Model-Based Design of an Electric Bus Lithium-Ion Battery Pack

In recent years, electric vehicles (EVs) are becoming more common and are utilizing higher capacity lithium-ion battery (LIB) packs on road ways around the world. These leaps in technological progress are the leading reason why advanced research and development into accurately modeling and designing LIB packs, structures, and simulation is critical. Current, widely accepted methods require incredibly complex models to undergo finite element modeling (FEM) analysis which increases development time. As a consequence of computation time, multi-scale and iterative battery pack design is not typically applied. While these complex practices are currently the standard, there have been efforts to develop homogenized FE models to increase computational speed. These advancements, which are based heavily on experimental results in the referenced documents, would permit an iterative process to be applied.

In order to achieve the ability to perform these iterative processes there must be homogenizations completed on the LIB models being used. Thus far, there have been various homogenization methods being used for LIBs at the various sublevels of an overall battery pack: jellyroll layers, cell level, module level, and pack level. Most studies to date have focused on small-scale experiments, as these are the backbone of all simplifications and typically have a significant impact on the overall model, such as internal layers and cell levels. Within the cell level experiments, there are studies that have addressed the different form factors of LIBs such as cylindrical cells [1–14], pouch cells [1,6,9,10,15–30], and prismatic cells [6,31–33]. In these studies, there have been various types of testing to conduct, such as but not limited to: crack prorogation [10], static and dynamic testing [8], thermal characteristics [6,11], etc. Testing on the internal layers of a LIB cell consist of mechanical testing of the cathode, anode, and separator layers [17,23,31,34].

The next stage is with respect to module level experimentation and modeling. As the module is the first sub-body below the pack, it can experience all the same types of mechanical damage as the pack but on a different scale. Zhang et al. performed a study focused on predicting state of health (SoH) based on machine learning and simulations. Impact tests on individual cells were performed and the results, as well as 3D scans of the cells, were analyzed and used in physical and electrical performance tests. A machine learning algorithm was then used to categorize the cells into three groups: safe, latent danger and unsafe. These results were then used in a module level study focused on impact testing where the previously described algorithm was able to deduce SoH based on impact criteria [35]. The next study, completed by Hu et al., focused on the deformation characteristics of packed cylindrical cells exposed to static or dynamic loading. This was the focus as cells within a LIB module are typically packed dense to maximize energy density within the module. It was determined that the behavior under static and dynamic loading varied drastically when displaced equally. As a result, the modules under dynamic loading were at much higher risk of catastrophic failure [36]. Another study focused on the electromechanical response of the module under various quasi-static and dynamic loadings with varying levels of protection. Two different punch heads were used at speeds of 0.06 mm/s and 50 mm/s against modules with and without cover plates. The resulting data provided detailed information of the behavior of a module when subjected to various low-speed impacts [37].

Pack level testing and simulations are not commonly performed as a result of the complexity of the internal structure of the pack. Scurtu et al. completed a series of simulations on a battery pack with and without shock absorption protection. Crash impact simulations were conducted at velocities ranging 7–21 m/s on the pack. The study concludes with the results of the experimentation and provides feedback based on the inclusion of shock absorption protection and geometry [38]. These findings shed a light on how critical various levels of protection are but were completed at a high cost using very complex models.

While experimental testing and simulations at each level are necessary and revealing, it is not feasible to perform this at the highest level of detail for all applications. Recognizing this, many studies implemented homogenization of cells, modules, packs, etc. to simplify the model and minimize simulation-based cost [1–4,15,16,18–21,31,32,34,39,40]. These simplified models have been used in a wide range of simulations to reduce the cost and time required to obtain accurate results and make necessary improvements.

Development of a LIB pack can be a lengthy process and one that can be improved as developments are constantly introduced. Starting from the initial iteration and continuing as new results are brought to light can further increase simulation time frames. A new method for LIB pack design is required to minimize this time and increase capability. This paper aims to solve this issue by creating a framework for an iterative method in order to accurately design necessary features for an electric bus being designed by national center for sustainable transportation technology in Institut Teknologi Bandung in Indonesia. This method utilizes the known methods of homogenization and enables the user to begin with an easily solvable simulation to obtain approximate stress/strain values which will then be used in more complex and detailed models.

