Reliability Oriented Design of Low Voltage Electrical Machines Based On Accelerated Thermal Aging Tests

In transport applications, electrical machines (EMs) are required to be highly reliable, in order to fulfill the intended mission profile over the expected lifetime. This task has been conventionally addressed through the adoption of safety-factors that might lead to an over-engineered EM. Only recently, few works have started championing a paradigm shift towards physics of failure methodologies, which allow to achieve an appropriate trade-off between optimal performance and demanded reliability figures. Thus, this paper proposes a reliability oriented methodology for low voltage (LV) EMs and outlines its critical implementation steps. Accelerated thermal aging (ATA) tests are preliminarily performed on custom made samples to assess the aging trend of the inter-turn insulation. The thermal endurance graph at different percentile values is then determined and a lifetime model suitable for variable duty motors is developed. Finally, this model is used to predict the inter-turn insulation cycles-to-failure of an EM installed on full-electric vehicle.


I. In t r o d u c t io n
Throughout the decades, the EM design has been gradually refined, and today, EM designers can count on several engineering tools, which allows highly-performing designs. Indeed, the performance oriented design method already enables the development of EMs that can achieve excellent operating performance values, in terms of both power density and efficiency [1,2]. In transport applications, these are essential features, because a compact and lightweight design is preferable. However, the safety-critical nature of mobile applications also imposes strict reliability figures [3,4].
From a lifetime prospective, the winding insulation system often represents a bottleneck, since uncontrolled over-temperatures are source of insulation degradation that compromise the dielectric properties [5]. In fact, studies revealed that approximately the 30% of the EM failures involve the winding insulation [6,7]. Focusing on the insulation system, the reliability constraints are usually met through an over-engineering strategy, which consists in using safety-factors, whose values come from rules of thumb and/or previous experience. Nevertheless, such practice can result in a low fill factor value that prejudices both weight and thermal management (i.e. heat dissipation) of the EM [8]. In addition, This work was partially funded from the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme under grant agreement no. 807081.
This work was also funded from the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation programme under grant agreement no 821023. by over-sizing the insulating material, the insulation system might greatly outperform the requested lifetime. Therefore, a contrast between reliability and operational performance occurs leading to a design choices' conflict.
An appropriate balance between reliability and performance is obtained via a paradigm shift from performance to reliability oriented EM designs [9,10]. The flowchart of the typical reliability oriented design is shown in Fig. 1, where the reliability is accounted since the early stage of the design (i.e. the reliability becomes a design objective) and it is assessed through lifetime models based on physics of failure (PoF) methods. The latter provide an accurate picture of the insulation degradation under specific stresses and the insulation system can be exactly defined in accordance with the reliability level demanded by the application under study (i.e. no safety-factors are needed). The reliability oriented design will then grant an improved adoption of insulating materials ensuring proper reliability figures while meeting the performance requirements, without compromising volume, weight and cost of the EM [11]. In this paper, the procedure for a reliability oriented EM design is outlined and the primary steps for its implementation are addressed. The inter-turn insulation of LV random-wound EMs is examined via an ATA test campaign. For the investigated enamelled wire, a multi-percentile Arrhenius graph (i.e. thermal endurance graph) is drawn and employed to determine the parameters of a lifetime model built according to Miner-Arrhenius law. The model, which is suitable for variable duty EMs, is consequently tuned on the required reliability level (i.e. percentile oftime-to-failure) and it is finally used to predict the cycles-to-failure and the loss-of-life of the inter-turn insulation belonging to a LV random-wound EM meant for a full-electric minivan.
II. Co n s id e r a t io n s a n d Stu d y Asse s s m e n t EMs rated below 700 Vrms (i.e. low voltage EMs) normally mount random-wound windings, where the inter-turn insulation is composed by a thin layer of enamel made of organic material (i.e. Type I insulation). Due to the chemical composition of the Type I insulation, the inter-turn insulation is normally identified as the weakest point in terms of failure probability [5], and for this reason, the preformed investigation purely focuses on such insulation system.
