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Half Bridge Converter Matlab Simulink

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Magnetizing Inductance And Hybrid Rectifier

Yohanes Leonaldo Sinaga1, Muhammad Daffa Pratama2, Dziki Early Al Husni3, Alberto Noris Simanjuntak4, Erlangga Satrio Jati5, Rizky Ajie Aprilianto6, Rizki Mendung Ariefianto7

Accepted June 06, 2026

Half-Bridge LLC Resonant converters are widely used in high-power supply applications due to their high efficiency and ability to operate at high frequencies. However, under hold-up conditions or during large fluctuations in input voltage, conventional topologies often experience reduced output stability and increased losses. Therefore, a method that can maintain efficiency and output voltage stability without excessively broadening the switching frequency range is required. To address this, this study proposes a Novelty Half-Bridge LLC Resonant Converter with Magnetizing Inductor and Hybrid Rectifier (NHB-LLCRC-MIHR), incorporating a magnetizing inductor (Lm) in the primary path and a MOSFET-based hybrid rectifier on the secondary side. The research methodology was conducted using MATLAB/Simulink simulation, focusing on five main areas, including optimal switching frequency conditions, operating thresholds, DC conversion ratio (Vo/Vs), comparison of output voltage with conventional topologies, and analysis of output voltage ripple. Simulation results demonstrate that NHB-LLCRC- MIHR can maintain a more stable output voltage, lower ripple, and increase efficiency compared to conventional converters. Thus, this topology shows significant potential for industrial applications that demand high efficiency and optimal power stability.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

Switching Frequency

This is an open access article under the CC BY-SA license.

Https://Doi.Org/10.52465/Joetex.V4I1.675

1.

Introduction

Balancing high frequency and high efficiency in hard-switching converters can increase switching frequency but often results in higher losses, increased heat dissipation, and reduced operational lifespan. Therefore, a soft-switching converter capable of achieving high frequencies by adding resonant elements is required. When voltage and current cross zero, the switches are controlled to turn on or off . The LLC resonant converter offers advantages in smaller volume, simpler structure, and a wide output range . This converter is highly valuable for various applications such as distributed power sources, power systems for computer hardware, and other industrial applications that demand efficient power conversion with precise control over voltage and current . The topology of the LLC resonant converter is divided into three parts: inverter, resonant network, and rectifier, with the structure of the resonant network being relatively fixed .

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

The Half-Bridge LLC Resonant Converter is a DC-DC power converter that utilizes resonance principles in inductive and capacitive elements to convert voltage with high efficiency and low electromagnetic interference. This topology uses two MOSFET switches in a half-bridge configuration to operate the LC resonant circuit, as well as a magnetizing inductor on the transformer to achieve ZVS, allowing the switches to operate without voltage during switching transitions. This significantly reduces the switching losses that commonly occur in conventional Pulse Width Modulation (PWM)-based converters. With improved thermal performance and stable output regulation, the Half-Bridge LLC Resonant Converter is an ideal choice for high-power, high- efficiency power supply applications .

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

The LLC resonance enables a smaller transformer size and lower costs, as its operating frequency is more flexible and can be adjusted according to system requirements, whereas in conventional PWM converters, input voltage fluctuations can significantly affect output voltage stability . The LLC resonant converter is considered an optimal choice due to its efficiency. However, a major challenge lies in the occurrence of large input voltage fluctuations during operation, particularly under transition or "hold-up" states. Such conditions frequently occur when the main power supply is lost, but the system must maintain a stable output voltage for a certain period. To overcome this issue, a more advanced control method is required one that can adjust voltage gain and switching frequency according to varying input conditions . The LLC resonant converter is one of the most popular isolated DC/DC converters, and it has been widely used in many different applications, including on-board battery charger, distributed power system, renewable energy generation system, server power supply, light emitting diode (LED) driver, and laptop adaptor . Proposed a two-bridge LLC resonant converter with an auxiliary switch, which adopts fixed-frequency PWM control and changes the effective input voltage of the resonator by adjusting the duty cycle of the auxiliary switch tube to achieve the stability of the output voltage. The topology can achieve soft switching in the full-load range. However, the normalized gain of this topology can only be adjusted to between 0.5 and 1, and the gain range is still limited.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