There are two major approaches in dealing with multi-scale analysis related to lithium-ion batteries: homogenization and submodeling. When the focus of analysis is on a larger scale, sometimes the details related to a smaller scale is not desired, therefore we assume homogenized mechanical properties throughout the model. These homogenized mechanical properties must exhibit the same overall behavior as the micro model. In various cases such as modeling a battery pack or module, homogenization is the only feasible way, because detailed modeling of a battery pack that houses thousands of batteries is not computationally possible. In cases where both detailed modeling and homogenization approaches are possible, homogenization can significantly reduce the computational time. The reverse procedure, submodeling, is when we are interested in getting more details from the model. Therefore, a smaller scale of the model (submodel) is chosen, all of the desired substructures are included in the model and proper boundary conditions are transferred from the present solution to the submodel. This approach can be very useful in studying the critical locations of a relatively large model in more detail. A schematic of typical homogenization/submodeling steps for lithium-ion batteries is depicted in Fig. 1.

The electric bus studied in the present work, has two battery packs, each comprised six modules. Each module contains 1008 cylindrical 18,650 lithium-ion batteries (see Fig. 2). Since including a detailed model of the entire battery pack in the finite element analysis is not computationally possible, a homogenization approach was required. The goal was to have a homogenized model of the battery pack with average mechanical properties similar to the detailed model. For this purpose, a set of four cylindrical cells were chosen from the module. Before performing homogenization on the four-cell level, characterization tests were conducted to find its mechanical properties and calibrate a material model to be used in the finite element model. In the literature, one of the most popular material models used for modeling jellyrolls of cylindrical cells has been the crushable foam model on LS-DYNA. For this material model, a nonlinear stress–strain curve can be defined in compression whereas, in tension, the behavior is linear up to a predefined tensile cutoff value. Different research groups have proposed various methods to calibrate jellyroll’s stress–strain curve from experimental data. One of these methods is based on principle of virtual work [41] which estimates average stress–strain curves from lateral compression test data. A similar approach has been used for this study. Figure 3(a) shows the compression test setup on the jellyroll and the calibrated stress–strain curve. In order to obtain the tensile cutoff value, tensile tests were also performed on jellyroll components (Fig. 3(b)) which resulted in an average cutoff value of about 17 MPa.

For the four-cell homogenization, the finite element model depicted in Fig. 4(a) was developed. Four cylindrical cells including the jellyroll and battery casing were considered to be between three rigid walls. Each cell included a jellyroll and a 0.25 mm aluminum battery casing with a yield strength of 450 MPa. A 0.5 mm copper plate, which serves as cooling channel in the battery module, was wrapped around the four cells. It was assumed to have a Young’s modulus of 110 GPa and a yield strength of 200 MPa. The copper plate and the battery casings were modeled using Material type 24 in the LS-DYNA library while, for jellyroll, crushable foam material model (type 63) was used. Polycarbonate sockets were modeled on both ends of the batteries using material type 24. These sockets were assumed to have an elastic modulus of 1.53 GPa and a yield strength of 63 MPa. A rigid plate applied compression on the cells at a constant displacement rate (Fig. 4(b)). The resulting force–displacement curve was used to find homogenized stress–strain curve (see Figs. 4(c) and 4(d)) by considering dimensions of the four-cell setup (40.4 × 40.4 × 66.75 mm³). For stress calculations, the area under compression was assumed to be (40.4 × 66.75 mm²) and the engineering strain values were found by considering the initial height to be 40.4 mm.

In order to have a homogenized model for the battery module, in addition to mechanical properties, average density is also needed. Since the load case being studied for the present electric bus and battery pack involves impact, density calculation is important and can affect the intensity of the impact and in general the design of battery pack connections. In this study, the mass of polycarbonate sockets is considered negligible compared with the batteries. The details of calculations are listed in Table 1. Based on the total number of batteries in each module, the total mass of the cells was estimated, and the homogenized density was calculated by considering the overall dimensions of the battery module.

