Soc Estimation Battery Matlab

Highlights

Dual time-scale state-coupled co-estimation of SOC, SOH and RUL for lithium-ion batteries

Ningbo Cai,Yuwen Qin,Xin Chen,Kai Wu

• The Deep Inter and Intra-Cycle Attention Network (DIICAN) method is proposed for the co-estimation of SOC, SOH, and RUL. • Convolutional neural networks are applied to automatically extract battery degradation-related embedding features from the raw BMS streaming data.

• The state degradation attention unit is combined with recurrent neural networks to extract the battery state evolving pattern for the SOH and RUL estimation over the whole lifespan. • SOH and SOC are coupled to account for the influence of battery aging on the SOC estimation. The SOC estimation accuracy is improved significantly over the battery lifespan.

Arxiv:2210.11941V1 [Eess.Sy] 20 Oct 2022

Dual time-scale state-coupled co-estimation of SOC, SOH and RUL for lithium-ion batteries via Deep Inter and Intra-Cycle

A Center Of Nanomaterials For Renewable Energy,

State Key Laboratory of Electrical Insulation and Power Equipment,

School Of Electrical Engineering,

bState Key Laboratory of Electrical Insulation and Power Equipment,

A B S T R A C T

Accurate co-estimations of battery states, such as state-of-charge (SOC), state-of-health (SOH,) and remaining useful life (RUL), are crucial to the battery management systems to assure safe and reliable management. Although the external properties of the battery charge with the aging degree, batteries’ degradation mechanism shares similar evolving patterns. Since batteries are complicated chemical systems, these states are highly coupled with intricate electrochemical processes. A state-coupled co-estimation method named Deep Inter and Intra- Cycle Attention Network (DIICAN) is proposed in this paper to estimate SOC, SOH, and RUL, which organizes battery measurement data into the intra-cycle and inter-cycle time scales. And to extract degradation-related features automatically and adapt to practical working conditions, the convolutional neural network is applied. The state degradation attention unit is utilized to extract the battery state evolution pattern and evaluate the battery degradation degree. To account for the influence of battery aging on the SOC estimation, the battery degradation-related state is incorporated in the SOC estimation for capacity calibration. The DIICAN method is validated on the Oxford battery dataset. The experimental results show that the proposed method can achieve SOH and RUL co-estimation with high accuracy and effectively improve SOC estimation accuracy for the whole lifespan.

1. Introduction

Due to the increasing shortage of resources, environmental pollution , the past decade has witnessed that the generation of electricity is rapidly increasing from non-predictable and variable renewable energy sources. Lithium- ion batteries with superior power and energy density, durability, and environmental protection have been widely applied in energy storage, and power systems such as water power, thermal power, wind power, and solar power stations, and so on. A high-efficiency battery management system (BMS) is usually deployed to facilitate a safe and wide range of battery operations. Accurate battery state-of-charge (SOC), state-of-health (SOH), and remaining useful life (RUL) estimation are key modules within BMS for ensuring the reliability, durability, and performance of batteries.

Generally speaking, the SOC estimation methods include basic, data-driven, and model-based methods. Basic methods include the looking-up table and Ampere-hour integral methods. Basic methods have been widely used in practical engineering due to the advantages of simple calculation and easy implementation, but are greatly affected by the working environment , rest time and accuracy of the initial value. The model-based method is to study the relationship between the internal mechanism and the external state, establish the model’s discrete expression, and then estimate the battery SOC recursively. The method generally owns the merits of real-time and closed-loop feedback.

Commonly used models can be roughly summarized into three types: electrochemical models (EM) , equivalent circuit models (ECM) , and electrochemical impedance models (EIM) . Although significant progress has been made in model-based methods, they rely on accurate prior knowledge of internal mechanisms, which is usually unavailable owing to the battery’s complex physical and chemical processes, as well as the noise and the diversity

Orcid(S):

First Author et al.: Preprint submitted to Elsevier

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DIICAN: Dual Time-scale State-Coupled Co-estimation of SOC, SOH and RUL for Lithium-Ion Batteries of the environment. Data-driven models depend only on historical data and do not need complicated equivalent or mathematical models. Hong et al. proposed an LSTM-based method for multi-forward-step SOC prediction for battery systems in real-world electric vehicles. Terala et al. used combined stacked bi-directional LSTM and encoder-decoder bi-directional long short-term memory architecture to improve on the existing methods of SOC estimation. In , a GRU model was proposed for accurate SOC estimation under dynamic driving conditions to solve the problems of time long-term dependencies and gradient disappearance or explosion.