In general, the analysis of the inter-turn insulation lifetime is performed via accelerated tests, where aging factors, as environmental (i.e. humidity, pressure, etc.), electrical, mechanical and thermal, are individually applied at greater level than that usually encountered during field operations [12]. Then, the lifetime at normal operations is extrapolated from the data collected in abnormal circumstances, using a lifetime probability distribution (e.g. Weibull distribution). However, in real applications, the aging factors (i.e. degrading stresses) act simultaneously on the insulation and a comprehensive lifetime estimation can only be given by multi-stress models [13,14], which are relatively complex to develop and implement. Additionally, it results challenging to precisely quantify the combined aging caused by the concomitant application of more aging factors, since the superimposition principle cannot be applied [15]. This issues is typically overcame by assuming a prevailing aging mechanism that predominantly affects the insulation lifetime, whilst other stresses feature a negligible impact on the lifetime consumption (i.e. secondary aging factors) [15,16]. Under such assumption, a single-stress lifetime model can be employed to estimate the lifetime of the inter-turn insulation.
In this work, the thermal stress is assumed as prevailing aging factor. Thus, the presented lifetime evaluation is based on a single-stress lifetime model, which can be only applied on partial discharges (PD) free EMs (rated below 700 Vrms), where the insulation aging is mainly due to the temperature.

A. PD Risk Evaluation
In LV random-wound EMs, the PD activity might be source of severe faults, because Type I insulating materials are not PD resistant [17]. In order to evaluate the risk of PD inception, the whole electric drive needs to be considered, due to the possibility of voltage enhancement at the EM terminals [18,19], According to the IEC standard [17], a PD free inter-turn insulation is gained when the peak voltage between two adjacent turns is lower than the minimum PD inception voltage (PDIVmlnt_t), which is given by (1).
In (1), EF is the enhancement factor, OF is the overshooting factor, VDC is the DC link voltage and K (tr ) is a coefficient function of the voltage rise time tr. The values of the factors in (1) can be selected from [17], based on both electric drive and magnet wire attributes. Considering an electric drive with the specifications listed below: 1) 270 V D C lin k voltage; 2) two-level power converter mounting silicon IGBT with 200 ns rise time and unipolar waveform; 3) cable connecting EM and power converter shorter than 10 m; the PDIVmint_t results equal to 330 Vrms (i.e. VDC -270, K(tr) = 1 , EF = 1.4 and OF -1.25 ), whereas the measured inter-turn PD inception voltage ranges from 480 Vrms to 500 Vrms, for the studied magnet wire. The PDIV measurements are taken with a transverse electromagnetic (TEM) antenna and the Techimp PD-Base1 post-processing software. Relying on the obtained findings, the PD risk is safely contained when the examined magnet wire is used in an electric drive that fulfils the specifications discussed above (i.e. PD free EM).

B. Motorettes and Magnet Wire
Accounting that the EM is free from PD, it is reasonable to assume the thermal stress as the main aging factor. Therefore, the thermal stress influence is evaluated via ATA tests where the temperature is constant. These tests are carried out on motorettes (i.e. specimens), which are available well earlier than the first set of EM prototypes. A single motorette has 6 slots equipped with a concentrated, double-layer winding, as depicted in Fig. 2. The motorette winding layout is detailed in Fig. 3, where the 6 coils per motorette are shown and every coil features 2 parallel strands, for assessing the inter-turn dielectric properties [20]. This assessment is performed during the diagnostic session. A Class 200, Grade 2, 0.4 mm diameter dual-coat magnet wire is used for winding the motorette. In particular, the magnet wire's insulating enamel is composed by two layers, where the inner one (i.e. base-coat) is made of modified polyester, while the outer one (i.e. over-coat) consists of polyamide-imide. Magnet wires with dual-coat are generally adopted in modern EMs, because they reveal enhanced abrasion resistance and heat-shock than single-coat magnet wires (i.e. monolithic coating). Indeed, the polyamide-imide over-coat grants a good abrasion resistance, whereas the modified polyester base-coat assigns high flexibility [21]. III. Ac c e l e r a t e d Ag in g Tests Ca m p a ig n Using the dual-coat magnet wire, a group of 15 motorettes is wound following the winding arrangement of Fig. 3. A Nomex® type slot-liner of 0.13 mm thickness is placed inside the slots, in order to avoid having the enamel surface touching directly the motorette's core. This expedient strengthens the phase-to-ground insulation system and prevents the enamel scratching when the coils are inserted in the slots.