In order to validate the homogenization procedure, since an experimental approach was not possible on the module level, a numerical approach was considered. A detailed model of a quarter of the module was developed including all of the batteries, copper plates, sockets, and module covers (see Fig. 5(a)). A similar quarter module was also modeled using a single homogenized part representing the batteries, copper plates and sockets (Fig. 5(b)). The models were crushed laterally (from one side) against a rigid wall at a constant displacement rate. Figures 5(c) and 5(d) show the deformation of both models. The resulting force–displacement curves are plotted in Fig. 5(e). Comparison of the two curves shows that, neglecting minor differences and oscillations, both models follow similar trends up to a displacement of about 60 mm.

The finite element model of the bus chassis including the battery packs was developed in LS-DYNA. Each battery pack was connected to the chassis frame using four 2-mm thick square tubes. In the finite element model of the chassis, in order to reduce the dynamic simulation time, most of the joints were defined using constrained nodal rigid bodies (CNRB), where several nodes from both parts were assumed to be part of a rigid body. In the initial simulation, a similar approach was followed for battery pack connections to get an initial estimation of forces at each connection between the tubes and the chassis. In the subsequent simulations, the bolts were modeled as spotwelds to achieve more accurate tensile and shear forces. In the Discussion section, the initial force estimations were used to design the fasteners and to improve the FE model.

The initial model for battery packs was comprised of homogenized solid blocks, representing the 1008 cylindrical cells, copper plates and sockets inside the modules and steel shells as the module casing. For the homogenized modules, crushable foam material with stress–strain curves found from four-cell homogenization was used. For each battery pack, eight constrained nodal rigid bodies were defined to connect the battery pack casing to the tubes and another eight CNRB connected the tubes to the chassis frame. Figure 6(a) shows the position of the battery pack on the tubes.

For the battery pack components, eroding single surface contact with soft 1 option was used. All other metal to metal contacts in the model were defined in one automatic single surface contact type. Figure 6(b) shows the FE model of the chassis including the two homogenized battery packs. The load case considered for this study was a side impact of chassis with a rigid pole. The initial velocity was set to 4.44 m/s.

In order to design a pack strong enough to survive an impact to the frame, an iterative approach was developed. This approach permits the designer more accuracy over time to ensure adequate design and factors of safety. The initial FE simulation including the homogenized battery modules where the connections to the chassis were through CNRB was analyzed to measure the forces in the three axes. While these are not perfectly accurate at this stage of design, they are representative enough to make initial design approximations and selections. The maximum of these force values, which was approximately 10 kN in sheer loading, was then used as a minimum force in all axes to determine a minimum fastener to be used to connect the lateral supports to the bus chassis. Typically, in automotive applications, Grade 8 steel bolts with a zinc or chromate plating are utilized for their high tensile strength properties while resisting corrosion. For this application a 5/8 in.–11 × 1.5 in. bolt in conjunction with a 5/8 in.–11 serrated flange lock nut were selected. The chassis, supports, and battery module were then modeled to test for dimensional continuity and can be seen in Fig. 7.

In the lateral supports, additional holes were drilled (seen in Fig. 7(b)) for insertion of the bolt and clearance for tooling. This resulted in four holes and two bolts per support, 16 holes/8 bolts per module, and 32 holes/16 bolts overall. Following the selection and placement of the fasteners to the model, a more accurate simulation should be conducted to increase the accuracy of the measurements. In order to achieve more accurate results for subsequent simulations a more detailed model is required. The battery pack was modified to include a top cover and bottom cover casing, internal support plates, and a battery solid that represents the array of cells within the module (Fig. 8). As for the material selection for the casing: Aluminum and Steel alloys were considered. Due to the geometry of the casing, it was determined that high pressure die-casting (HPDC) would be suitable for Aluminum parts and investment casting (IC) would be appropriate for Steel parts. Further research showed that an optimal aluminum alloy would be Aluminum Alloy 218 due to its high strength values and resistance to corrosion while still being readily available in the HPDC process. Similarly, an optimal steel material was selected as Stainless Steel 304 for strength and corrosion resistance while being readily available in IC applications. Following these additions another simulation was structured to provide more detailed results based on the updated models and fasteners utilization.

