Cooling of electric machines is a key to increasing power density and improving reliability. This paper focuses on the design of a machine using a cooling jacket wrapped around the stator. The thermal contact resistance (TCR) between the electric machine stator and cooling jacket is a significant factor in overall performance and is not well characterized. This interface is typically an interference fit subject to compressive pressure exceeding 5 MPa. An experimental investigation of this interface was carried out using a thermal transmittance setup using pressures between 5 and 10 MPa. The results were compared to currently available models for contact resistance, and one model was adapted for prediction of TCR in future motor designs.
Cooling of electric machines is an important factor in increasing power density. Components within an electric machine such as the magnets and wire insulation experience reduced performance or reliability when exposed to temperatures beyond their thermal specifications . Therefore, heat must be removed from these components to limit the temperature to which they are exposed. Typically, heat must flow through several components and material interfaces or contacts before the heat can be extracted from the motor through convective cooling. For this reason, the convective cooling approach for the machine can impact the path of heat transfer through the electric machine, resulting in certain materials or interfaces having a larger impact on the overall thermal management of the electric machine. Examples of some thermal management approaches that have been applied to electric machines are summarized in Ref. .
The choice of convective cooling technology depends on the electric machine's performance requirements, intended application, and available coolants. The research described in this paper focused on a new electric machine design cooled with a high-performance cooling jacket integrated into the machine case using water–ethylene glycol, as shown in Fig. 1.
Because the machine of interest used a high-performance cooling jacket for heat removal, the heat flow path through the machine was predominantly radial. A parameter sensitivity study was performed on a preliminary design of the electric machine using a thermal finite element analysis model to determine which thermal resistances were most significant. To perform the study, the thermal properties of each material or interface were decreased by 20%, and the change in maximum temperature was reported. The thermal sensitivity analysis indicated that the dominant thermal resistances for heat conduction through the machine were the stator lamination stack and the thermal contact resistance (TCR) between the stator and case . For this reason, there was a need to experimentally measure the in-plane lamination thermal conductivity and the TCR of the stator-to-case interface.
The coolant jacket for the electric machine was mounted to the stator through an interference fit between the coolant jacket and stator. For the machine of interest, the stator-to-case interference fit resulted in a compressive pressure on the joint ranging from 5.52 to 9.65 MPa. The laminated silicon steel used in the stator gives the outer diameter of the stator a ridged surface. The inner diameter of the case in contact with the stator is a machined aluminum surface. Examples from a similar electric machine are shown in Fig. 2, showing the stator's outer diameter surface and the cooling jacket's inner diameter surface.
There are a number of models and experimental data for calculating TCR. The simplest use an effective air gap with suggestions for values based on surface roughness [4,5]. Using these techniques yields a pressure-independent TCR ranging from 840 to 1400 mm2 K/W. Theoretical models will take into account factors such as the pressure on the joint, the hardness of the two materials, the surface roughness, and interstitial gas [6,7]. Using such a model gives a pressure-dependent TCR ranging from 354 to 244 mm2 K/W for the 5.52–9.65 MPa pressure range. The disadvantage of such a model is the requirement to obtain upward of 15 parameters, some of which may be obscure or difficult to obtain or require specialized equipment to measure. Finally, extrapolating from previously published experimental data  gives a TCR of 157–149 mm2 K/W for the same pressure range.
The large range in the calculated TCR values (149–1400 mm2 K/W) causes a challenge in the electric machine thermal design. A TCR of 150 mm2 K/W corresponds to a temperature drop across the stator-to-jacket interface of 5 °C–10 °C. A TCR of 1400 mm2 K/W across the same interface results in a temperature drop about seven times higher. Therefore, obtaining an accurate value for the stator-to-case TCR is critical in the thermal design of case-cooled electric machines.
This paper presents an experimental method to measure thermal contact resistance at pressures representing interference fits. Pressures from 5.52 to 9.65 MPa and two types of commonly used machine laminations were studied. The experimental data were used to select a model that can be used with easily obtained parameters, while giving an accurate result that can be used in relevant electric machine thermal models.