For a given aging temperature, the ATA test is performed on a group of 5 motorettes. Therefore, a total number of 30 coils is thermally aged since each motorette features 6 coils. Although 10 samples are recommended by technical standard [22], a higher number is adopted to enhance the statistical validity of the study. Further, the significant number of samples allows to mitigate the inevitable discrepancies due to the random-wound nature of the winding.
The ATA test procedure is sketched in Fig. 4, where the corresponding flowchart is reported. At groups of 5, the samples are fitted in a ventilated oven and they are aged at three temperatures higher than 200 °C (i.e. dual-coat magnet wire's thermal class). In particular, the aging temperatures of 270, 250 and 230 °C are chosen and the samples are exposed to several thermal cycles, whose duration is listed in Table I according to the considered temperature level. Once the thermal exposure is completed, the oven is turned off and the samples are cooled down until ambient temperature. Reached the room temperature, the samples are moved out from the oven and the inter-turn insulation is evaluated (i.e. diagnostic session). The diagnostic session consists in a pass/fail test, namely AC hipot test [23,24], which is conducted through the dissipation factor tester (i.e. Megger® Delta 4000). During this test, a 500 Vrms sinusoidal voltage at 50 Hz is applied for 1 minute between the parallel paths of the same coil [22], e.g. terminals "# lA l_ a" and "#lA l_ b " of Fig. 3. Here, the diagnostic voltage amplitude is set equal to the PDIV value of the magnet wire (i.e. 500 Vrms) to derive a more conservative lifetime estimation. Since the dielectric breakdown is selected as end-of-life criterion, the coil is established 'dead' when it does not withstand the diagnostic voltage (i.e. insulation breakdown occurs) and the end-of-life is assumed occurring at the middle of the last exposure. Therefore, the time-to-failure is determined as the sum of the total thermal exposure time minus half of the thermal cycle period. After completing the diagnostic session, all the 'still-alive' coils are ready for the next thermal cycle and the ATA test at a specific temperature value ends when all the specimens fail the AC hipot test. IV. Tests Ca m p a ig n Resu l t s An d Mu l t i-Pe r c e n t il e A r r h e n iu s G r a p h The collected time-to-failures are post-elaborated via a two-parameter Weibull distribution and its cumulative distribution function (CDF) F (t£) is expressed by (2), where a is the scale parameter (i.e. the 63.2% percentile of the lifetime), ¡3 is the shape parameter (i.e. inverse of the data scatter) and t £ is the generic time-to-failure.
These parameters are obtained using a graphical approach relying on the linear regression method. As first step, the Weibull CDF is linearized, as described in (3).
The auxiliary variables x and y, defined in (4) and (5) respectively, are introduced and the Weibull CDF is rearranged as detailed in (6).

x -ln(ti)
The latter expression, i.e. (6), represents the equation of a straight line with /3 • ln(a) as y-axis intercept and /3 as slope. For each recorded time-to-failure t £, the Weibull CDF is estimated by the median rank estimator, according to the Benard's approximation (7) [12], where N is the samples' population, while i is the ith insulation breakdown.