The initial FE simulation discussed in the Finite element modeling and pack design section, led to an initial design of battery modules (top and bottom covers), supporting plates, and fasteners. Using the new design, the FE model was updated to find stresses, strains and forces in the battery modules and fasteners with more accuracy (see Figs. 9(a) and 9(b)). In this model, the bolts connecting the tubes to the chassis were modeled using beam-type spotwelds with the same diameter as the bolts. Each module comprises 1008 cylindrical 18650 batteries that are positioned vertically. All these batteries were homogenized into a single block inside each module. The top and bottom supporting plates were assumed to be 1 mm thick steel materials. The top and bottom covers were made of steel 304 (as described in Finite element modeling and pack design section) with a thickness of 1.2 mm. Flanges of the top and the bottom covers had merged nodes. The supporting plates were attached to the covers using tied contacts. Similar contacts were defined between the stacked modules.

The bottom cover of the lower module was also tied to the four supporting tubes. An initial velocity of 4.44 m/s was applied to the entire chassis including the battery packs assembly before impacting onto a rigid pole. A second simulation was performed by replacing material models of module covers and supporting plates with Aluminum alloy 218 which are also suitable for die-casting with acceptable yield and ultimate strengths.

The total time for the first model to reach from the initial velocity to maximum deformation was about 80 ms. Figure 9(c) shows the chassis at maximum deformation. Since the battery packs were not directly impacted by the rigid pole, severe deformation of the modules was not expected. von Mises stress contour for the chassis main frame and the supporting structure of the battery pack is plotted in Fig. 9(d) which shows a maximum stress of 492.2 MPa on the frame. Similarly, a plot for the metal parts of the battery pack shows local maximum stresses of 232 MPa (Fig. 9(e)), while overall, the stresses for a major part of the battery pack do not exceed 200 MPa. This suggests that in case there is no added complexity in the manufacturing process, a lower density material such as aluminum can be used for battery module parts. Subsequent simulation using Aluminum 218 material for the module parts shows a maximum von Mises stress of 274 MPa. In order to find out how much load is applied to the bolts connecting the pack supports to the chassis frame, shear forces were plotted for the beams representing the spotwelds. Figure 10 shows that 14 out of 16 spotwelds remain below 20 kN for the majority of the impact duration. Two of the spotwelds (number 8 and 10 which are closest to the rigid pole), however, show higher shear forces of up to 38 kN which is expected given the severity of the deformation in the chassis at this location. Failure in a number of these fasteners is not necessarily catastrophic and in many circumstances (depending on the loading scenario) can be beneficial for the battery pack, since in those cases the deformation of chassis frame will not cause sever deformation in the battery pack, thus it reduces chances of battery failure and thermal runaway.

One of the most important parts of the analysis of the battery pack, when homogenization is involved in the process, is following the reverse approach, i.e., submodeling. Homogenization, as explained before, leads to an overall similar deformation of the detailed model. However, stresses and strains of the lower scale model cannot be extracted without submodeling. It should be noted that the submodeling procedure explained here is not exactly what is usually referred to in the literature. In the commonly used submodeling procedure, a piece (submodel) of the larger model is selected, usually to study in more detail. The submodel is then usually re-meshed using finer element sizes. Both the coarse-mesh submodel and fine-mesh submodel have similar or close-enough boundaries so that the exact deformation can be transferred from the original model to the boundaries of submodel. In this study, a different submodeling approach was used, mostly to get an estimate of the stresses and strains in individual batteries in the pack without performing a detailed modeling of the entire battery pack. The procedure is explained schematically in Fig. 11(a). First, the maximum strain is found in the homogenized battery pack model. It is then assumed that the four-cell model (that was used initially for homogenization) is going through the same strain value. The strain is converted to the displacement assuming the four-cell model is being deformed in the lateral direction. Values of stresses and strains are then estimated from the four-cell model. Figure 11(b) shows logarithmic strain values of the homogenized modules for the Aluminum pack model which shows a maximum value of 0.354 (equivalent to a volumetric strain of 0.298). Since the impact was indirect, the strain values were not significant. However, in order to check stress and strain values in each cylindrical cell, one needs to apply the same maximum strain values to the original four-cell model that was initially used for homogenization. In this case, a strain value of 0.298 is equivalent to a displacement of about 12.04 mm (dimension of the four-cell model: 40.4 mm). Applying the displacement to the four-cell model results in the stress/strain values plotted in Figs. 11(c) and 11(d) for the jellyrolls (battery casings, copper plate and sockets are not shown in the plots). This dual multi-scale approach i.e., homogenization and submodeling can be expanded to more levels. In this case, one can have another level of submodeling to find the stresses and strains in the jellyroll components such as anode, cathode, and separator layers.