Experimental Apparatus and Procedures
To measure the TCR of the case-to-stator interference fit, a high-pressure transmittance setup was constructed in accordance with ASTM International (ASTM) Method D5470  using a high-capacity hydraulic clamp, as shown in Fig. 3 . The setup includes a lamination coupon with the laminations stacked horizontally. The laminations are sandwiched between two 4-mm-thick aluminum contact plates that simulate the aluminum case. The aluminum contact plates on the top and bottom of the fixture are pressed against copper metering blocks with thermal grease applied at the interface. The setup was validated against both an existing thermal transmittance setup at the National Renewable Energy Laboratory for lower pressures described by Narumanchi et al.  and a xenon flash diffusivity measurement system using the 4-mm-thick aluminum contact plates to be used in the experiment. The setup uses resistance temperature detectors (RTDs) placed into the copper metering blocks located on the top and bottom of the test sample. Heat is provided to one side of the sample through electrical heaters inserted into an aluminum heater block. The test apparatus is thermally isolated from the large pneumatic press using a cold plate on the bottom. Both cold plates are cooled with a bath circulator using plain water.
For the experiments, the laminations were manufactured with a tolerance of 0.1 mm. A stabilizing rig was built to hold the laminations together. The stabilizing rig provided a method to hold the laminations level without welding or adhesion such that the surface was “self-leveling.” The stabilizing rig consisted of an aluminum frame with thermally insulating Teflon bumpers held against the lamination stack with set screws.
The objective of the experiment was to measure the TCR between the steel laminations and the aluminum contact plate in addition to the lamination thermal conductivity parallel to the in-plane direction of the laminations. The primary test factors for the experiment included pressure and lamination material. The sample temperature ranged from 45 °C to 115 °C. A temperature gradient must be applied to the sample to obtain results using the thermal transmittance method, and the temperature was limited by the safe operating temperature of the heaters in the heater block shown in Fig. 3. The highest safe temperature was used to maximize the heat flux across the sample to improve the accuracy of the measurement results. Electric machines will operate across a wide range of temperatures, but the impact of temperature on the thermal contact resistance was not included as part of the design space of this experiment.
The pressures applied during the tests were intended to represent an interference fit between the case and stator where the stator diameter is larger than the inner diameter of the case. The pressure was calculated based on the geometry of the UQM prototype electric machine. The tested pressures covered a range of values that encompassed the pressure estimate of the UQM prototype machine, which included 5.52 MPa, 6.89 MPa, 8.27 MPa, and 9.65 MPa. Each data point at the listed pressure was repeated three times to aid in the measurement uncertainty analysis. Thermal contact resistance is affected by hysteresis or the loading history of the contact. Thermal cycling, load cycling, and extended time under load can reduce thermal contact resistance . To minimize hysteresis effects, measurements were taken immediately after thermal steady-state was reached. Steady-state was defined by a maximum temperature change of less than 0.03 °C for a 10-min period. Pressures were only increased throughout each test (i.e., a higher-pressure test could not precede a test at lower pressure).
The high pressures involved necessitated investigation into whether the surface of the contact plate would become indented from the lamination coupon surface. This was done by using a laser profilometer to scan the surface and then using spatial two-dimensional fast Fourier transform to transform the surface data into the frequency domain. Analyzing the surface in the frequency domain allows differentiation between tool marks and indentation caused by the lamination coupon surface. If the experiment caused an indentation in the aluminum, it would necessitate replacing the aluminum for each experimental test to ensure repeatability. Whether or not the aluminum plates could be reused affects the number of experiments that can be performed due to the potential expense of having to cut or refinish plates for each repetition should they not be reusable. The laminations were also tested for possible work hardening by comparing thermal properties before and after application of pressure.
Two types of laminations were used: 29-gauge M15 material and 0.2-mm high-frequency material from JFE Steel Corporation. Both laminations were laser cut to get the shapes needed. The different edges are the result of different feed rates and/or intensity used by the vendor in the cutting process to ensure samples were not damaged due to thinner laminations being more brittle. Figure 4 shows the edges of the two lamination materials included in the experimental measurements. The JFE material is thinner, and the resulting edge has a serrated appearance.
Surface Properties of Contact Plates.