Recent research on LLC resonant converters has mainly targeted wider voltage-gain regulation, higher efficiency, and improved soft-switching under abnormal input conditions. A hybrid control strategy proposed based on an improved fruit fly optimization algorithm that combines hybrid phase-shifted and frequency- modulated control for an LLC converter in X-ray machines. MATLAB simulation and prototype verification showed improved stability and reduced conduction loss, but the method still depends on control tuning rather than structural enhancement . A phase-shifting adaptive LLC converter proposed with PSM/PFM hybrid control, where ZVS was maintained over a wide voltage-gain range and turn-off loss was reduced, yet the solution again relied on control adaptation to extend the operating range . Method proposed by experimentally showed that, for a 22 kW, 40 kHz LLC converter, shifting the DC-link operating point so the converter spends about 75% of the grid period above resonance increased average efficiency from 97.66% to 97.70% and reduced resonant-capacitor stress, while still leaving below-resonance loss as a key limitation.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

Study by used sampled-data analysis to derive a discrete state-space model that improves accuracy for LLC operation below resonance, whereas proposed a state-trajectory-based synchronous rectification method for CLLC converters and validated it on an 800 W prototype with 97.38% rated efficiency. However, these studies mainly address modeling or secondary-side loss reduction separately. A remaining gap in the literature is the lack of an integrated topology-level solution that simultaneously improves hold-up behavior, output-voltage stability, ripple, and efficiency within one converter structure.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

This study aims to evaluate the performance and advantages of the proposed converter NHB-LLCRC- MIHR, particularly in the context of operation with PWM control. The main focus of this research is to analyze the impact of implementing an auxiliary switch (Qa) on the primary side on power conversion efficiency, voltage gain, and the reduction of conduction losses caused by current in the magnetizing inductor.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

Additionally, this study examines the dynamic characteristics of the RLC circuit forming the resonant tank, as well as the role of PWM duty cycle in maintaining output voltage stability and efficiency under varying DC input conditions. The research is conducted through simulation using MATLAB/Simulink, with the experimental design. Each parameter is analyzed through circuit simulation results under various load and input variations, providing a comprehensive overview of the advantages and application potential of the proposed converter compared to conventional topologies.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

2.

Method

The NHB-LLCRC-MIHR topology is an advancement of the half-bridge LLC resonant converter with a Qa as presented , incorporating two key innovations: the addition of a Lm in the primary path and the implementation of a hybrid rectifier on the secondary side. The magnetizing inductor, which is integrated in series with the primary winding (NP), serves to extend the ZVS operating range, enhance energy transfer

12

flexibility, and suppress RMS current, thereby reducing conduction losses and increasing efficiency . On the secondary side, two diodes in the rectifier are replaced by two MOSFETs (M3 and M4) operated synchronously at the same frequency as the primary switches, allowing for current rectification with lower voltage losses and faster switching response compared to conventional diodes. The combination of the resonant tank (Lr-Cr), the use of a MOSFET-based hybrid rectifier, as well as the output filter (Co) and load resistor (Ro), results in a converter capable of maintaining output voltage stability, reducing ripple, and significantly improving power efficiency, making this topology highly ideal for high-power and maximum-efficiency applications .

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

2.1 Resonant Network

The operating principle of this converter focuses on the use of LLC resonance involving the inductor and capacitor in the resonant network. When the switch is first opened, the inductor current initiates a resonance cycle with the capacitor. During this resonance process, the inductor and capacitor together generate a resonant frequency sufficient to ensure the switches operate under ZVS, thereby reducing power losses commonly found in conventional switches. At the ZVS condition, the voltage across the switch approaches zero, so no high voltage is applied during switching transitions, which decreases switching losses and enhances converter efficiency . In the LLC–LC resonant converter, ZVS operation is achieved for all power devices under all operation conditions without using active auxiliary circuits, which are usually used in soft switching PWM converters .