Battery aging, usually in the form of capacity fade and resistance growth, is one of the most challenging issues for system safety. Typically, SOH refers to the current health condition of a LIB compared to its initial degradation state. By contrast, RUL is defined as a remaining lifespan from the current cycle to the end of life (EOL) based on its current degradation state. Some model-based approaches are mainly to analyze the physical and chemical principles of internal degradation mechanism and establish mathematical models to characterize the process of capacity degradation for SOH and RUL prediction. Numerous methods for extracting health indicators (HIs) have been explored in the recent literature. Indirect HIs extraction methods typically find hidden variation laws and statistical information during the battery operating process. Sun et al. combined incremental capacity analysis (ICA) and bidirectional long short-term memory (Bi-LSTM) neural networks based on health characteristic parameters to predict the SOH of lithium-ion batteries. used battery terminal voltage during the later stage of the charging process as the input of the sparse auto-encoder and abstracted compressive feature of battery voltage to obtain battery SOH, achieving a good accuracy with adaptability to the capacity fading diversity and voltage differences among different battery cells. Hong et al. proposed a dilated CNN-based neural network architecture for predicting the remaining useful life of lithium-ion batteries, which boosted the remaining useful life prediction. Deng et al. used features extracted from discharge capacity curves to achieve degradation pattern recognition and transfer learning, which can effectively improve SOH estimation accuracy. These relevant research results are flexible and accurate and clearly reflect the advantages of the data-driven method.

Monitoring SOC, SOH, and RUL over time is a challenging goal since SOC and SOH are highly coupled with intricate electrochemical processes. With the aging of the battery, the capacity of the battery will gradually decrease, and the characteristics of external measurable parameters may change, which will pose a great challenge to the estimation of SOC. Zou et al. proposed an effective multi-time-scale estimation algorithm for a class of nonlinear systems with coupled fast and slow dynamics using the developed reduced-order battery models. Hu et al. proposed a SOC and SOH co-estimation scheme that is capable of predicting the voltage response in the presence of initial deviation, noise, and disturbance against battery degradation. Che et al. established an improved dynamic recurrent neural network (DRNN) with the ability of dynamic mapping to improve the estimation accuracy of the SOC and SOH under different conditions. Song et al. proposed a joint lithium-ion battery state estimation approach with high accuracy and robustness that takes advantage of the least-square-support-vector-machine and unscented-particle-filter.

Some feature extraction methods often require additional manpower consumption, such as incremental capacity analysis (ICA), differential voltage analysis (DVA) and differential thermal voltammetry (DTV) . Although these HFs have been proven to be highly related to the battery aging process, their adequacy and availability under different working conditions should be considered. In addition, capacity degradation will significantly decrease the accuracy of state estimation, and the accurate state of charge relies on the correction of the maximum available capacity of the battery. The unified data-driven co-estimation method for SOC, SOH, and RUL of battery is crucial work for the modern BMS. To solve the above problems, a dual time-scale state-coupled co-estimation method is adopted in this research, named Deep Inter and Intra-Cycle Attention Network (DIICAN). The key contributions of the present work

Are Summarized As Follows:

• The unified state-coupled co-estimation method, DIICAN, is proposed to estimate SOC, SOH, and RUL in battery life cycles according to the inter-cycle and intra-cycle features. The inter-cycle features are used for the SOH-RUL estimation, while the intra-cycle features are for the estimation of SOC.

• Convolutional neural networks are utilized to map raw battery measurements directly to battery degradation- related embedding features automatically to reduce the error caused by manual feature extraction. • The state degradation attention unit accurately reveals the battery state evolving patterns to represent the battery degradation and achieve the SOH and RUL co-estimation over the whole lifespan.

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DIICAN: Dual Time-scale State-Coupled Co-estimation of SOC, SOH and RUL for Lithium-Ion Batteries

Augru

Augru

Figure 1: The overall architecture of the DIICAN co-estimation method. • The influence of battery degradation on SOC estimation is considered. Battery degradation-related state in the SOH estimation is used for the capacity calibration in the SOC estimation. The accuracy of SOC estimation is improved significantly over the battery lifespan.

The paper is organized as follows. In Sec. 2, the proposed DIICAN method is presented. The training process of the DIICAN method is discussed in Sec. 3. The experimental results and the performance analysis are given in Sec. 4. Finally, Sec. 5 gives the concluding remarks.

Table 1

The inter and intra-cycle feature set.

1

2. Dual time-scale state-coupled co-estimation: Deep Inter and Intra-Cycle Attention

Network

The BMS streaming data has two temporal structures, inter-cycle and intra-cycle timescales. The inter-cycle sequence contains all the information for SOH and RUL while the intra-cycle time series data is used for the estimation of SOC within a cycle. The Deep Inter and Intra-Cycle Attention Network (DIICAN) is proposed to extract battery multiple states and model battery states’ evolving process based on the two intra-cycle and inter-cycle temporal structures. As illustrated in Fig. 1, DIICAN has the three modules: feature extraction module (FEM), temporally structured recurrent module (TRM) and state-coupled regression module (RM).