The points having as x-axis coordinate the time-to-failure t £ (experimental data) and the relative F ( t£) (estimated Weibull CDF) as y-axis coordinate are located on the probability plotting paper. Afterwards, the most appropriate straight line fitting these points is drawn relying on the linear regression methodology (e.g. least squares method). Thus, the Weibull probability plot, which allows to evaluate the probability of failure at a generic time instant, is obtained and the associated a and /3 parameters are found. In Figs. 5, 6 and 7, the Weibull probability plots are shown (with 95% confidence interval) for the considered aging temperatures, i.e. 230,250 and 270 °C respectively. The resulting shape and scale parameters are given in Table II, along with the time-to-failure at 10% (i.e. B10) and 50% (i.e. B5Q) percentile. The lifetime percentile values Bp express the time when a given percentage of samples will 'die', e.g. B50 indicates the time-to-failure related to the 50% failure probability.    Knowing the Weibull probability distribution, the time-to-failures at several percentiles are determined for each ATA temperature and the Weibull CDFs are plotted, as illustrated in Fig. 8. Then, the Weibull CDFs are used to extrapolate the multi-percentile Arrhenius graph, which delivers the lifetime in normal operating conditions for different percentiles (i.e. reliability levels). Assuming a certain percentile (e.g. 50% percentile), the correspondent thermal endurance line (e.g. Arrhenius graph at 50% percentile) is sketched by interpolating the three time-to-failures of the CDFs at the selected percentile value. By repeating this procedure for various percentiles, the multi-percentile Arrhenius graph is accomplished, as reported in Fig. 9, where only 10% and 50% percentiles are considered, for the sake of drawing clarity. In spite of the percentile chosen for Fig. 9, any percentile could have been employed, because this value is related to the level of reliability demanded by the application at hand (i.e. design requirement). It is worthy to underline that low percentile values lead to stringent reliability constraint.  Based on the outcome of the statistical analysis, a single-stress thermal lifetime model is built to forecast the life of the EM's inter-turn insulation under variable duty operations. The multi-percentile Arrhenius graph of Fig. 9 can be described through (8), which is the Arrhenius equation.
In (8), LBp{d) is the life at the generic constant temperature 6 for the percentile Bp, L0_Bp is the life at the reference temperature 0O -Bp f°r the same percentile B p , while RBp is a characteristic parameter of the insulating material. Assuming the thermal class as reference temperature, i.e. temperature that guarantees 20,000 hours of continuous operation, the Arrhenius's equation (8) is rearranged as in (9), which represents the lifetime model for continuous duty EMs (i.e. operating at constant temperature).

LBp(8) = 20,000 ■ e -fisp-i
Considering 10% and 50% percentiles, the parameter RBp and the thermal class 0Q-Bp are graphically obtained from Fig. 9 and the obtained values are summarized in Table III. For variable duty EMs (i.e. operating at variable temperature), the lifetime model is developed by combining the cumulative damage law (i.e. Miner's law) and the Arrhenius' law [25]. Assuming a generic time-variable temperature profile 6(t) featuring Atcy6ie as time duration (i.e. cycle's period), the loss-of-life per cycle, i.e. LFcycle_Bp, at a predetermined percentile Bp is quantified by (10).

IF,
_ r e c y c le The time-variable temperature profile can be divided in infinitesimal interval dt, thus, the corresponding insulation loss-of-life LBp[9i(t)] (i.e. loss-of-life per infinitesimal interval dt) is calculated by (9), since the temperature 6((t) is constant during dt [26]. Considering Miner's law [25], the number of cycles-to-failure KBp at a given percentile is computed according to (11).
Therefore, the insulation total life Ltot can be expressed by (12) ( 12) and a breakdown of the inter-turn insulation will occur if the cumulative loss-of-life equals 1 (i.e. unitary value).