Two surfaces for the contact plates were tested and compared to determine the significance of the surface finish. The first was a factory-ground surface with no special treatment with an average surface roughness of 0.6 μm. In an actual machine case, the inner surface is lathed to a specified tolerance. Ideally, the second surface would exactly replicate a lathed machine pattern. However, it was not possible to exactly duplicate a lathed machine pattern on a flat surface without specialized equipment. Instead, the second surface approximated a lathed surface by machining the aluminum contact block surface with a fly cut. Fly cutting results in surface tooling (ridges) similar to what would be obtained with lathing; using a very large bit results in nearly straight ridges. The feed speed gives control over the surface roughness and was adjusted to match the surface roughness of the stator case, which was 1.6 μm. Figure 5 shows a surface topography map of the fly cut surface obtained using a laser profilometer. The data were postprocessed in matlab to obtain the area-average surface roughness.
Data Analysis Procedure.
RGL represents the thermal grease layer between the copper metering blocks and the contact plates shown in Fig. 3. The grease layer improves the thermal contact between the copper metering block and contact plate. RCP represents the thermal resistance of the aluminum contact plate shown in Fig. 3. The thermal resistance of the contact plate was characterized using a xenon flash transient technique. RLS represents the thermal resistance of the lamination stack coupon shown in Fig. 3.
The challenge with the thermal transmittance setup is that the measurement uncertainty is a fixed percentage of Rtot. Therefore, care must be taken to minimize the subtractions from Rtot to obtain the value of interest, in this case, TCR. Care must also be taken to minimize variations in Rtot due to variations of individual layers (e.g., grease layer thickness).
Results and Discussion
The experimental results are described in the following sections. To validate the experimental design and the test procedure, a series of preliminary tests was performed. The results of the preliminary testing provided confidence in the experimental approach. Once the experimental design was finalized, the experimental results were recorded as described in the following.
Preliminary Test Results.
Before the high-pressure tests were conducted, an initial test was performed on the existing thermal transmittance setup to check if the random uncertainty of the measurement would be acceptable before constructing the high-pressure setup. The test yielded an acceptable uncertainty and work proceeded to build the high-pressure experimental setup.
The thermal resistance of the grease layer in Eq. (4) was determined experimentally as described previously. The results of the measurements are shown in Table 1. The result is the average of three experiments. The values are small compared to the expected measurements. It is worth noting that the thermal resistance decreases with pressure, which follows the expected behavior.
To test for indentations in the contact plates, the experiment was performed at 9.65 MPa for the same temperature and time conditions used in the experiment. The surface was then analyzed using a spatial two-dimensional fast Fourier transform technique. Transforming the surface data into spatial frequency space allows simple differentiation between a potential indentation due to a lamination stack and existing tool marks that both run in the same direction. There was no indication of any indentation or change in surface properties due to the experiment. Samples were also periodically analyzed throughout the experiment to ensure that no cumulative damage occurred to the plate surface that would affect results. In addition, the laminations were tested on the xenon flash before and after the preliminary test to ensure no thermal property changes due to potential work hardening had occurred.
To highlight the effect the lathed surface on the interior of the case had on the contact resistance, a series of tests was run using a smooth contact plate and the fly-cut contact plate. The results are shown in Fig. 7. For the TCR calculation in Fig. 7, a value for the lamination coupon was calculated based on the known bulk thermal properties of the laminations as a preliminary estimate. As seen in Fig. 7, the surface finish significantly impacts the measured contact resistance. For this reason, the tests proceeded with the fly-cut surface to more closely represent the lathed surface properties.
Thermal Property Experimental Results.
Figure 8 shows a plot of the data for the M15 29-gauge lamination coupons at the lowest of the four pressures tested. Three data points were collected for each of the three coupon thicknesses. The data were fit with a first-order curve with the curve fit data points weighted according to the systematic error of the experiment. The thermal properties for both the lamination stack and the stator-to-case contact resistance were extracted using the slope and intercept of the fit, respectively, using Eqs. (3) and (4).