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

2.2 Half-Bridge LLC Resonant Converter in Hold-Up Mode In hold-up mode, when a sudden drop in input voltage occurs, the Qa is activated with PWM control to maintain stable output voltage using the energy stored in the link capacitor. The current in the resonant inductor (Lr) increases as Qa is turned on, and this energy is then delivered to the load once Qa is turned off. This PWM method enables control of the output voltage gain without the need to significantly widen the switching frequency range, thus maintaining efficiency and allowing for a reduction in link capacitor size. A similar approach was also proposed in , emphasizing the importance of additional PWM control to maintain stability and efficiency during hold-up conditions without significantly increasing system complexity. By actively controlling the duty cycle of the secondary-side auxiliary MOSFET in a PWM-LLC resonant converter, wide voltage regulation can be achieved while maintaining fixed resonant frequency operation and Zero-Voltage Switching (ZVS) for all MOSFETs . The transformer in the LLC resonant converter plays a critical role in high-voltage applications, as its parasitic capacitance and leakage inductance significantly affect soft-switching conditions, voltage gain, and overall efficiency of the converter .

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

2.3 Magnetizing Inductor

According to , the role of the Lm in the LLC resonant converter topology is crucial, as Lm not only functions as an energy storage element during the switching cycle but also determines the resonance characteristics and ZVS capability. The greater the value of Lm relative to the Lr, the flatter the resulting gain curve, so that frequency variations do not drastically affect the output voltage conversion ratio. The magnetizing inductor Lm participates in resonance, improving the stability and efficiency of the LLC resonant converter .

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

2.4 Hybrid Rectifier

The hybrid rectifier approach provides a new degree of control freedom on the secondary side, enabling more adaptive output voltage regulation and current sharing among parallel modules. The hybrid rectifier is also effective in suppressing switching losses and increasing efficiency, particularly during light-load operation or in multi-converter (interleaved) systems that require balanced current distribution. Experimental results show that this method can maintain converter stability and high performance, while minimizing output fluctuations under various operating conditions .

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

2.5 Zero Voltage Switching

ZVS is a condition where the power switch, such as the main MOSFET in a Half-Bridge LLC Resonant Converter, is activated when the drain-source voltage approaches zero volts, thus eliminating switching losses caused by the overlap of voltage and current. ZVS is achieved naturally through resonance between Cr and Lm, which generates sufficient current to discharge the internal parasitic capacitance of the switch during the gate-off period. When one switch turns off, the magnetizing inductor current empties the opposing switch’s Coss, so that the voltage across the switch reaches zero when it is turned on again. This condition not only increases efficiency by reducing switching losses and thermal stress on the switches but also lowers electromagnetic interference (EMI). Studies such as support that appropriate resonance design and magnetizing inductance are critical to ensuring ZVS, thereby achieving high efficiency and optimal performance in LLC resonant converters.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

2.6 Operational Characteristics And Gain (Fr/Fs)

The gain characteristics of the Half-Bridge LLC Resonant Converter are highly dependent on the ratio of switching frequency (Fs) to resonant frequency (Fr). Thus, proposed using PWM control on Qa during hold-up mode, keeping the main switching frequency close to the optimal resonant frequency while regulating gain via the PWM duty cycle. This approach maintains high efficiency without significantly widening the switching frequency range, ensuring that the transformer and resonant tank design remain optimal. This is in line with the findings of , which emphasize the importance of resonance design and adaptive control for high efficiency and stable output.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