Temporal Attention

Figure 2: The structure of the feature extraction module. 2.1. Inter and intra-cycle feature representations The BMS streaming data is made of the continuous measurement of the battery external electrical and thermal performance that contains the information of the battery states and characterize the battery degradation. For battery states, one is the intra-cycle states such as state of charge (SOC), the other is the inter-cycle states such as state of health (SOH) and remaining of useful life (RUL). Therefore, the BMS streaming time series data can be decomposed into the inter-cycle and intra-cycles features that represent the two temporal structures within the cycles and between the cycles.

For the SOH and RUL estimation, all the features are embedded in the sequence of charging or discharging curves. The relationship between battery V/I/T curves and battery health status is very difficult to establish in the full battery lifetime. The inter-cycle features, 퐗푖= {푋푖, 푋푖+1, ⋯, 푋푖+퐿−1}, are the sequences of voltage, current and temperature (V/I/T) curves in the battery charging/discharging processes measured by BMS within different cycles, which typically

2 , ⋯, 푇푑

푁} in the 푖푡ℎcycle. Although the BMS streaming are recorded at the same sampling rate, the total time duration could vary for different batteries and in different cycles. Given that the charged and discharged capacity increases monotonously, the battery V/I/T curves are normalized as the functions of capacity ratio.

As a result, the inter-cycle feature 퐗푖are re-labelled with the capacity indices to remove the temporal sampling rate discrepancy. On the other hand, for the SOC estimation, the intra-cycle features, 퐱푗, are the sequences of voltage, First Author et al.: Preprint submitted to Elsevier

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DIICAN: Dual Time-scale State-Coupled Co-estimation of SOC, SOH and RUL for Lithium-Ion Batteries current and temperature measurement points (V/I/T) within a discharging cycle. The intra-cycle feature sequence is defined as 퐱푗= {푥푗, 푥푗+1, ⋯, 푥푗+푙} which 퐱푗are 푙historical V/I/T points. The inter-cycle and intra-cycle features for the battery state forecasting in DIICAN are presented in Table 1.

2.2. Feature Extraction Module

The feature extraction module is vital to identify the features that can accurately and completely cover the information of each original historical step and the correlation between the attributes. For SOC estimation it applies one fully connected layer (FC) for embedding each feature point 퐱퐣into 퐞퐣. The relationship between battery V/I/T curves and battery health status is very difficult to perceive owing to the complex electrochemical reactions and mechanisms inside the batteries. Thus, SOH-RUL estimation consists of complex structures for the input data 퐗퐢during one cycle to generate the embedding features 퐄푖associated with battery degradation. The details of the convolution structures are presented below.

(B) Group Conv2D

Figure 3: The Conv2D and group Conv2D. Traditionally, convolutional neural networks (CNNs) have been widely used in the computational vision field. Sun et al. applied the CNN architecture to the time series prediction with excellent performance. The convolution operation is good at capturing the temporal correlation of local information, and the convolution kernel coefficient can flexibly adjust the size of the receptive field to obtain more features of input data in different time scales. Inspired by that, CNNs are utilized to extract degradation-related features hidden in battery V/I/T curves comprehensively and automatically; meanwhile, feature and temporal attention block is adopted to enhance the performance. Each input vector 퐗퐢∈ℝ푁×푀×1 is treated like a color image as the input of a two-dimensional convolutional neural network.

Fig. 2 indicates the complex 2DCNN structure for SOH-RUL estimation. The convolution layer is computed as convolving the input feature maps with filters. Taking the 푘푡ℎlayer for an example, the input of the 푘푡ℎlayer can be denoted as 퐗푘= {푋푘

And 푋푘

푠is the 푠푡ℎfeature map. The filters of the 푘푡ℎlayer are denoted as 퐖푘= {푊푘

푂}, Where 푂Denotes The

filter number, as well as the output channel number, and 푊푘 푠is the 푠푡ℎ2D convolutional filter. The Conv2D structure

(2)

where ⊗denotes the convolution between two sets, ∗denotes the convolution operation between a filter and the input feature maps. After each Conv2D layer, the rectified linear unit (ReLU) activation function 푓(푥) = max(0, 푥) is applied. As shown in Fig. 3(b), the group convolution is a special case of a sparsely connected convolution . In group convolution, the input feature maps 퐗푘are divided into 퐺groups equally as the number of filters, i.e., First Author et al.: Preprint submitted to Elsevier

Σ

Σ

Figure 4: The feature and temporal attention maps.

퐺⊗퐗푘

퐺}.