As described previously, the thermal resistances of the grease and contact plate are subtracted from the intercept to obtain the contact resistance. To calculate the uncertainty of the measurements, the curve fit is weighted on systematic error, which includes RTD calibration error, estimated spatial temperature variation calculated using a thermal finite element model of the setup, and RTD location error. The RTDs were calibrated to a National Institute of Standards and Technology traceable reference probe using a static temperature calibration bath. The curve fit yields random error and the 95% confidence interval (U95) is calculated [12,13]. Figure 9 summarizes the results for both the stator-to-case contact and the bulk thermal conductivity for the laminations as calculated from the slope-intercept technique.
The results shown in Fig. 9 are generally consistent with expectations, which give confidence in the technique. The thermal conductivity of the laminations does not vary with pressure and is near the bulk value measured with the xenon flash technique of 22 W/m K for both materials. The contact resistance decreases with increasing pressure. The contact resistance is significantly lower than what is predicted by effective air gap models, but agrees well with pressure-dependent models for TCR. The uncertainty in the results shown by the error bars in Fig. 9 precludes making further conclusions about the results. However, there is a clear trend of pressure dependence, and the different surface of the JFE as shown in Fig. 4 may impact TCR.
where k is the harmonic mean of the thermal conductivities of the two materials; C and n are coefficients, which are 1.13 and 0.94, respectively ; σ is the centerline average roughness of the two contacting surfaces and is 1.25σRMS; σRMS is the root mean square of the average surface roughness of the two contacting surfaces; tan Θ is the mean slope of the surface asperities; P is the applied pressure; and H is the contact microhardness of the softer of the two materials. P and H have units of MPa.
Figure 10 shows a comparison of the model to the data for both sets of laminations. The model shows good agreement with the data. Although not included in the plot, the model agrees with the preliminary test at 0.22 MPa. The range of 150–250 mm2 K/W is on the lower end of the estimates of 149–1400 mm2 K/W for the interface. More importantly, it reduces the uncertainty of the value by 90%, which leads to more accurate machine design.
Thermal contact resistance calculated by the model agrees reasonably well (17% difference) with the experimental results reported by Kulkarni et al.  for 13.28 MPa, but the model results are lower than their results when extrapolating to higher pressures (21–39 MPa). Note that values were not given for the material and surface properties, so it is possible they differed from what is presented here.
The TCR between machine laminations and an aluminum cooling jacket under interference loading was measured using a simulated stack within a high-pressure ASTM D5470 setup. The results for two commonly used machine lamination types are presented and compared to existing contact resistance models. It was found that the TCR ranged from 150 to 250 mm2 K/W for interference fit pressures between 5.52 and 9.65 MPa. A model was presented with parameters that can be obtained using standard equipment and agrees closely with the experimental data.
Pressure-independent models (such as effective air gap models) are valid for pressures below 500 kPa. For pressures exceeding 500 kPa, the air gap model overestimates TCR proportional to the pressure. For the interference fit pressures investigated, the pressure-independent models overestimated TCR by a factor of four to seven compared to the pressure-dependent model presented. The model presented was validated to 10 MPa, but should be valid for any pressure well below the material yield point.
The stator-to-case TCR is a critical parameter in high-performance and compact machine designs, especially those that depend on case cooling. Without an accurate value for the stator-to-case TCR, the cooling system may be optimized incorrectly or additional expense invested in alternative cooling or oversizing the motor that may not be necessary. This work helps electric machine designers accurately estimate the stator-to-case TCR for a range of electric machines without having to resort to expensive experimental tests or overly conservative estimates.
We acknowledge financial support for the work provided by Susan Rogers and Steven Boyd, Technology Managers for the Electric Drive Technologies Program, Vehicle Technologies Office, U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE). The significant contributions from Doug DeVoto (NREL) and Charlie King (NREL) to the project are acknowledged.
This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308 with the Alliance for Sustainable Energy, LLC, the Manager and Operator of the National Renewable Energy Laboratory.
- C =
- H =
- hg =
gaseous fluid conductance
- hs =
solid spot conductance
- k =
- n =
- P =
- R =
- RTD =
resistance temperature detector
- tanΘ =
mean asperity slope
- TCC =
thermal contact conductance (1/TCR)
- TCR =
thermal contact resistance
- δ =
mean surface separation
- σ =