was made for a range of temperatures from 20 o C to 180 o C. The oven hysteresis was measured at 0.1 o C, while the thermocouple offset was measured at 0.33 o C. The temperature sensor uncertainty was calculated using: eqn. 9! The temperature uncertainty was calculated at 0.35 o C. Conversely the uncertainty in the voltage and current were measured at and respectively. The uncertainty of the heat load supplied was calculated using: eqn. 10! The uncertainty of heat input was found to be 4mW at low heat flux and up to a maximum of 33 mw at the higher heat flux values. The uncertainty of the heat flux was found to be between 1 W/m 2 and 14 W/m 2 and was estimated using: eqn. 11! In which the u(a) is the absolute uncertainty of the area, estimated as 7.8 m using: eqn. 12! Finally the uncertainty in thermal contact resistances was found using: eqn. 13! The uncertainty value of the thermal contact resistances was measured as m 2 K/W. Hence the uncertainty in thermal contact conductance measured 18 W/m 2 K. 4. Test Results and Discussion Test results showing the variation of thermal contact conductance with heat flux and contact pressure are shown in Figure 3. As expected, the thermal contact conductance increases as the shrink fit pressure increases. However at a constant shrink fit pressure the thermal contact conductance was also found to increase with heat flux. An arbitrary correlation of conductance with heat flux is shown for various shrink fit pressures. Each setup was found to reach a critical heat flux value, after which the thermal contact conductance flattens out. It was also noted how with larger the shrink fit pressures it takes a higher heat flux before the thermal contact conductance flattens out. For any particular shrink fit pressure, the critical heat flux can be correlated to a quadratic equation as follows: eqn. 14! The variation of the maximum temperature (reached at the inner cylinder) with heat flux is shown in Figure 4. The component temperature is a result of the input power, the thermal capacity of the assembly, the heat transferred from the inner cylinder to the outer cylinder and the heat transferred from the outer cylinder to ambient air by natural convection. The heat flux and temperature were correlated with a quadratic trend line as follows: eqn. 15! The data has an R 2 value of The experimental data was also compared to conductance values used to simulate real machines in [6, 25]. The effective air gaps shown in [6] were converted to a conductance value by equating: eqn. 16! The machine efficiencies and dimensions were obtained from the manufacturer data [33] and are shown in Table 5. The steady state heat flux was estimated by assuming that the loss from each machine was distributed at 80% stator, 20% rotor. Machine Description Efficiency Heat Flux q [W/m 2 ] Effective gap x [mm] hc [W/m 2 K] 4 kw TEFC IM MA112M4 85% kw TEFC IM MA132M4 88% kw TEFC IM MA160L4 90% kw TEFC IM MA200L4 91% kw TEFC IM M250M4 93% kw TEFC IM M132 85% kw TEFC IM M250 93% Table 5: Details of machines used to compare the thermal contact conductances. 5

6 While the lack of information on the shrink fit pressure of the actual machines makes it difficult to make definite deductions, the following remarks can be made:! All points fall beyond the critical heat flux line. This matches expectations as these values correspond to the steady state conductance values.! While it is noted that some points fall below the 0 MPa line, this could be due to a light press fit rather than a shrink fit. The rest of the points fall within the flattened conductance values of 0 MPa and 52 MPa. The upper tensile stress of aluminium is approx. 50 MPa (depending on the type of alloy used for the casing). However manufacturers may be cautious not to exceed this limit.! The variations in values compared is likely due to the variables that are unaccounted for in the chart such such as the different properties of silicon steel and the surface roughness. A better comparison could be achieved through a non-dimensional conductance such as proposed in [14, 15, 21, 23]: eqn. 17! In which, k and m are the effective surface roughness, conductivity and the surface slope asperity. However such a comparison would require more detailed investigation on the material and surface properties. 5. Conclusion In high current density machines, the stator-housing thermal contact resistance is on the main heat path of the electrical machine. Current lumped parameter network models assume a fixed single value for the thermal contact resistances across the whole machine operating range. However this paper provided experimental evidence showing that the thermal contact resistance not only varies with contact pressure but is also affected by the heat flux and the resultant component temperature. Hence the common notion that the thermal contact resistances is a single value, set during the machine assembly and can be applied across the whole operation range of the machine is oversimplified. When thermal modelling of a transient application is required, the thermal contact resistances must hence be set so that it is a function of heat flux. The paper provides correlations of how the thermal contact resistances in a shrink fit assemblies vary with contact pressure and heat flux and compares them to values used in thermal modelling of real machines. However we would caution machine designers from the direct application of the values presented, as more research to explore the effects of surface and material properties on contact conductance is required. Acknowledgements The authors would like to thank Seifert-MTM Systems Malta Ltd. for their generous funding. The support of Mr Cleveland Williams, Mr Maurice Keeble-Smith, Dr Igor Dyson, Dr Kalin Dragnevski and Mr Robin Vincent during the various stages of the experimental work is also acknowledged and appreciated. Figure 3: Chart showing measurements of how the thermal contact conductance varies with contact pressure and heat flux.! 6

7 Figure 4: Chart showing the variation of temperature with heat flux for all shrink fit assemblies.! Figure 5: Chart comparing the experimental results with thermal contact resistance from other machines 7

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