(3)

The group Conv2D reduces the computational cost by partitioning the input features into 퐺mutually exclusive groups producing its own output feature maps. The computational cost is reduced by a factor 퐺to be 푂×푁

퐺.Each Group

represents one feature, which means that each convolution is operated on one feature. With the feature map 퐗퐾transformed by three group Conv2D layers, a feature/temporal attention map 퐁푖are generated with the feature attention block 필퐹and temporal attention block 필푇. As shown in Fig. 4, the feature/temporal

(4)

where ⊙denotes the element-wise multiplication. During multiplication, attention values are broadcasted accordingly. A feature attention map is inferred by exploiting the inter-feature relationship. To weight the relevance of features,

(5)

where 휎denotes the sigmoid function and MLP denotes the multilayer perceptron. To compute the feature attention efficiently, feature dimension is squeezed. By aggregating features with both average-pooling and max-pooling operations simultaneously, the feature attention block ends up with MLP and sigmoid function.

Furthermore, temporal attention is computed along the time dimension. As shown in Fig. 4, the temporal attention

(6)

where 휎denotes the sigmoid function, ∥is a concatenation operation and 5×1 represents a convolution operation with the 5×1 kernel filter. To compute the temporal attention maps, this paper applies the average-pooling and max-pooling First Author et al.: Preprint submitted to Elsevier

2

Figure 5: The structure of the temporally structured recurrent module. operations along the feature dimension and concatenates them to generate efficient feature descriptors 퐴푣푔푃표표푙(∙) and 푀푎푥푃표표푙(∙). Applying pooling operations along the temporal dimension is effective in highlighting informative temporal regions. With the concatenated feature descriptor, a temporal attention map 퐌푇is generated through one convolution layer.

Finally, the dimension reshaping block consists of one Conv2D layer with a 1 × 1 kernel filter and one adaptive 2D average pooling layer. The feature/temporal attention map 퐁푖is flattened into the inter-cycle embedding features 퐄푖.

2.3. Temporally Structured Recurrent Module

The temporally structured recurrent module is developed to extract battery state evolution pattern. As illustrated in Fig. 5, it has the many-to-one structure with the gated recurrent unit (GRU), GRU with attentional gate (AUGRU) and the state degradation attention (SDA) unit. It takes the states 퐒푖as input which can be either the inter-cycle embedding features 퐄푖or intra-cycle embedding features 퐞푗.

Discharge Capacity (Mah)

Figure 6: The capacity degradation curves of eight cells in the Oxford dataset. The sequence of the inter-cycle and intra-cycle embedding features 퐒푖−푑−1, 퐒푖−푑, ⋯, 퐒푖are concatenated and fed into GRU, and then the sequence of hidden states 퐡1

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DIICAN: Dual Time-scale State-Coupled Co-estimation of SOC, SOH and RUL for Lithium-Ion Batteries embedding features are fed into AUGRU to measure how much the battery states deviate from the initial battery states.

푖−1 And 퐡1

푖denote the hidden states in and out of the GRU, respectively. Inspired by the biological systems of humans that tend to focus on the distinctive parts when processing large amounts of information, Firat et al. , the attention mechanism is used to improve the efficiency and accuracy of perceptual information processing. In order to extract battery state evolution pattern by measuring the deviation of the embedding feature 퐒푖at 푖푡ℎfrom the embedding feature 퐒0 at the initial cycle, the initial battery embedding features

퐒0 And Hidden States 퐡1

푖are fed into the state degradation attention (SDA) unit. As demonstrated in Fig. 5, the SDA consists of two fully connected layers. 퐡1

푖⊖퐒0 Are Concatenated

and fed into the SDA to compute the attention weight associated with the battery degradation in Eq. 8,

(8)

where ∥is a concatenation operation, ⊖denotes element-wise minus and 푎푡푡represents the state degradation attention unit. Aiming to accurately account for the battery degradation degree, we use the absolute attention weights instead of the relative attention weight distribution and the softmax normalization of attention weights is abandoned.

Cycle 8000

Figure 7: The discharge voltage curves of all the cycles in the full lifespan for Cell 1 in the Oxford dataset. Then, AUGRU is used to calculate the hidden states. As shown in Fig. 5, it combines the attention mechanism and the GRU update gates together to learn the battery state deviation, which is defined as,

(9)

where the superscript 2 represents the AUGRU, ∗means scalar-vector product 퐳2

푖, And 퐡2

푖−1 indicate the hidden states of AUGRU. The attention weight is added as the attentional update gate which keeps original dimensional information of update gate, and decides the importance of each dimension. AUGRU models the battery state degradation smoothly. The last hidden state 퐡2

푖From

the AUGRU is fed into the state-coupled regression module. First Author et al.: Preprint submitted to Elsevier

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

0.150

Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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