Table 2 lists comparison of various factors between the models with battery packs made of Steel 304 and Aluminum 218. Some factors such as shear forces in bolts and impact accelerations are very identical in both models. Other factors such as stresses in the metal parts of the battery pack and consequently the strains in the homogenized modules are slightly higher for the Aluminum model, but the difference is not more than 20 percent. The difference in mass, however, is significant and since the weight is one of the most important factors from different points of view such as energy consumption, this makes the Aluminum model to be the better design for the present loading scenario. One of the advantages of the low weight of Aluminum model can be seen in the stress level of the chassis frame which is dropped from 492 MPa in the Steel model to 478.2 MPa in the Aluminum model. However, it should be noted that deformability of the Aluminum casing, can cause significantly larger deformations in the batteries that might raise safety issues.

In this study, a multi-scale framework was proposed to design battery packs and fasteners of an electric bus. The focus of this research was on the methodology and the validity of the design/analysis procedure as opposed to the actual detailed design of all of the battery pack parts and fasteners. Rigorous design of the battery pack requires consideration of other loading scenarios, corrosion, fatigue, and many other factors which were beyond the scope of the present work. The proposed multi-scale framework involves a three-step procedure. Homogenization, FE simulation, and submodeling:

• Homogenization is implemented by using cell level mechanical properties to find average mechanical properties for the module/pack.

• The homogenized properties make it possible to run simulations on the models with entire battery packs that otherwise would not be possible since including the details of individual cells would requires tens of millions of elements.

• After running the main simulation, the submodeling approach is used to go back to cell level (at the desired locations of the module) and estimate stress/strain values of the cell.

This multi-scale approach was applied to an electric bus lithium-ion battery pack. Cell level mechanical properties, which were previously calibrated using various experimental and analytical methods, were utilized to develop a finite element model of battery modules and packs. The pack model, with its metal parts, attachments and supporting structures was combined with the bus chassis model to study the effects of impact with a rigid pole on the chassis and battery assembly. This iterative procedure makes it possible to improve the design of various parts of the structure if needed. The proposed method can be expanded to include more levels. Maximum strains in a battery module are used to find deformation and stress/strain values of battery cell, which in turn can be used to estimate the stresses in jellyroll component layers.

It should be noted that in case one prefers to apply the classical computational homogenization approach [17], the mesh size in the battery pack’s homogenized model in the full vehicle (bus) simulation should be the same size as the detailed representative volume element (RVE) and one can directly apply the deformation gradient from one homogenized element to the corresponding RVE. However, in that case, the element size for the homogenized model would have been too large to capture details of deformation. In the approach used in this study, the smaller element size of the homogenized pack allows a higher fidelity representation of the battery pack and a local deformation in such a pack will go beyond what could be captured with a larger mesh. Therefore, when the maximum deformation is extracted from a smaller element, a more conservative evaluation of potential failure in the RVE will be achieved.

The authors would like to acknowledge the funding from multiple sources for this research. This includes support of Temple University Startup funds, MIT Industrial battery consortium, Office of Naval Research Contract N000141912351, and from USAID SHERA Award AID-497-A-16-00004. This research includes calculations carried out on HPC resources supported in part by the National Science Foundation through major research instrumentation grant number 1625061 and by the U.S. Army Research Laboratory under contract number W911NF-16-2-0189.

Furthermore, the authors are thankful to Professor Sigit Santosa of Institute Technology Bandung (ITB) and his team for providing the bus model used in this study.

There are no conflicts of interest.