Using the multi-percentile Arrhenius graph (i.e. Fig. 9), the developed lifetime model (10) is tuned on a particular percentile (e.g. 10%, 50%, etc.), which depends on the reliability level required. This model is then utilized as life prediction tool in the reliability oriented EM design (i.e. Fig. 1). Indeed, knowing the duty cycle of the EM, the associated losses are evaluated based on the EM preliminary design and they are applied in input at thermal model, e.g. lumped parameter thermal network [27][28][29]. The latter provides the winding temperature profile that is given as input to the lifetime model. The predicted lifetime expressed in terms of cycles-to-failure or time-to-failure is then compared against the reliability specification, which is a design constraint, in order to verify whether or not the EM preliminary design fulfils the targeted reliability level. If the mentioned check provides a positive outcome, the EM designer can safely finalize the EM design and move to the prototyping of the EM. Conversely, the preliminary designed EM would require an update to meet both reliability and performance constraints. The applicability and practical utilization of the implemented lifetime model is addressed in the next section.

VI. Au t o m o t iv e Ca s e -Stu d y
A full-electric minivan powered by two twin EMs, is considered as case-study. The mechanical power developed by each EM is transferred to the wheelbase through a gearbox. Therefore, the minivan transmission architecture features one EM per vehicle axle allowing an adequate availability level by exploiting the redundancy concept [30,31]. The EM is an interior permanent magnet synchronous machine (IPMSM) with 20 poles and 24 slots [32]. From a preliminary EM design, the IPMSM geometry is obtained and it is shown in Fig. 10. Focusing on the single electric drive, whose parameters are listed in Table IV, a two-level power converter  supplies the IPMSM through a 3 m long cable. Based on the  specifications o f Table IV, the electric drive meets the PD-free requirements introduced in Section II.A. Thus, the lifetime model presented in Section V is employed assuming the thermal stress as prevailing aging factor. Such model enables the prediction of both cycles-to-failure and loss-of-life of the inter-turn insulation.  An extra urban driving cycle (EUDC) is cyclically performed during a time period of 1 hour and the corresponding EM losses are applied to the EM thermal model in order to estimate the hot-spot temperature of the winding. Considering an inlet cooling liquid temperature of 40 °C and an environmental temperature of25 °C, the resulting hot-spot winding temperature profile is reported in Fig. 11. Looking at the temperature profile (red continuous line in Fig. 11), the temperature o f 200 °C, which corresponds to the thermal class of the magnet wire, is sometimes exceeded causing an excessive loss-of-life. Therefore, the lifetime model developed according to the Miner-Arrhenius (10) is used to predict the hourly loss-of-life for both 50% and 10% percentile. The predicted trends are depicted in Fig. 11, while in Table V, the cycles-to-failure and the loss-of-life are also given. The lifetime assessment allows to assert that if 13700 EMs perform the EUDC for one hour, then the 10% would fail due to a thermal aging induced inter-turn breakdown. Although the only thermal stress is accounted for in the investigation, these results are conservative, since it is unlikely that the minivan is only driven on extra urban roads. Referring to Fig. 1, the EM can be manufactured in case the cycles-to-failure prediction complies with the reliability target. If this condition is not satisfied, EM preliminary design should be further improved. It is important to underline that the obtained predictions are consistent with the values expected by an EM for traction applications (i.e. 300000 km or 10000 h) [33]. VII. Co n c l u s io n s A reliability oriented EM design methodology is introduced with the purpose of limiting the safety-factors adoption. Indeed, the discussed approach allows to simultaneously meet performance and reliability requirements typical of EMs for transportation applications. In particular, the presented study investigates the thermal aging of the inter-turn insulation employed in LV random-wound EMs. ATA tests were preliminary carried out for developing a single-stress thermal lifetime model based on Miner-Arrhenius law. The built lifetime model can be tuned at a predetermined percentile and it is suitable for variable duty EMs. Both applicability and feasibility of the described methodology were proven by discussing an automotive case-study.
Although the investigation was performed on a specific magnet wire, the main steps to develop a lifetime model for a different enamelled wire were given. The discussed single-stress lifetime model represents just the first step towards the PoF methodology applied at EM. As future work, multi-stress lifetime models are going to be built aiming at a more comprehensive lifetime prediction.