Figure 2 illustrates the MATLAB/Simulink implementation of the proposed NHB-LLCRC-MIHR converter, which is organized into four main functional blocks, a monitoring section, a primary switching stage, a resonant tank, and a secondary hybrid rectifier. The monitoring block records the key electrical variables used in the analysis, especially the input voltage, output voltage, and DC conversion ratio. The primary stage operates the inverter switches, while the resonant network, consisting of Lr, Cr, and Lm, shapes the energy- transfer process and supports soft-switching operation. On the secondary side, the hybrid rectifier improves rectification performance by reducing conduction and reverse-recovery losses. Table 1 summarizes the component values used in the simulation, namely the 250 V DC source, Lr = 120 uH, Cr = 22nF, Lm = 360 uH, Co= 3 uF, and Ro = 1000 ohm. These values were selected to define the resonant behavior, output filtering, and load condition of the converter.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

Figure 2. NHB-LLCRC-MIHR simulation with MATLAB/simulink Tabel 1. Main parameters of proposed converter.

360Uh

The proposed method was evaluated through MATLAB/Simulink simulation by sweeping the switching frequency and load condition, then comparing the proposed topology with the conventional converter. In line with the reference work by In-Ho Cho et al., the nominal-state operation is expected to stay close to the resonant point for maximum efficiency, while the hold-up state uses the auxiliary switch (Q_a) with PWM control to increase the voltage gain without excessively widening the switching-frequency range. The main performance metrics used in the evaluation are resonant frequency, output voltage, DC conversion ratio, efficiency, output ripple, and settling behavior. These metrics make it possible to verify whether the proposed converter achieves higher output stability, lower loss, and faster recovery than the conventional topology.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

The resonant frequency equation calculates the frequency at which the inductor and capacitor in a resonant circuit naturally oscillate, with Lr representing the resonant inductance and Cr representing the resonant capacitance.

half-bridge-converter-matlab-simulink Diagram
Figure: System Model & Simulation Flow for Half Bridge Converter Matlab Simulink

(1)

Hence, the resonation inductance (𝐿𝑟) is determined to be 120 µH and the resonation capacitance (𝐶𝑟) is 22 nF. As we get this equations. Based on these values, the product of the inductance and capacitance, which is a key parameter in determining the resonant behavior of the circuit, can be calculated as follows:

(3)

By applying equations (1), the resonant frequency is found to be 97.953 kHz, indicating the frequency at which the circuit naturally oscillates with maximum energy transfer. The design of an NHB-LLCRC-MIHR circuit simulation uses MATLAB/Simulink software, based on the conventional topology reference , which was then modified by adding a Lm and a MOSFET-based hybrid rectifier on the secondary side. The designed circuit was tested under various switching frequencies and load conditions, with output parameters such as voltage, current, ripple, and response time to steady-state being measured. The experimental data were directly compared with the conventional topology to identify the advantages of the proposed innovations, and all results were interpreted comprehensively based on the main performance parameters as well as the phenomena observed during testing.

3.

3.1 Resonant Frequency

The first test focused on characterizing the impedance of the series resonant tank, which consists of a resonant capacitor (Cr = 22 nF) and a resonant inductor (Lr = 120 μH). Using simulations in Simulink, a frequency sweep was performed in the range of 80 kHz to 120 kHz to observe the impedance and phase behavior of the circuit. The impedance magnitude graph shows a minimum point at a frequency of approximately 97.953 kHz, which corresponds to the theoretical calculation using the resonance formula.

At this resonant frequency, the circuit impedance reaches its minimum value due to the cancellation of inductive and capacitive reactance, resulting in a purely resistive circuit with only minor resistive losses remaining. Below the resonant frequency, the circuit exhibits capacitive characteristics with the current leading the voltage, while above the resonant frequency, the circuit is inductive with the current lagging behind the voltage.

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.

ansys-airbag-injury-simulation Diagram
Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

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).

ansys-airbag-injury-simulation Diagram
Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

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.

ansys-airbag-injury-simulation Diagram
Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

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).

ansys-airbag-injury-simulation Diagram
Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

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.

ansys-airbag-injury-simulation Diagram
Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

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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